Pavane For a Warped Princess
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Maurice Ravel's Pavane pour une infante défunte has a more complex harmonic structure than Pachelbel's Canon. Pavane takes advantage of the vanishing syntonic comma (81/80) in traditional systems of tuning (meantone, and later equal temperament). In this lattice diagram, which shows the basic harmonic structure of Pavane, note how the same notes appear on both the left and right sides of the diagram. In just intonation, or other non-meantone tunings, the pitches on one side are not identical to the ones on the other side with the same name.
G#
(A) E B F# C#
C G D A (E)
Eb Bb F (C)
Ab
Since the original Pavane uses the pitches on both sides of the diagram interchangeably, some of the retuned versions have dissonant "wolf" fifths where the music wraps around from one side to the other. This is especially noticeable in the A major chords around 1:15 and 1:45. In other words, the retuned versions have only 13 distinct pitches per octave (at most; I manually edited the pitch bend to distinguish G# from Ab, but the other 12 notes were automatically retuned). Given enough time and patience, these files could be adjusted by hand to eliminate wolf fifths. As of now, only the 5-limit JI version has a hand-adjusted version available (see the link below the main list).
minor major perfect "wolf"
ET Temperament third third fifth fifth
8 300.0 450.0 750.0 600.0
18 333.3 400.0 733.3 600.0
10 360.0 360.0 720.0 600.0
25 336.0 384.0 720.0 624.0
17 inconsistent (352.9) 352.9 705.9 635.3
32 inconsistent (337.5) 375.0 712.5 637.5
15 porcupine 320.0 400.0 720.0 640.0
37 porcupine 324.3 389.2 713.5 648.6
59 porcupine 325.4 386.4 711.9 650.8
46 diaschismic 313.0 365.2 704.3 652.2
22 diaschismic 327.3 381.8 709.1 654.5
42 314.3 400.0 714.3 657.1
29 schismic 331.0 372.4 703.4 662.1
27 311.1 400.0 711.1 666.7
34 diaschismic 317.6 388.2 705.9 670.6
41 schismic 322.0 380.5 702.4 673.2
53 schismic 317.0 384.9 701.9 679.2
5-limit JI 315.6 386.3 702.0 680.4
65 schismic 313.8 387.7 701.5 683.1
72 ampersand 316.7 383.3 700.0 683.3
7 342.9 342.9 685.7 685.7
26 meantone 323.1 369.2 692.3 692.3
45 meantone 320.0 373.3 693.3 693.3
19 meantone 315.8 378.9 694.7 694.7
50 meantone 312.0 384.0 696.0 696.0
31 meantone 309.7 387.1 696.8 696.8
43 meantone 307.0 390.7 697.7 697.7
12 meantone 300.0 400.0 700.0 700.0
17 inconsistent 282.4 (423.5) 705.9 705.9
64 inconsistent (300.0) 393.8 693.8 712.5
47 306.4 383.0 689.4 714.9
52 inconsistent (300.0) 392.3 692.3 715.4
35 308.6 377.1 685.7 720.0
40 inconsistent (300.0) 390.0 690.0 720.0
5 240.0 480.0 720.0 720.0
33 327.3 400.0 690.9 727.3
28 300.0 385.7 685.7 728.6
23 313.0 365.2 678.3 730.4
21 inconsistent (285.7) 400.0 685.7 742.9
16 300.0 375.0 675.0 750.0
14 inconsistent (257.1) 428.6 685.7 771.4
9 266.7 400.0 666.7 800.0
5-limit JI (adjusted)
1-TET
11-note Zireen scale (kleismic MOS, generators: 318.4c, 1203.0c)
19-limit JI
