List of MOS scales in 17edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
m Moved from category "MOS" to "MOS scales"
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Replaced table with template
Line 44: Line 44:
* 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, 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.
* [[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.
 
{{MOSes in EDO|EDO=17}}
{| class="wikitable"
! colspan="21" |Single-Period Scales for 17 Equal Division of the Octave
|-
! colspan="17" |Steps for Generators 16\17 and 1\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="16" |16
| 1
| 1L 1s
| 16:1
|
|
|-
| colspan="15" |15
| 1
| 1
| 1L 2s
| 15:1
|
|
|-
| colspan="14" |14
| 1
| 1
| 1
| [[1L 3s]]
| 14:1
|
|
|-
| colspan="13" |13
| 1
| 1
| 1
| 1
| [[1L 4s]]
| 13:1
|
|
|-
| colspan="12" |12
| 1
| 1
| 1
| 1
| 1
| [[1L 5s]]
| 12:1
|
|
|-
| colspan="11" |11
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 6s]]
| 11:1
|
|
|-
| colspan="10" |10
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 7s]]
| 10:1
|
|
|-
| colspan="9" |9
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 8s]]
| 9:1
|
|
|-
| colspan="8" |8
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 9s]]
| 8:1
|
|
|-
| colspan="7" |7
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 10s]]
| 7:1
|
|
|-
| colspan="6" |6
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 11s]]
| 6:1
|
|
|-
| colspan="5" |5
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 12s]]
| 5:1
|
|
|-
| colspan="4" |4
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 13s]]
| 4:1
|
|
|-
| colspan="3" |3
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 14s]]
| 3:1
|
|
|-
| colspan="2" |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
|
|
|-
! colspan="17" |Steps for Generators 15\17 and 2\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="15" |15
| colspan="2" |2
| 1L 1s
| 15:2
|
|
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
| 1L 2s
| 13:2
|
|
|-
| colspan="11" |11
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 3s]]
| 11:2
|
| bleu[4]
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 4s]]
| 9:2
|
| bleu[5]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 5s]]
| 7:2
|
| bleu[6]
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 6s]]
| 5:2
|
| bleu[7]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 7s]]
| 3:2
|
| bleu[8]
|-
| 1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="17" |Steps for Generators 14\17 and 3\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="14" |14
| colspan="3" |3
| 1L 1s
| 14:3
|
|
|-
| colspan="11" |11
| colspan="3" |3
| colspan="3" |3
| 1L 2s
| 11:3
|
|
|-
| colspan="8" |8
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[1L 3s]]
| 8:3
|
| machine[4]
|-
| colspan="5" |5
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[1L 4s]]
| 5:3
|
| machine[5]
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[5L 1s]]
| 3:2
| machinoid
| machine[6]
|-
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |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
|
|
|-
! colspan="17" |Steps for Generators 13\17 and 4\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="13" |13
