Brad Mehldau TRIO: BLues and Ballads Nonesuch Records released the Brad Mehldau Trio’s Blues and Ballads, the trio’s first new release since 2012’s Where Do You. Here is Brad Mehldau's solo on 'Not You Again' a tune based on the changes to 'There Will Never be Another You' from John Scofield's record Works for Me Brad Mehldau - Not You Again (Solo) no chords Jazz Transcriptions An online forum to share transcriptions. Email pdf files to [email protected] Evans Brad Mehldau Brad. Resignation by Brad Mehldau. Brad mehldau collection six transcriptions pdf. PDF Also we have an excellent. Rains brad mehldau pdf J. WrenfroW 27, 3, transcription, pdf.When It Rains - Brad Mehldau 16. Brad Mehldau Trio - Number 19 (transcribed). Pdf files (with corrections. Brad Mehldau – Transcriptions Part 2. Motivic Strategies in. Brad Mehldau Collection - Six Transcriptions.pdf - Download as PDF File (.pdf) or read online. The reason I have made 2 handed transcriptions of certain lead sheets is because Mehldau is so creative with his left hand, making it necessary to document how he supports melody. I hope you enjoy these, sorry again for the delay, I have received many emails requesting these transcriptions.

Start display at page:
Download 'My Workouts: Brad Mehldau, independence, deep learning'
  • Lily Underwood
  • 2 years ago
  • Views:

Transcription

1 My Workouts: Brad Mehldau, idepedece, deep learig Adrea La Matia Bachelor s thesis Savoia Uiversity of Applied Scieces Bachelor s degree (UAS)

2 SAVONIA UNIVERSITY OF APPLIED SCIENCES THESIS Astract Adrea La Matia, 2017 This work is licesed uder the Creative Commos Attriutio-ShareAlike 3.0 Uported Licese. To view a copy of this licese, visit

3 CONTENTS 1 INTRODUCTION What s this aout Who s Brad Mehldau What s idepedece Music ad laguage Spaced Repetitio Software (SRS) Deep learig, oredom, flow Music Workouts INDEPENDENCE FROM STYLE AND GENRE CONVENTIONS HANDS INDEPENDENCE Both hads play chords with the same rhythm Both hads play chords with a differet rhythm Both hads play a melody with the same rhythm Both hads play a melody with a differet rhythm Oe had plays chords, the other oe a melody Three voices RHYTHMIC AND METRIC INDEPENDENCE Rhythmic displacemet Polyrhythms / polymeters Odd meters INDEPENDENCE FROM HARMONY, OR PLAYING OUT INDEPENDENCE FROM STRICT PRACTICING INDEPENDENCE FROM EVERYTHING BUT THE PRESENT MOMENT CONCLUSION AND COMING SOON..63 REFERENCES..63 APPENDICES Appedix 1 All The Thigs You Are, 7/4 drums solo ackgroud, Brad Mehldau Trio Appedix 2 Black Hole Su, arragemet ased o Brad Mehldau Trio s versio Appedix 3 Coutdow, drop2 voicigs workout Appedix 4 Giat Steps, upper structure voicigs workout Appedix 5 Goodye Storyteller (for Fred Myrow) / Exit Music (for a Film) medley Appedix 6 Lodo Blues, Brad Mehldau Trio Appedix 7 Wid, full score Appedix 8 Wid, piao reductio Appedix 9 Woderwall, Brad Mehldau Trio

4 4 1 INTRODUCTION 1.1 What s this aout This work is a recollectio ad gatherig of my ideas aout music i geeral, ad aout studyig improvisatio o the piao i particular. These thoughts have ofte led to experimetig ew methods, ecause, as Bill Evas (1966) wisely tells us, a serious jazz player is ultimately goig to teach herself/himself. Especially whe we cosider improvisatio as a fudametal part of music, ifiite possiilities meas ifiitely differet paths for reachig them. That s why, as music studets ad teachers, I thik it s importat to share our ow fidigs; music evolves as a collaorative effort. I the last few years, the piaist who has iflueced me the most is Brad Mehldau. That s why you saw his ame i the title, ad you re goig to see it may more times if you keep readig. 1.2 Who s Brad Mehldau I m ot goig to waste my time ad yours y writig a ad versio of Mehldau s life s story; if you re iterested go read it o Wikipedia, or o Brad s persoal we page (liks i the Refereces sectio). What s importat here is that he is the most ifluetial jazz piaist of the last 20 years (Chie 2013). There s a reaso ayody would say somethig like that. There are may iovative elemets i his playig; the most importat are his use of the left had ad his mastery of dyamics, polyphoy, polyrhythms, polymeters ad odd meters. 1.3 What s idepedece I ve chose the word idepedece as a uderlyig theme for this thesis. It mostly meas freedom. Before we dig ito the more practical stuff, I d like to go over some ideas that will provide a key to iterpret this work ad etter uderstad my approach to studyig music. Feel free to skip these ad go straight ahead to the mai cotet at Page Music ad laguage Music ad laguage have somethig i commo, we ve proaly all heard it from time to time. Both are forms of commuicatio, ca e writte ad put ito soud. Eve some of the termiology is used i oth fields; thik of phrases, call ad respose. Scietists have ee studyig this coectio. Neuroscietist Airuddh D. Patel (2010) has

5 5 writte a ig ook o the suject. A team of researchers at Joh Hopkis Uiversity moitored the rai of 11 piaists as they improvised from iside a MRI, tradig fours with aother musicia i the room. The sytactic areas of the rai where very active, ut the sematic areas were t workig at all. The parts of the rai used y spoke ad musical commuicatio were overlappig, eve though they were ot exactly the same. (Bisceglio 2014.) Also musicias have ee woderig aout this similarity. Bass player Victor Woote (2012) thiks we should lear music i a similar way to how we leared our first laguage. May of us thik music is somethig that should e leared followig a strict disciplie, uder the guidace of a teacher. Istead, it s proaly etter to sped more time playig rather tha practicig, acceptig mistakes ad avoidig too may rules. Whe childre lear to speak, they do t do it y learig grammar rules. They just lear y listeig ad talkig with more advaced speakers. I the same way egiers should e allowed to play with more advaced players. Beig iterested i oth music ad laguages, I ve come across some methods ad cocepts used i laguage learig, which i some way have iflueced my way of studyig music. While studyig Japaese I came across SRS, Spaced Repetitio Software, which I ve ee usig for some years. Learig aout Japaese culture, I foud out aout the aciet Chiese oard game of go, which i tur led me to Google DeepMid s AI AlphaGo ad the cocept of deep learig. Turs out deep learig is used also i the atural laguage processig field, so we re ack to laguage ad the circle is closed (Wikipedia) Spaced Repetitio Software (SRS) Spaced repetitio is a learig techique ased o the spacig effect, a learig pheomeo studied i the field of psychology. We re proaly all familiar with how crammig for a exam i the last days will assure that we ll have already forgotte almost everythig a couple of weeks after the exam. This is exactly what spaced repetitio is aout. It s ee oserved that a piece of kowledge is retaied more easily ito log-term memory if we review it after icreasigly loger itervals of time, as opposed to reviewig it may times i a shorter period. This cocept has ee used to develop Spaced Repetitio Software (SRS), like Supermemo or Aki. SRS is a evolutio of flashcards, those cards where you have somethig writte o oe side, ad you must rememer what s o the other side. For example, i the cotext of vocaulary learig, you could have a word i your ative laguage o the questio side, ad the correspodig word i the laguage you re learig o the aswer side (or vice versa). SRS is ot used oly for laguage learig, ut also i other fields where you have to memorize a ig amout of iformatio, which ca e divided ito small eough pieces; it s used y medicie studets ad programmers (Kisella). By makig the flashcard system ito a software, it ecomes much more versatile. If you see a word you like while

6 6 watchig a movie, you ca take a screeshot of that scee ad iclude it ito your cloze deletio flashcard. The more you coect the ew iformatio to previous memories ad emotioal states, the easier it is to rememer it (Woziak 1999). SRS also keep track of whe you have to review each oe of your cards. What happes is: you lear a card for the first time, the you review it the ext day; if you got it right the ext review is goig to e after some days, the after some weeks, ad so o as the itervals etwee reviews grow igger ad igger (eve years igger). After seeig the aswer side of the card, you ca give yourself feedack aout how easily you rememered it, ad this will chage the legth of the time iterval efore the ext review. If you do t rememer the card, the learig cycle starts agai from the egiig, so you ll see it the ext day, ad so o. This way you ca focus just o the material you keep forgettig, istead of havig to go over everythig every time. If you forget a card too may times, to avoid spedig too much time o it the card gets marked as a leech ad gets suspeded. This is a very importat poit: if you wat to lear efficietly, you have to let go of ay perfectioist tedecies you might have. Perfectioism ad oredom are your most dagerous eemies (Khatzumoto Jue 2011). If we still thik aout laguage learig, it does t make sese to kow 100% of 1000 words if i the same time you could have memorized 90% of 2000 words. Havig used SRS for some years, I ve also fatasized aout a software that would implemet spaced repetitio to study piao voicigs; I ve writte a article aout it a couple of years ago (2015), ut it s still just a fatasy. The most importat lesso to lear from spaced repetitio is this: whe thikig for the log-term, it s etter to orgaize you studies so that you do t keep studyig the same material over ad over i a short period of time. If you have more time it s etter to cocetrate o may differet sujects, rather tha a sigle oe. You ca switch from oe to aother durig oe study sessio, or i the course of oe week. You should t wait too log etwee study sessios with the same topic though, otherwise the progress you already made could e partly lost. Ad do t switch sujects so quickly that you do t have time to dig ito them. This is the est way to iteralize ay material: fidig a equilirium etwee studyig a sigle thig so ofte that your progress per hour rate starts decliig sigificatly, ad studyig it so ifrequetly that you lose part of the progress you already made. Thus space repetitio provides a framework o which you ca uild your workout strategy Deep learig, oredom, flow I March 2016 a computer program eat a 9-da professioal go player for the first time. It may ot seem like a ig deal, sice chess programs who ca defeat champios have ee aroud sice the 1980s. But go is a game with may more possiilities tha chess, eve though the rules are simpler. I fact, the possiilities are so may, that they exceed y far the estimated total umer of atoms i the uiverse. It would e almost ifiitely log to calculate

7 every possiility y rute force, like chess software does. This differece etwee the two 7 games meas that go players have to rely much more o ituitio, whereas chess players are more aalytical. AlphaGo, developed y DeepMid, is a self-learig AI, which is ased o a deep learig eural etwork algorithm. Martiez (2016) does a excellet jo of explaiig how deep learig works, so I suggest you watch his video o the Computerphile YouTue chael if you re iterested. I ll try to give you the gist of it. Covetioal software takes a iput (oe or more values), has a set of istructios aout what to do with that iput (a algorithm), ad y followig these istructios it produces a output. Pretty straightforward (or ot, cosiderig the amazig thigs that ca e doe with just that). A deep learig algorithm takes the iput values, ad istead of just followig a set of rules, it kid of makes his ow coectios. For example, it ca try to comie a set of values, ad the comie the result of that with aother set of values, ad so o for may levels (hece deep). After all those levels, a output is produced. That output is the judged, either y the programmer, or automatically y the machie; i a game of go for example it could e that the output correspods to the fial score of the game, so the higher the etter. Out of all those itermediate coectios etwee values ad set of values that it has created, the machie lears which oes it should keep, ecause they have produced a etter value. Some deep learig algorithms are called artificial eural etworks precisely ecause these extremely complicated coectios are similar to the oes etwee the euros i our rais. This machies usually lear y themselves, ad the programmer has o idea aout what is happeig i the deeper layers. AlphaGo was first programmed with the asic rules of the game, ad it was fed data from thousads of games played y strog amateurs. After that, it was copied ad it was made play agaist itself 30 millio times. (Altraide 2016.) Deep learig is eig implemeted i fields like computer visio, speech recogitio, atural laguage processig ad medicie. This rapidly developig techology has so may differet applicatios, that it s oth excitig ad scary. But let s come ack to music. Music, like a laguage, is a highly complicated suject. Therefore it makes o sese to try to lear it oly y rute force. What I mea y this will e clearer i each specific example, ut i geeral I m thikig aout exercises which try to memorize may differet possiilities, with the aim of kowig at least somethig very well. This is a good strategy, especially at the egiig whe you do t have much, ad aythig is etter tha othig. Later o these exercises should oly e see as you feedig data to your rai, which is useful; ut similarly to whe we feed data to a deep eural etwork, we should t expect to have ay idea aout what is goig o i the rai, ad how or whe the results of that data will come out as output, ad what that output will e. For example, if we lear a trascriptio, we should t try to use parts of it i our ow solos. If we force it, it just souds uatural a fake. It s good to aalyze the trascriptio ad uderstad what could we do to achieve a similar effect, ut if somethig good will come out of it, it will do so at its ow time. Aythig which is practiced attetively ad regularly will make its appearace durig improvisatio i its ow time. Tryig to hurry the process ca cause the improvisig to soud too premeditated, or it may disrupt the flow i a way which greatly icreases the tedecy toward metal locks ad mistakes

