Scale of the Day: F Ionian diminished 5

The F Ionian diminished 5 Scale as you would find it on any conventionally tuned equal tempered instrument.

Scale of the Day: A Mixolydian

The A Mixolydian Scale as you would find it on any conventionally tuned equal tempered instrument.

Scale of the Day: E Pythagorean Construct #1, Lydian Mode

The E Pythagorean Construct #1, Lydian Mode Scale.

Scale of the Day: E Flat Dorian mapped to the Square-root of 2

The E Flat Dorian mapped to the Square-root of 2 Scale.

Scale of the Day: E Flat Dorian diminished 4

The E Flat Dorian diminished 4 Scale as you would find it on any conventionally tuned equal tempered instrument.

Scale of the Day: G Sharp Aeolian

The G Sharp Aeolian Scale as you would find it on any conventionally tuned equal tempered instrument.

Scale of the Day: D# Phrygian

The D Sharp Phrygian Scale as you would find it on any conventionally tuned equal tempered instrument.

Composer birth aniversaries:

Dizzy Gillespie. Everything about Gillespie's composition and performance is just hot. Astonishing dexterity of ideas and execution. He's a true icon of American music.

Fred Hersch. So far, all I've heard of Hersch is Songs We Know: Fred Hersch and Bill Frisell. And there's plenty there for me to admire. I look forward to hearing more from this creative pianist.

Scale of the Day: E Lydian mapped to the Square-root of 2

E Lydian mapped to the Square-root of 2 Scale.

Composer birth aniversaries: Charles Ives. Possibly the most important figure and role model for the "American Maverick" tradition of American music composition. Ives was very much in my mind as I completed my third string quartet last year as I was quoting hymn tunes in a collage style similar to his Sonatas for Violin and Piano.

Scale of the Day: E Flat Lydian

Interval content of the E Flat Lydian Scale.

Nature Via Nurture

Nature Via Nurture: Genes, Experience and What Makes Us Human by Matt Ridley

I finished reading Nature Via Nurture last night. It's an impressive presentation of how human development is a product of both and how the political/social/scientific debates about the primacy of one over the other has been an oversimplification and misunderstanding. There's a lot of good supporting argument in the form of current scientific research and history. Ridley does a good job of keeping things interesting and disciplined at the same time. It's a good read if you've ever tried raising someone who shares your genes.

Scale of the Day: E Lydian augmented 5

The E Lydian augmented 5 Scale as found on any conventionally tuned equal tempered instrument.

Scale of the Day: G Ionian

The G Ionian Scale as you would find it on any convetionally tuned equal tempered instrument. Also known as the "G Major Scale."

Scale of the Day: E Square-root of 2 Axis, Construct #1, Lydian Mode

The E Square-root of 2 Axis, Construct #1, Lydian Mode Scale.

Composer birth anniversary observance:

Larry Polansky. I recommend checking out the epic piano composition Lonesome Road - The Crawford Variations.

The Confusion

The Confusion by Neal Stephenson.

Last night I completed reading The Confusion by Neal Stephenson. It is volume 2 of 3 of the Baroque Cycle which should really be thought of as a single, 3000 page novel that the publisher has broken up into three large volumes.

Neal Stephenson has developed a great story telling sensibility. He has a great ability to write quality dialogue and present compelling characters with believable motivations. And he's always done well at telling a story with a large cast of characters. Daniel Waterhouse is easily one of my favorite fictional characters in anything I've ever read. I'm fond of the entire Waterhouse clan from Cryptonomicon (the fictional offspring of Daniel of the Baroque Cycle). It's a pleasure to experience such a lengthy tale that is populated by such great characters. Stephenson has clearly immersed himself in the period of the 17th century and makes it vibrant.

I'll have to comment more completely on this particular work once I've finnished reading volume three (which I plan to dive into immediately). So far I've been impressed with Stephenson's growth as a novelist over the span of his output.

Scale of the Day: E Flat Mixolydian mapped to the square-root of 2

The E Flat Mixolydian mapped to the square-root of 2 Scale.

Scale of the Day: E Flat Mixolydian augmented 4

The E Flat Mixolydian augmented 4 Scale as you would find it on any conventionally tuned equal tempered instrument.

Composer birth anniversary observance:

LaMonte Young. Young's music and ideas are particularly important/valuable to me. He looms large in the landscape of experimental intonation practitioners. The Well Tuned Piano in particular taps into my obsessions with just intonation, epic piano composition and minimalism. It also stimulated my current thinking in just systems that add or subtract prime factors as a means of coloring the end result.

Scale of the Day: G Dorian

The G Dorian Scale as you would find it on any conventionally tuned equal tempered instrument.

Today is the anniversary of the birth of two more composers who have inspired me:

Art Tatum was clearly in an elite group of intimidatingly gifted jazz pianists. Brimming with talent and inventiveness he revealed some incredible territory for piano improvisation.

