Harmonic Études, Op.4

No.1 No.2 No.3 No.4 No.5 No.6 No.7 No.8 No.9 No.10 No.11 No.12




Harmonic Étude No.1

"Diatonic Circles"

Op.4, No.1

for String Quartet


Date Duration Listen
Download
12 March 2005 2'51" Realization (.MP3) Score (.PDF)
3.93 MB 90 KB



Harmonic Étude No.2

being a descent through the circle of fifths using all possible 3- and 4-voice chords exactly once, ordered by decreasing dissonance according to an adjusted Hindemithian analysis

Op.4, No.2

for Piano


Date Duration Listen
Download
6 May 2011 4'00" Realization (.MP3) Score (.PDF)
5.51 MB 50.6 KB



Harmonic Étude No.3

on a randomly-generated tone row

Op.4, No.3

for Flute, Oboe, Clarinet, Bassoon, and Horn


Date Duration Listen
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2 June 2011 1'21" Realization (.MP3) Score (.PDF)
1.85 MB 44.8 KB



Harmonic Étude No.4

Op.4, No.4

for String Quartet


Date Duration Listen
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7 June 2011 2'33" Realization (.MP3) Score (.PDF)
3.51 MB 94.9 KB


This is a strict variation on the structure used to compose Harmonic Étude No.2: it contains every possible 4-voice chord exactly twice and every possible 3-voice chord exactly four times. The chords are again indexed to always move from greater to lesser dissonance, but this time they are filtered to appear in discrete groups containing either the same note in the treble voice or the same note in the bass voice (this is what creates the ostinato drones and pedal points that become increasingly prominent as the piece advances). The groups themselves are sorted so that they smoothly appear in series from the smallest group (a single 3-voice chord with an A natural in the bass) to the largest group (the 84 consecutive chords at the very end, each containing a C natural in the bass). As in Étude No.2, all melodic elements independent of chordal constructions are anticipations and/or fragments of the individual voices in the chord progressions immediately adjacent. The composition, finally, is tonal (according to a Hindemithian scheme), governed by the root tone C natural, and divided into ten roughly equal sections according to a plan a diatonician might recognize as I-V-I-V-IV-VI-V-I-V-I.

I toyed with the idea of making this a movement in a larger work, but obstinate ideological prejudice, alas, prevents me from authoring extended works in tonal environments. I have complete faith that the serial method - fully informed and guided by the evolving contrapuntal wisdom of all previous stages in the development of the art - represents the solid future of Western Art Music. Let the current piece remain forever nothing more than a curious didactic study of the complete harmonic potential inherent in all 4-voice writing.




Harmonic Étude No.5

Op.4, No.5

for Orchestra


Date Duration Listen
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8 July 2011 3'19" Realization (.MP3) Score (.PDF)
4.56 MB 128 KB


Here we see yet another variation on the idea underlying Harmonic Études No.2 and No.4: every possible 3- and 4-voice chord is used in this piece exactly once. Yet again, they are consistently moving from dissonance to consonance, but according to the following scheme: using an adjusted Hindemithian analysis (I consider the tritone considerably less dissonant, than he did, and place it between the major sixth and the minor seventh on that scale), I divided the 210 available chords into six equal groups of 35 - with Group Six being the 35 most dissonant and Group One being the 35 most consonant, etc - then created 35 sets of 6 chords each: one from Group Six, followed by one from Group Five, Group Four, Group Three, Group Two, and Group One in each set. Each individual set of chords thus moves from extreme dissonance to extreme consonance. Additionally, the first set took from each group the chord in the 35th position of that group, i.e., the most dissonant of each individual group. The second set of chords took the 34th chord from each group, i.e., the secondmost dissonant ones, and so on, until the final set of six chords contained the most consonant available chords from each of the six separate groups. Thus the individual sets of chords move internally from dissonance to consonance on the micro scale, and the entire collection of 35 sets also moves smoothly from dissonance to consonance on the macro scale. Yet again, the piece is tonal, governed by the root tone A natural, with each individual set of six chords modulating along a thoroughly conventional pattern not particularly worth specifying; and the incidental melodic passages are strictly mined variations of voices discovered in the immediately adjacent chords themselves.

