13edo scales: Difference between revisions

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Note on terminology: I often use "cofourth", "cothird", and "cosecond" for octave complements of a fourth, third or second in place of sixth, seventh and eighth. The terms describe their melodic behavior being similar to octave complements of fourths, thirds, and seconds, and work in both archaeotonic and oneirotonic contexts.
Since 13 is prime, [[13edo]] has more MOS scale types than 12edo; somewhat amazingly, all of them have a good number of consonant chords if you know where to look.


Both archaeotonic and oneirotonic modes are partly analogous to diatonic modes, though some of them sound more like combinations of different modes.
== Overview ==


===Archaeotonic===
The intervals themselves are not very alien except near the middle of the octave, just a bit darker compared to their 12edo counterparts. They are familiar enough that they can be given pseudo-diatonic names:
The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common.


===Oneirotonic===
{| class="wikitable center-all right-2"
The darker, damper, more "minory" cousin of archaeotonic. Only 2 out of 8 oneirotonic modes (Dylathian and Ilarnekian) are "major" in the sense of having a major third, and both sound pretty bittersweet.
|-
! Degree
! Cents
! Pseudo-Diatonic Category
|-
| 0
| 0.00
| Unison (P1)
|-
| 1
| 92.31
| Minor second (m2)
|-
| 2
| 184.62
| Major second (M2)
|-
| 3
| 276.92
| Minor third (m3)
|-
| 4
| 369.23
| Major third (M3), Diminished fourth (d4)
|-
| 5
| 461.54
| Minor fourth (m4)
|-
| 6
| 553.85
| Major fourth (M4), Minor tritone (mᴛ)
|-
| 7
| 646.15
| Minor fifth (m5), Major tritone (Mᴛ)
|-
| 8
| 738.46
| Major fifth (M5)
|-
| 9
| 830.77
| Minor sixth (m6), Augmented fifth (A5)
|-
| 10
| 923.08
| Major sixth (M6)
|-
| 11
| 1015.38
| Minor seventh (m7)
|-
| 12
| 1107.69
| Major seventh (M7)
|-
| 13
| 1200.00
| Octave (P8)
|}


Like in archaeotonic, seconds and thirds are similar in consonance to 12edo seconds and thirds, and similarly cothirds and coseconds are similar to diatonic sixths and sevenths.  
My ([[User:IlL|Inthar's]]) subjective perception of the relative consonance of different intervals from the most consonant to the most dissonant (octave equivalents are not taken into account):
*''Basals'' (the most consonant): major second, major and minor thirds
*''Glitterers'' (intermediate, buzzy consonance): major and minor fourths, major and minor sixths, major and minor sevenths, minor ninth
*''Flarers'' (the most dissonant): minor and major fifths, the most dissonant and categorically ambiguous intervals.


Perfect fourths (21/16) are dissonant, but they work a lot like diatonic perfect fourths do e.g. in "sus24" chords that resolve down to thirds, and can also be spread out to make convincing 4:9:21 chords. Minor fifths (approximating 11/8) work like tritones and they like to resolve inward to a third. Major fifths (16/11) are the opposite: they like to resolve outward to a cothird. Unlike in 12edo, there is a major difference in quality between fourths and fifths, and their octave inversions. Perfect fourths and minor fifths are more consonant than their inversions major fifths and perfect cofourths; they can also both be spread out to make them more consonant, whereas their inversions cannot.
Cheat sheet of important [[MOS]] scale types with 9 notes or fewer:


