3-limit scales
48 scales
| File | Description | Notes | Period (ยข) | Limit | Source |
|---|---|---|---|---|---|
| 081_E8 | Enharmonic tetrachord 282429536481/274877906944 * 70368744177664/68630377364883 * 81/64 | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 120_E14 | Enharmonic tetrachord 282429536481/274877906944 * 134217728/129140163 * 8192/6561 | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 249_C17 | Chromatic tetrachord 256/243 * 2187/2048 * 32/27, Gaudentius | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 454_D15 | Diatonic tetrachord 256/243 * 9/8 * 9/8, Pythagoras? | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 456_D15 | Diatonic tetrachord 2187/2048 * 65536/59049 * 9/8, Anonymous | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 482_R6 | Reduplicated tetrachord 2187/2048 * 16777216/14348907 * 2187/2048, Palmer | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| 485_R9 | Reduplicated tetrachord 256/243 * 256/243 * 19683/16384 | 3 | 498.0 | 3 | Divisions of the Tetrachord |
| pseudo_Odo_octatonics | pyth. 3-limit 5ths chain of 8 pitch-classes: Bb-F-C-G-D-A-E-B | 8 | 1200.0 | 3 | Mailing lists |
| pyth_17 | 17-tone Pythagorean scale | 17 | 1200.0 | 3 | Mailing lists |
| synmav1 | First 81/80&135/128 scale Pythagorean | 7 | 1200.0 | 3 | Mailing lists |
| xen03-wilson-positive-05 | Positive, linear-mapped intonational system, 5 notes | 5 | 1200.0 | 3 | Xenharmonikon |
| xen03-wilson-positive-07 | Positive, linear-mapped intonational system, 7 notes | 7 | 1200.0 | 3 | Xenharmonikon |
| xen03-wilson-positive-12 | Positive, linear-mapped intonational system, 12 notes | 12 | 1200.0 | 3 | Xenharmonikon |
| xen06-london-ditone-diatonic | Tuning for 'Eight Pieces for Harp in Ditone Diatonic' | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-chalmers-tritriadic-54-64-81 | Tritriadic scale built from 54:64:81 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-chalmers-tritriadic-64-81-96 | Tritriadic scale built from 64:81:96 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-01 | Marwa permutation 1 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-02 | Marwa permutation 2 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-03 | Marwa permutation 3 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-04 | Marwa permutation 4 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-05 | Marwa permutation 5 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-02-06 | Marwa permutation 6 from Figure 2, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen09-wilson-marwa-05-01 | Marwa permutation 1 from Figure 5, Pythagoras 256/243 9/8 9/8 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-01 | Purvi modulation 1 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-02 | Purvi modulation 2 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-03 | Purvi modulation 3 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-04 | Purvi modulation 4 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-05 | Purvi modulation 5 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-06 | Purvi modulation 6 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen10-wilson-purvi-01-07 | Purvi modulation 7 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-diamond-81-64 | Triadic diamond for M=81/64, D=3/2 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-diamond-81-64-tetrachord | Upper tetrachord 256/243 * 2187/2048 * 32/27 of triadic diamond for M=81/64, D=3/2 | 3 | 498.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-diamond-8192-6561 | Triadic diamond for M=8192/6561, D=3/2 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-diamond-8192-6561-tetrachord | Upper tetrachord 2187/2048 * 134217728/129140163 * 19683/16384 of triadic diamond for M=8192/6561, D=3/2 | 3 | 498.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-32-27 | Triadic reversed diamond for M=32/27, D=3/2 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-32-27-tetrachord | Tetrachord 9/8 * 256/243 * 9/8 of triadic reversed diamond for M=32/27, D=3/2 | 3 | 498.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-81-64 | Triadic reversed diamond for M=81/64, D=3/2 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-81-64-tetrachord | Tetrachord 256/243 * 19683/16384 * 256/243 of triadic reversed diamond for M=81/64, D=3/2 | 3 | 498.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-8192-6561 | Triadic reversed diamond for M=8192/6561, D=3/2 | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-chalmers-triadic-reversed-diamond-8192-6561-tetrachord | Tetrachord 2187/2048 * 16777216/14348907 * 2187/2048 of triadic reversed diamond for M=8192/6561, D=3/2 | 3 | 498.0 | 3 | Xenharmonikon |
| xen15-gilson-eratosthenes-diatonic | Eratosthenes' Diatonic (or Ptolemy's Diatonic Ditonaion) | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-gilson-generalized-pythagorean-3-2-12 | Generalized Pythagorean Scale, 3/2 stacked 12=7+5 times | 12 | 1200.0 | 3 | Xenharmonikon |
| xen15-gilson-generalized-pythagorean-3-2-5 | Generalized Pythagorean Scale, 3/2 stacked 5=3+2 times | 5 | 1200.0 | 3 | Xenharmonikon |
| xen15-gilson-pythagorean-chromatic | Pythagorean Intonation Chromatic Scale (PICS) | 12 | 1200.0 | 3 | Xenharmonikon |
| xen15-gilson-pythagorean-diatonic | Pythagorean Intonation Diatonic Scale (PIDS) | 7 | 1200.0 | 3 | Xenharmonikon |
| xen15-gilson-pythagorean-pentatonic | Pythagorean Intonation Pentatonic Scale (PIPS) | 5 | 1200.0 | 3 | Xenharmonikon |
| xen18-ayers-table-23 | Inverted Geometric Means Between 1/1 and 2/1 Produce a Symmetrical Scale | 9 | 1200.0 | 3 | Xenharmonikon |
| xen18-schulter-pythagorean | 12-note Pythagorean tuning | 12 | 1200.0 | 3 | Xenharmonikon |