xen18-ayers-table-23
Inverted Geometric Means Between 1/1 and 2/1 Produce a Symmetrical Scale
Properties
| Notes | 9 |
|---|---|
| Period | 1200.0 ¢ |
| Just | 3-limit |
| Source | Xenharmonikon 18 |
| Reference | Lydia Ayers, Making Scales from Mathematical Means, Xenharmonikon 18 (2006), p.208 |
| Author | Lydia Ayers |
| Article | 40 scales |
| Tone | Tone (¢) | Step | Step (¢) |
|---|---|---|---|
| 256/243 | 90 | 256/243 | 90 |
| 9/8 | 204 | 2187/2048 | 114 |
| 32/27 | 294 | 256/243 | 90 |
| 4/3 | 498 | 9/8 | 204 |
| 3/2 | 702 | 9/8 | 204 |
| 27/16 | 906 | 9/8 | 204 |
| 16/9 | 996 | 256/243 | 90 |
| 243/128 | 1110 | 2187/2048 | 114 |
| 2/1 | 1200 | 256/243 | 90 |
Parent scales
| File | Notes | Max diff (¢) |
|---|---|---|
| xen03-wilson-positive-12 | 12 | 0.0 |
| xen18-erlich-helmholtz-12 | 12 | 1.0 |
| xen18-erlich-garibaldi-12 | 12 | 1.9 |
| schisdia5 | 12 | 2.0 |
| mistyschism2 | 12 | 2.0 |
| mistyschism3 | 12 | 2.0 |
| raintree | 12 | 2.0 |
| akj19_12 | 12 | 3.4 |
| xen18-erlich-dominant-12 | 12 | 4.8 |
| pyth_17 | 17 | 0.0 |
Child scales
| File | Notes | Max diff (¢) |
|---|---|---|
| synmav1 | 7 | 0.0 |
| xen09-wilson-marwa-02-04 | 7 | 0.0 |
| xen10-wilson-purvi-01-04 | 7 | 0.0 |
| xen15-chalmers-triadic-reversed-diamond-32-27 | 7 | 0.0 |
| xen03-wilson-positive-05 | 5 | 0.0 |
| xen15-gilson-pythagorean-pentatonic | 5 | 0.0 |
| xen18-erlich-helmholtz-05 | 5 | 0.5 |
| xen18-erlich-helmholtz-07 | 7 | 0.6 |
| xen18-erlich-garibaldi-05 | 5 | 0.8 |
| xen18-erlich-garibaldi-07 | 7 | 1.3 |
Raw file
! xen18-ayers-table-23.scl ! Inverted Geometric Means Between 1/1 and 2/1 Produce a Symmetrical Scale 9 ! 256/243 9/8 32/27 4/3 3/2 27/16 16/9 243/128 2/1 ! ! Lydia Ayers ! Making Scales from Mathematical Means ! Xenharmonikon 18 (2006), p.208 ! ! [info] ! source = Xenharmonikon ! whole_number = 18