Anyone who didn't know I generally work in serial environments might be tempted to accuse me of inexcusably arbitrary methods. But the fixed and mathematically-determined harmonic elements of this piece are not all: the appearance and disappearance of the various choirs in the orchestra are also predetermined according to an arbitrary pattern:

Choir 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Flutes & Oboes
Clarinets & Bassoons
Horns
Trumpets
Trombones & Tuba
Strings

In retrospect, I might be tempted to consider this decision a mistake, insofar as it considerably complicated the compositional process and occasionally forced me to ask the trombones and tubas to execute tasks definitely more suited to nimbler and brighter instruments. But such, alas, is the price one must pay for sticking like glue to intellectually arbitrary schemes.




Harmonic Étude No.6

"Minimalist Mandalas"

Op.4, No.6a

for String Quartet


Date Duration Listen
Download
31 July 2011 16'54" Realization (.MP3) Score (.PDF)
23.2 MB 972 KB

Op.4, No.6b

for String Orchestra


Date Duration Listen
Download
31 July 2011 16'54" Realization (.MP3) Score (.PDF)
23.2 MB 1.14 MB

Op.4, No.6c

for Piano and Orchestra


Date Duration Listen
Download
31 July 2011 16'54" Realization (.MP3) Score (.PDF)
23.2 MB 2.33 MB


More than simply another variation on the idea already familiar from earlier études, this Étude No.6 actually employs exactly the same progression of every possible 3- and 4-voice chord found in No.5, exploding the 3'19" they required in that piece to a minimalist monster almost 17 minutes in length. It is presented in three different versions: the string quartet for which it was originally conceived; a logically-irresistible adaptation for string orchestra; and a full-blown extravanganza for piano and orchestra. The adaptation for strings adds a little oomph and support for the cellos from the contrabasses moving in tied whole notes underneath, but for my money the quartet version is purer and more elegant; of course, anyone who knows me already knew I would say that.

The full orchestration leaves something to be desired, to my ear. It is a little ponderous and muddy in places (despite having had the voice-leading checked and re-checked within an inch of its life), while the string versions seem to move along nicely throughout. Considering that both string versions were written essentially in a single, full working day, while the subsequent orchestration occupied me for nearly a week afterward, one may sympathize with my desire to be finally done with it and stop eternally trying to make new subtle improvements. Seemingly every fifth or sixth editorial decision concerning the orchestration led to hours and hours of tedious, close work across hundreds and hundreds of measures: the full score of the orchestration is 271 pages long, even with empty measures compressed to nothingness. Such may be the essential nature of minimalism, but surely a mere étude should not become a life's work.

I recommend setting the volume control absolutely as low as practicable from the beginning, particularly if one is braving the version for piano and orchestra. The piece begins pianissimo possibile and builds in a long crescendo over ten minutes to a full tutti fortissimo possibile. This may at least have the virtue of blowing any possible dust off the leads to one's speakers, if taken unaware. Praemonitus, praemunitus.




Harmonic Étude No.7

"Minimalism Marries a Tone Row"
(and a randomly-generated one, at that)

Op.4, No.7a

for String Quartet


Date Duration Listen
Download
5 August 2011 11'36" Realization (.MP3) Score (.PDF)
15.9 MB 532 KB

Op.4, No.7b

Octet for Wind and Strings


Date Duration Listen
Download
5 August 2011 11'36" Realization (.MP3) Score (.PDF)
15.9 MB 812 KB


Notwithstanding all the whining above about the tediously close and time-consuming detail work necessary to produce finished minimalist compositions, one outstanding task in that genre still needed to be undertaken - marrying minimalism to a serial environment - and it seemed wisest to attack the matter while still freshly familiar with the database scripts I wrote to create the harmonic skeleton for the Études No.6. Truth be told, I am now firmly convinced that adding a fair number of error-trapping subroutines to these scripts to govern the basic rules of voice-leading would permit me to reach a point where I could pass any succession of tones - whether tonal or serial - to these scripts and produce reasonably complete minimalist pieces immediately, one after another, all day long: with one click, as lying advertisers everywhere love to say. Which is about as good a reason as any why it shouldn't be done.

