List of MOS scales in 17edo: Difference between revisions
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→Mosses by generator pair: Temperament[note_count] fields were wrongly calculated and fixed |
→Mosses by generator pair: Updated according to current TAMNAMS names |
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* The table denotes each family using a [[Horogram#Rectangular%20Horogram|rectangular horogram]], starting with 1L 1s and [[MOS Diagrams|adding notes]] until every note is added. | * The table denotes each family using a [[Horogram#Rectangular%20Horogram|rectangular horogram]], starting with 1L 1s and [[MOS Diagrams|adding notes]] until every note is added. | ||
* For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator. | * For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator. | ||
* [[TAMNAMS]] names are used wherever possible. Scales with at least four notes have clickable links to their corresponding mos page. | * [[TAMNAMS]] names are used wherever possible, except for scales with 4 or fewer notes and 1L ns scales for tidiness. Scales with at least four notes have clickable links to their corresponding mos page. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 524: | Line 524: | ||
|[[4L 1s]] | |[[4L 1s]] | ||
|4:1 | |4:1 | ||
| | |manual | ||
|huxley[5] | |huxley[5] | ||
|- | |- | ||
| Line 538: | Line 538: | ||
|[[4L 5s]] | |[[4L 5s]] | ||
|3:1 | |3:1 | ||
| | |gramitonic | ||
|huxley[9] | |huxley[9] | ||
|- | |- | ||
| Line 608: | Line 608: | ||
|[[3L 1s]] | |[[3L 1s]] | ||
|5:2 | |5:2 | ||
| | |tetric | ||
|maqamic/hemif[4] | |maqamic/hemif[4] | ||
|- | |- | ||
| Line 701: | Line 701: | ||
|[[3L 5s]] | |[[3L 5s]] | ||
|4:1 | |4:1 | ||
| | |checkertonic | ||
|sqwares[8] | |sqwares[8] | ||
|- | |- | ||
| Line 818: | Line 818: | ||
|[[5L 7s]] | |[[5L 7s]] | ||
|2:1 | |2:1 | ||
| | | | ||
|supra[12] | |supra[12] | ||
|- | |- | ||
| Line 897: | Line 897: | ||
|[[2L 7s]] | |[[2L 7s]] | ||
|5:1 | |5:1 | ||
| | |balzano | ||
|progress[9] | |progress[9] | ||
|- | |- | ||
Revision as of 21:57, 18 November 2022
Since 17 is a prime number, any interval can be repeatedly stacked to produce new intervals until all 17 tones are included. This page lists and visualizes the scales produced this way.
Diagram of mosses of 17edo
The following diagram is a visualization of some of the mosses available in 17edo. See moment of symmetry scales for background on this type of linear scale, and see horogram for background on this type of diagram.
| generator | temperament |
|---|---|
| 2\17 | Bleu |
| 3\17 | Machine |
| 4\17 | Huxley |
| 5\17 | Maqamic/hemif |
| 6\17 | Skwares |
| 7\17 | Supra |
| 8\17 | Progress |
See also: 17edo neutral scale
Mosses by generator pair
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:
- The table denotes each family using a rectangular horogram, starting with 1L 1s and adding notes until every note is added.
- For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
- TAMNAMS names are used wherever possible, except for scales with 4 or fewer notes and 1L ns scales for tidiness. Scales with at least four notes have clickable links to their corresponding mos page.
