Rhythm: The Music of the Spheres

"Music is a hidden arithmatic exercise of the soul, which does not know that it is dealing with numbers, because it does many things by way of unnoticed conceptions which with clear conception it could not do. Those who believe that nothing can happen in the soul of which the soul is not conscious are wrong. For this reason the soul, although not realizing that it is involved in mathematical computation, still senses the effect of this unnoticeable forming of numbers either as a resultant feeling of well-being in the case of harmonies or as discomfort in the case of disharmonies."
Gottfried Wilhelm Leibniz

Rhythm is the basis of harmonic proportions and intervals, fundamental physical mechanisms. This harmonious equilibration was expounded upon by Pythagoras, father of Philosophy. Pythagorean thought formed the basis of the philosophy of Plato, and later Neo-Pythagoreans and Platonists, and greatly influenced the development of western science.

Pythagoras laid the foundation for a holistic science which integrated spiritual, ethical, and metaphysical, as well as practical techniques. Pythagoras is famous for his axiomatic viewpoint that "there is geometry in the humming of the strings. There is music in the spacing of the spheres." From Plotinus we hear, "All music based upon melody and rhythm, is the earthly representative of heavenly music."

And from Sufi Hazrat Inayat Khan,

"When one looks at the cosmos, the movements of the stars and planets, the law of vibration and rhythm, all perfect and unchanging, it shows that the cosmic system is working by the law of music, the law of harmony; and whenever that harmony in the cosmic system is lacking in any way, then in proportion disaster comes to the world, and its influence is seen in the many destructive forces which are manifest there. The whole of astrological law and the science of magic and mysticism behind it, are based upon music."

Pythagoras systematized the laws which allow the creation of stringed instruments: musical scale intervals (octaves, fifths, fourths, thirds). He recognized that these fundamentally abstract relationships pervade all creation--even matter irself. In music, as in nature, a wave is a shape in motion. Each note has a wave-shape.

The octave comes from exactly doubling, or halving the string length, that is in 1:2 proportion, while the harmonious fifth has a 2:3 ratio and the fourth 3:4. There is also the less obvious 4:5 interval of the third, and even less obvious consonances.

Any tone in the overtone scale is higher than the preceding tone by precisely one whole number. These are the so-called harmonics. The lower the proportions of the numbers, the stronger the consonance, the more harmonious the sound of the two tones together. The primal polarity ratio of 1:2 is the most harmonious to our ears which are biologically geared to seven basic laws of harmony based on the primal law of whole-number quanta (which prevails in physics as well as music):


1. the overtone scale

2. the interval proportions

3. the division of the octave into twelve semitones

4. the difference between consonance and dissonance, the consonance growing as the proportion of the numbers gets smaller

5. the difference between major and minor, the major proportion being the most frequent by far

6. the predominance of the 1:2 polarity, the octave

7. the law of the Lambdoma (a column of numbers written in the form of the Greek letter lambda, whose right leg consists of whole numbers going from one to infinity while the left leg contains the fractions of these same whole numbers, so that the coordinates of the open isosceles triangle follow the scale of overtones or undertones). There are correspondences in physics, acoustics, arithmatic, geometry, crystallography, cybernetics, theology and philosophy, the genetic code and I Ching.

The Mysticism of Sound: Music, The Power of the Word, and Cosmic Language (Sufi Message of Hazrat Inayat Khan Ser: Vol. 2)

Max Beckman- 'On My Painting'

"My aim is always to get hold of the magic of reality and to transfer this reality into painting -- to make the invisible visible through reality. It may sound paradoxical, but it is, in fact, reality which forms the mystery of our existence.
What helps me most in this task is the penetration of space. Height, width, and depth are the three phenomena which I must transfer into one plane to form the abstract surface of the picture, and thus to protect myself from the infinity of space. My figures come and go, suggested by fortune or misfortune. I try to fix them divested of their apparent accidental quality."

"When spiritual, metaphysical, material, or immaterial events come into my life, I can only fix them by way of painting. It is not the subject which matters but the translation of the subject into the abstraction of the surface by means of painting. Therefore I hardly need to abstract things, for each object is unreal enough already, so unreal that I can only make it real by means of painting."