8 8 i executio. (Dois 1994, 127.) This is exactly why listeig to a lot of music is so importat. Especially if you have traied your ears well ad you re ale to recogize which otes are eig played. You re essetially feedig a lot of precious, good quality data (hopefully you liste to good stuff) to your rai, which i tur, without you eve kowig it, will some day regurgitate all that greatess, recomied ad trasformed with your persoal sigature style, ito your ow playig. Back to practicig. It s importat that it does t ecome too stiff, ecause it could ecome orig. The prolem of oredom. The geeral attitude is that eve if somethig is orig, you have to suffer to gai somethig good. This is just a romatic/christia/asia/samurailike idea, ut it s ot true. What is true, is that it s etter to do somethig, tha to do othig. But if you isist with somethig that oviously does t iterest or etertai you, proaly i the ed you will have leared somethig, ut you will have wasted so much time i the process, that you could have leared way more if you just had doe somethig iterestig ad fu. Khatzumoto is the ower of the AJATT (All Japaese All The Time) wesite, ad he leared Japaese from zero to fluecy i a year ad a half, without attedig ay Japaese class, ad while eig a full time IT egieer studet. I really like what he says aout oredom (March 2011): Boredom meas stop doig this ad start doig somethig else. Boredom is pai. You do t keep your had o the hot stove ecause it uilds character, you take it away efore you really hurt yourself. It s importat to uderstad that this does t mea laziess, it s just a more efficiet way to lear. It s ot just ecause I, or Khatzumoto (who s he ayway), say so; it s ecause psychologists ad scietists say so. Flow is the metal state of operatio i which a perso performig a activity is fully immersed i a feelig of eergized focus, full ivolvemet, ad ejoymet i the process of the activity. We all kow how short is our attetio spa. Sice i flow every sigle ouce of our attetio is focused o the activity we re performig, this is the est state ot oly for learig (employed for example i Motessori schools) ut also for improvisig music. (Wikipedia.) The lesso to lear from deep learig algorithms is that we ca t hope to tackle complex prolems like improvisatio oly with aalysis. Aalysis is importat, ut it s oly together with ituitio that we ca get the est results. So do t over-aalyze everythig, ad do t try to force the learig process; a ig part of it is happeig without your awareess of it. Play more tha you practice, or at least the same amout of time. Usig my ow words from the Music Workouts Faceook page s Aout sectio, Story field: So much is time itrisic to music, our art ca reach its peak oly whe we are etirely ito the momet. What we create i this state of mid, we could t imagie efore, ad caot completely explai. If the most fasciatig thigs are the oes we do t expect or comprehed, the why do we reletlessly try to figure out more ad more aout music By pushig the lie etwee coscious ad sucoscious further ad further, we are ale to reach deeper ito ucharted territory every time we cross it. I other words, the more we uderstad, the more what we play sucosciously evolves accordigly. (La Matia, 2015.) The lesso to lear from the cocept of flow is that we should avoid oredom. Practicig somethig we already kow is also ad tedecy, though (Dois 1994, 127). We should fid a good alace; our workouts should e challegig eough to keep us iterested ad

9 9 allow us to actually lear somethig ew, ut they should t e so difficult that we ed up overthikig ad ot havig fu. We should also e flexile. At Page 6 we talked aout how space repetitio ca e a framework with which to uild our workout strategy. But whe we re actually studyig we should t e afraid to modify our plas ased o how we feel at the momet. If we see that we re eig lessed with a flow state of mid, we should play somethig that ca take full advatage of it (see also Page 61 aout freefall workout). If we otice that i a particular day we get really ored with a particular workout we should switch to aother oe, eve if it is t what we plaed for that day s sessio. Oe of the advatages of havig may sujects to study is that we ca switch etwee them. We should e flexile also i the cotext of a sigle workout. A workout should t e stiff; it s always possile to evolve gradually towards completely free improvisatio. So if after a while we get ored, little y little we ca get rid of some of the rules we estalished for that workout, ad play more ad more freely. Do t give up too soo, ut do t eat your head stuorly agaist a stoe wall either. There is a reaso why we say play music. It s supposed to e fu Music Workouts A word aout words. I m usig the term workout whe referrig to exercises or practice routies. This is related to a project of mie called Music Workouts; it s a platform for sharig my ow study methods, ad to discuss them with fellow musicias. You ca check it out o Faceook (2015). 2. INDEPENDENCE FROM STYLE AND GENRE CONVENTIONS If music is like a laguage, composig is like writig, ad improvisig is like speakig without writig a speech eforehad. Therefore it is atural to assume that improvisig is a fudametal elemet of music, ecessary to achieve a deeper uderstadig of it. Improvisatio was commo also i Wester art music, at least util the 19 th cetury. The it ecame somehow less commo, ad owadays it s almost completely disappeared. I thik this is a great loss for classical musicias; eve though they might ot realize it, it could give freshess to the performace (eve if it s ot improvised), ad it could help whe composig. I a iterview with his rother Harry, Bill Evas (1966) recalls how, efore eig itroduced to jazz ad improvisatio, he could play itelligetly a difficult piece, ut could t play a sigle ote without a score. I that same iterview he said that he cosiders jazz ot much as a style, ut as a process, i the sese that jazz has rought ack what was lost i classical music: improvisatio. Evas thiks that whe teachig jazz (improvisatio), oe should t teach style, ut istead try to teach those astract cocept of music which are idepedet from ay style. I thik this is a really valid statemet, ecause i the cotext of improvised music the musicia who has a

10 10 persoal soud is always appreciated. If we teach jazz as a style, we are already restrictig our studets creativity ad cripplig their search for a persoal voice. Of course, oth as a egier ad as a professioal, it s oly healthy to steal what we like from our colleagues, ut as teachers we should ever say: Your lies were good, ut they do t quite fit with the tue s style; this is a eop tue so you should play more like yada yada yada. If your teacher says somethig like this to you, just igore it, or say a uch of ugly words to him/her; you re proaly etter off studyig y yourself, tha with a ad teacher. Brad Mehldau, a all-aroud musicia, is a really good example of idepedece from style. He s always evolvig, tryig ot to get stuck playig i the same way all the time. The style of his improvisatio has evolved. The style of his compositios has evolved. Take Elegiac Cycle (1999), piao solo with a classical vie, the Highway Rider (2010) a mix of pop ad jazz with a orchestra, ad ow The Old Shade Tree from his ew duo alum (2017) with madoliist ad vocalist Chris Thile, which has some folk flavors. The trio ad piao solo formatios are always preset (though ever the same), ut there s space for experimetatio i may differet geres, like the electroic duo Mehliaa (2014) with drummer Mark Guiliaa. I additio to his ow compositios, Mehldau does t play oly jazz stadards, or pieces from other jazz artists. He plays covers from artists as diverse as Soudgarde, Nirvaa, Massive Attack, The Verve, Radiohead, Pik Floyd, Beatles, Jimi Hedrix, Nick Drake, Jeff Buckley ad Johaes Brahms amog others. Ad whe he goes to Viea (2010) to play a piao solo cocert o a Steiway, he plays with a Grateful Dead T-shirt. How cool is that! I his improvisatio he icorporates elemets from everywhere, ad therefore he s eyod styles. He eve steals a great deal from classical music, which is somethig more of us should do, ecause there is a lot of iterestig stuff there. The fact that some classical musicias so jazz is ot a good reaso to do their same mistake, ad miss out o classical music. A example of Mehldau s classical ifluece is the mid-lowig solo that he played i Athropology with the Mehldau Rossy Trio i Barceloa (o a piao that I ve heard was almost uplayale) i 1993 (yes, he was oly 23). At aout 4:50 Brad starts to play a polyrhythmic lie with oth hads i the ass register, somehow remiiscet of Tristao s Turkish Mamo (1955), ad the tha at aout 5:00 he trasforms it ito a typically Bachia phrase. It s amazig. 3. HANDS INDEPENDENCE Now we start to get ito the more practical stuff. Hads idepedece. I may differet ways. Firstly, from each other. Everyoe who has ever played the piao kows how difficult is to split your rai, ad play two differet thigs with your hads. Whe playig thoroughly writte music, somehow we are ale to use muscle memory to ypass i part this prolem. Sice our hads kow where they are goig, we ca mostly avoid the prolem of really

11 11 cocetratig o the two separate thigs we are playig. Of course with experiece we lear to overcome the mere mechaicaless of the process, ad develop a aility to truly hear ad feel oth thigs at the same time. Whe we itroduce improvisatio, thigs ecome much more complicated. Ad of course there could e more tha two thigs goig o, eve if we just have to hads. Let s call these thigs voices, ad let s say they ca e either melodies, or rhythmic patters, or chords, or sigle repeated otes (pedals). Thik of Bach s C- fugue i the first Well-Tempered Clavier (BWV 849): we ca have as may as five voices goig o. The it ecomes practically impossile to feel every sigle voice, ad you have to chose which oes are more importat, ad cocetrate o those. You have to e sure that this is ot just i your head, ecause the listeer, too, has to e give the possiility to split his listeig mid, ad appreciate those voices goig o at the same time, oth i their idividuality, as i their iterweavig comiatio. To achieve this, we have to use dyamics to rig out the voices we thik deserve the most attetio at ay give momet. Otherwise, if we keep the dyamics flat, the voice that s goig to catch the attetio is usually the highest. Ad that s orig. Speakig aout Bach, oe who s really good at rigig out the voices is Gle Gould. Do you kow who else is a master of voices ad their dyamics Exactly. Me. Just jokig. Talkig aout our Brad. Elegiac Cycle (1999) is a masterpiece i this sese. Brad is a master also of hads idepedece from their covetioal roles. I jazz piao the covetioal roles would e more or less: - solos: right had plays melody, left had plays chords - i a ad without ass: left had plays the ass, right had plays chords or melody Ad this is ecause the masters of the past played this way. I thik ot eve oe of my teachers ever suggested the possiility of playig melodies with the left had, apart from whe doulig the melody played y the right had. Proaly they thought that I could t eve play the covetioal stuff, so why other. Which makes sese. But i this way, we are asically just teachig style. While we should istead try to teach the geeral priciples of music, like Bill said i the last chapter. It s ot just a questio egalitariaism or fightig discrimiatio. It s a questio of usig everythig we have. Sure we ca make great music without ay of this. Brushy Oe Strig (2013) has a wicked groove with just oe strig o his guitar. Still, thik aout Rahsaa Rolad Kirk (1972), ad how he wated so adly to play more tha just oe lie at a time, that he played as may as three saxophoes together; it s so much easier to do that o the piao, still some piaists do t eve try. It s a it like whe you say to your childre: Come o, fiish what you ve got i your plate, you kow that childre i Africa die of starvatio, so do t waste your food!. I the same way you ca say: Come oe, use oth of your hads like you mea it, play every sigle key of that piao; you kow poor Brushy has oly oe strig, so do t waste your istrumet s potetial like that!. So, we should give studets every weapo availale, ot precludig them ay possiility right from the start. I do t thik these cocepts should e saved for advaced players oly. If oe is iterested i developig more his left had ad a differet style of playig, while should we try to coform her/him to the orm While at the same time we are i a field, where the

