Schoenberg the thesis, Partch the antithesis...

The 45th movement of Symphony No. 2 is now finished (except for future edits). It’s kind of short, but maybe it needs to be that way.




It took me a while to get started, but about a day to actually write.

One of my main goals as a composer has been to reconcile two opposite musical schools:

• the masters of the twelve-tone system of the common-practice period and thereafter, from Bach to Schoenberg
• the ideas of Partch (and Helmholtz through him), who wished to return music to a pre-equal temperament ideal of natural harmony using the overtone and undertone scales; also the extended-meantone work of Vicentino and (maybe) Gesualdo

I have advocated 72 equal temperament as a compromise between the two: it’s twelve-tone multiplied by six, and it approximates Partch’s 43-tone just scale very accurately. This piece, which is for string quartet though part of a large symphonic project, is another example of my works in that tuning.

The violin plays a 31-tone row, as an expression of microtonal serialism:

• B Bd D‡ Fd C‡ D Db C# C B‡ G# Bb A Ad Cd F‡ F# A‡ A# G‡ Eb Ab Dd D# Ed E E‡ Gb F Gd G
  (‘‡’  = half sharp; ‘d’ = half flat)

The cello repeats it later in retrograde inversion. Though originally intended to be atonal, it ended up being in a vague G major, even using the appropriate key signature.

The beginning is an example of tonality flux—it has a major third, G–B, transform into a minor third by small movements of the two violins in opposite directions (33.33 cents, precisely), to G‡–Bd. The rest of the movement is harmonization of the row using various otonal and utonal chords, with major and minor tonalities extended to twelve harmonics or subharmonics, instead of the traditional six.

I also originally wanted a fugue, but it does end in a “fuguing tune”-like canon. (There’s another idea I took from old shape-note hymnody, besides using the notehead shapes as a microtonal notation.) However, the still-unfinished 43rd movement (New Mexico) is to be a fugue using a 19-tone row, also in 72-tone.

The 31- and 19-tone scales are derived by simple formulas: n*(72/31) rounded to the nearest whole number, and n*(72/19) also rounded to the nearest whole number. I’ll also need to explain these systems further at a future time (I have written something about them before).