Pinetone: Difference between revisions
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We could tune the scale in many different ways. The TE tuning given above consists of 7 large steps of 146.6352c, 1 medium step of 63.1434c, and 4 small steps of 27.4197c. | We could tune the scale in many different ways. The TE tuning given above consists of 7 large steps of 146.6352c, 1 medium step of 63.1434c, and 4 small steps of 27.4197c. | ||
We could instead tune to [[POTE tuning|POTE]] no-7 ptolemismic, resulting in a very similar 7L 1m 4s = (146.7247c, 63.1818c, 27.4363c). There are also least squares and minimax. I hope to figure those out. | We could instead tune to [[POTE tuning|POTE]] no-7 ptolemismic, resulting in a very similar 7L 1m 4s = (146.7247c, 63.1818c, 27.4363c). | ||
For reference, the 5-limit JI tuning of (27/25, 25/24, 250/243) is equal to (133.2376c, 70.6724c, 49.1661c). There are also least squares and minimax. I hope to figure those out. | |||
We could also tune to edos. Tuning to [[15edo]], [[22edo]] or [[29edo]] collapses the scale to a [[Porcupine]][8] scale, and tuning to [[19edo]] or [[31edo]] tempers the scale to a Meantone[12] scale. We can retain three step sizes if we tune to [[27edo]] (using 27e), [[34edo]], or to [[41edo]]. | We could also tune to edos. Tuning to [[15edo]], [[22edo]] or [[29edo]] collapses the scale to a [[Porcupine]][8] scale, and tuning to [[19edo]] or [[31edo]] tempers the scale to a Meantone[12] scale. We can retain three step sizes if we tune to [[27edo]] (using 27e), [[34edo]], or to [[41edo]]. | ||
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41edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c) | 41edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c) | ||
== Chords == | |||
=== Porcutone diatonic === | |||
Since the scale is built from 6/5 3/2 9/5 2/1, it is the most readily available tetrad, containing a 4:5:6 major triad and a 10:12:15 minor triad. To tonal harmony we can use tertian chords in the diatonic scale, leading to: | |||
* D minor 10:12:15 | |||
* E minor 10:12:15 | |||
* F major 4:5:6 | |||
* G major 4:5:6 | |||
* A porcupine diminished / meantone minor 15:18:22 | |||
* B diminished 25:30:36 | |||
* C porcupine diminished / meantone major (has a neutral third) 27:33:40 | |||
Tertian tetrads: | |||
* D minor 7 10:12:15:18 | |||
* E minor 7 10:12:15:18 | |||
* F major 7 but it's actually a major neutral 7 chord 12:15:18:22 | |||
* G porcupine major 7 / meantone dominant 7 20:25:30:36 | |||
* A porcupine half-dim 7 / meantone minor 7 45:54:66:80 | |||
* B half diminished 7 25:30:36:45 | |||
* C porcupine half-dim 7 / meantone major 7 (has a neutral third) 27:33:40:50 | |||
9 chords: | |||
* D 10:12:15:18:22 | |||
* E 33:40:50:60:72 | |||
* F 36:45:54:66:80 | |||
* G 20:25:30:36:45 | |||
* A 45:54:66:80:100 | |||
* B 25:30:36:45:54 | |||
* C 27:33:40:50:60 | |||
11 chords: | |||
* D 30:36:45:54:66:80 | |||
* E 33:40:50:60:72:90 | |||
* F 36:45:54:66:80:100 | |||
* G 20:25:30:36:45:54 | |||
* A 45:54:66:80:100:120 | |||
* B 25:30:36:45:54:66 | |||
* C 27:33:40:50:60:72 | |||
13 chords: | |||
* D 30:36:45:54:66:80:100 | |||
* E 33:40:50:60:72:90:108 | |||
* F 36:45:54:66:80:100:120 | |||
* G 20:25:30:36:45:54:66 | |||
* A 45:54:66:80:100:120 | |||
* B 25:30:36:45:54:66:80 | |||
* C 27:33:40:50:60:72:90 | |||