12 12 exceptio to the orm ad origiality are what s valued. We ca say that Mehldau s hads are eve idepedet from their covetioal positios. What I mea y that is, he ofte plays cross-hadedly, with the left crossig over the right or vice versa. It s othig ew, there are coutless classical pieces where you re supposed to cross your hads. But I would t say that it s commo i jazz. While it may seem like a poitless trick, it s actually really useful, for example whe you have a cotiuous patter goig o i the middle register, played y oe had, ad you wat to play somethig over it, or uder it. You could just cotiue the patter with the other had, ad there would o eed to cross, ut it s actually much more easy, ad it souds more atural, to let the same had cotiue the same patter. I was playig the trascriptio y Adré (2011, ) of Goodye Storyteller (for Fred Myrow) from Elegiac Cycle (1999), ut I had t ee listeig to it for a while. It was really difficult to play the lower ass otes at ar (miutes 4:56 ad 5:01 i the recordig) with the left had, ad at the same keep up the left had roke chord patter. The I was watchig a video o YouTue of a live versio of that same piece (Mehldau 1999), ad I oticed that i may occasios Brad was reachig over with his right had to play ass otes, as the left had cotiued with its patter (at 1:38, 3:20, ad 3:39 i the video). You ca see that eve from other videos of the same sog, like the oe from the Jazz i Marciac festival (Mehldau 2011). The, whe I listeed to the alum versio agai, I realized that those ass otes I was havig troule with had actually ee played y the right had reachig over. It was really clear, ecause of the dyamics (those ass otes are quite loud, proaly Brad wated to emphasize them) ad ecause the left had patter just cotiues o i such a atural way, that would e impossile if oe were to play those otes with the left had. Which rigs us to a iterestig questio, which is very similar to the age-old chicke-or-egg questio: which came first, the music or the hads It seems quite straightforward that the music should come first, i our mid, ad e expressed idepedetly from the hads, meaig whe a idea is or, it does t matter which had plays it, as log as it gets played. The hads are just a meas to traslate a thought ito soud. Especially whe there are more tha two voices, very ofte it happes that a voice i the middle gets played alteratively y oth hads. Goig ack to Bach, his fugues ad his Three-part ivetios ofte require us to switch hads ad cotiue playig the same voice with the other had. Also a elemet that was efore played y oe had, ca e played y the other oe, it depeds o which had is usy, which had is closer. Brad i that same video of Goodye Storyteller (for Fred Myrow) (1999) at 3:47 plays with the left had a figure he just had played with his right had reachig over at 3:42, ecause his right had was too usy at that momet, ut he still felt that importat ass lie movemet i his head, ad had to play it somehow. So, ack to our chicke-or-egg questio, does music come always first Actually I do t thik so. I thik listeig is importat. I do t just mea listeig to others people playig. I mea listeig to what we play, to the various voices, the movemet of each part. Sometimes, very ofte actually if you re rave eough, you play somethig really good y chace, ad if you

13 13 are ale to catch it with your ear, ad recogize that it s gold, you the keep it alive ad play with it. I this case first come the hads, ad the the music. I kow that it s still your mid that cotrol your hads, ut some thigs always always are semi-automatic, eve i improvisatio. Whe somethig good comes y chace from those semi-automatic had movemets/rai processes, if you re ale to catch, you ca make good music with it. Soo we ll go through some workouts more i detail, ut first I d like to tell you aout some more geeral, deep learig-like methods I tried i the past years (for more o deep learig see also Page 7). I wated to improve my aility to play more voices at oce, with a good commad of dyamics; I wated to improve my aility to liste to more voices at oce; I wated to improve my hads idepedece. Intel d915gse2 motherboard manual. I also felt I eeded to improve my prima vista skills i every toality, so Bach s Well-Tempered Clavier (BWV ) felt like the perfect choice. Ad the fugue is such a iterestig format, ad so fittig to improvisatio, sice it s ased o coutless differet variatios of a simple theme (which we d call riff ack there i the dark side). I started readig the first volume; I d just go through it, playig each piece oly oce, ad the startig agai from the egiig. Of course this could happe over the course of weeks, ecause I was also studyig other stuff i the meatime. This way I was sure to rely less o muscle memory ad more o readig aility, thus developig a more geeral skill for playig multiple voices (ot writig ay figerig umer dow ad so o). This was proaly also very good from a spaced repetitio poit of view, sice some time was passig efore I played agai the same piece, maye that allowed me to get what I could from it ad store it more securely ito log-term memory (for more o spaced repetitio see Chapter X). The after some time (more tha oe year for sure) I wet o to the secod volume, ad kept playig a couple of favorites from the first oe from time to time. I do t mea to say this would e good for ayoe; I actually do t eve kow if it was good for me, sice we are ot ale to pipoit exactly from where does our improvemet come, ad it may come after a very log time ayway. Still, it makes sese to study such material, which has the precise characteristics we re seekig to acquire. Ad sice there s o shortage of highquality material i classical music, it does t hurt to look ito that, too; we do t eed to e separated ayway. Aother method I tried is somethig I was forced to do y circumstaces, ut it tured out to e quite iterestig. Three gigs were comig up, with three differet ads. I did somethig wrog, proaly practiced too much or too itesively, ad my right had ecame quite sore. I could t take a week-log reak from playig, ecause the gigs were comig up ad we had the last rehearsals efore that. So I just stopped usig the right had. They were all ads with a ass player, so I did t have to play too much stuff i differet registers ayway. I foud that quite challegig ad fu. You get a ew perspective o thigs, you may have to play a it less, ut ew ideas keep comig. It s a good way to develop our aility at iterchagig hads roles. Plus, my right had improved ad I was ale to play the gigs, so I killed two irds with oe stoe. I do t like killig irds actually; still that was a fatastic way to trai. Never over-

14 14 practice efore a cocert y the way. That time I also tried aother thig, which souds really Asia-martial-arts-traiig style. Ad it s really geeral ad deep learig. But maily I did it to stop the pai, that first time at least. I was still usig my right had for everyday tasks, ut it was really tese, so I decided to stop usig it completely. Thigs like eatig with spoos ad forks, rushig teeth, pour driks from a ottle, use the computer s mouse or trackpad ad so o..all with the left had. It s fuy ecause you feel dum/metally impaired, all those thigs seemed so easy ut they are ot! If you feel particularly da Vicia you ca eve try writig, ut that s some ext level stuff. Ayway, as usual I have o way of kowig if it actually helped develop my left had s playig skills, ut I like to thik that y usig it more ofte for all kids of stuff, a geeral improvemet i the figers fie motor skills takes place i the rai. Now let s move o to more specific workouts. Let s go through differet situatios. Eve though Mehldau ca keep at least 4 voices at the same time, we ll keep it a it simpler ad cosider oly cases with a maximum of 3 voices goig o. I real life these will ofte overlap ad chage quickly ito oe aother, ut for the sake of our study it s easier to try them out oe at a time. Oe had is playig chords. Oe had is playig a melody. Both hads play chords with the same rhythm. Both hads play chords with a differet rhythm. Both hads play a melody with the same rhythm. Both hads play a melody with a differet rhythm. Oe had plays chords, the other oe plays a melody. Three voices goig o, usually chords, a melody ad a ass lie. As you see a ig discrimiatig factor is rhythm, whe it s ot the same for oth hads we eed to study also rhythmic idepedece. We are goig to skip the first two cases, ecause we do t eed hads idepedece there, sice oly oe had is playig. For may of the situatios i the ext suchapters we ll talk aout differet cotext, like playig piao solo or playig with at least a ass player. Ayway the mai cocepts are goig to e valid regardless, ad we must rememer to keep a certai flexiility aout our ow role i differet formatios. What I mea is that, eve though some ehaviors are commo sese, we should t take them as asolute rules. Whe playig with a ass player, we usually do t play i the ass register, ecause that s where the ass player usually is, so if we re oth i the same area the soud could ecome muddy. But sometimes that effect ca e sought o purpose. Ad what if the ass player goes up i the middle register for a while The if we also stay there we ll have the same prolem. So istead of estalishig for ourselves a safe to-do-ot-to-do list, we should just liste to what s happeig, ad play what s eeded at the momet. Joh Medeski metios somethig similar i the 9 th track of the alum made from the Maria McPartlad s Piao Jazz radio show (2006). He recalls a previous episode of the show that he had recorded, where Joae Brackee was asked aout playig with ass ad with drums. She simply

15 15 aswered that she listeed to the whole thig, ad tried to put i whatever was t there, what eeded to e there. If you re iterested i learig aout jazz piao I suggest you check out other episodes of McPartlad s show. You ca fid a uch of them o the NPR s site (2017), ad some have ee released commercially as alums, like the oe with Medeski ad the oe with Brad Mehldau (2007). I the 3 rd track of the alum, Coversatio, Mehldau ad McPartlad discuss aout gettig a lot of voices movig at the same time, somethig which Mehldau ad his teacher Fred Hersch ca do really well. [McPartlad:] [ ] watig to have several voices goig at oe time, ad ot havig, like, the melody lie ad the chord chages [ ] lies goig o i all directios [ ] sort of like a cotraputal thig almost. [Mehldau:] [ ] actually really voice lead ad ot just get ito this thig of like you say, your left had almost kid of ecomig just as claw. [ ] I thik it s just somethig that s ice to do whe you re playig the piao, ecause you ca! It s almost like that s a great thig to do o the istrumet, cause it s all out i frot of you, you kow, ad you just get to try that out if you ca, ut it s tough, ad I always feel like I m always workig o that. [McPartlad:] [ ] Well, that s proaly harder to do tha just poudig away with your left had, ut it sure is effective, gee, I loved it! (McPartlad, 2007.) I the ext suchapters we ll see how harmoy ad melody are ot so clearly separated. By chord I mea somethig that gives a harmoic ackgroud, without takig too much attetio i a way. Sometimes it ca e eve a melodic patter, most of the time cotiuous ad repetitive; so that there s ever actually two otes played together. But as log as it s ot the mai focus of attetio, ad it takes care of defiig some harmoy, let s call it chord. Melody istead is the focus of attetio, ad it s fuctio is more melodic tha harmoic. So a lock chord phrase i a solo ca actually e cosidered a melody, rather tha chords. Here s Mehldau talkig aout harmoy. What s really fasciatig to me ad great aout music is harmoy. You kow, people thik a lot i terms of, you kow, how does a improviser or a musicia or a composer sort of idetify themselves, ad ofte people thik of melody. You kow, what type of melody do you write, you kow, ca you write a great melody. [ ] Whe I thik of ayoe from Schuert, or Brahms, all the way through, you kow, the Beatles, for jazz certaily Coltrae, Duke Elligto; people like that, they were really great harmoists. You kow, i the sese that they wrote these great melodies, ut the melodies would t have ee too much if there was t this harmoy uder it that ofte times is this sort of thig, that s mixig a very simple melody with harmoy that, somethig that s ot as simple, you kow, sort of has a darker side to it, so it sort of mixes the two together. (Mehldau 1999, Nicolas Klotz s documetary.) Before proceedig to the ext chapter let s talk aout the cocept of seeig a scale. Whe we improvise ofte we choose a specific group of otes to play, ased o the harmoy we wat to geerate. So, usig this group of otes we uild melodies ad chords. To a certai extet it does t matter too much which otes of that group we play, if we re ot talkig aout the mai melody. So for chords ad melodic patters with a harmoic fuctio, if we ca just hit somethig from that group with the right rhythm, it ll do the jo. The piao gives us a very ig advatage i this task: everythig is clearly visile efore us, so we should trai to e ale to clearly see those separate group of otes o the keyoard, ad play some of them. Keep i mid that whe tryig out these workouts you should feel free to chage thigs ad experimet; I tried to reverse everythig ad thik aout may differet comiatios, ut I m sure there are may I did t thik aout. Ad we re cosiderig oly 3 voices maximum, so if you ca do 4 the possiilities are eve more.

16 16 The whole idea from which to start is that hads roles are completely iterchageale. From here we start experimetig. This might ot e true for everyody, ut I fid that i practice hads roles are ot perfectly iterchageale. For example if you play a melody at the ass ad some harmoy over that, you might have to play a melody with less tesios ad more chord otes for it to soud good (much like it happes whe playig a walkig ass lie). But sometime it works just fie to have more asic harmoy i the right had, ad tesios i the left, for example here there s a stuig melody from the edig of Bela Bartok s Bear Dace from 10 Easy Pieces, Sz.39 (1908), where the right had plays a plai D major triad, while the left had melody is ased o a D altered domiat (AKA super Locria mode) (Figure 1). FIGURE 1. Bear Dace, r.h. D major triad, l.h. super Locria mode Creatig a melody o the spot require a lot of metal power, so doig somethig we re ot used to i the meatime (like playig chords with the right had) ca e really challegig at first. I elieve this is worth it, though. I love music i which powerful melodies appear i every part of the harmoy, from the ottom to the top. If you do t kow what that souds like ad you wat to get the idea, I suggest you liste to a piece I composed, Wid; writte for choir or sigig esemle, it s a study o how the theme melody (Figure 2) ca e siged alteratively y each of the four voices. FIGURE 2. Wid, theme melody You ca fid the full score at the ed (Appedix 7), ad you ca liste to it while watchig the score, i which the voice who s sigig the theme melody has ee highlighted (La Matia 2014). Cosiderig the piao, oly y havig melodies also i the middle ad ass registers ca we truly appreciate the whole spectrum of toes that this woderful istrumet has to offer. We already metioed Tristao. He also liked to play melodies i the middle-ass register, like you ca hear i his solos o Lie Up ad East Thirty Secod Street from Leie Tristao (1956). That soud, the roudess of it, is somethig I do t wat to throw away without eve tryig.