"In my opinion all important things in art since Ur of the Chaldees, since Tel Halaf and Crete, have always originated from the deepest feeling about the mystery of Being. Self-realization is the urge of all objective spirits. It is this Self for which I am searching in my life and in my art.
Art is creative for the sake of realization, not for amusement; for transfiguration, not for the sake of play. It is the quest of our Self that drives us along the eternal and never-ending journey we must all make."

"Color, as the strange and magnificent expression of the inscrutable spectrum of Eternity, is beautiful and important to me as a painter; I use it to enrich the canvas and to probe more deeply into the object. Color also decided, to a certain extent, my spiritual outlook, but it is subordinated to light and, above all, to the treatment of form. Too much emphasis on color at the expense of form and space would make a double manifestation of itself on the canvas, and this would verge on craft work. Pure colors and broken tones must be used together, because they are the complements of each other."

Excerpts from the lecture , given at the New Burlington Galleries, London, in 1938. (source: Herbert)

Max Beckman


Carlos Valdez senior and Matisse

Being the only son of a painter I grew up listening to my father's ideas about the mystical experience of art. As a kid I was bored out of my skull when he would start rambling on and on about art, but as I grew older I realized that pops had given my a pretty good artistic education. I just applied everything he talked about to Jazz music. It would behoove every Jazz musician to take some time to study the writings of the masters. Visual artists often have more developed philosophic concepts about the artistic process. There are many books by painters that have profoundly influenced my concepts of music.

A few of these books are:
Concerning the Spiritual in Art
by Wassily Kandinsky,

Kandinsky: The Art of Abstraction

Here's a note my father sent me about abstract expressionism. Carlos senior could be described as an abstract expressionist painter, so here's what he has to say about one of his favorite painters- Matisse.

"You mentioned being an abstract expressionist player-

So what if a line bleeds through or some canvas shows?

Matisse worked those elements intuitively, brought them along with the rest of the painting.

They had as much rich distilled feeling as anything else in the painting.

Did this make the painting complex? no

condensed his elements fantastically- some wonderful works are nothing
but a few scratches.

He said that he wanted an art free of all troubling subject matter-
what he really wanted was to be in his oriental paradise, and he did get there.

Imagine decades of
that experience of beauty.

He called it in his characteristically concise way- expression.

I can't
understand how he was ever recognized-his work is so subtle.

Contemporaries talk
of seeing him scrape away works of fantastic beauty- that's not what he was after.

He said that
he experienced god at those times when he did something that he was not capable of, but he felt cheated that that was as close as he could come.

I found this Matisse quote-
"Instinct must be thwarted just as one
prunes the branches of a tree so that it will grow better."

but you know he got his major jollies when he worked-intuitively.

Maybe he meant something different than it seems.

I think that Matisse followed the sense of what mattered to himself in his art no
matter what.

He learned everything he could about painting then simply left himself open to what might happen.

He was suicidal at times in despair over being unable to do what he needed to d
o. He lived through 2 world wars where artists were starving- but if he could identify with it it stayed in. This can be seen in the work just after the fauvist period. Once that was solidly established, which I believe involved cultivating his nervous system as a tibetan monk would do- through the practice of painting.

He went to the light and ultimately transcended himself.

The matisse flower is actually a tamed demon.


Liner notes for my new CD w/Pere Soto

Tim Price wrote the liner notes for Oasis, my new CD project with guitarist/composer Pere Soto. We're still shopping the CD to European record labels and have a few leads so far. We found a record label that really likes, but can't afford the advance we need. They are acting as our agent at the MIDEM international music industry convention. I'm just trying to be patient.
I wanted someone who really understood my playing to write the notes. Tim knew all the teachers I studied with. I also felt that he really appreciated the direction I was headed as well as the musical influences that had shaped my playing. He have been trading our music for years but have never met in person. I'm very happy with how the liner notes turned out. He really understood what we were trying to do with this CD.