The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as O-J-K-M, representing both 8:10:11:13 and 13:16:18:21, but it only represents 13:16:18:21 in other oneirotonic-supporting tunings such as [[31edo]]).
{| class="wikitable center-all right-2"
|-
! MOS type
! Generator
! Most common consonant triad
! Most common consonant tetrad(s)
|-
| archeotonic (2222221)
| major second (2\13)
| 4:5:9
| 4:5:9:11, 4:5:9:13
|-
| Father pentatonic (32323)
| minor fourth (5\13)
|
|
|-
| oneirotonic (21221221)
| minor fourth (5\13)
| 4:9:21. Also important: 4:5:9 and its minor counterpart 0-3-15.
| Basic triads with added 6ths and 7ths
|-
| Lovecraft nonatonic (212121211)
| minor third (3\13)
| 4:11:13
| 4:9:11:13
|-
| Sephiroth decatonic (1313131)
| major third (4\13)
| 4:5:13
| 4:5:13:21
|}


Basic chord progressions can move by perfect fourths or major seconds: J major-M minor-P minor-Ob major-J major (in Ilarnekian) or J major-K major-O major-M major-J major (in Dylathian)
== Archaeotonic (6L 1s) ==


===Chords===
The archaeotonic scale is one of the two pseudo-diatonic scale types in 13edo. It is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics.
Oneirotonic provides unique tetrads taking every second degree of the scale, JLNP or KMOQ. They're quite spicy, might want to try different voicings?


J-L-K (4:5:9) and its minor counterpart J-Lb-K work well with an added cothird or cosecond, even when the resulting chord does not approximate an obvious JI chord.
Being a 7-note scale, the unison to octave interval categories remain the same as in the diatonic scale, except that we now have major fourths (6\13, approx. 11/8) and minor fourths (5\13, approx. 21/16), and their inversions minor and major fifths. An interesting feature is that you can switch whether you perceive an interval as minor or major by approaching it from opposite directions: for example, a minor sixth can be made to sound like a diatonic major sixth by walking up whole-whole-half-whole-whole steps from the tonic or like a diatonic minor sixth by walking down two whole steps.


todo: try added cofourths or fifths, describe chords with two additions or more
=== Scale ===
 
Sortable table of intervals in the Lobonian mode. (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.)
 
{| class="wikitable right-1 right-2 sortable"
|-
! Degree
! Cents
! Note name on J
! Approximate ratios
! #Gens up
|-
| 1, 8
| 0.00, 1200.00
| J
| 1/1, 2/1
| 0
|-
| 2
| 184.62
| K
| 9/8, 10/9, 11/10, 19/17, 21/19
| +1
|-
| 3
| 369.23
| L
| 5/4, 11/9, 16/13, 26/21
| +2
|-
| 4
| 553.85
| M#
| 11/8, 18/13, 26/19 
| +3
|-
| 5
| 738.46
| Ob
| 17/11, 20/13, 26/17, 32/21
| +4
|-
| 6
| 923.08
| Pb
| 8/5, 13/8, 18/11, 21/13
| -2
|-
| 7
| 1015.38
| Qb
| 9/5, 16/9, 20/11, 34/19, 38/21
| -1
|}
 
=== Chords ===
 
The root-major third-major ninth (approximating 4:5:9; J-L-K in Kentaku notation) and its minor equivalent root-minor third-major ninth (J-Lb-K in Kentaku notation) may be considered equivalents of root-third-fifth chords in diatonic music. Archeotonic scales have 6 such triads, 5 "major" and 1 "minor". The 11th and 13th harmonics are also plentiful, as already noted by Cryptic Ruse; 4 roots have the 11th harmonic over them and 5 roots have the 13th harmonic over them.
 
The chord spelled root-major third-major fourth-minor sixth in archeotonic nomenclature occurs twice in archeotonic. It can be interpreted both as an 8:10:11:13 and as a 13:16:18:21 (which can be revoiced as 8:9:13:21), thanks to the way 13edo conflates higher-limit JI intervals together.
 
Archeotonic offers fairly familiar-sounding chord progressions by major seconds, thirds, and (both major and minor) fourths. One example is root-major third-two major thirds-root (spelled J major - L major - N# major - J major in J Ryonian), where the (two major thirds) is a 21/16 minor fourth away from the root.
 