17 Both hads play chords with the same rhythm. This is asically voicigs study. Of various approaches I read or heard aout, the oe I like most is Dois (1994). It s asically a way to go through every possile voicig you could ever play o the piao. If oly you had eough time. It s very aalytic ad methodical, almost scietific; ut also really slow. Oe cocept o which Dois is very kee o is liearity i harmoy, which ca already e see i the title of aother ook of his, Jazz arragig ad composig a liear approach (1986). Here are some iterestig words from the preface The aim i this coceptio is to give each istrumet i the esemle a lie which is as melodic as possile. [ ] Sometimes it may e possile to give each hor a tueful ad melodically idepedet lie while, at the same time, creatig a strog sese of harmoic movemet. I thik it is importat to give each istrumet a good lie for two reasos. First, whe each musicia i the esemle has a part which makes musical sese ad is fu to play, everyoe will e ale to play the music with much more ethusiasm ad covictio. Secod, whe the idividual lies move i a clear ad covicig maer, the faric of the music is stroger ad richer. (Dois 1986, 8.) Harmoy as the uio of eautiful melodies. As we saw efore (see Page 15) melody ad harmoy are ot two clearly separated etities. This is why group improvisatio works; eve if the ass player ad piaist decide to play a differet sustitutio o a particular chord, the logicality ad covictio of their sigle lies will make the esemle soud good. Mehldau is also o this way of thikig i his iterview with McPartlad o her show Piao Jazz (2007). Liearity i harmoy meas eig ale to liste to the iteral movemets of harmoy, of the sigle voices, ot just churig out a chord after aother, as if they were separate etities; the ed result is somethig o a completely differet level, soudig very atural ad sustatial. Someoe could call this thikig aout the chords horizotally, istead of vertically. If we are workig o a chord progressio, it does t make much sese to liste to how chords soud i a asolute maer; istead we should liste more attetively to how they evolve ito each other. Eve Bach could soud harsh if you were to liste to a sigle, isolated momet. If the sigle lies soud etter, also the collective ed result should soud etter. Voice leadig, ad ot oly i the top voice. I ca give you a example of how I used this cocept i a luesy outro for a piao trio arragemet of Body ad Soul. I got to the first versio (Figure 3) y thikig aout asic drop2 voicigs.

18 18 FIGURE 3. Body ad Soul, luesy outro, asic drop 2 voicigs The I listeed to the movemets of the sigle voices, ad chaged them so that they souded etter y themselves, regardless of how ucovetioal the resultig voicigs may seem at first (Figure 4). You ca try them ad judge y yourself which oe souds etter. FIGURE 4. Body ad Soul, luesy outro, more liear harmoy Aother key cocept i Dois piao harmoy ook (1994) is simplicity, sice it starts y studyig structures made of four differet otes, avoidig ay doulig. Dois prefers to play oe ote with the left had ad three otes with the right, which allows you to keep the same figerig whe addig a ass ote (1994, 11). Ulike him I like to play two otes with each had, ecause it s dyamically more alaced ad it s easier to add otes to the right had, for example doulig the secod ote from the top oe octave higher, which adds mass to these voicigs. Playig voicigs i a alaced way helps with certai compig styles, as we ll see later (Page 24). Dois (1994, 9) also says that voicigs should e trasposed i all keys without lookig at the ook; I disagree. Trasposig voicigs you re learig for the first time is complicated ad slow, ad overthikig is poitless, as we said efore (Page 8). It s

19 19 est to fid a alace etwee the material eig challegig eough to keep you iterested ad learig, yet ot so difficult that you d just strai without havig fu, thus slowig your progress. If you re good eough at readig sheet music, you should take advatage of that. You will assimilate the trasposed voicigs more easily ad quickly if you just read them. With this i mid I wrote two exercises: oe (Appedix 3) with less commo drop2 voicigs o Coutdow s chages, the other (Appedix 4) with upper structure voicigs o Giat Steps chages. It s stylish to cocetrate o voicigs with a small umer of otes; somethig reow ad appreciated y may i jazz, play-fewer-otes-ut-the-right-oes kida thig. But Dois method is also very slow. So to speed thigs up we ca lear to see the chord toes (see Page 15) ad improvise voicigs o the fly (see also Page 61 aout freefall workout), ad we ca comie voicigs. The way I wat to use hads idepedece here is y havig them play differet oe had voicigs together. So idepedece here is helpig us dividig a sigle ig etity ito two smaller compoets, which are more easily elaorated y our rai. It s easier ad more effective to comie already possessed kowledge ito ew iformatio, tha it is to create somethig ew altogether. Comie three ote ad four ote voicigs, for example three ote quartal voicigs i the left hads ad four ote voicigs i the right, or vice versa. Also, comie two triads or a triad ad a two otes chord to form upper structure voicigs, ad try to reverse every comiatio you try, meaig that you d switch what you play with your right ad you left had. Dois also writes aout comiig smaller voicigs ito igger structures (1994, 110). We re ot goig to go over every kid of comiatio here, ut I ll metio oe that I like, ad I thik it s relatively easy to uild: voicigs with a three or four ote close positio chord i the left had, ad octaves i the right had (or octaves with somethig i etwee, like a fourth, fifth, third or triad). This lock chords are really good also for soloig, ecause the doulig of the top ote gives it eve more power. Ad thik aout Hacock s lock chords, like these oes (Figure 5) I trascried from his solo i Drifti from Taki Off (1962).

20 20 FIGURE 5. Hacock s lock chords from Drifti I the left had there s some 3 or 4 otes chord, ad i the right had there s a octave, which could e filled with somethig (like a 4 th, a 5 th or triad). The doulig at the top ote gives it stregth, so you ca play eautiful lies with this. By the way, you ca otice how we ca fid a very similar kid of voicigs i Clair de lue, the third movemet of Deussy s Suite ergamasque (Figure 6). So rememer to steal from everyoe, eve from classical musicias! FIGURE 6. Deussy s lock chords i Clair de lue Aother thig to keep goig i parallel to the Dois aalytical method to make progress faster, is a deep learig related thig. Ofte I ve ee said, you have to kow for certai some voicigs, the you start usig them, the you lear others, use them too, ad so o. I other words try to play oly voicigs you kow for sure. But istead I thik you should play also voicigs you do t kow, ut just create o the spot, or play ituitively. Whe we talked

21 21 aout deep learig (Page 7) we metioed how ituitio it s the est way to tackle largely complex prolems. As we ve see, the piao harmoy prolem is so ig, it could y itself take up the etirety of our lifetime. So we should just play aroud with it, gettig little y little a geeral uderstadig of how a certai shape would soud. For example, we would kow that a certai shape i the right had ad a certai shape i the left had soud a certai way i a certai register, apply the shape to the group of otes we are cosiderig (see also Page 15 aout seeig a scale). We ca the use these improvised voicigs eve i real life, whe playig real music. Ad y that I mea whe we play with, or for, someoe. Also, try to e cool ad ot e too covetioal with harmoy (see also Page 58 aout playig out). Talkig aout voicigs, do t automatically exclude ay of them. Those with a mior secod o top are ofte avoided y default, for example; ut liste how good they soud i this ackgroud for drums solo (Figure 7). FIGURE 7. Mehldau s ackgroud for drums solo i All The Thigs You Are This is take from Mehldau s live versios of All The Thigs You Are, you ca liste to it either from 4:49 util the ed i the Jazz Festival Vitoria-Gasteiz versio (2006), or from 10:13 util 11:24 i the Art of the Trio 4: Back at the Vaguard (1999). I ca give two examples of ot-so-covetioal chords I stumled oto, liked, ad kept for my arragemets. I Figure 8 you ca spot a A7 quartal voicig with 3 ad oth 9 ad 9. Ad I thik it souds great ad really lues.

22 22 FIGURE 8. Bar 36: A7 voicig with 3, 9 ad 9 (Body ad Soul) Ad here from ar 5 through 8 you ca see a eautiful voice leadig etwee voicigs ased o fifths, from a How Deep Is the Ocea arragemet of mie (Figure 9). FIGURE 9. Bars 5 8: fifths ased chords (How Deep Is the Ocea) Next we take a rief look at large voicigs with lots of sixths ad seveths, which work very well i uildig solo piao arragemets. I guess you could call them doule-drop2 drop3 voicigs, ecause from the close positio the secod ote from the top is dropped two octaves lower, ad the third ote from the top is dropped oe octave lower. They are relatively simple (it s just four otes), ut have a really full soud (they re so spread apart), ad really good voice leadig. I like to move just some of the voices at the same time, ad every oce i a while play aroud with oe at a time, play little melodies. Here s a example (Figure 10). FIGURE 10. Large, doule-drop2 drop3 four ote voicigs for solo piao (All of You) Like it happeed here, voice-leadig harmoy ofte goes more easily dowwards. Tryig ot to play the same thigs over ad over, it ca e good to fid some progressios that go upwards istead. I Figure 11 there s a example of a upward progressio o the rhythm chages.

23 23 FIGURE 11. Upward chord progressio (rhythm chages) Write dow cool voicigs ad cadeces you happe to like. I Figure 12 there s a example of a cadece I ve played y mistake, liked ad writte dow for future referece. It would otherwise e a typical IV- I cadece, ut it has a peculiar ass lie I really like. FIGURE 12. A cadece I live with a eautiful ass movemet Here are two voicigs which I ve stole from Mehldau ecause I like them very much (Figure 13). The chord i the first ar is used i The Falco Will Fly Agai, from Highway Rider (2010); see also Figure 17 at Page 25 for the whole comp patter. The chord i the secod ar is used for example i Resigatio from Elegiac Cycle (1999); it ca also e see as a maj7 chord with the major third at the ass, ut I prefer to see it as mior. FIGURE 13. A couple of really cool Mehldau s voicigs Of course I stole those chords ad started usig them, for example I used the first oe i Wid s (2014) edig (Figure 14). FIGURE 14. Wid s edig, Dadd4 chord I ve stole from Mehldau Also try to e creative with how you use chords. I Figure 15 there s a excerpt from my trascriptio of Hacock s solo i Drifti from Taki Off (1962), where he uses arpeggiated chords as a color.

24 24 FIGURE 15. Excerpt from Hacock s Drifti ; arpeggiated chords add color Thikig aout Brad, he surely uses chords i may differet creative ways; ut if I had to metio oe, it would e the piao solo techique where he repeats chords every sixteeth ote, chagig some thigs little y little ad evidecig voices or melodic lies i the middle of that eautiful mess. Harmoy like a potet, iridescet wall of soud. A idea so simple, yet so effective. We ca hear it i Bittersweet symphoy (2010), from the egiig util aout 3:50, whe it chages ito roke chords, ad the progressively ito melodic repetitive patters with harmoic fuctio (see also Page 39). I Goodye Storyteller (for Fred Myrow) from Live i Marciac (2011) we have a similar passage, ut i iverse order, with roke chords ecomig repeated sixteeth otes chords at aout 5:52, ad cotiuig likewise util the ed of the ext track, Exit Music (for a Film). These two sogs are actually fused together i this particular live versio, which gave me the idea for the arragemet you ca fid at the ed (Appedix 5). 3.2 Both hads play chords with a differet rhythm. We could proaly fit may more thigs ito this chapter, ut I d like to talk aout oe i particular. It s a compig style that i some way mimics oth guitar ad drums. First you have to alace your two-haded voicigs more or less equally etwee your two hads, ad y that I mea that each had should have approximately the same umer of otes. This feels quite atural to me; as I metioed efore (see Page 18) I usually play two otes with each had whe I m playig drop2 four otes voicigs. The it s easy to add extra otes ad fid somethig that will work with this compig style. Oce you have your alaced voicigs, just make rhythms with your hads, like you would do whe playig drums. I this case, rather tha rhythmic idepedece we should talk aout rhythmic co-depedece, sice the hads are creatig a rhythmic patter together. With this techique it s easier to achieve a good groove ad also emulate typical guitar compig rhythms. Here I made the piao versio of the acoustic guitar comp at the egiig of Woderwall (Oasis 1995) (Figure 16).

