A Bridge Principle for Harmonic Maps

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Sign in to Purchase Instantly. Usually ships within 1 week. Overview This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. Product Details Table of Contents.

The Analysis of Harmonic Maps and Their Heat Flows

Table of Contents Preface vii Organization of the book ix Acknowledgements xi 1 Introduction to harmonic maps 1 1. Show More. Average Review.

Modality is the opposite of functional harmony where phrases resolve with voice leading rules. Modal playing has opened another huge and rich area for jazz improvisation to explore and when we map jazz solos these different approaches have to be noted. Michael Brecker often uses superimposed triads over a simple harmonic framework as in the following example over a simple Cm7 chord. These triads can create more tension and also add movement to a static underlying harmony.

These few examples serve just as a starting point for discussing the mapping process and to reveal some of the syntax tools of the language. In a sense although we are looking for Parker — ism, Sonny — isms, Trane — isms, Brecker — isms, etc, arriving into any — isms, for the new developing player when he thrives to realize his personal voice, we need to see all these under the proper perspective into a harmonic and melodic framework. Pattern - isms can describe the players and the styles and can be extremely useful for players or computer systems, but when they acquire harmonic, melodic, voice leading etc.


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Another different subject is to examine sound. This is a very important aspect that has changed a lot in jazz history. As players develop more harmonic information they tend to rely on sound nuances less and they play with uniform sound, while traditional jazz players had a lot of expressive colors in their playing. This will become very evident when we examine ballad playing, where vibrato, subtone and other more human like vocal effects are evident on the old school cats.

We should examine samples from players to detect crucial aspects that are responsible for certain texture and timbre effects they produce. Also harmonic tension can be produced by just sound itself. Difference in attack, articulation, bending, vibrato, timbre can make just a strategically placed note very important in a jazz solo and can create excitement. Players like Miles Davis where able to express a lot with very few notes.

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We can store favorite phrases from great players that characterize their playing and together with the topics and approaches touched upon above, these phrases will gain the necessary direction and harmonic meaning. What is regarded as beautiful in a jazz solo is a matter of a big discussion with players and listeners and especially with the greats that are still alive.

This discussion will get us deep into the insights of this great art form and will shed light on many gems of the language. And usually his phrases describe the underlying harmony very well. We can do with as many functional or modal phrases we can find from the repertoire and vocabulary, which is easily accessible with many transcribed solos available. The important thing is to isolate the phrases and map their meanings adding the descriptor values.

That way we can identify his special way of playing like when we talk about mannerisms in speech. The use of pre-learned patterns is also very important and self evident when we listen to many great players but this is only used partially. We could also plan how patternistic, modal, bebopish, thematic, linear, melodic, fragmental, bluesy etc we want the new solo to be and in that manner we could create many interesting and contrasting new improvisations.

In short here are some descriptors that can acquire values:. To conclude I could suggest that we can focus on 3 main areas. One task will be the mapping itself that needs a lot of detailed work for every phrase, sound and approach. Third area is to start working with visual or other performing arts and connect the mappings with analogous valued descriptors. We can present these descriptors for discussion and evaluation to jazz greats, while a method of evaluation has been discussed in relation to also presenting these mapping values to audience.

If we can succeed in emulating, up to a point, the processes behind a jazz player, as a real time improviser, then we will be getting closer to making a computer system, that reproduces an improvisation, react in a more creative way. Dimitri Vassilakis May revision. The tritone, as a multi-vehicle for harmonic movement, will be examined, under a new light, comparing its use in functional, modal and blues harmony: As the 11th harmonic F comes high in the harmonic series.

If we continue to built the full chord until we get to the tonic C, we get: C-E-G-B-D-F -A-C and again we are faced with the same problem of having two minor 3rds in a row. See how the 7 th resolves to the 3 rd on: bar 8 to bar 9 from Bb to A, bar 10 to 11 from A to G, bar 11 to 12 from D to C , bar 12 to 13 from G to F, bar 14 to 15 from F to E… He achieves a nice rhythmic and melodic flow combining diatonic playing, nice swing phrasing, voice leading and rhythmic variety. The system remains you with the Tutorial and possible books based for database in the new selection system.

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A Bridge Principle for Harmonic Diffeomorphisms between Surfaces | SpringerLink

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