I shall certainly be happy to incorporate minimalist techniques into sections of future compositions as the spirit moves me, but probably these two current études will be my last purely minimalist works for a good, long time. Unless thousands of demonstrators mass outside my home and demand more of them, of course, that is. In which case I may simply pack up my meager belongings and move to an undisclosed location in the middle of the night, because there are so many much more pressing problems in this world deserving of mass demonstrations of passion. Don't you think?




Harmonic Étude No.8

"The Palindrome"
on a randomly-generated tone row

Op.4, No.8

for Wind Sextet


Date Duration Listen
Download
9 August 2011 7'41" Realization (.MP3) Score (.PDF)
10.5 MB 128 KB


Brilliantly nicknamed "The Palindrome," because the second (and last) 199.5 measures of the piece are an exact mirror image of the first 199.5. 'Nuff said.




Harmonic Étude No.9

on a randomly-generated tone row

Op.4, No.9

Quartet for Violin, Oboe, Cor Anglais, and Violoncello


Date Duration Listen
Download
27 October 2011 6'12" Realization (.MP3) Score (.PDF)
8.51 MB 119 KB


You wouldn't believe how many times the instrumentation and prospective scope of this slender little bagatelle changed during the realization of it, so I won't tell you.




Harmonic Étude No.10

Op.4, No.10

for String Quartet


Date Duration Listen
Download
13 December 2011 12'16" Realization (.MP3) Score (.PDF)
16.8 MB 407 KB


This is a different take on the same germ of an idea underlying Études Nos. 2, 4, and 5; it contains every possible 3- and 4-voice chord, ordered first by identity in the soprano voice and second by descending dissonance, repeated in 17 major sections expressing the full gamut of Hindemithian tonality: from A, up through the circle of fifths (E, B, F#, C#, G#, D#, A#, F, C, G, D) and then precipitously back down enharmonically (Bb, Eb, Ab, Db, Gb) to the so-called relative minor of the original tonal center.

The piece is structurally and texturally minimalist, but not thematically so. Nevertheless, no "composer" or "artist" appealed to any Muse for melodic inspiration at any point in the process of construction. The location, duration and frequency of every single note here (save for adjustments of register to improve voice-leading or accomodate individual instruments' ranges) was determined strictly by successive global application of mathematical processes informed by simple rules: the first of which was that identical adjacent notes in any voice should invariably be tied or consolidated to create rhythmic variety in the lines and thus relieve the tedium of the unrelenting 4-voice chorale structure at the piece's architectural foundation. This same tedium was also mitigated structurally, as the following paragraph exhaustively details.

To recapitulate and advance: the thematic, i.e., melodic logic of the piece is straightforward and continues uninterrupted from beginning to end, but the textural logic is palindromic and minimalist. Of the 17 major sections, the 9th - i.e., central - one is both the shortest in duration and the densest, being the only one consisting entirely of 4-voice writing. All eight of the remaining sections on each side of it (each of which are themselves texturally palindromic [containing five subsections, the third of which is also always its own shortest and densest, in 4-voice writing]) are extended by adding either introductions or postludes to each remaining 4-voice subsection: consisting of deconstructed versions of its own "mirror" substructure (i.e., subsection 1 pairs with subsection 5, 2 with 4, 4 with 2, and 5 with 1) with one entire voice and portions of two other remaining voices deleted, thus thinning the textures in these sub-subsections to alternating patterns of 3-, 2-, and 1-voice passages. Finally, the four major sections at each end of the composition - beginning and end - are additionally thinned and lengthened by tacking further introductions or postludes to them fashioned from "exploded" versions of the previously ignored 3rd, central, subsection, with all four voices staggered so they never appear in anything more dense, than 2-voice counterpoint. To summarize and simplify, then: the whole advances in gently undulating waves of 1-, 2-, 3-, and 4-voice counterpoints, gradually becoming denser, with shorter harmonic pulses, until the densest and quickest, central section; after which the order reverses and the texture gradually thins and lengthens to the conclusion.