| Single-Period Scales for 17 Equal Division of the Octave | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps for Generators 16\17 and 1\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 16 | 1 | 1L 1s | 16:1 | |||||||||||||||||
| 15 | 1 | 1 | 1L 2s | 15:1 | ||||||||||||||||
| 14 | 1 | 1 | 1 | 1L 3s | 14:1 | |||||||||||||||
| 13 | 1 | 1 | 1 | 1 | 1L 4s | 13:1 | ||||||||||||||
| 12 | 1 | 1 | 1 | 1 | 1 | 1L 5s | 12:1 | |||||||||||||
| 11 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 6s | 11:1 | ||||||||||||
| 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 7s | 10:1 | |||||||||||
| 9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 8s | 9:1 | ||||||||||
| 8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 9s | 8:1 | |||||||||
| 7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 10s | 7:1 | ||||||||
| 6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 11s | 6:1 | |||||||
| 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 12s | 5:1 | ||||||
| 4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 13s | 4:1 | |||||
| 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 14s | 3:1 | ||||
| 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 15s | 2:1 | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 15\17 and 2\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 15 | 2 | 1L 1s | 15:2 | |||||||||||||||||
| 13 | 2 | 2 | 1L 2s | 13:2 | ||||||||||||||||
| 11 | 2 | 2 | 2 | 1L 3s | 11:2 | bleu[4] | ||||||||||||||
| 9 | 2 | 2 | 2 | 2 | 1L 4s | 9:2 | bleu[5] | |||||||||||||
| 7 | 2 | 2 | 2 | 2 | 2 | 1L 5s | 7:2 | bleu[6] | ||||||||||||
| 5 | 2 | 2 | 2 | 2 | 2 | 2 | 1L 6s | 5:2 | bleu[7] | |||||||||||
| 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1L 7s | 3:2 | bleu[8] | ||||||||||
| 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 8L 1s | 2:1 | subneutralic | bleu[9] | ||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 14\17 and 3\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 14 | 3 | 1L 1s | 14:3 | |||||||||||||||||
| 11 | 3 | 3 | 1L 2s | 11:3 | ||||||||||||||||
| 8 | 3 | 3 | 3 | 1L 3s | 8:3 | machine[4] | ||||||||||||||
| 5 | 3 | 3 | 3 | 3 | 1L 4s | 5:3 | machine[5] | |||||||||||||
| 2 | 3 | 3 | 3 | 3 | 3 | 5L 1s | 3:2 | machinoid | machine[6] | |||||||||||
| 2 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 6L 5s | 2:1 | machine[11] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 13\17 and 4\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 13 | 4 | 1L 1s | 13:4 | |||||||||||||||||
| 9 | 4 | 4 | 1L 2s | 9:4 | ||||||||||||||||
| 5 | 4 | 4 | 4 | 1L 3s | 5:4 | huxley[4] | ||||||||||||||
| 1 | 4 | 4 | 4 | 4 | 4L 1s | 4:1 | manual | huxley[5] | ||||||||||||
| 1 | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 3 | 4L 5s | 3:1 | gramitonic | huxley[9] | ||||||||
| 1 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 4L 9s | 2:1 | huxley[13] | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 12\17 and 5\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 12 | 5 | 1L 1s | 12:5 | |||||||||||||||||
| 7 | 5 | 5 | 1L 2s | 7:5 | ||||||||||||||||
| 2 | 5 | 5 | 5 | 3L 1s | 5:2 | tetric | maqamic/hemif[4] | |||||||||||||
| 2 | 2 | 3 | 2 | 3 | 2 | 3 | 3L 4s | 3:2 | mosh | maqamic/hemif[7] | ||||||||||
| 2 | 2 | 2 | 1 | 2 | 2 | 1 | 2 | 2 | 1 | 7L 3s | 2:1 | dicotonic | maqamic/hemif[10] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 11\17 and 6\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 11 | 6 | 1L 1s | 11:6 | |||||||||||||||||
| 5 | 6 | 6 | 2L 1s | 6:5 | ||||||||||||||||
| 5 | 5 | 1 | 5 | 1 | 3L 2s | 5:1 | antipentic | sqwares[5] | ||||||||||||
| 4 | 1 | 4 | 1 | 1 | 4 | 1 | 1 | 3L 5s | 4:1 | checkertonic | sqwares[8] | |||||||||
| 3 | 1 | 1 | 3 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 3L 8s | 3:1 | sqwares[11] | |||||||
| 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 3L 11s | 2:1 | sqwares[14] | ||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 10\17 and 7\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 10 | 7 | 1L 1s | 10:7 | |||||||||||||||||
| 3 | 7 | 7 | 2L 1s | 7:3 | ||||||||||||||||
| 3 | 3 | 4 | 3 | 4 | 2L 3s | 4:3 | pentic | supra[5] | ||||||||||||
| 3 | 3 | 3 | 1 | 3 | 3 | 1 | 5L 2s | 3:1 | diatonic | supra[7] | ||||||||||
| 2 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 5L 7s | 2:1 | supra[12] | ||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||
| Steps for Generators 9\17 and 8\17 | Mos | Step Ratio | TAMNAMS Name | Temperament | ||||||||||||||||
| 9 | 8 | 1L 1s | 9:8 | |||||||||||||||||
| 1 | 8 | 8 | 2L 1s | 8:1 | ||||||||||||||||
| 1 | 1 | 7 | 1 | 7 | 2L 3s | 7:1 | pentic | progress[5] | ||||||||||||
| 1 | 1 | 1 | 6 | 1 | 1 | 6 | 2L 5s | 6:1 | antidiatonic | progress[7] | ||||||||||
| 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 5 | 2L 7s | 5:1 | balzano | progress[9] | ||||||||
| 1 | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 2L 9s | 4:1 | progress[11] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 1 | 1 | 3 | 2L 11s | 3:1 | progress[13] | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2L 13s | 2:1 | progress[15] | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17edo | 1 | ||