In 1974, Robert Morris and Daniel Starr famously enumerated every all-interval twelve-tone row. 

Inspired by their work, and in around 1979 in unpublished works, I generated an analogous catalog of what one might call the all-trichord rows, meaning rows, which together with two of their untransposed rotations, and in "first-species counterpoint," produce a sequence of all twelve distinct trichord classes.  By the standards of the day, this 
involved very substantial computational search.  But lately I have vastly expanded that calculation, now allowing transposition, retrograde and inversion of the rotations. Some of these new rows provide the basis of my recent pieces.   

The catalog of all-trichord rows runs to about 300 more or less, depending upon the accounting for symmetries.  That makes these rows quite rare among all the twelve-tone rows.  This rarity suggests my original compositional conception but unrealized at the time: a museum-like installation where a listener might walk in a large space from sonic exhibit to sonic exhibit, and experience the different ways these rows fit together and do their thing.  

So here are just three typical exhibits, realized now as works for chamber orchestra.  In each, the basic row first gets a plain but lapidary statement, and then the rotated forms fade in, statistically speaking, and eventually the rows likewise fade out in the order in which they entered, leaving finally a statement of the basic row.  By design, this treatment could loop seamlessly as one "display," as per my original conception.

0    1    9    4   10    5    2    8    7    6    3   11

Written in October 2025. Violin and orchestra.
Seated Balinese Woman, Arthur John Fleischmann.

Violin Concerto 2 (ii)

18 THE DISTANT PAST

19 GO ON A FORAY

20 FEAR→SORROW

03 - MORE...

13 - SILENT

02.2ND MOV： PSYCHO-FIELD

03.3RD MOV： ANGELO

06.RIDDHE

The track "dEvilGODfamily復活動 ＜X9＞" from the "THE SEVEN DEADLY SINS: PRISONERS OF THE SKY ORIGINAL SOUNDTRACK" album.

Composer: Hiroyuki Sawano
Arranger: Hiroyuki Sawano

All rights go to Hiroyuki Sawano, VV-ALKLINE and any other associated copyright owners.

劇場版 七つの大罪 天空の囚われ人 オリジナル・サウンドトラック

dEvilGODfamily復活動 ＜X9＞

13 - SILENT

T_Tistory

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