"When one considers what makes a meeting of two master musicians interesting, there are several common factors that can be observed throughout the history of jazz. The interest is found in the contrast between a common vocabulary and lineage but interpreted individually which of course is one of the main facets of jazz. In other words, there is enough similarity for some semblance of a unified approach, but at the same time enough differences to attract interest. With David Valdez and Pere Soto the unity and differences are clearly demonstrated.
Stylistically, David and Pere approaches are very distinct. They both stretch the rhythm and harmony, but in completely different ways. David seems to slip and slide around within the framework of a tune in with a wide range of articulations and intervallic choices. He plays with the beat creating a kind of spiraling vortex of sounds. One of the very best modern day alto players!

Pere Soto dives straight into the center of the harmony and pulse using his
incredible imagination to create a universe of its own within the structure of the tune. Speed and dexterity are fundamental to his style .Ya know, when I close my eyes and listen to him, it’s amazing.

Finally, there is the sheer joy and camaraderie the David Valdez and Pere Soto of playing and listening to each other. Classic! This disc is stellar and packed with just the kind of experience needed, which is to the advantage of the listener because it brings a relaxed informality to the recording.

Pere in his own wa
y has extended the language on his instrument to a level prominent enough to have a major effect. It has been my feeling that with our culture's emphasis upon and rewarding of conformity rather than originality has been increasingly stifled in the past decade or so. You won't hear that stifled approach here! In his playing you hear the history of jazz!

David Valdez can do so much and has always struck me as rather distinctive on that level as well. He tends to go more directly head to head inside the music. Maybe this translates musically to more chances taken, more densely packed lines, more roughness and use of combinations in the sound.

Most of these tunes allow the artists to use their common language, as a vehicle for creativity and self-expression. It is a vital source of listening experience, I've known Valdez for years musically, and his playing is a vital asset to this music. This disc combines a kind of textural austerity with the sometimes forbiddingly jagged melodies that just make you return to it daily, the results are very attractive.

This new recording by these two modern day masters is a step in a well-needed direction. This excellent project brings together highly respected players whose paths have crossed before in various configurations over the years. As a unit, they authoritatively and creatively play the music on this disc with great personal integrity coupled with intensity and energy, formidable chops and intelligence that recalls the forward thinking.

Hear It! It is something very special.

Tim Price

Here is a link to the title track Oasis.

Cannonball Spectacular!

This Cannonball transcription site is out of control, truly amazing, and totally Kick-ass, unless of course you don't love Cannonball. Doc Stewart put these solos together. Doc has a Cannonball tribute band and he actually plays the transcriptions.
Nice work Doc, thanks!


"This page is a comprehensive list containing the title and recording date of every RELEASED song - past or present - that Cannonball Adderley plays a solo on. The following recordings were/are available in either LP, EP, 45rpm, CD, DVD, casette, 8-track, or VHS formats. If the song name is in red, that means the recording exists but I haven't found it yet. Black means I have the recording. Links are provided to some of my transcriptions and session tables."

I found this on Steve Neff's site. Steve has just started a very promising Jazz blog, and has some nice material on his main site, like clips of him playing lots of different mouthpieces (including a nice early Babbit Link I recently sold him).


Michael Brecker Dies at 57, the voice of the modern saxophone

Published: January 14, 2007
New York Times

Michael Brecker, a saxophonist who won 11 Grammy Awards and was among the most influential musicians in jazz since the 1960s, died yesterday at a hospital in New York City. He was 57 and lived in Hastings-on-Hudson, N.Y.

The cause of death was leukemia, said Darryl Pitt, his manager.

Having taken a deep understanding of John Coltrane’s saxophone vocabulary and applied it to music that merged with mainstream culture — particularly jazz fusion and singer-songwriter pop of the 1970s and 80s — Mr. Brecker spread his sound all over the world.

For a time, Mr. Brecker seemed nearly ubiquitous. His discography — it contains more than 900 albums — started in 1969, playing on the record “Score,” with a band led by his brother, the trumpeter Randy Brecker. It continued in 1970 with an album by Dreams, the jazz-rock band he led with his brother and the drummer Billy Cobham.