Pharoah Sanders. Message From Home has been spinning in my CD player quite a bit the past few months. He taps into a spirituality that cannot be co-opted or maligned. He is the surviving practitioner of the uncompromising truth and personal journey that began with John Coltrane's A Love Supreme and Albert Ayler's Love Cry. The title of the recent Ayler box set acknowledges as much with its title: Holy Ghost; Trane was the Father, Pharoah was the Son. I was the... . Unlike Coltrane and Ayler, Sanders managed to avoid leaving this world through madness and self-destruction. He has continued to record over the past few decades (and hasn't taken on the same cult-figure status bestowed on the "martyred contemporaries").

Scale of the Day: E Flat Aeolian

The E Flat Aeolian Scale as you would find it on any conventionally tuned equal tempered instrument. The Aeolian is often referred to as the "natural minor" scale.

Scale of the Day: F Lydian

The F Lydian Scale as you would find it on any conventionally tuned equal tempered instrument.

Today is the anniversary of the birth of two more composers responsible for works that inspire me. The great jazz drummer Art Blakey. Art Blakey and the Jazz Messengers with Thelonius Monk (Atlantic, 1958) is one of those classic recordings no serious jazz buff should be without. The other composer b-day observed today is the great trumpet player Lester Bowie. He is probably best known for his work with the Art Ensemble of Chicago and involvement with the astonishingly inspiring AACM. I remember catching a set at the Apollo Theatre in New York City of Jack DeJohnette and Lester Bowie playing together back in 1987. He was truly one of the great creative improvisers on that instrument. I recommend checking out Fast Last and Rope-a-dope.

Scale of the Day: E Octave subdivided: 2 equal [2 equal/2 equal]

The E Octave subdivided: 2 equal[2 equal/2 equal] scale. Long name for a simple scale. The octave is divided into to equal tempered parts (1200.00 cent octave is divided in half with an interval of 600.00 cents) and the two intervals on either side are divided in half as well (resulting in an octave divided into four equal parts of 300.00 cents each).

Today is the anniversary of the birth of two inspiring (and stylistically contrasting) composers: Thelonius Monk was a tremendous jazz pianist and composer (Off Minor and 'Round Midnight spring to mind) and Stephen Scott is the composer of a significant body of works for bowed piano. Check them both out.

Scale of the Day: E Flat Ionian mapped to the Square-root of 2

The E Flat Ionian mapped to the Square-root of 2 Scale. All the intervals of the standard E Flat Ionian Scale (mapped to the octave as per standard practice) are halved to fit within the square-root of 2 (a.k.a. the equal tempered "tritone").

Scale of the Day: E Flat Ionian diminished 5

The E Flat Ionian diminished 5 Scale as you would find it on any conventionally tuned equal tempered instrument. Note the augmented second between the diminished 5 and major 6. Augmented seconds are great for breaking up the sea of major/minor 2nds in standard diatonic scales.

Scale of the Day: F Sharp Mixolydian

The F Sharp Mixolydian Scale as you would find it on any conventionally tuned equal tempered instrument. 

Scale of the Day: E Flat Dorian

The E Flat Dorian Scale as you would find it on any conventionally tuned equal tempered instrument.

Troubling Terms

Today is the birthday of “downtown” composer and hero Glenn Branca. Check out his symphonies if you haven’t heard them yet.

Here’s a list of some harmonic terminology that strikes me as unfortunate. Much of my quarrel with these terms stems from three basic reasons: (1) there’s a bias toward diatonic tonality that obscures less traditional concepts, (2) these terms are so common that they take on a vivid, concrete meaning early in the study of music and (3) the numerical values within the names are at odds with the physics of the sound they describe.

Octave

This is perhaps the most maddening term as it is such an important and common interval in music globally. The oct- prefix that implies that the number 8 is an important descriptor of the interval. There are 8 diatonic steps between the root and the “octave.” Which renders the term quaint in non-diatonic contexts. It is the origin of the “8va” notation that indicates something is to be played an octave higher than written. However, when something two octaves higher the notation is “15va” as opposed to “16va” as two octaves are actually 8 + 7 diatonic steps (the “root” of the second octave isn’t counted whereas the “root” of the first is).

Harry Partch avoided using the term “octave” by simply referring to its frequency ratio: 2/1. This is descriptively more accurate. One wishes that this interval had a name that emphasized the number 2 such as “bi-ative” or “di-ative.” But for better or worse the term “octave” has stuck and even I can’t escape using it and having it mean 2/1 in a vivid manner within my own conception of harmony.

The harmonic sound of the 2/1 is strongly "consonant." Only the unison sounds more "consonant." The harmonic relationship between pitches an octave apart is so strong that they share the same letter name, or pitch-class. The harmonic implication is that they share the same harmonic function. This is true in about 99.9% of all music in the world. Scales replicate their interval patterns at the octave and set-theory is built upon the concept that octaves are "equivalencies" suitable as an orchestration device that adds no new harmonic content.