25 25 FIGURE 16. Woderwall itro, guitar comp, piao versio Mehldau uses ofte this techique. I Figure 17 you ca check out the asic comp rhythm of his compositio The Falco Will Fly Agai, from Highway Rider (2010). FIGURE 17. The Falco Will Fly Agai, asic piao comp I The Old Shade Tree from Mehldau s ad Chris Thile s duo alum (2017) this compig style appears may times throughout the etire duratio of the tue, mixed ad fused together with melodies ad other compig techiques. 3.3 Both hads play a melody with the same rhythm. A very well kow techique that falls ito this category is to doule the right had melody with the left had, oe or more octaves lower. This is really effective, ut sice it s pretty straightforward ad widely used ad taught, I m ot goig to say aythig more aout it. Liste to a super example y Mehldau, i Athropology from Whe I Fall i Love (1993) he doules the theme ad solo melodies, from the egiig util 1:27 oe octave lower, the from 1:27 util 2:03 two octaves lower. Our mai topic i this chapter is goig to e whe the two melodies are actually differet from each other. There s the special case, where the rhythm oth hads play is fixed, like a ostiato. A example could e a motuo like the oe i Figure 18.

26 26 FIGURE 18. A motuo If you re iterested i Cua music ad motuos I suggest you check out Reeca Mauleó- Sataa s ook (2005). We are goig to develop a cocept we already talked aout, seeig the scales as zoes (see Page 15). Classical piaists practice their scales i parallel ad cotrary motio. By cotrary motio I mea whe the hads go i opposite directios (Figure 19). FIGURE 19. /nero-recode-patent-activation-crack/. C major scale, cotrary motio I do t kow why they do it, ut this is actually a step i the directio we re goig to take. First let s play melodies at a fixed distace; the itervals ca e diatoic or chromatic (Figure 20) FIGURE th itervals, oe chord The let s try the same workout (with a differet iterval) o a chord progressio (Figure 21). FIGURE th itervals, chord progressio (All The Thigs You Are) Our workout here cosists of simply playig whatever otes, with whatever rhythm, as log as they are part of our chose group of otes. A few thigs to keep i mid aout this: try ot to play the same ote at the same time with oth hads, ecause that would weake the harmoic effect start with smaller group of otes, like chord toes, ad the move o to larger oes, like scales start y takig just oe group of otes at a time, the later move o to chord

27 27 progressios, so that the group of otes which you are cosiderig keeps chagig together with the uderlyig harmoy oe had ca e harmoically simpler the the other, for example oe could play just chord toes, while the other oe plays otes from a scale start with the hads close to oe aother, ad take advatage from eig ale to easily see what keys oth of them are hittig as you start to get cofidet, try to progressively icrease the space etwee the hads, to the poit where you ca focus your eyes oly o oe had at a time, forcig yourself to kow what you re playig without lookig at it too much (like learig to type without lookig at the keyoard) This workout is really just playig aroud ad gettig a feel of how two melodies ca fit together. Sice it s so geeral, you really do t eed a writte example, ut just to e clearer I made some ayway. First let s play just chords toes over oly oe chord (Figure 22). FIGURE 22. Two melodies, same rhythm, chord toes, oe chord The let s play scale otes, over oly oe chord at a time (Figure 23). FIGURE 23. Two melodies, same rhythm, scale otes, oe chord The chord toes over a chord progressio (Figure 24). FIGURE 24. Two melodies, same rhythm, chord toes, chord progressio (lues) The scale otes over a chord progressio (Figure 25). FIGURE 25. Two melodies, same rhythm, scale otes, chord progressio (Wave) The let s try movig the hads farther away from each other, ad playig chord toes with the left, ad scale otes with the right (Figure 26).

28 28 FIGURE 26. Two melodies, same rhythm, far away, left plays chord toes, right plays scale otes, chord progressio (All The Thigs You Are) OK, so ow we kow what we re workig o. Let s hear a example from the master. I Urequited from Methey/Mehldau (2006), at 1:50 durig Methey s solo Mehldau comps y playig melodies, which sometimes are played y oth hads simultaeously with the same rhythm. We ve ee very geeric i this chapter, ut ow let s see oe specific case. This is a techique that works really well whe playig piao solo. Its fuctio is proaly more harmoic tha melodic, ut it s poitless to discuss these formalities sice we ve see that we ca t clearly draw a lie etwee those two categories. This techique cosists i playig cotiuously otes of the same value (for example all eighth otes, or all sixteeth otes), repeatig the sigle otes a certai umer of times (like two or three), with the last repetitio eig o the eat. At the same time the hads are movig quite ofte i opposite directios, so if the left goes up, the right goes dow, ad vice versa. Liste to a example y Mehldau i his Goodye Storyteller (for Fred Myrow), from Elegiac Cycle (1999), from 4:12 util aout 4:40, ad the agai with differet ote values from 6:12 util 6:20. To get a etter uderstadig you ca check out the trascriptio of that i Adré s ook (2011, , 185). Here s a excerpt from that trascriptio (Figure 27). FIGURE 27. Goodye Storyteller (for Fred Myrow) repeated otes two hads patter from Mehldau s solo Rememer that it does t have to e perfect, ad chromaticisms are welcome. Here s a example I made of this techique, o the chord chages from Soudgarde s Black Hole Su, from their alum Superukow (1994). You ca otice how i some poits I chage oe had s harmoy earlier or later tha the other had s (Figure 28).

29 29 FIGURE 28. Black Hole Su repeated otes two hads patter s example 3.4 Both hads play a melody with a differet rhythm. This is asically the same thig of the last chapter, ut evolved. There ca e may differet cases. Oe really cool thig to do is to play a sort of call ad respose etwee hads. It does t ecessarily have to e just oe had playig at a time; they could e playig together, ut alteratively would get more cocetratio (y the player) ad attetio (y the listeer). This shift of focus from oe had to aother ca e uderlied with the use of dyamics (the voice we focus o has more volume) ad with rhythmic complexity (the voice we do t focus o is rhythmically mootoous ad repetitive). I Brad s reditio of Bittersweet symphoy (2010), at aout 5:45 the left had plays the mai melody, while the right is playig somethig rhythmically mootoous with more of a harmoic fuctio. Soo after that, the right ecomes gradually the ceter of attetio. This is a example of shift of focus i oly oe directio. We have a call ad respose situatio oly whe the focus shifts more quickly from oe had to the other. As a workout we ca try a similar approach to the oe at Page 26 ad followig. With all that i mid, let s take a lues structure ad improvise melodies with oth hads, with a call ad respose itet. We ca also decide to fix the legth of each call ad respose, as if we were

30 30 tradig fours with our admates; so for example each call ad each respose would last two ars, or ars (Figure 29). FIGURE 29. Two melodies, differet rhythm, call ad respose (lues) Aout hads playig melodies with differet rhythms; let s cosider the particular cases whe oth hads are playig fixed rhythms. This is similar to what we saw i Figure 16 at Page 25, ad Figure 17 at Page 25; it s ot exactly the same, though. I all these cases the two hads uild a complex rhythm together, ut here each had s rhythm is importat also o its ow; that has to come out i our playig. To develop this skill of rhythmic idepedece (ad co-depedece) l like to play together two differet istrumets parts from the same tue, tryig to rig out oth rhythms. Here are the ass ad guitar riffs from Dave Hollad s How s Never, from Gateway s Homecomig alum (1995) (Figure 30). FIGURE 30. How s Never, guitar melody ad ass lie Aother particular case is whe oly oe had is playig a fixed rhythm, while the other oe has a more variegated rhythm. We have this whe the left had plays walkig ass while the right had soloes. Practicig walkig ass with your left had aloe is extremely useful. You ca get a deeper uderstadig of a tue s harmoic progressio, ad you ca improve your left had melody playig techique. The whe you re used to it you ca add o top of the walkig ass some chords or a solo melody. Whe you eed to cocetrate o a solo melody, the walkig ass lie is oviously goig to ecome simpler ad more predictale. As Earl Fatha Hies suggests us i his educatioal video (Hies.d.), if your hads are ig eough, you ca oost your walkig ass y playig teths (Figure 31). FIGURE 31. Boost your walkig ass lie y playig 10 th itervals

31 Ayway, walkig ass techiques are very well kow ad taught; there s proaly tos of good quality material o walkig ass already availale, so we re goig to move o. 31 Sice our premise is that hads roles are iterchageale (see Page 16), it makes sese to try to reverse this walkig ass plus solo, so that the right had s melody has a fixed rhythm (every quarter ote for example). I Figure 32 we have a example of a walkig ass lie plus melody. FIGURE 32. Walkig ass plus melody (Stella By Starlight) The we ll reverse it ad get somethig like Figure 33. FIGURE 33. Walkig ass plus melody, reversed (Stella By Starlight) It ca e that oth hads form a patter together. This ca mea i some cases they oth play fixed rhythms, which comied together form a patter. Oe example is this two hads patter (Figure 34) from Deussy s Doctor Gradus ad Parassum, first piece of the suite Childre s Corer (L. 113). FIGURE 34. Doctor Gradus ad Parassum, two hads patter It s asically arpeggiated lock chords, so it ca e easily used i a melodic way, like lock

32 32 chords. Here s a example I made of this patter applied to Ifat Eyes chord chages (Figure 35). FIGURE 35. Deussy s two hads patter applied to Ifat Eyes (B ad C part) These patters ca sometimes e more of a color tha a melody, like the oe from Hacock we saw i Figure 15, Page 24. For developig these kid of more variegated approaches to playig melodies what s est i my opiio is to play free (see also Page 61). Ad of course stealig from other musicias ideas is also great, as we saw with the Deussy patter. Aother case of oth hads playig melodies ut with differet rhythm is whe they form a polyrhythm together. I m very fod of polyrhythms, ad a couple of years ago I made a YouTue video aout some 2:3 ad 4:3 polyrhythm workouts with the metroome; check that out if you re iterested (2015). That video s focus is playig polyrhythmically agaist aother rhythm: the metroome s, or a admate s rhythm i real-life situatios. Here, though, we re talkig aout you playig agaist yourself; for example i the case of a 4:3 or 3:4 polyrhythm, oe of your hads would e playig i three, ad the other oe i four. Mehldau is also fod of this kid of stuff. I that versio of Athropology we already metioed (1993), durig the first part of his solo Rossy at the drums plays polyrhythmically agaist the his rother at the ass, with Mehldau mostly followig the ass s rhythm, while sometimes playig alog with the drums, like at 1:15. I the same tue, from 5:00 to 5:10 he proaly plays some polyrhythmic figure etwee his two hads; I ca t e sure aout what is it actually, ut it souds great. A example of polyrhythm etwee hads that is easier to idetify is foud i Goodye Storyteller (for Fred Myrow), from Elegiac Cycle (1999). As Adré otes (2011, 170), i the solo part Mehldau uses progressively smaller ote values for the accompayig arpeggios,

33 33 acceleratig from eighth otes to eighth ote triplets, sixteeth otes ad sextuplets of sixteeth otes. He returs ack to eighth otes oly efore the fiale theme. May of those passages iclude polyrhythms etwee hads. At 3:38 the left had arpeggios accelerate from eighth otes to eighth ote triples, while the right had still plays eighth otes. The at 4:00 the left keep playig eighth ote triplets, ad the right plays sixteeth otes; the after a while the left starts playig sixteeth otes, too. You ca more easily follow all this from Adré s trascriptio (2011, ). Here s a workout I tried for traiig polyrhythms etwee hads. I played it o a lues structure, ut asically you ca try it o whatever harmoy you wat, possily startig out with sigle chords sice it could e quite challegig. I start y playig a walkig ass lie i 4/4 with the left had, ad simultaeously half ote triplets with the right had. The every oce i a while you try to switch those two without losig your tempo, so that you would e playig half ote triplets with the left had ad quarter otes with the right (Figure 36). FIGURE 36. 3:4 ad 4:3 polyrhythms workout (lues) You ca try this also with other polyrhythms, like 2:3 (Figure 37). FIGURE 37. 3:2 ad 2:3 polyrhythms workout (lues) 3.5 Oe had plays chords, the other oe a melody. Whe oe had plays chords ad the other had a melody, they could e playig the same rhythm, or a differet rhythm. Thik of Evas soloig style; very ofte he plays a melody with the right had, while the left had is playig chords with almost exactly the same rhythm as the right had s melody, emphasizig it ad addig volume. We ca hear it for example i My Romace (take 1) from

34 34 Waltz for Dey (1962), from 2:24 util 3:15. Techiques that add volume to the piao, makig it more similar to a wid solo istrumet, were eve more commo i times whe there was t eough electroic amplificatio to e heard over the drums. I a educatioal video piaist Earl Fatha Hies says his melodies could t e heard whe playig with a ad, so he rought to promiece a techique called trumpet style (Hies.d.), which cosists i playig melodies with octaves. So please e flexile ad keep i mid that i all these workouts, whe we talk aout melody you could play octaves, aother harmoic iterval or eve chords. Thik aout those Hacock s lock chords we saw i Figure 5, Page 20. Agai, harmoy ad melody are ot clearly separated cocepts (see Page 15). Back to Evas, let s try that solo techique of his we were just talkig aout, with the right had playig a melody (solo or theme) ad the left had playig chords with roughly the same rhythm. A example i Figure 38. FIGURE 38. Evas s style: l.h. chords with same rhythm as r.h. melody (Nardis) Ad the of course let s reverse it, with the left had playig a solo melody ad the right had playig chords with roughly the same rhythm (Figure 39). FIGURE 39. Evas s style reversed: r.h. chords with same rhythm as l.h. melody (Nardis) The cotrary of the Eva s style we just saw would e to play chords mostly durig pauses i the melody, as a sort of call ad respose. Here s a example with the right had playig a melody (Figure 40).

