1-- Full Disclosure: there are three meas. where one violin double-stops (jargon for simultaneously playing two notes at once), resulting in 9 “P”s for meas. 11, 33 & 47. For each of these, the “extra” “P” duplicates a “P” played by some other violin; and the double-stops are for “voicing” and emphasis only, and do not add “harmonic” information. To avoid even more detail in an already cluttered landscape, these 9 “P” “agg”s are subsumed within the 1 - 8 “agg” categories.
2-- Some of these “P”s are the open strings of the violin. I would argue that they be played as such, to provide a color contrast reinforcing their primacy. I am less sanguine about the use of the “PC” octave harmonics.
4-- As a sometime violinist, I may be predisposed to first think horizontally, then vertically; nevertheless, one can not deny the existence of these repeated “P”s, or “PC”s, tolling with Schubertian poignancy. NB: red and blue horizontals are NOT to be played more loudly. These lines denote continuity ONLY! As each violin nominally plays at the same loudness, loudness is solely a function of the number of violins simultaneously playing a specific “P”.
meas. 1 - 12: “PC”s = D E A in entry order; more fruitfully thought of as two superimposed Perfect 5ths.
Two areas of “PC” “major second” clusters (any pair of “PC”s that form -- after reducing the octaves-- a “major 2nd” are referred to as “PC major 2nds”) in:
meas. 56 - 60: the triad F A C;
The diminished triad F# A C of meas. 30 - 37;
meas. 43 - 48 “PC”s = G E♭ A.
Pairs of “PC” major 2nds (in this case C/D/E), are formed by the superimposition of four P5ths. The superimposition of four P5ths also can form triads, but the bifurcation of the span differs.
A “PC” semitone dyad is any interval relation that can be reduced to a minor 2nd (i.e. F/E, no matter the octave displacement). These dyads result from the superimposition of five P5ths.
“PC” semitone triunes (meaning three in one) clusters are defined as a group of 2 adjacent “PC” semitones (E/F/F#), no matter the octave displacement. They require the superimposition of seven P5ths.
10-- “Triad” is used only in the intervallic sense i.e. these are NOT tonics, dominants, medians, etc. However, within an “agg”, triads can (and do) function as attractants to the other “PC”s of that “agg”.
11-- The last triad (2nd inversion G♭ major) first appears in meas. 31, and thereafter in an alternative spelling (F# major - meas. 68 etc); so the refreshing and surprising deceptive cadence of the last 2 bars is not quite the new thought one might think.
12-- Ex. 21 helps clarify the “PC” specifics.
13-- Wherever possible, use triads as the basis. Given two or more triads, decide how they “interlock”, leaving the remaining “P”s to “fall out”. If no triads present, use P5ths as the basis. Should two (or more) meas. have one or more “P”s or “PC”s in common, these should remain constant across meas., unless ABSOLUTELY NO CHOICE.
For major 2nds (both singly, and especially if paired), one must decide if these are large or small whole tones (204 vs 182 cents, adjusted for all octave displacements). Given a triadic context, that becomes fairly obvious.
Paired Major/minor triads require the use of the 70 cent semitone for the minor-major 3rd interval. For other uses of minor 2nds, one needs to decide between large or small semi-tones (112 vs 70 cents, adjusted for octave displacements).
One should probably avoid Zalzal’s “middle finger”.
14-- Nine “PC”s appear in this extract. The missing “PC”s are A♮; D#/E♭; & B♮. That the last two, (used somewhat sparingly thruout) fail to appear, is perhaps not surprising; but the missing A♮ is odd, given its primacy. Perhaps a case “of the curious incident of the dog in the night-time”?
15-- The congruences are: that the red brackets of ex.14 all start, and with one exception, finish, to the right of the pink swath; two grey pillars (ex.15) coincide with the start and termination of an ochre oval (meas. 73 and 84); and that there are five green ovals (ex.17) on either side of the pink swath.
Acknowledgements: Wong Jing Men Jamie formed all the examples, plus a myriad of others, fallen by the wayside. Anton Vishio provided insightful, useful, comments. Elaine Vella Catalano (http://elainevellacatalano.com) did the web work. To all, my deepest appreciation, and many thanks.