----------------------------------------------- ASCII score for _La Pacifica_ Composed in Zest-24, Soft Diatonic on Bb ----------------------------------------------- Here is a keyboard map showing the steps used in this notation for the piece _La Pacifica_. The scale is a soft diatonic version of a medieval Dorian mode, featuring some large steps of around 237 cents (C*-Eb) and 250 cents (G*-Bb) equal to about half of a fourth. Bb C C* Eb F G G* Bb 0 204.190 254.465 491.621 708.379 900 950.276 1200 204.190 50.276 237.155 216.759 191.621 50.276 249.724 A scale file for Manuel Op de Coul's outstanding and free software program Scala, and some information generated by Scala, follow the ASCII score. In this score, the "free voicing" of the keyboard texture which shifts between three and four parts is indicated by rests, shown with the symbol "r" and arbitrarily assigned to one of the lines. Generally each note in a given part is sustained until another note or rest occurs in that part, or a section is concluded. While the first section through measure 34 is in a fairly regular and flowing triple rhythm, the concluding measures 35-44 are slower and freer, with the notation giving a general idea. In one performance on keyboard, I found that the first section took about 58 seconds, and the second about 28 seconds -- or about 1:26 for the whole piece. These times will somewhat vary from performance to performance and interpretation to interpretation, of course. Following conventions in MIDI notation, I have used C5 to represent middle C. m5 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | Bb5 G*5 G5 G*5 C*6 C6 Bb5 C*6 C6 C*6 Eb6 F5 G5 F5 Eb5 C*5 G*5 Bb5 C6 Bb5 Bb4 C5 C*5 Eb5 F5 Eb5 m10 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | Eb6 C*6 C6 C*6 Bb5 C6 Bb5 G5 G5* Bb5 r G*5 Bb5 r Bb5 G*5 G5 r G5 F5 G5 F5 Bb5 G5 G*5 F5 G5 F5 Eb5 F5 Eb5 F5 Eb5 C*5 C5 C5 Bb4 C5 Bb4 m15 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | F5 G*5 G5 ' r F5 G5 ' F5 G5 G*5 G5 F5 Bb4 C*5 C5 ' Bb4 C*5 C5 Eb5 C*5 Eb5 F5 Bb4 C5 ' Bb4 C5 C*5 C5 Bb4 m20 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | C*6 C6 C*6 C6 F5 G*5 Bb5 Bb5 Bb5 C6 Bb5 C6 Eb5 C*5 F*5 Eb5 Eb5 F5 G*5 F5 G*5 F5 Bb4 C*5 Eb5 Eb5 Eb5 F5 Eb5 F5 m25 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | r C*6 Eb6 ' C6 C6 Bb5 C6 Bb5 ' F5 G5 G*5 G*5 Bb5 G*5 Bb5 ' F5 F5 Eb5 F5 Eb5 ' m30 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 || C6 C6 C*6 Bb5 C6 Bb5 G5 G*5 Bb5 G*5 Bb5 Bb5 Bb5 G*5 G5 r G5 F5 G5 F5 G5 G5 G*5 F5 G5 Eb5 F5 Eb5 F5 Eb5 F5 Eb5 Eb5 C*5 C5 C5 Bb4 C5 Bb4 (slower) m35 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | Eb6 C*6 F6 Bb5 G*5 C6 Bb5 F5 Bb4 m40 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 || C6 C*6 C6 C6 Bb5 F6 G5 G*5 G5 G5 Bb5 Bb5 F5 F5 Bb4 Bb4 --------------------------------- Scala file and tuning information --------------------------------- The soft diatonic scale for _La Pacifica_ is a subset of the Zest-24 tuning system described in some papers like these: First, here is a Scala file for this seven-note set, which rather resembles a scale in the Scala archive, diat_enh6.scl. ! zest24-diat_enh6_Bb.scl ! Soft neomedieval Dorian like diat_enh6.scl (~200-50-250 cents) 7 ! 204.18965 254.46549 491.62069 708.37930 900.00000 950.27584 2/1 Here is listing of steps with Zest-24 keyboard locations added at the right hand. Soft neomedieval Dorian like diat_enh6.scl (~200-50-250 cents) 0: 1/1 0.000 unison, perfect prime Bb 1: 204.190 cents 204.190 C 2: 254.465 cents 254.465 C* 3: 491.621 cents 491.621 Eb 4: 708.379 cents 708.379 F 5: 900.000 cents 900.000 G 6: 950.276 cents 950.276 G* 7: 2/1 1200.000 octave Bb Here is a list of intervals above each step as we "rotate" the choice of a step on which to begin. Soft neomedieval Dorian like diat_enh6.scl (~200-50-250 cents) 1/1 : 204.2 254.5 491.6 708.4 900.0 950.3 2/1 204.2: 50.3 287.4 504.2 695.8 746.1 995.8 2/1 254.5: 237.2 453.9 645.5 695.8 945.5 1149.7 2/1 491.6: 216.8 408.4 458.7 708.4 912.6 962.8 2/1 708.4: 191.6 241.9 491.6 695.8 746.1 983.2 2/1 900.0: 50.3 300.0 504.2 554.5 791.6 1008.4 2/1 950.3: 249.7 453.9 504.2 741.3 958.1 1149.7 2/1 2/1 One type of interval taking a prominent role in _La Pacifica_ is the very small minor sixth, as it is here treated, at about 746.1 cents, available at F-C* and C-G*. This is actually identical to the diminished sixth of Zarlino's 2/7-comma meantone (e.g. G#-Eb in a regular 12-note tuning) from which Zest-24 is derived, and almost precisely equal to a just ratio of 20:13 (~745.786 cents). Gene Ward Smith terms the 20:13 a "ratwolf" in a meantone temperament he describes, almost identical as he notes to Zarlino's 2/7-comma, where the diminished sixth or "Wolf fifth" is set at precisely this ratio. In the context of _La Pacifica_, the "near-ratwolf" characteristically expands like a more usual minor sixth to an octave in progressions like this: G*5 Bb5 C*5 Eb6 C*6 Eb6 G5 F5 C5 Bb5 C6 Bb5 Eb5 F5 G*5 Bb5 F5 Eb5 or C5 Bb4 or F5 Eb5 These progressions could be considered as intonational variants on directed resolution in 13th-century Western European music like these: F5 G5 E5 D5 E5 F5 G5 C5 D5 D5 E5 D5 A4 G4 or A4 G4 Margo Schulter 1 February 2007