=== Modal harmony ===
 
The 7 archeotonic modes each sound like one part of the scale (the part with the unique small step) is diatonic and thus can evoke various modes of the diatonic scale. The modal harmony of the unmodified archeotonic scales is otherwise simpler than diatonic modal harmony due to the dearth of small steps. To get more complex modal harmony, you could contrast major and minor intervals of the same interval class by playing the same melody in a different mode (like you can do in [[porcupine]]), and you could make 12edo-like chromatic modifications to spice things up.
 
== Oneirotonic (5L 3s) ==
:''Main article: [[5L 3s]]''
[[File:Oneirotonic_Scale_-_Dylathian_in_L.png|alt=Oneirotonic Scale - Dylathian in L.png|800x135px|Oneirotonic Scale - Dylathian in L.png]]
 
[[:File:Oneirotonic_Scale_-_Dylathian_in_L.svg|Oneirotonic Scale - Dylathian in L.svg]]
 
[[:File:13edo-fretboard-template.svg|13edo-fretboard-template.svg]]
 
== Switching between archeo- and oneirotonic ==
 
Pseudo-diatonic music in 13edo can easily use both archeotonic and oneirotonic, switching back and forth between a 7-note mode and a corresponding 8-note one as the situation requires.
 
=== Twin modes ===
 
The most obvious way to do this is to exploit the fact that an oneirotonic mode and an archeotonic mode based on the same tonic may share up to 6 notes; replace the "1 2 1" in the oneirotonic mode with a "2 2". Six of the 8 oneirotonic modes have a "twin" archeotonic mode that keeps the same tonic, listed below from brightest to darkest:
 
{| class="wikitable center-all"
|+ Oneiro-Archeo Twin Modes
! Oneirotonic || ↔ || Archeotonic
|-
| Dylathian  2 2 1 2 2 1 2 1 || ↔ || Oukranian  2 2 1 2 2 2 2
|-
| Illarnekian  2 2 1 2 1 2 2 1 || ↔ || Ryonian    2 2 2 2 2 2 1
|-
| Ultharian  2 1 2 2 1 2 1 2 || ↔ || Tamashian  2 1 2 2 2 2 2
|-
| Mnarian    2 1 2 1 2 2 1 2 || ↔ || Karakalian  2 2 2 2 2 1 2
|-
| Hlanithian  1 2 2 1 2 1 2 2 || ↔ || Zo-Kalarian 1 2 2 2 2 2 2
|-
| Sarnathian  1 2 1 2 2 1 2 2 || ↔ || Lobonian    2 2 2 2 1 2 2
|}
This operation might change the mood of the scale drastically. For example, Mnarian, a "minor" mode, becomes Karakalian, a "major" mode.
 
== Nonatonic (4L 5s) ==
 
Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also [[support]]s bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. Similar scales also exist in 22edo and 31edo with flatter generators, but they use a [[Orwell|different temperament]] and won't approximate the 13th harmonic.
 
=== Scale ===
 
The brightest mode is LsLsLsLss or 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11.
 
Sortable table of LsLsLsLss (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.):
 
{| class="wikitable right-1 right2 sortable"
|-
! style="text-align:right" | Degree
! Cents
! Note name on J
! Approximate ratios
! # generators up
|-
| 1, 10
| 0.00, 1200.00
| J
| 1/1, 2/1
| 0
|-
| 2
| 184.62
| K
| 9/8, 10/9, 11/10, 19/17, 21/19
| +5
|-
| 3
| 276.92
| Lb
| 7/6, 13/11, 20/17, 19/16, 22/19
| +1
|-
| 4
| 461.54
| M
| 13/10, 17/13, 21/16, 22/17
| +6
|-
| 5
| 553.85
| M#/Nb
| 11/8, 18/13, 26/19
| +2
|-
| 6
| 738.46
| N#/Ob
| 17/11, 20/13, 26/17, 32/21
| +7
|-
| 7
| 830.77
| O
| 8/5, 13/8, 18/11, 21/13
| +3
|-
| 8
| 1015.38
| P#
| 9/5, 16/9, 20/11, 34/19, 38/21
| +8
|-
| 9
| 1107.69
| Q
| 17/9, 19/10, 21/11, 32/17, 36/19, 40/21
| +4
|}
 
=== Modal harmony ===
 
The nonatonic scale can be thought of as a (chromatically altered) octatonic scale with one note added.
The 6-generators-up mode 0-2-3-5-6-7-9-10-12-13 contains an octatonic MODMOS 0-2-3-5-7-9-10-12-13 (Celephaïsian with a sharpened 6th degree).
 