His long list of sideman work from then on wended through hundreds more records, including those by Frank Zappa, Aerosmith, James Brown, Paul Simon, Joni Mitchell, Lou Reed, Funkadelic, Steely Dan, John Lennon, Elton John, and James Taylor, as well as (on the jazz side) Chick Corea, Pat Metheny, Gonzalo Rubalcaba, and Papo Vasquez. His 11 Grammys included two for “Wide Angles,” his ambitious last album, released in 2003 with a fifteen-piece band he called the Quindectet.

His highest achievements were his own albums, both under his own name (starting in 1986) and with the Brecker Brothers band, as well as his early 80s work with the group Steps Ahead. Mr. Brecker was scheduled to tour with a reunited version of Steps Ahead in the summer of 2005 when his condition was publicly announced — initially as myelodysplastic syndrome, a bone-marrow disorder, which finally progressed to leukemia — and much of his work had to stop.

Mr. Brecker grew up in a musical family in Philadelphia; his father was a lawyer who played jazz piano. He started playing the clarinet at the age 6, switched to alto saxophone in the eighth grade, and finally settled on tenor saxophone in the tenth. He started to attend Indiana University — as did his brother Randy. After initially pursuing a music degree and then briefly switching to pre-med, he quickly discovered he preferred to be playing music. He left for New York at 19.

For most of the 1970s and through the mid-80s he worked hard in studio sessions, becoming a fixture on albums by the Southern California pop singer-songwriter movement, including those by Jackson Browne and Joni Mitchell. But for hard-core jazz enthusiasts, it was his work of the early 80s — on Steps Ahead’s first two albums, when the band was simply called Steps — as well as Chick Corea’s “Three Quartets,” from 1981, and Pat Metheny’s “80/81,” from 1980, that cemented his reputation as a great player.

His tone was strong and focused, and some of his recognizable language echoed Coltrane’s sound. But having worked in pop, where a solo must be strong and to the point, Mr. Brecker was above all a condenser of exciting devices into short spaces. He could fold the full pitch range of the horn into a short solo, from altissimo to the lowest notes, and connect rarefied ideas to the rich, soulful phrasing of saxophonists like Junior Walker.

In the 1980s and 1990s he experimented with the electronic wind instrument called the EWI, which allowed him to blow through an electronic hornlike device, play a range of sampled sounds, and multitrack them in real time. He began experimenting with the instrument again in the last few years.

With the onset of his illness, he and his family called for bone-marrow donors at international jazz festivals, synagogues, and Jewish community centers around America; tens of thousands responded. Working sporadically over the last year, he managed to complete his final album two weeks ago, Mr. Pitt said.

He is survived by his wife, Susan, of Hastings-on-Hudson; his children, Jessica and Sam, of Hastings-on-Hudson; his brother, Randy, of Manhattan; and his sister, Emily Brecker Greenberg, of Philadelphia.


Django's Castle videos

My partner in crime Pere Soto just posted a bunch of videos on YouTube of his Gypsy Jazz project Django's Castle. Check out his two fingered version of Nuages to get an idea of what Django was working with.

Pere Soto plays Django


More Slonimsky questions...

Q: Carlos,
Hey, can you elaborate more on this idea of "resolving" your harmonic lines? Obviously things like taking the leading tone of a dominant to the tonic make sense to me, but in your last email regarding Slonimsky you said the following....

"Just make sure you resolve them strongly, you'd be amazed what you
can actually get away with and still sound good."

and ..

"Tonal harmony is after all mainly about forward motion, so the lines
found in TSMP offer away to still retain forward motion while playing
outside. It just becomes a matter of being able to resolve these
lines in a logical way...."

A: Charles McPherson has an exercise that he makes his students do. He has them play totally outside over dominants and then land on a strong chord-tone on beat one of the next resolving bar. He says if you resolve on the downbeat with a strong chord tone you can play anything and it will sound like Bebop. This is just about true, even though it does sound quite extreme.

