Xenharmonikon 15 — Bruce R. Gilson
A Numerical Theory of Scale Invention
47 scales
| File | Description | Notes | Period (¢) | Limit |
|---|---|---|---|---|
| xen15-gilson-archytas-chromatic | Archytas' Chromatic | 7 | 1200.0 | 7 |
| xen15-gilson-archytas-diatonic | Archytas' Diatonic (or Ptolemy's Diatonic Tonaion) | 7 | 1200.0 | 7 |
| xen15-gilson-archytas-enharmonic | Archytas' Enharmonic | 7 | 1200.0 | 7 |
| xen15-gilson-aristoxenus-chromatic-hemiolon | Aristoxenus' Chromatic Hemiolon | 7 | 1200.0 | 37 |
| xen15-gilson-aristoxenus-chromatic-malakon | Aristoxenus' Chromatic Malakon | 7 | 1200.0 | 29 |
| xen15-gilson-aristoxenus-chromatic-tonikon | Aristoxenus' Chromatic Tonikon (or Eratosthenes' Chromatic) | 7 | 1200.0 | 19 |
| xen15-gilson-aristoxenus-diatonic-malakon | Aristoxenus' Diatonic Malakon | 7 | 1200.0 | 19 |
| xen15-gilson-aristoxenus-diatonic-syntonon | Aristoxenus' Diatonic Syntonon | 7 | 1200.0 | 19 |
| xen15-gilson-aristoxenus-enharmonic | Aristoxenus' Enharmonic | 7 | 1200.0 | 19 |
| xen15-gilson-didymus-chromatic | Didymus Chromatic | 7 | 1200.0 | 5 |
| xen15-gilson-didymus-diatonic | Didymus' Diatonic | 7 | 1200.0 | 5 |
| xen15-gilson-eratosthenes-diatonic | Eratosthenes' Diatonic (or Ptolemy's Diatonic Ditonaion) | 7 | 1200.0 | 3 |
| xen15-gilson-eratosthenes-enharmonic | Eratosthenes' Enharmonic | 7 | 1200.0 | 23 |
| xen15-gilson-generalized-just-1 | Ten note just scale, two rows and five columns of chart on p.119 | 10 | 1200.0 | 5 |
| xen15-gilson-generalized-just-2 | Scale based on product (25/24)**2 * (21/20)**3 * 16/15 * (8/7)**3 = 2 | 9 | 1200.0 | 7 |
| xen15-gilson-generalized-just-3 | Scale based on product (21/20)**3 * (16/15)**2 * (15/14)**3 * (10/9)**2 = 2 | 10 | 1200.0 | 7 |
| xen15-gilson-generalized-pythagorean-11-8-11 | Generalized Pythagorean Scale, 11/8 stacked 11=5+6 times | 11 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-11-8-13 | Generalized Pythagorean Scale, 11/8 stacked 13=6+7 times | 13 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-11-8-24 | Generalized Pythagorean Scale, 11/8 stacked 24=11+13 times | 24 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-11-8-37 | Generalized Pythagorean Scale, 11/8 stacked 37=17+20 times | 37 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-13-8-10 | Generalized Pythagorean Scale, 13/8 stacked 10=7+3 times | 10 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-13-8-3 | Generalized Pythagorean Scale, 13/8 stacked 3=2+1 times | 3 | 1200.0 | 13 |
| xen15-gilson-generalized-pythagorean-13-8-7 | Generalized Pythagorean Scale, 13/8 stacked 7=5+2 times | 7 | 1200.0 | 13 |
| xen15-gilson-generalized-pythagorean-15-8-10 | Generalized Pythagorean Scale, 15/8 stacked 10=9+1 times | 10 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-15-8-11 | Generalized Pythagorean Scale, 15/8 stacked 11=10+1 times | 11 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-15-8-32 | Generalized Pythagorean Scale, 15/8 stacked 32=29+3 times | 32 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-15-8-43 | Generalized Pythagorean Scale, 15/8 stacked 43=39+4 times | 43 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-18-17-12 | Generalized Pythagorean Scale, 18/17 stacked 12=1+11 times | 12 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-3-2-12 | Generalized Pythagorean Scale, 3/2 stacked 12=7+5 times | 12 | 1200.0 | 3 |
| xen15-gilson-generalized-pythagorean-3-2-41 | Generalized Pythagorean Scale, 3/2 stacked 41=24+17 times | 41 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-3-2-5 | Generalized Pythagorean Scale, 3/2 stacked 5=3+2 times | 5 | 1200.0 | 3 |
| xen15-gilson-generalized-pythagorean-3-2-53 | Generalized Pythagorean Scale, 3/2 stacked 53=31+22 times | 53 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-5-4-28 | Generalized Pythagorean Scale, 5/4 stacked 28=9+19 times | 28 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-5-4-59 | Generalized Pythagorean Scale, 5/4 stacked 59=19+40 times | 59 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-7-4-26 | Generalized Pythagorean Scale, 7/4 stacked 26=21+5 times | 26 | 1200.0 | |
| xen15-gilson-generalized-pythagorean-7-4-5 | Generalized Pythagorean Scale, 7/4 stacked 5=4+1 times | 5 | 1200.0 | 7 |
| xen15-gilson-just-chromatic | Just Intonation Chromatic Scale (JICS) | 12 | 1200.0 | 5 |
| xen15-gilson-just-diatonic | Just Intonation Diatonic Scale (JIDS) | 7 | 1200.0 | 5 |
| xen15-gilson-just-pentatonic | Just Intonation Pentatonic Scale (JIPS) | 5 | 1200.0 | 5 |
| xen15-gilson-ptolemy-chromatic-malakon | Ptolemy's Chromatic Malakon | 7 | 1200.0 | 7 |
| xen15-gilson-ptolemy-chromatic-syntonon | Ptolemy's Chromatic Syntonon | 7 | 1200.0 | 11 |
| xen15-gilson-ptolemy-diatonic-hemiolon | Ptolemy's Diatonic Hemiolon | 7 | 1200.0 | 11 |
| xen15-gilson-ptolemy-diatonic-malakon | Ptolemy's Diatonic Malakon | 7 | 1200.0 | 7 |
| xen15-gilson-ptolemy-diatonic-syntonon | Ptolemy's Diatonic Syntonon | 7 | 1200.0 | 5 |
| xen15-gilson-pythagorean-chromatic | Pythagorean Intonation Chromatic Scale (PICS) | 12 | 1200.0 | 3 |
| xen15-gilson-pythagorean-diatonic | Pythagorean Intonation Diatonic Scale (PIDS) | 7 | 1200.0 | 3 |
| xen15-gilson-pythagorean-pentatonic | Pythagorean Intonation Pentatonic Scale (PIPS) | 5 | 1200.0 | 3 |