=== Musical examples ===
 
[https://www.youtube.com/watch?v=x4Yesl8n6gc Brusselator Sprouts (by Xotla)] (The main riffs are in this scale, although key changes and notes outside the 9 note subset are used too.)
 
== Sephiroth heptatonic (3L 4s) ==
The symmetric 1313131 mode:
{| class="wikitable right-1 right-2 sortable"
|-
! Degree
! Cents
! Note name on J
! Approximate ratios
! #Gens up
|-
| 1, 8
| 0.00, 1200.00
| J
| 1/1, 2/1
| 0
|-
| 2
| 92.31
| Kb
| 17/16, 18/17, 19/18, 20/19, 21/20, 22/21
| +1
|-
| 3
| 369.23
| L
| 5/4, 11/9, 16/13, 26/21
| +2
|-
| 4
| 461.54
| M
| 13/10, 17/13, 21/16, 22/17
| +3
|-
| 5
| 738.46
| Ob
| 17/11, 20/13, 26/17, 32/21
| +4
|-
| 6
| 830.77
| Pb
| 8/5, 13/8, 18/11, 21/13
| -2
|-
| 7
| 1107.69
| Q
| 17/9, 19/10, 21/11, 32/17, 36/19, 40/21
| -1
|}
 
{{Navbox scale gallery}}
 
[[Category:13edo]]
[[Category:Lists of scales]]
[[Category:Guitar]]

Latest revision as of 06:02, 20 March 2026

Since 13 is prime, 13edo has more MOS scale types than 12edo; somewhat amazingly, all of them have a good number of consonant chords if you know where to look.

Overview

The intervals themselves are not very alien except near the middle of the octave, just a bit darker compared to their 12edo counterparts. They are familiar enough that they can be given pseudo-diatonic names:

Degree Cents Pseudo-Diatonic Category
0 0.00 Unison (P1)
1 92.31 Minor second (m2)
2 184.62 Major second (M2)
3 276.92 Minor third (m3)
4 369.23 Major third (M3), Diminished fourth (d4)
5 461.54 Minor fourth (m4)
6 553.85 Major fourth (M4), Minor tritone (mᴛ)
7 646.15 Minor fifth (m5), Major tritone (Mᴛ)
8 738.46 Major fifth (M5)
9 830.77 Minor sixth (m6), Augmented fifth (A5)
10 923.08 Major sixth (M6)
11 1015.38 Minor seventh (m7)
12 1107.69 Major seventh (M7)
13 1200.00 Octave (P8)

My (Inthar's) subjective perception of the relative consonance of different intervals from the most consonant to the most dissonant (octave equivalents are not taken into account):

  • Basals (the most consonant): major second, major and minor thirds
  • Glitterers (intermediate, buzzy consonance): major and minor fourths, major and minor sixths, major and minor sevenths, minor ninth
  • Flarers (the most dissonant): minor and major fifths, the most dissonant and categorically ambiguous intervals.

Cheat sheet of important MOS scale types with 9 notes or fewer:

MOS type Generator Most common consonant triad Most common consonant tetrad(s)
archeotonic (2222221) major second (2\13) 4:5:9 4:5:9:11, 4:5:9:13
Father pentatonic (32323) minor fourth (5\13)
oneirotonic (21221221) minor fourth (5\13) 4:9:21. Also important: 4:5:9 and its minor counterpart 0-3-15. Basic triads with added 6ths and 7ths
Lovecraft nonatonic (212121211) minor third (3\13) 4:11:13 4:9:11:13
Sephiroth decatonic (1313131) major third (4\13) 4:5:13 4:5:13:21

Archaeotonic (6L 1s)

The archaeotonic scale is one of the two pseudo-diatonic scale types in 13edo. It is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics.