The dynamic levels, while also palindromic and moving by steps, follow a slightly different logic, consisting of two great waves meeting and overlapping at the central major section, which - together with the very first and the very last major sections - represents the quietest passages in the entire piece: pp-p-mp-mf-f-mf-mp-p-pp-p-mp-mf-f-mf-mp-p-pp.

In short, the whole composition easily "could have, should have" been entirely computer-generated at a single go by the programming equivalent of a Mozart, but in the real world of this lesser mortal the patient computer had to wait at several major stages while yours truly laboriously examined the feedback already produced and puzzled out strategies for improving the next result. The whole is an intricately comprehensive and balanced harmonic étude, after all - not an improvisation. If it tickles the imagination of any sentient being even slightly, it will have served its purpose in full.




Harmonic Étude No.11

Minimalist Reconstruction of an Intermezzo
by Johannes Brahms (Op.118, no.2)
Op.4, No.11

for orchestra


Date Duration Listen
Download
19 July 2012 8'22" Realization (.MP3) Score (.PDF)
11.5 MB 565 KB


Um, yes, well, see, this is note-for-note Johannes Brahms' A-Major Intermezzo for Piano, Op.118, No.2. Each of the 124 measures of the original composition has been exploded or deconstructed into a successive string of its own voices, making of each individual measure a new melody lasting anywhere from two to eight measures, depending on the density of harmonic elements in the model piece. The 124 "new" melodies are then introduced one-by-one, as ostinati figures, into the "reconstructed" score, at four measure intervals, following an arbitrary, repetitive pattern of voices invented by the étudist. Strict mathematical patterns are also applied in such a way as to periodically gradually remove voices from the mix in order to prevent the monotony of full tutti passages from utterly dominating the piece. The orchestra is allowed to swell to full tutti, thus, on only three occasions in the piece - and the first two times it happens only last for four full measures each. At all other times, the total number of sounding voices is either gradually rising or gradually subsiding - and the general timbres of voices sounding is constantly changing.

Other than the above few slight alterations in the original Brahms piece, the tempo has been changed from Andante teneremente to Presto spassionato. Why, you ask? Well, that, my friend, is a trade secret.




Harmonic Étude No.12

Serial Gloss on a 13th-century Carol, "Tempus adest floridum"
Op.4, No.12

for orchestra


Date Duration Listen
Download
29 November 2013 7'38" Realization (.MP3) Score (.PDF)
10.4 MB 292 KB


This miniscule bagatelle, less than 8 minutes in length, took over two years to compose. Two Novembers in a row, I took up the idea for it, fiddled around trying to script some easy solution to the problem of marrying a tone row to a delightful medieval tune in a chorale setting, discovered myself facing enormous numbers of alternate counterpoints (none of which particularly fit the bill), finally reconciled myself to the fact that the ultimate solutions to the puzzle would only be found in extended brute-force winnowing of potential fragments by ear, and - recognizing time constraints made it impossible to complete the project in time for Christmas of whatever year - put everything back on the shelf and went back to composing less strenuously demanding pieces. This was the third November I tried to complete the thing; and the third time was the proverbial charm.

It is, of course, incumbent to remark that the famous lyrics about Good King Wencelaus were a 19th-century invention, and that the original carol tune was intended to be sung as a celebration of Spring. None of that bears on the piece as here presented, however, since the setting is entirely instrumental. ;p

The original tune appears here in ten chorales: four three-voice, and six four-voice, settings. The accompaniments in each of these chorales are entirely original, i.e., there is no repetition of any material within, or among, them, other than that of the original melody itself. The bridges and introductory sections are populated primarily by the tone row, with occasional fragmentary quotes from the carol.

The extended efforts involved in creating this lilliputian essay - coupled with the fact that it is the twelfth of its kind - suggests it as a fit final destination for the entire series of Harmonic Études. Farewell, then, to my Opus Number 4. Composing the various pieces within it spanned almost nine years. Where does the time go?




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