| colspan="4" |4
| 1L 1s
| 13:4
|
|
|-
| colspan="9" |9
| colspan="4" |4
| colspan="4" |4
| 1L 2s
| 9:4
|
|
|-
| colspan="5" |5
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| [[1L 3s]]
| 5:4
|
| huxley[4]
|-
| 1
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| [[4L 1s]]
| 4:1
| manual
| huxley[5]
|-
| 1
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| [[4L 5s]]
| 3:1
| gramitonic
| huxley[9]
|-
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |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
|
|
|-
! colspan="17" |Steps for Generators 12\17 and 5\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="12" |12
| colspan="5" |5
| 1L 1s
| 12:5
|
|
|-
| colspan="7" |7
| colspan="5" |5
| colspan="5" |5
| 1L 2s
| 7:5
|
|
|-
| colspan="2" |2
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| [[3L 1s]]
| 5:2
| tetric
| maqamic/hemif[4]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| [[3L 4s]]
| 3:2
| mosh
| maqamic/hemif[7]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| colspan="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
|
|
|-
! colspan="17" |Steps for  Generators 11\17 and 6\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="11" |11
| colspan="6" |6
| 1L 1s
| 11:6
|
|
|-
| colspan="5" |5
| colspan="6" |6
| colspan="6" |6
| 2L 1s
| 6:5
|
|
|-
| colspan="5" |5
| colspan="5" |5
| 1
| colspan="5" |5
| 1
| [[3L 2s]]
| 5:1
| antipentic
| sqwares[5]
|-
| colspan="4" |4
| 1
| colspan="4" |4
| 1
| 1
| colspan="4" |4
| 1
| 1
| [[3L 5s]]
| 4:1
| checkertonic
| sqwares[8]
|-
| colspan="3" |3
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| [[3L 8s]]
| 3:1
|
| sqwares[11]
|-
| colspan="2" |2
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| colspan="2" |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
|
|
|-
! colspan="17" |Steps for Generators 10\17 and 7\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="10" |10
| colspan="7" |7
| 1L 1s
| 10:7
|
|
|-
| colspan="3" |3
| colspan="7" |7
| colspan="7" |7
| 2L 1s
| 7:3
|
|
|-
| colspan="3" |3
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
| [[2L 3s]]
| 4:3
| pentic
| supra[5]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| 1
| colspan="3" |3
| colspan="3" |3
| 1
| [[5L 2s]]
| 3:1
| diatonic
| supra[7]
|-
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| colspan="2" |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
|
|
|-
! colspan="17" |Steps for Generators 9\17 and 8\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="9" |9
| colspan="8" |8
| 1L 1s
| 9:8
|
|
|-
| 1
| colspan="8" |8
| colspan="8" |8
| 2L 1s
| 8:1
|
|
|-
| 1
| 1
| colspan="7" |7
| 1
| colspan="7" |7
| [[2L 3s]]
| 7:1
| pentic
| progress[5]
|-
| 1
| 1
| 1
| colspan="6" |6
| 1
| 1
| colspan="6" |6
| [[2L 5s]]
| 6:1
| antidiatonic
| progress[7]
|-
| 1
| 1
| 1
| 1
| colspan="5" |5
| 1
| 1
| 1
| colspan="5" |5
| [[2L 7s]]
| 5:1
| balzano
| progress[9]
|-
| 1
| 1
| 1
| 1
| 1
| colspan="4" |4
| 1
| 1
| 1
| 1
| colspan="4" |4
| [[2L 9s]]
| 4:1
|
| progress[11]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| [[2L 11s]]
| 3:1
|
| progress[13]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |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
|
|
|}
 