Being a 7-note scale, the unison to octave interval categories remain the same as in the diatonic scale, except that we now have major fourths (6\13, approx. 11/8) and minor fourths (5\13, approx. 21/16), and their inversions minor and major fifths. An interesting feature is that you can switch whether you perceive an interval as minor or major by approaching it from opposite directions: for example, a minor sixth can be made to sound like a diatonic major sixth by walking up whole-whole-half-whole-whole steps from the tonic or like a diatonic minor sixth by walking down two whole steps.

Scale

Sortable table of intervals in the Lobonian mode. (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.)

Degree Cents Note name on J Approximate ratios #Gens up
1, 8 0.00, 1200.00 J 1/1, 2/1 0
2 184.62 K 9/8, 10/9, 11/10, 19/17, 21/19 +1
3 369.23 L 5/4, 11/9, 16/13, 26/21 +2
4 553.85 M# 11/8, 18/13, 26/19 +3
5 738.46 Ob 17/11, 20/13, 26/17, 32/21 +4
6 923.08 Pb 8/5, 13/8, 18/11, 21/13 -2
7 1015.38 Qb 9/5, 16/9, 20/11, 34/19, 38/21 -1

Chords

The root-major third-major ninth (approximating 4:5:9; J-L-K in Kentaku notation) and its minor equivalent root-minor third-major ninth (J-Lb-K in Kentaku notation) may be considered equivalents of root-third-fifth chords in diatonic music. Archeotonic scales have 6 such triads, 5 "major" and 1 "minor". The 11th and 13th harmonics are also plentiful, as already noted by Cryptic Ruse; 4 roots have the 11th harmonic over them and 5 roots have the 13th harmonic over them.

The chord spelled root-major third-major fourth-minor sixth in archeotonic nomenclature occurs twice in archeotonic. It can be interpreted both as an 8:10:11:13 and as a 13:16:18:21 (which can be revoiced as 8:9:13:21), thanks to the way 13edo conflates higher-limit JI intervals together.

Archeotonic offers fairly familiar-sounding chord progressions by major seconds, thirds, and (both major and minor) fourths. One example is root-major third-two major thirds-root (spelled J major - L major - N# major - J major in J Ryonian), where the (two major thirds) is a 21/16 minor fourth away from the root.

Modal harmony

The 7 archeotonic modes each sound like one part of the scale (the part with the unique small step) is diatonic and thus can evoke various modes of the diatonic scale. The modal harmony of the unmodified archeotonic scales is otherwise simpler than diatonic modal harmony due to the dearth of small steps. To get more complex modal harmony, you could contrast major and minor intervals of the same interval class by playing the same melody in a different mode (like you can do in porcupine), and you could make 12edo-like chromatic modifications to spice things up.

Oneirotonic (5L 3s)

Main article: 5L 3s

Oneirotonic Scale - Dylathian in L.png

Oneirotonic Scale - Dylathian in L.svg

13edo-fretboard-template.svg

Switching between archeo- and oneirotonic

Pseudo-diatonic music in 13edo can easily use both archeotonic and oneirotonic, switching back and forth between a 7-note mode and a corresponding 8-note one as the situation requires.