Q: Related question.....do you use diminished stuff freely against dominants resolving to both Major and Minor, or just for dom's resolving to Major? I've heard both suggested....and can you specifically tell me how you resolve a diminished scale, like do you actually try to resolve each dissonance (flat 9, sharp 9, sharp 11....) or just go to the Lydian mode/melodic minor of the tonic and leave it at that?

A: I do use diminished modes when resolving to major or minor chords. To determine what chord-scales are available I only look at the root motion of the chord that the dominant resolves to. If the root motion is going down a fifth (up a fourth) then anything is fair game, no matter what chord quality the resolution is. Yes, there are scale choices that are smoother as far as voice leading when resolving to a minor chord, like a harmonic minor scale from the fourth or and altered dominant scale.

Remember that if the dominant chord is moving down a half-step in root motion you only should play a Lydian dominant (even if the #11 isn't notated) because it is functioning as a tritone!

Berklee teaches that certain tensions are available for each of the secondary dominant chords:

V7/II b9, 9,#9, b13
V7/III b9,#9, b13
V7/IV 9, 13
V7/V b9, 9,#9, 13
V7/VI b9, #9, b13

The most important thing is to watch for root motion! Where do the dominants move to?
Don't worry about resolving individual tensions, this will drive you nuts and slow you down.
Some people would argue with me, remember I consider myself a post-bop player, which to me is like an abstract expressionist painter. The rules are a bit more relaxed and I'm looking to use a more 'painterly technique', I don't want photo-realism in my playing. So what if a few lines bleed over or if some canvas shows? You could follow stricter rules than I do as far as finding scales for chords, but mine keep you out of trouble and I can always break them if they get too constraining.

Q: Also, other than Bird, what specific solos would you prescribe for an intermediate level aspiring improviser on alto to learn by ear and transcribe? How about tenor?

A: I usually get intermediate level students working on Sonny Stitt transcriptions, both alto and tenor. Stitt is very clear rhythmically and he has nice long lines. Early Phil Woods is also a good altoist for transcription, the Phil and Quill records.

Q: And what about more advanced concepts,
are there some specific examples you could point me to for my students that aren't too long or too fast but that would show in detail some specific stuff. Most of the stuff I have them do is Bird and Lester, but you don't get into more far out harmonic stuff with them. Some I've graduated to Dexter, but I'm trying to get them onto some newer material. Cannonball? Who else and what else?......If you could toss out a handful or so that would be great....

A: How about Dick Oatts, Grossman or Rick Margitza for 3-tonic lines, Jerry Bergonzi for use of pentatonics and digital patterns, Kenny Garrett for triads and pentatonics used for outside playing. Try to find examples that are rhythmically straightforward, since complex rhythmic figures are the bane of young transcribers.

Q: Also, the Gary Campbell article is great on the blog, and I've seen the book. I seem to remember it being detailed but mostly covering the triad pairs being practiced up and down in their various inversions. Are there other ways to use these that sound good?

A: Gary does offer many examples of situations for triad pairs in his book. Triad pairs can also be used to play outside. Kenny Garrett does this very well. You can use one triad that fits the chord alternating with a triad that doesn't fit at all, this slips you in and out of tonal harmony.
Triads are so strong that they can supersede any chord progressions. Once you learn to create lines that shift inversions as they move between triads you can then use these lines to navigate outside harmony. Triadic lines are so strong that you can use them over any changes regardless of how they fit over the changes.

Q: Also, I worked with one of my former students who's in the jazz program at USC yesterday, he's now studying with Jason Goldman. Ever heard of this guy? Anyways, my kid was using the bis key for b flats exclusively, so I questioned him about it. He said his teacher told him to do it this way. So, since you do the same, I ask you, is this orthodox technique? I make my students master the side b flat, particularly for chromatic stuff, and then show them how to use the bis for leaps, like g minor or b flat major. Isn't that the way it's generally taught? What did Viola teach?

A: Joe V taught the use of both for different situations. Joe had a very pragmatic approach to technical questions. He always want you to find the most comfortable and smoothest fingerings for any given situation. The less motion, the better. There is usually one fingering that is clearly mechanically and ergonomically superior, just slow things down, watch your fingers and see which fingering feels best.