It is possible to theorize and practice in harmonic environments that do not extend this property to the 2/1 (1200.00 cent octave). My Piano Concerto No. 1 is an example of this. The piano is tuned so that there is no pair of notes 1200.00 cents (2/1) apart. Some of the open strings in the string section are tuned 1200.00 or 2400.00 cents apart from notes found on the re-tuned piano. But these “octaves” are not treated as harmonic equivalencies. Instead, the triative (3/1, a.k.a. the 1901.96 cent just perfect twelfth) takes on this harmonic role. Scales replicate their sequence of intervals at the triative and the piano is tuned so that every perfect twelfth (the octave + perfect fifth) is exactly 1901.96 cents apart. I’ll admit that this is a contrived harmonic system (which is part of the thrill of composing with it). It is a great exercise to compose something that completely renders the traditional meaning/concept of the term “octave” meaningless. It forces a different facility with the “letter names” of pitches.

Whole-tone

Why is the 200.00-cent interval (the major second) regarded as “whole?” How arbitrary is that? Again, there’s a diatonic prejudice at work here. The first diatonic interval away from the root of a “major” scale happens to be this interval and it happens to be the most common sequential interval in a scale made up of five “whole-tones” and two “semi-tones.” Unfortunately, this term has taken on a vivid meaning in my ears and I can’t escape calling the scale that divides the octave into six equal parts as the whole-tone scale.

Semi-tone or Half-step

Why is the 100.00-cent interval (the minor second) regarded as “half” or “semi?” It’s an extension of the fallacy of the “whole-tone.” And again it has a vivid meaning to my ears and conception of harmony even if an octave divided into twelve equal parts is the “chromatic” scale as opposed to the more consistent name: semi-tone scale.

Tritone

This is an intriguing fallacy. Again it’s the extension of the “whole-tone” issue being applied to an interval made up of three such “whole tones.” But there’s an even deeper fog at work with this interval. At 600.00 cents wide it’s an enharmonic stand-in for both the augmented fourth and the diminished fifth. In an equal tempered system these two intervals are sonically identical even if they serve radically different harmonic functions. And this ambiguity is put to good use in tonal syntax when the augmented or diminished chord is used to modulate to different key centers.

In just intonation the “tritone” takes on an interesting property. Typically, the augmented fourth and the diminished fifth have an equivalent harmonic relationship to the tonic (that is, in harmonic space they are the same distance away from the 1/1). However, they are relatively unrelated to each other (the harmonic distance between the augmented fourth and diminished fifth typically being twice the distance between the augmented fourth and the 1/1 or the diminished fifth and the 1/1). This is true of any pair of intervals that are inversions of one another (as is the case with the augmented fourth and the diminished fifth). But it is the only pair of intervals related by inversion that also share an enharmonic equivalence in equal temperment.

Intervals as Seconds, Thirds, Fourths, etc.

All the interval names that attach diatonic numerical values to them share the same problem of diatonic bias. And anyone who spends time learning music develops vivid conceptions of the sound associated with seconds, thirds, fourths, etc. I’m not sure what solution for this terminology would be pragmatic. There are an infinite number of intervals out there and it’s easier to think in terms of a finite set. The “solution” isn’t as simple as the substitution 2/1 for octave. A major second could be 200.00 cents, 9/8, 8/7, 11/10, etc. And this is true for all interval classes. It's the diatonic bias that seems unfortunate here.

Quarter-tone

Quarter-tone is a further extension of the “whole-tone” problem. Perhaps it should just be called the 50.00 cent interval.

Micro-tone

Actually, micro-tone is not a bad term. I’m just sad that there’s no vocabulary for discussing intonation other than as a “deviation” from dominant common practice. It seems inherently more valuable to describe things additively by what they are rather than subtractively by what they are not.

Perhaps I’ll become “radicalized” enough to adopt a language that is mathematically “pure.” But I’ve basically absorbed the good and the bad terms born from a predominantly diatonic tradition. “Octave,” “semi-tone,” “tritone,” etc. all evoke something conceptually concrete as I’ve developed a working familiarity with how they sound. It becomes a choice of abandoning a flawed language in favor of something “accurate” at the expense of being the only person fluent (and thus defeating the communicative properties of language) or striving to communicate ideas within a vocabulary inherently hostile to my own sensibilities. In the end it seems best to strive toward sound while maintaining a delicate truce with verbal language. Words always seem to come up short compared to the directness of experience. There will always be a vast body of ideas that cannot be conveyed by words alone.

Scale of the Day: E Octave Divided into 2 Equal Parts

The E Octave Divided into 2 Equal Parts Scale as you would find it on any conventionally tuned equal tempered instrument. This scale is could be described as harmonicly impoverished as the 1200 cent octave is a vast distance to divide into only two parts.