Twin modes

The most obvious way to do this is to exploit the fact that an oneirotonic mode and an archeotonic mode based on the same tonic may share up to 6 notes; replace the "1 2 1" in the oneirotonic mode with a "2 2". Six of the 8 oneirotonic modes have a "twin" archeotonic mode that keeps the same tonic, listed below from brightest to darkest:

Oneiro-Archeo Twin Modes
Oneirotonic ↔ Archeotonic
Dylathian 2 2 1 2 2 1 2 1 ↔ Oukranian 2 2 1 2 2 2 2
Illarnekian 2 2 1 2 1 2 2 1 ↔ Ryonian 2 2 2 2 2 2 1
Ultharian 2 1 2 2 1 2 1 2 ↔ Tamashian 2 1 2 2 2 2 2
Mnarian 2 1 2 1 2 2 1 2 ↔ Karakalian 2 2 2 2 2 1 2
Hlanithian 1 2 2 1 2 1 2 2 ↔ Zo-Kalarian 1 2 2 2 2 2 2
Sarnathian 1 2 1 2 2 1 2 2 ↔ Lobonian 2 2 2 2 1 2 2

This operation might change the mood of the scale drastically. For example, Mnarian, a "minor" mode, becomes Karakalian, a "major" mode.

Nonatonic (4L 5s)

Generated by 3\13, the 276.9-cent minor third approximating 13/11, this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the bithotrilu temperament that tempers out the bithotrilu comma 1352/1331 = [3 0 0 0 -3 2⟩, aka "lovecraft temperament".) 17edo also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. Similar scales also exist in 22edo and 31edo with flatter generators, but they use a different temperament and won't approximate the 13th harmonic.

Scale

The brightest mode is LsLsLsLss or 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11.

Sortable table of LsLsLsLss (Harmonics are in bold; this is useful for seeing a chord's complexity when you sort the intervals according to the generator chain.):

Degree Cents Note name on J Approximate ratios # generators up
1, 10 0.00, 1200.00 J 1/1, 2/1 0
2 184.62 K 9/8, 10/9, 11/10, 19/17, 21/19 +5
3 276.92 Lb 7/6, 13/11, 20/17, 19/16, 22/19 +1
4 461.54 M 13/10, 17/13, 21/16, 22/17 +6
5 553.85 M#/Nb 11/8, 18/13, 26/19 +2
6 738.46 N#/Ob 17/11, 20/13, 26/17, 32/21 +7
7 830.77 O 8/5, 13/8, 18/11, 21/13 +3
8 1015.38 P# 9/5, 16/9, 20/11, 34/19, 38/21 +8
9 1107.69 Q 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 +4

Modal harmony

The nonatonic scale can be thought of as a (chromatically altered) octatonic scale with one note added.

The 6-generators-up mode 0-2-3-5-6-7-9-10-12-13 contains an octatonic MODMOS 0-2-3-5-7-9-10-12-13 (Celephaïsian with a sharpened 6th degree).

Musical examples

Brusselator Sprouts (by Xotla) (The main riffs are in this scale, although key changes and notes outside the 9 note subset are used too.)

Sephiroth heptatonic (3L 4s)

The symmetric 1313131 mode:

Degree Cents Note name on J Approximate ratios #Gens up
1, 8 0.00, 1200.00 J 1/1, 2/1 0
2 92.31 Kb 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 +1
3 369.23 L 5/4, 11/9, 16/13, 26/21 +2
4 461.54 M 13/10, 17/13, 21/16, 22/17 +3
5 738.46 Ob 17/11, 20/13, 26/17, 32/21 +4
6 830.77 Pb 8/5, 13/8, 18/11, 21/13 -2
7 1107.69 Q 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 -1


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JI scales 12-tone JI • Combination product set • Constant structure • Harry Partch-related • Maximal harmony epimorphic • MOS transversal • Non-octave JI • Wakalix • Z-polygon transversal • Other JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS • 12-tone tempered • Chromatic pair • Clipper • Double mode • Essentially tempered • Fantasy detemper • Marvel woo • Meantone • Min ambiguity • MOS cradle • Negri-9 • Neutral third • Non-octave tempered • Scalesmith systematic • Ternary • Other tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo • 11 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 33 • 34 • 35 • 36 • 37 • 38 • 40 • 41 • 42 • 43 • 46 • 49 • 53 • 72 • 80
All other scale gallery pages are included in Category:Lists of scales
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