35 35 FIGURE 40. Call ad respose, r.h. solo (Have You Met Miss Joes) Ad the oe with the left had playig a melody (Figure 41). FIGURE 41. Call ad respose, l.h. solo (Have You Met Miss Joes) Let s cosider some cases where the hads play differet rhythms from oe aother. It could e that oth hads are playig fixed rhythms. This is quite similar to what we saw i Figure 16 (Page 25), Figure 17 (Page 25) ad Figure 30 (Page 30). The hads are i fact creatig a rhythm together, eig rhythmically co-depedet rather tha idepedet. May compig rhythms fall ito this category, like this asic ossa ova compig (Figure 42). FIGURE 42. Basic ossa ova compig (Wave) Whe oth hads fixed rhythms have differet legths, it tur ito a good polymeters workout (for more aout polymeters see Page 52). Here s oe example: the right had s patter lasts for two 3/4 ars, while the left had s lasts five eighth otes (Figure 43).

36 36 FIGURE 43. Polymeter, patters of differet legths, r.h. two 3/4 ars, l.h. 5/8 I these cases it s ot worth it to write the rhythms i a easier to read way, ecause I feel like it s a way etter workout if you just do it without readig, tryig to feel the two differet patters iterweavig. You ca recycle the same patter just y chagig the meter, which gives it a differet feel; for example i Figure 44 there s the same patter ut i 12/8 meter. FIGURE 44. Polymeter, patters of differet legths, r.h. 12/8, l.h. 5/8 If the meter i which we re playig does t match with the legth of either patter, the it adds eve a third elemet to the polymetric texture (Figure 45). FIGURE 45. Polymeter, either patter s legth matches with the meter Whe oly oe had is playig a fixed rhythm we get a etter chace to study rhythmic idepedece. I felt I could maage to keep a simple rhythm with the left had, while improvisig somethig with the right. But I had o idea how much more difficult it ca e to do the opposite! Eve keepig the most simple rhythm with the right had, like quarter otes o 4/4, ca e super challegig for me. Ayway, let s try these out. The first workout cosists i playig chords with the left had i a steady quarter ote rhythm, while the right had plays a melody (Figure 46) FIGURE 46. L.h. chords fixed rhythm, r.h. melody (Doa Lee) The as usual we re goig to reverse it, switchig hads roles (Figure 47).

37 37 FIGURE 47. R.h. chords fixed rhythm, l.h. melody (Doa Lee) Let s try with a differet rhythm: this time we re goig to play chords o the upeats of two ad four (Figure 48). FIGURE 48. L.h. chords fixed rhythm, r.h. melody (Stella y Starlight) Ad the let s reverse it (Figure 49). FIGURE 49. R.h. chords fixed rhythm, l.h. melody (Stella y Starlight) It ca also e that the had keepig a fixed rhythm is playig a melody, like whe playig walkig ass ad chords (Figure 50). FIGURE 50. There Will Never Be Aother You, walkig ass ad chords Sice we re explorig as may possiilities as we ca thik of, let s try reversig that too, playig a melody with a fixed rhythm with the right had, ad chords with free rhythm with the left had (Figure 51). FIGURE 51. There Will Never Be Aother You, walkig ass ad chords, reverse The there s the case where either had keeps a fixed rhythm. So asically we ca do the

38 similar workouts to those we just saw, oly without ay fixed rhythm. Here s a example (Figure 52). 38 FIGURE 52. R.h. chords free rhythm, l.h. melody (Beatrice Sam Rivers) We ca still keep the tempo, ut it s really useful to play also without tempo, explorig attetively ad thoroughly each chord s harmoic ad melodic possiilities ad comiatios. Aother thig to keep i mid: chords do t have to e four otes voicigs. I fact, oe workout that I like is playig a melody from oe scale with oe had, ad three otes quartal voicigs with the other oe. I fid it s really good for improvig scale-seeig ailities (see Page 15), sice the quartal harmoy is quite idefiite, it s more aout the soority of the mode rather tha the soority of the sigle chords. Therefore it s easier to start studyig quartal voicigs i a scalar motio. As usual, start with oe chord at a time, ad the practice o progressios. With quartals I usually make symmetrical progressios, like chords which are a mior or major third apart from each other (Figure 53). FIGURE 53. L.h. quartal voicigs scalar motio, r.h. melody, Doria modes Ad rememer, eve though I wrote it i 4/4 you ca play it i aother meter or without tempo. Now let s reverse hads of course (Figure 54). FIGURE 54. R.h. quartal voicigs scalar motio, l.h. melody, Doria modes The let s try to move from oe chord to aother i a o-scalar fashio, y larger itervals; ad without keepig ay fixed rhythm (Figure 55). FIGURE 55. R.h. quartal voicigs o-scalar motio, freer rhythm, l.h. melody, Doria modes

39 39 Aother thig: chords do t have to e literally chords. Oce agai, we see how melody ad harmoy are ot two clearly separated cocepts (see Page 15). A chord ca e aythig with a maily harmoic fuctio. Eve a melody with a predomiatly harmoic fuctio ca take the place of chords. Broke chords are somethig i etwee. Traditioally roke chord meas a sequece of sigle otes origiated from oe chord. Arpeggios are oe kid of roke chords. Here I take the term with a wider meaig, icludig also situatios where a chord has ee roke ito smaller chords, possily played quickly after oe aother. This device is used very ofte y Mehldau, especially i his solo playig. Here are some workouts I wrote o the chages from Massive Attack s Teardrop from Mezzaie (1998). First some roke chords, which are made respectively from the 1 st with the 3 rd, ad the 2 d with the 4 th otes form the top of the origial chords (Figure 56). FIGURE 56. Teardrop, r.h. roke chords 13-24, l.h. melody The some that comie respectively the 1 st with the 4 th, ad the 2 d with the 3 rd form the top of the origial chords (Figure 57). FIGURE 57. Teardrop, r.h. roke chords 14-23, l.h. melody Keep i mid those were just examples, you ca use whatever comiatios you like, eve use may of them at oce i a freer way, similarly to what you see i Figure 58.

40 40 FIGURE 58. Teardrop, r.h. varied roke chords, l.h. melody The ext passage would e whe the roke chords are actually made from sigle otes, creatig therefore a melody with a predomiatly harmoic fuctio. I fid playig some accets here ad there helps give it a more harmoic sese. I Figure 59 there s a example, as you see the accets i the first half of each ar are always the same, so as to create a rhythmic patter. FIGURE 59. Teardrop, r.h. melodic roke chords (harmoic melody), l.h. solo melody We already metioed a couple of examples where Mehldau makig this progressive trasitio from chords to roke chords to melody with harmoic fuctio, or vice versa (see Page 24). 3.6 Three voices. Three voices. They could e melodies, chords, riffs, ass otes, or somethig else, or i etwee. To get used to takig care of three voices at oce, I like to just take some tue I kow well, the take from it three simple elemets I wat to play with, ad mix them i every way I ca thik of. It s easier to explai with a example, so let s take Radiohead s Exit Music (For a Film) from OK Computer (1997). The three elemets we re startig with are the vocal melody, guitar chords with their rhythmic patter, ad ass otes. First let s play the melody o top, the chords i the middle ad the ass otes at the ottom (Figure 60).

41 41 FIGURE 60. Exit Music (For a Film), melody top, chords middle, ass ottom The let s start mixig; let s move the melody to the middle ad the chords to the top (Figure 61). FIGURE 61. Exit Music (For a Film), chords top, melody middle, ass ottom Same thig, ut with melody ad ass otes a octave higher (Figure 62). FIGURE 62. Exit Music (For a Film), chords top, melody middle, ass ottom Sice the melody is i the middle, it ca e played y either had; so ow let s try to play it with the right had. The chords ca e a little smaller to make it easier (Figure 63). FIGURE 63. Exit Music (For a Film), chords top, melody middle (r.h.), ass ottom I this case the left had is pretty idle, just playig a few ass otes. Let s try to employ it a it more the, playig some ass lies every oce i a while, especially whe there are pauses i the mai melody (Figure 64).

42 42 FIGURE 64. Exit Music (For a Film), chords top, melody middle (r.h.), ass ottom (with more ass lies ad fills) Goig o like this we ca try may other comiatios, ad keep workig o the oes we like most. There s ot much improvisatio here, this kid of workout is more aout arragig, comiig simple thigs i fresh ew ways. At the same time, though, we are developig our solo piao skills, ad our aility to thik ad play, more voices, at the same time. Now let s play Coldplay s Speed of Soud, from XY (2005). This time we re goig to take also a riff as oe of the elemets (voices); it s the riff i the itro, which fits also i the verse ecause the chords are the same. So, first the melody o top, the riff i the middle, ass otes at the ottom (Figure 65). FIGURE 65. Speed of Soud, melody top, riff middle, ass ottom The let s move the melody to the middle, ad the riff to the top (Figure 66). FIGURE 66. Speed of Soud, riff top, melody middle, ass fixed rhythm ottom The let s move the riff to the ottom, ad the melody to the top; i the middle let s play chords (Figure 67).

43 43 FIGURE 67. Speed of Soud, melody top, chords middle, riff ottom The, keepig the riff at the ottom, let s move the melody to the middle, ad the chords to the top (Figure 68). FIGURE 68. Speed of Soud, chords top, melody middle, riff ottom Ad like efore, we ca mix eve more of course, these were just a few examples. Let s take aother tue, Part of Your World from the 1989 Disey movie The Little Mermaid; you ca watch the origial clip o YouTue (Beso 2014). The elemets we re startig with are the vocal melody o top, a riff from the itro i the middle, ad ass otes at the ottom. I the sogs that riff stops after a while, ut we ca keep it goig for as log as we like, of course adaptig it to the chord chages (Figure 69). FIGURE 69. Part of Your World, melody top, riff middle, ass ottom The let s move the riff to the top, ad the melody to the middle (Figure 70).

44 44 FIGURE 70. Part of Your World, riff top, melody middle, ass ottom The let s move the riff to the ottom ad the melody to the middle; as a third elemet let s add to the top sigle otes with harmoic fuctio (Figure 71). FIGURE 71. Part of Your World, sigle otes top, melody middle, riff ottom The istead of those sigle otes we ca also try playig small chords (Figure 72). FIGURE 72. Part of Your World, chords top, melody middle, riff ottom The let s move the melody to the ottom, the riff to the top, ad the sigle otes with harmoic fuctio to the middle (Figure 73).

45 45 FIGURE 73. Part of Your World, riff top, oe ote middle, melody ottom The, istead of the riff, let s try playig chords at the top (Figure 74). FIGURE 74. Part of Your World, chords top, sigle otes middle, melody ottom The istead of those log chords let s play roke chords, like those we talked aout at Page 39 (Figure 75). FIGURE 75. Part of Your World, quarter otes roke chords top, sigle otes middle, melody ottom The let s play them faster, as eighth otes (Figure 76).

46 46 FIGURE 76. Part of Your World, eighth otes roke chords top, sigle otes middle, melody ottom Now some rhythmic variatios. At Page 32 we talked aout polyrhythms etwee hads; see also Figure 36 (Page 33) ad Figure 37 (Page 33). Let s take what we had i Figure 70, Page 44; we ll modify the theme melody, so that it forms a polyrhythmic texture with the riff (Figure 77). FIGURE 77. Part of Your World, riff top, 3:4 polyrhythmic melody middle, ass ottom Aother kid of rhythmic variatio is rhythmic displacemet; for more aout it see Page 49. Let s go ack to what we had i Figure 71, Page 44; we ll displace the riff at the ottom so that it starts a eighth ote earlier (Figure 78).

