! _For Kathleen Schlesinger: Forms of Tonality_, composition in just ! intonation system with 12 notes combining F-B chain in Pythagorean ! with Avicenna's version of "Soft Diatonic," 14:13:12 division of 7:6 ! in equable or arithmetic fashion -- tetrachords of 28:26:24:21, also ! suggesting the _harmoniai_ of Kathleen Schlesinger, whose music uses ! ratios of 14:11 and 13:11 now also favored in neo-medieval music. The ! scale: 1/1, 14/13, 9/8, 7/6, 81/64, 21/16, 4/3, 3/2, 21/13, 27/16, ! 7/4, 243/128, 2/1. ! Thanks to George Secor for pointing out to me a JI tuning of a scale ! almost identical to Avicenna's, with a harmonic division (12:13:14) ! of 7:6; to Paul Erlich for the theme of "Forms of Tonality"; and to ! Jacky Ligon for a very superparticular kind of encouragement in ! exploring scales with arithmetic divisions. ! The piece opens with mm. 1-4, then mm. 5-6 for the first ending, and ! then repeats mm. 1-4 with mm. 7-8 for the second ending. The "v" ! symbol shows a note lowered from Pythagorean by a comma of Archytas, ! as George Secor has named it, 64:63 (~27.26 cents). The choice of ! the opening sonority D4-F(v)4-Bb4 might depend on the timbre, since ! in some "pastelized" textures 1:1-21:16-14:9 can be quite smooth. A ! basic three-voice texture sometimes expands to four voices. ! 1 & 2 & | 1 & 2 ' | 1 2 & | 1 2 ' | ! Bb4 A4 G4 A4 E4 Fv4 F4 G4 ! Eb4 D4 ! F(v)4 E4 D4 E4 C#4 C4 D4 ! D4 C#4 C4 Bb3 A3 A3 Bb3 A3 G#3 G3 ! [1st time, da capo] ! 1 2 | 1 2 :|| ! F4 F4 G4 F4 ! Eb4 E4 F4 ! C#4 C4 B3 C4 ! A3 G#3 G3 F3 ! [2nd time] ! 1 2 | 1 2 | ! F4 F4 E4 F4 ! Eb4 D4 F4 ! C#4 C4 B3 C4 ! A3 G#3 G3 F3 ! Use scale pythavi2.scl (Pythagorean F-B, Avicenna's soft diatonic) ! 0 tempo 650_000 0 timesig 2/2 0 program 54 0 exclude 16 0 exclude 10 0 velocity 64 0 load pythavi2.scl ! 1 0 note 10 240 240 note 9 960 1200 note 7 240 1440 note 9 480 1920 note 4 480 2400 note 5 480 2880 note 6 480 3360 note 7 480 3840 note 6 480 4320 note 6 480 4800 note 7 480 5280 note 6 480 5760 note 10 240 6000 note 9 960 6960 note 7 240 7200 note 9 480 7680 note 4 480 8160 note 5 480 8640 note 6 480 9120 note 7 480 9600 note 6 480 10080 note 6 480 10560 note 4 480 11040 note 6 480 ! 2 2880 note 3 480 4320 note 3 480 4800 note 4 480 8640 note 3 480 10080 note 3 480 10560 note 2 480 ! 3 0 note 5 480 480 note 4 480 960 note 2 480 1440 note 4 480 1920 note 1 480 2400 note 1 480 2880 note 0 480 3360 note 2 480 3840 note 1 480 4320 note 0 480 4800 note -1 480 5280 note 0 480 5760 note 5 480 6240 note 4 480 6720 note 2 480 7200 note 4 480 7680 note 1 480 8160 note 1 480 8640 note 0 480 9120 note 2 480 9600 note 1 480 10080 note 0 480 10560 note -1 480 11040 note 0 480 ! 4 0 note 2 480 480 note 1 240 720 note 0 240 960 note -2 480 1440 note -3 480 1920 note -3 480 2400 note -2 240 2640 note -3 240 2880 note -4 480 3360 note -5 480 3840 note -3 480 4320 note -4 480 4800 note -5 480 5280 note -6 480 5760 note 2 480 6240 note 1 240 6480 note 0 240 6720 note -2 480 7200 note -3 480 7680 note -3 480 8160 note -2 240 8400 note -3 240 8640 note -4 480 9120 note -5 480 9600 note -3 480 10080 note -4 480 10560 note -5 480 11040 note -6 480