[[Category:17edo]]
[[Category:17edo]]
[[Category:MOS scales]]
[[Category:MOS scales]]

Revision as of 21:13, 4 December 2023

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.

17edo_horograms.jpg

17edo horograms.pdf

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.

This page lists all moment of symmetry scales in 17edo.

Single-period MOS scales

Generators 9\17 and 8\17
Step visualization MOS (name) Step sizes Step ratio
├────────┼───────┤ 1L 1s 9, 8 9:8
├┼───────┼───────┤ 2L 1s 8, 1 8:1
├┼┼──────┼┼──────┤ 2L 3s 7, 1 7:1
├┼┼┼─────┼┼┼─────┤ 2L 5s (antidiatonic) 6, 1 6:1
├┼┼┼┼────┼┼┼┼────┤ 2L 7s (balzano) 5, 1 5:1
├┼┼┼┼┼───┼┼┼┼┼───┤ 2L 9s 4, 1 4:1
├┼┼┼┼┼┼──┼┼┼┼┼┼──┤ 2L 11s 3, 1 3:1
├┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┤ 2L 13s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 10\17 and 7\17
Step visualization MOS (name) Step sizes Step ratio
├─────────┼──────┤ 1L 1s 10, 7 10:7
├──┼──────┼──────┤ 2L 1s 7, 3 7:3
├──┼──┼───┼──┼───┤ 2L 3s 4, 3 4:3
├──┼──┼──┼┼──┼──┼┤ 5L 2s (diatonic) 3, 1 3:1
├─┼┼─┼┼─┼┼┼─┼┼─┼┼┤ 5L 7s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 11\17 and 6\17
Step visualization MOS (name) Step sizes Step ratio
├──────────┼─────┤ 1L 1s 11, 6 11:6
├────┼─────┼─────┤ 2L 1s 6, 5 6:5
├────┼────┼┼────┼┤ 3L 2s 5, 1 5:1
├───┼┼───┼┼┼───┼┼┤ 3L 5s (checkertonic) 4, 1 4:1
├──┼┼┼──┼┼┼┼──┼┼┼┤ 3L 8s 3, 1 3:1
├─┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ 3L 11s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 12\17 and 5\17
Step visualization MOS (name) Step sizes Step ratio
├───────────┼────┤ 1L 1s 12, 5 12:5
├──────┼────┼────┤ 1L 2s 7, 5 7:5
├─┼────┼────┼────┤ 3L 1s 5, 2 5:2
├─┼─┼──┼─┼──┼─┼──┤ 3L 4s (mosh) 3, 2 3:2
├─┼─┼─┼┼─┼─┼┼─┼─┼┤ 7L 3s (dicoid) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 13\17 and 4\17
Step visualization MOS (name) Step sizes Step ratio
├────────────┼───┤ 1L 1s 13, 4 13:4
├────────┼───┼───┤ 1L 2s 9, 4 9:4
├────┼───┼───┼───┤ 1L 3s 5, 4 5:4
├┼───┼───┼───┼───┤ 4L 1s 4, 1 4:1
├┼┼──┼┼──┼┼──┼┼──┤ 4L 5s (gramitonic) 3, 1 3:1
├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤ 4L 9s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 14\17 and 3\17
Step visualization MOS (name) Step sizes Step ratio
├─────────────┼──┤ 1L 1s 14, 3 14:3
├──────────┼──┼──┤ 1L 2s 11, 3 11:3
├───────┼──┼──┼──┤ 1L 3s 8, 3 8:3
├────┼──┼──┼──┼──┤ 1L 4s 5, 3 5:3
├─┼──┼──┼──┼──┼──┤ 5L 1s (machinoid) 3, 2 3:2
├─┼─┼┼─┼┼─┼┼─┼┼─┼┤ 6L 5s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 15\17 and 2\17
Step visualization MOS (name) Step sizes Step ratio
├──────────────┼─┤ 1L 1s 15, 2 15:2
├────────────┼─┼─┤ 1L 2s 13, 2 13:2
├──────────┼─┼─┼─┤ 1L 3s 11, 2 11:2
├────────┼─┼─┼─┼─┤ 1L 4s 9, 2 9:2
├──────┼─┼─┼─┼─┼─┤ 1L 5s (antimachinoid) 7, 2 7:2
├────┼─┼─┼─┼─┼─┼─┤ 1L 6s (onyx) 5, 2 5:2
├──┼─┼─┼─┼─┼─┼─┼─┤ 1L 7s (antipine) 3, 2 3:2
├┼─┼─┼─┼─┼─┼─┼─┼─┤ 8L 1s (subneutralic) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 16\17 and 1\17
Step visualization MOS (name) Step sizes Step ratio
├───────────────┼┤ 1L 1s 16, 1 16:1
├──────────────┼┼┤ 1L 2s 15, 1 15:1
├─────────────┼┼┼┤ 1L 3s 14, 1 14:1
├────────────┼┼┼┼┤ 1L 4s 13, 1 13:1
├───────────┼┼┼┼┼┤ 1L 5s (antimachinoid) 12, 1 12:1
├──────────┼┼┼┼┼┼┤ 1L 6s (onyx) 11, 1 11:1
├─────────┼┼┼┼┼┼┼┤ 1L 7s (antipine) 10, 1 10:1
├────────┼┼┼┼┼┼┼┼┤ 1L 8s (antisubneutralic) 9, 1 9:1
├───────┼┼┼┼┼┼┼┼┼┤ 1L 9s (antisinatonic) 8, 1 8:1
├──────┼┼┼┼┼┼┼┼┼┼┤ 1L 10s 7, 1 7:1
├─────┼┼┼┼┼┼┼┼┼┼┼┤ 1L 11s 6, 1 6:1
├────┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 12s 5, 1 5:1
├───┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 13s 4, 1 4:1
├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 14s 3, 1 3:1
├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 15s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Retrieved from "https://en.xen.wiki/index.php?title=List_of_MOS_scales_in_17edo&oldid=128440"