47 47 FIGURE 78. Part of Your World, sigle otes top, melody middle, displaced riff ottom The let s displace i the same way also the sigle otes with harmoic fuctio at the top; we ll leave the melody i its place, otherwise there would t e aythig left to stad out agaist the displaced elemets (Figure 79). FIGURE 79. Part of Your World, displaced sigle otes top, melody middle, displaced riff ottom At Page 12 we talked aout playig cross-hadedly, which makes thigs easier whe we wat to keep a voice goig o i the middle, ad the play alteratively over ad uder it. Switchig hads i the middle of a cotiuig voice is quite difficult; it will soud more atural if the had playig the cotiuig voice i the middle it s always the same, while the other had cross over it whe eeded. Let s try this o Massive Attack s Teardrop from Mezzaie (1998). Oe had plays the riff i the middle, the other had plays solos, alteratively over ad uder it. Solos ca e melodies, chords, a mix of them, whatever. We ca try this oth ways: with the right had i the middle ad the left had crossig over, the vice versa, with the left had i the middle ad the right had crossig over (Figure 80).

48 48 FIGURE 80. Teardrop, riff middle (r.h. or l.h.), solos alteratively top ad ottom (l.h. or r.h.) Now istead of the riff let s play chords i the middle (Figure 81). FIGURE 81. Teardrop, chords middle, solos top ad ottom alteratively Oe of the elemets ca also e a pedal poit, which is a ote that does t chage while the surroudig harmoy chages. It s usually foud i the ass, ut it could e also the melody at the top; thik of Atôio Carlos Joim s Sama de Uma Nota Só (AKA Oe Note Sama). Pedal poits ca e eve i the middle of the harmoy. Mehldau has used this techique i may occasios i his solo playig; Adré calls it toic pedal i his ook (2011, 171). He metios some examples from Mehldau s recordigs, which I ll report here, so that you ca liste to how this techique souds whe played y a master. You ca hear it i Resigatio from Live i Marciac (2011), i Blackird from Love Sogs with vo Otter (2010), ad i Goodye Storyteller (for Fred Myrow), from Elegiac Cycle (1999). I sog I like to play this i is Ifat Eyes; a ote that fits well throughout the chord chages is B. Let s try playig a B pedal poit i the middle with oe had, ad improvised solos ad chords over ad uder it with the other had (Figure 82). FIGURE 82. Ifat Eyes, B pedal middle, solos ad chords top ad ottom Sice the had playig the pedal has ot too much to do, it ca play also other thigs i the meatime. The pedal poit is a very simple elemet, so we ca also try to play it alteratively with the left or the right had, whichever oe is closer ad less usy. Now let s play pedal poits ad chords i the middle with oe had, while the other had plays solos alteratively over ad uder it (Figure 83).

49 49 FIGURE 83. Ifat Eyes, B pedal ad chords middle, solos top ad ottom alteratively Here eds this chapter aout hads idepedece, the logest i this work. Before movig o to the ext oe I ll metio more examples from Mehldau s playig that iclude thigs metioed i this chapter. I Teardrop from 10 Years Solo Live (2015), from 2:12 util 4:15, there are aout four voices goig o; there s a riff, some ass, melodies at the ass, melodies ad chords over the riff. Proaly Mehldau is playig the riff ad sometime the ass with the left had, ad the middle-ass melodies ad the high chords ad melodies with the right had; ut we ca t tell for sure, he could eve e switchig hads i the middle of oe voice. I the versio of Goodye Storyteller (for Fred Myrow) from Klotz s documetary (Mehldau 1999), from 5:03 util 5:33 he plays three or four voices; the right had starts playig a trill, ad at the same time over that also sigle otes that form a lie, ad the left had i the meatime plays a cotiuous roke chord compig. I Make peace from the duo alum with Methey (2006), Brad starts his solo at aout 4:00 with a melody played y the right had, as the left plays chords with strog voice leadig ad sometimes melodic lies that go together with, or respod to, the right s melody (like at 4:13-4:20). The from 4:35 util 5:45 the right had plays chords, ad the left had takes care of the middle ad ass voices, sometimes playig a melody i the middle, sometimes ass otes ad rhythmic chord patters etwied with the right had s. The from 5:45 util the ed of the solo it s the right agai that takes care of the melody. 4. RHYTHMIC AND METRIC INDEPENDENCE I love all kids of rhythmic illusio ad cofusio. I this chapter we ll go through some pheomea related to rhythm ad meter. We ve already talked aout rhythmic idepedece (see Page 14, Page 24, Page 30 ad Page 36). We ve metioed also rhythmic displacemet; ow we re goig to dig ito it more deeply. 4.1 Rhythmic displacemet I heard aout it from a educatioal video y Ari Hoeig ad Johaes Weidemueller (2009). Hoeig is the guru of rhythmic ad metric mischievousess; I suggest you check out Hoeig s educatioal material ecause it s rilliat (Hoeig.d.). Also, liste to Waye Kratz. Rhythmic displacemet cosists i movig a rhythmic patter so that it starts earlier, or later.

50 50 Whe the eat is divided ito three parts, we have three possiilities for displacemet; whe the eat is divided ito four we have four possiilities, ad so o. I Figure 78 (Page 47) ad Figure 79 (Page 47) we had Part of Your World, which was divided i groups of four eighth otes; we displaced some elemets oe eighth ote earlier. Now a example of rhythmic displacemet i the opposite directio. I ve ee playig electric piao i guitarist Toi Taskie s project; we recorded fusio versios of Erik Satie s Trois Gossiees. Bassist Heri Laitie composed a eautiful ass riff for Gossiee No. 2, usig rhythmic displacemet. Here s the idea from which he started (Figure 84). FIGURE 84. Heri Laitie s ass riff s origi It s a really straightforward ass riff, which I had already heard may times efore. We ca write it also i 4/4 (Figure 85). FIGURE 85. Heri Laitie s ass riff s origi 4/4 The idea was to have a Afro compig, so let s write it i 12/8 (Figure 86). FIGURE 86. Heri Laitie s ass riff s origi 12/8 Now the part which makes it super cool: let s displace it a eighth ote later (Figure 87). FIGURE 87. Heri Laitie s ass riff, rhythmic displacemet Ad the let s rewrite it with a differet sudivisio; each eat is clearly separated, this makes it easier to read (Figure 88). FIGURE 88. Heri Laitie s ass riff, rhythmic displacemet, easier to read What s really cool aout this kid of rhythmic tricks, is that you ca use them to create illusios. To hear that a elemet is displaced, there has to e aother, o-displaced elemet, agaist which we ca hear the displacemet. I love it whe a sog starts with a sigle elemet with a easily recogizale rhythm, ad the aother elemet comes i, ad oly the you otice that the first elemet is t what you thought it was. I our versio of Gossiee No. 2 after the first theme Heri plays the ass riff i Figure 88; ut he plays aloe, so istictively everyoe thiks that he s actually playig the o-displaced riff i Figure 84. The drummer Atti-Pekka Rissae comes i, ut he plays together with Heri, i such a amiguous way

51 51 that oody thiks they re oth displaced. The, little y little, A-P starts to e less amiguous ad comes ack to playig o the o-displaced eats, ultimately evolvig ito a full-low shuffle compig. Here there are more examples of rhythmic displacemet; these are from my video aout practicig polyrhythms with the metroome (2015). We re displacig the stride-like left had compig, while the right had melody stays the same. The tue is Straight No Chaser. Sice we re playig it with swig eighth otes, which are approximately ased o a triplet, we have a total of three possiilities for displacemet, icludig the origial, o-displaced versio. Let s start with that (Figure 89). FIGURE 89. Straight No Chaser, stride-like compig, o displacemet The let s displace the compig oe triplet eighth ote earlier (Figure 90). FIGURE 90. Straight No Chaser, stride-like compig displaced oe triplet eighth ote earlier The the last optio availale: displacig the compig oe triplet eighth ote later (Figure 91). FIGURE 91. Straight No Chaser, stride-like compig displaced oe triplet eighth ote later Whe I m playig solo piao I like to displace the left had compig every oce i a while. Let s try displacig a arpeggiated compig, while soloig over it. The tue is Black Hole Su y Soudgarde, from their alum Superukow (1994) (Figure 92). FIGURE 92. Black Hole Su, rhythmically displaced arpeggio compig

52 52 Mehldau does somethig similar i Resigatio from Elegiac Cycle (1999); Adré metios it i his ook, callig it rhythmic shifts i the ass (2011, 61). So may of the workouts i the previous chapter ca e displaced; let s try with the oe from Figure 47, Page 37 (Figure 93). FIGURE 93. R.h. chords displaced oe triplet eighth ote earlier, l.h. solos (Doa Lee) The let s displace it i the opposite directio (Figure 94). FIGURE 94. R.h. chords displaced oe triplet eighth ote later, l.h. solos (Doa Lee) These were just examples, there are may other possiilities; experimet as much as you like. 4.2 Polyrhythms / polymeters Aother rhythmic pheomeo we already talked aout is polyrhythms (see Page 32 ad Page 46). Some make a distictio etwee polyrhythms ad polymeters: polyrhythms are measure-preservig, while polymeters are eat-preservig; the there are polytempi, which do t preserve either measures ot eats (Wikipedia). I m ot a stickler for omeclature, so how we call them it does t matter much, ut the distictio itself is iterestig ecause it presets us two ways to explore those pheomea. The whole idea of havig two or more meters, ad therefore two tempi, goig o at the same time, is as fasciatig as havig two or more voices goig o at the same time. Mehldau also likes this cocept; here s a trascript from Nicolas Klotz s documetary (Mehldau 1999) where Mehldau talks aout his trio work, ad how they like to two pulses goig o at the same time: It s pretty specific what I m doig, I thik, especially with the trio, you kow. We have the regular pulse that s goig o ad the we have aother pulse, that would seem to e urelated to that, ad the idea is to make your phrases ad your melodies i that other pulse, i that other tempo; ut that time is

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Professional Networking

Professioal Networkig 1. Lear from people who ve bee where you are. Oe of your best resources for etworkig is alumi from your school. They ve take the classes you have take, they have bee o the job market

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Determining the sample size

Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

More information

Hypothesis testing. Null and alternative hypotheses

Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

More information

Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio

More information

Lesson 17 Pearson s Correlation Coefficient

Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

Snap. Jenine's formula. The SNAP probability is

Sap The game of SNAP is played with stadard decks of cards. The decks are shuffled ad cards are dealt simultaeously from the top of each deck. SNAP is called if the two dealt cards are idetical (value

More information

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).

BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly

More information

The second difference is the sequence of differences of the first difference sequence, 2

Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for

More information

Solving Inequalities

Solvig Iequalities Say Thaks to the Authors Click http://www.ck12.org/saythaks (No sig i required) To access a customizable versio of this book, as well as other iteractive cotet, visit www.ck12.org CK-12

More information

Key Ideas Section 8-1: Overview hypothesis testing Hypothesis Hypothesis Test Section 8-2: Basics of Hypothesis Testing Null Hypothesis

Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, P-value Type I Error, Type II Error, Sigificace Level, Power Sectio 8-1: Overview Cofidece Itervals (Chapter 7) are

More information

Math C067 Sampling Distributions

Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters

More information

Building Blocks Problem Related to Harmonic Series

TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite

More information

Example Consider the following set of data, showing the number of times a sample of 5 students check their per day:

Sectio 82: Measures of cetral tedecy Whe thikig about questios such as: how may calories do I eat per day? or how much time do I sped talkig per day?, we quickly realize that the aswer will vary from day

More information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,

More information

Mathematical goals. Starting points. Materials required. Time needed

Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios

More information

AQA STATISTICS 1 REVISION NOTES

AQA STATISTICS 1 REVISION NOTES AVERAGES AND MEASURES OF SPREAD www.mathsbox.org.uk Mode : the most commo or most popular data value the oly average that ca be used for qualitative data ot suitable if

More information

I. Chi-squared Distributions

1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

Simple Annuities Present Value.

Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

Basic Elements of Arithmetic Sequences and Series

MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

More information

Week 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable

Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5

More information

THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3, n

We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =, This model icludes the assumptio that the ε i s are a sample

More information

6. p o s I T I v e r e I n f o r c e M e n T

6. p o s I T I v e r e I f o r c e M e T The way positive reiforcemet is carried out is more importat tha the amout. B.F. Skier We all eed positive reiforcemet. Whether or ot we are cosciously aware of

More information

Lecture 4: Cauchy sequences, Bolzano-Weierstrass, and the Squeeze theorem

Lecture 4: Cauchy sequeces, Bolzao-Weierstrass, ad the Squeeze theorem The purpose of this lecture is more modest tha the previous oes. It is to state certai coditios uder which we are guarateed that limits

More information

Wes Montgomery Harmonization Techniques

Wes Motgomery Harmoizatio Techiques Belo is oe scale choice that Wes Motgomery icorporates over a mior 7 chord This particular scale is a Doria Mode ith a added chromatic etee the 7 ad Root This is cosidered Download picture style untuk canon 600d t3i.

More information

Module 4: Mathematical Induction

Module 4: Mathematical Iductio Theme 1: Priciple of Mathematical Iductio Mathematical iductio is used to prove statemets about atural umbers. As studets may remember, we ca write such a statemet as a predicate

More information

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

More information

Lesson Plans for Teachers

Lesso Plas for Teachers Kidergarte - Grade 3 Copyright 2012 by Little Pickle Press LLC Table of Cotets Quite uique! Streeeetch ad grooow.. Overview 3 Activity Set 1 What Is a Brai ad What Does It Do?

More information

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations

CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad

More information

Handling. Collection Calls

Hadlig the Collectio Calls We do everythig we ca to stop collectio calls; however, i the early part of our represetatio, you ca expect some of these calls to cotiue. We uderstad that the first few moths

More information

Sum and Product Rules. Combinatorics. Some Subtler Examples

Combiatorics Sum ad Product Rules Problem: How to cout without coutig. How do you figure out how may thigs there are with a certai property without actually eumeratig all of them. Sometimes this requires

More information

How to use what you OWN to reduce what you OWE

How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.

More information

Standard Errors and Confidence Intervals

Stadard Errors ad Cofidece Itervals Itroductio I the documet Data Descriptio, Populatios ad the Normal Distributio a sample had bee obtaied from the populatio of heights of 5-year-old boys. If we assume

More information

1. C. The formula for the confidence interval for a population mean is: x t, which was

s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form. D. Use the rule : p-value

More information

Recursion and Recurrences

Chapter 5 Recursio ad Recurreces 5.1 Growth Rates of Solutios to Recurreces Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer. Cosider, for example,

More information

Divide and Conquer. Maximum/minimum. Integer Multiplication. CS125 Lecture 4 Fall 2015

CS125 Lecture 4 Fall 2015 Divide ad Coquer We have see oe geeral paradigm for fidig algorithms: the greedy approach. We ow cosider aother geeral paradigm, kow as divide ad coquer. We have already see a

More information

The Forgotten Middle. research readiness results. Executive Summary

The Forgotte Middle Esurig that All Studets Are o Target for College ad Career Readiess before High School Executive Summary Today, college readiess also meas career readiess. While ot every high school

More information

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

More information

Descriptive statistics deals with the description or simple analysis of population or sample data.

Descriptive statistics Some basic cocepts A populatio is a fiite or ifiite collectio of idividuals or objects. Ofte it is impossible or impractical to get data o all the members of the populatio ad a small

More information

1 Computing the Standard Deviation of Sample Means

Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

The Importance of Media in the Classroom

01-TilestoVol09.qxd 8/25/03 3:47 PM Page 1 1 The Importace of Media i the Classroom As teachers, we have a wealth of iformatio from which to choose for our classrooms. We ca ow brig history ito the classroom

More information

Discrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13

EECS 70 Discrete Mathematics ad Probability Theory Sprig 2014 Aat Sahai Note 13 Itroductio At this poit, we have see eough examples that it is worth just takig stock of our model of probability ad may

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

Properties of MLE: consistency, asymptotic normality. Fisher information.

Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout

More information

G r a d e. 2 M a t h e M a t i c s. statistics and Probability

G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

Sequences and Series

CHAPTER 9 Sequeces ad Series 9. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their

More information

Soving Recurrence Relations

Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Listing terms of a finite sequence List all of the terms of each finite sequence. a) a n n 2 for 1 n 5 1 b) a n for 1 n 4 n 2

Pdf To Jpg

74 (4 ) Chapter 4 Sequeces ad Series 4. SEQUENCES I this sectio Defiitio Fidig a Formula for the th Term The word sequece is a familiar word. We may speak of a sequece of evets or say that somethig is

More information

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

More information

CS103X: Discrete Structures Homework 4 Solutions

CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible six-figure salaries i whole dollar amouts are there that cotai at least

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

Elementary Theory of Russian Roulette

Elemetary Theory of Russia Roulette -iterestig patters of fractios- Satoshi Hashiba Daisuke Miematsu Ryohei Miyadera Itroductio. Today we are goig to study mathematical theory of Russia roulette. If some

More information

WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12

WidWise Educatio T rasformig the Eergy of Wid ito Powerful Mids A Curriculum for Grades 6 12 Notice Except for educatioal use by a idividual teacher i a classroom settig this work may ot be reproduced

More information

Section 11.3: The Integral Test

Sectio.3: The Itegral Test Most of the series we have looked at have either diverged or have coverged ad we have bee able to fid what they coverge to. I geeral however, the problem is much more difficult

More information

BINOMIAL EXPANSIONS 12.5. In this section. Some Examples. Obtaining the Coefficients

652 (12-26) Chapter 12 Sequeces ad Series 12.5 BINOMIAL EXPANSIONS I this sectio Some Examples Otaiig the Coefficiets The Biomial Theorem I Chapter 5 you leared how to square a iomial. I this sectio you

More information

Impact your future. Make plans with good advice from ACT. Get Set for College 1. THINK 2. CONSIDER 3. COMPARE 4. APPLY 5. PLAN 6.

Impact your future Get Set for College 1. THINK 2. CONSIDER 3. COMPARE 4. APPLY 5. PLAN 6. DECIDE Make plas with good advice from ACT. 1. Thik Thik about yourself ad your college eeds Do you start thigs

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

Modified Line Search Method for Global Optimization

Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

Ideate, Inc. Training Solutions to Give you the Leading Edge

Ideate, Ic. Traiig News 2014v1 Ideate, Ic. Traiig Solutios to Give you the Leadig Edge New Packages For All Your Traiig Needs! Bill Johso Seior MEP - Applicatio Specialist Revit MEP Fudametals Ad More!

More information

A Resource for Free-standing Mathematics Qualifications Working with %

Ca you aswer these questios? A savigs accout gives % iterest per aum. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%

More information

Quadratics - Revenue and Distance

9.10 Quadratics - Reveue ad Distace Objective: Solve reveue ad distace applicatios of quadratic equatios. A commo applicatio of quadratics comes from reveue ad distace problems. Both are set up almost

More information

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

More information

CS100: Introduction to Computer Science

I-class Exercise: CS100: Itroductio to Computer Sciece What is a flip-flop? What are the properties of flip-flops? Draw a simple flip-flop circuit? Lecture 3: Data Storage -- Mass storage & represetig

More information

GOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS

GOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS I the sprig of 2008, Stadig Together agaist Domestic Violece carried out a piece of collaborative work o domestic violece

More information

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

More information

Setting Up a Contract Action Network

CONTRACT ACTION NETWORK Settig Up a Cotract Actio Network This is a guide for local uio reps who wat to set up a iteral actio etwork i their worksites. This etwork cosists of: The local uio represetative,

More information

ABCs. of Diabetes Care

ABCs of Diabetes Care Stayig healthy whe you have diabetes ca be challegig. But the more you focus o the positive results of a healthy diet, medicatio routie ad regular exercise, the easier it will be

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

PUBLIC RELATIONS PROJECT 2016

PUBLIC RELATIONS PROJECT 2016 The purpose of the Public Relatios Project is to provide a opportuity for the chapter members to demostrate the kowledge ad skills eeded i plaig, orgaizig, implemetig ad evaluatig

More information

Betting on Football Pools

Bettig o Football Pools by Edward A. Beder I a pool, oe tries to guess the wiers i a set of games. For example, oe may have te matches this weeked ad oe bets o who the wiers will be. We ve put wiers i

More information

5: Introduction to Estimation

5: Itroductio to Estimatio Cotets Acroyms ad symbols.. 1 Statistical iferece.. Estimatig µ with cofidece.. 3 Samplig distributio of the mea.. 3 Cofidece Iterval for μ whe σ is kow before had.. 4 Sample

More information

The Fundamental Forces of Nature

Gravity The Fudametal Forces of Nature There exist oly four fudametal forces Electromagetism Strog force Weak force Gravity Gravity 2 The Hierarchy Problem Gravity is far weaker tha ay of the forces! Why?!?

More information

Application and research of fuzzy clustering analysis algorithm under micro-lecture English teaching mode

SHS Web of Cofereces 25, shscof/20162501018 Applicatio ad research of fuzzy clusterig aalysis algorithm uder micro-lecture Eglish teachig mode Yig Shi, Wei Dog, Chuyi Lou & Ya Dig Qihuagdao Istitute of

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments

Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 6-12 pages of text (ca be loger with appedix) 6-12 figures (please

Brad Mehldau Albums

More information

1 Correlation and Regression Analysis

1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

Agenda. Outsourcing and Globalization in Software Development. Outsourcing. Outsourcing here to stay. Outsourcing Alternatives

Outsourcig ad Globalizatio i Software Developmet Jacques Crocker UW CSE Alumi 2003 [email protected] Ageda Itroductio The Outsourcig Pheomeo Leadig Offshore Projects Maagig Customers Offshore Developmet

More information

Arithmetic Sequences and Partial Sums. Arithmetic Sequences. Definition of Arithmetic Sequence. Example 1. 7, 11, 15, 19,.., 4n 3,..

3330_090.qxd 1/5/05 11:9 AM Page 653 Sectio 9. Arithmetic Sequeces ad Partial Sums 653 9. Arithmetic Sequeces ad Partial Sums What you should lear Recogize,write, ad fid the th terms of arithmetic sequeces.

More information

Covariance and correlation

Covariace ad correlatio The mea ad sd help us summarize a buch of umbers which are measuremets of just oe thig. A fudametal ad totally differet questio is how oe thig relates to aother. Stat 0: Quatitative

More information

Spss Lab 7: T-tests Section 1

Spss Lab 7: T-tests Sectio I this lab, we will be usig everythig we have leared i our text ad applyig that iformatio to uderstad t-tests for parametric ad oparametric data. THERE WILL BE TWO SECTIONS FOR

More information

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.

5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers

More information

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is

0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values

More information

Get advice now. Are you worried about your mortgage? New edition

New editio Jauary 2009 Are you worried about your mortgage? Get advice ow If you are strugglig to pay your mortgage, or you thik it will be difficult to pay more whe your fixed-rate deal eds, act ow to

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

Tenants handbook Booklet 4. Paying your rent. June 2015

Teats hadbook Booklet 4 Payig your ret Jue 2015 Your Ret ad other charges Payig your ret ad other charges is a coditio of your teacy. If you do ot pay, you will have broke your teacy agreemet with us.

More information

(VCP-310) 1-800-418-6789

Brad Mehldau Transcription Pdf To Word

Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.

More information

The Euler Totient, the Möbius and the Divisor Functions

The Euler Totiet, the Möbius ad the Divisor Fuctios Rosica Dieva July 29, 2005 Mout Holyoke College South Hadley, MA 01075 1 Ackowledgemets This work was supported by the Mout Holyoke College fellowship

More information

Section 1.6: Proof by Mathematical Induction

Sectio.6 Proof by Iductio Sectio.6: Proof by Mathematical Iductio Purpose of Sectio: To itroduce the Priciple of Mathematical Iductio, both weak ad the strog versios, ad show how certai types of theorems

More information

8.1 Arithmetic Sequences

MCR3U Uit 8: Sequeces & Series Page 1 of 1 8.1 Arithmetic Sequeces Defiitio: A sequece is a comma separated list of ordered terms that follow a patter. Examples: 1, 2, 3, 4, 5 : a sequece of the first

More information

Hypergeometric Distributions

7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you

More information

Brad Mehldau Radiohead

Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

More information

Engineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51

Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log

More information

Research Method (I) --Knowledge on Sampling (Simple Random Sampling)

Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact

More information

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

More information

4.1 Sigma Notation and Riemann Sums

Pdf To Word Converter Free Download

0 the itegral. Sigma Notatio ad Riema Sums Oe strategy for calculatig the area of a regio is to cut the regio ito simple shapes, calculate the area of each simple shape, ad the add these smaller areas

Brad Mehldau Piano

More information