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Added more to this page. It's a sandbox, so I decided to add 29L 12s.
 
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{{interwiki|en=MOS scale|de=MOS-Skala|es=|ja=MOSスケール|ro=G2S}}{{Beginner|Mathematics of MOS}}An '''MOS''' (sometimes '''mos'''; originally pronounced "em-oh-ess," but sometimes also pronounced "moss"; plural '''MOSes''' or '''mosses''') or '''moment of symmetry''' is a [[periodic scale]] in which ascending by any given number of steps is equivalent to ascending by either the period or one of two possible intervals. We can denote step patterns of mosses by writing L for each large step and s for each small step.


The [[5L 2s|diatonic scale]] is a classic example of an MOS scale. It has 7 steps: 5 large ones (whole tones) and 2 small ones (diatonic semitones). Writing out the pattern of the major mode, we get LLsLLLs. The other modes are rotations of this pattern (e.g. LsLLsLL is the minor mode.) The melodic minor scale, which is not a mode of the diatonic scale, (LsLLLLs) is not a MOS since it has three kinds of fifths: perfect, diminished, and augmented; and so ascending by four steps is equivalent to ascending by one of three possible intervals.
{{nowrap|''Iθ''{{"}} + ''bθ''{{``}} + ''mgL'' sin(''θ'') {{=}} 0}}


See the [[catalog of MOS]] for a collection of MOS scales.
702


== Naming ==
fafshdtharsgdasjdkhajsgdh
Any MOS can be clearly and uniquely specified by giving its [[signature]], i.e. the number of small and large steps, which is typically notated e.g. "5L 2s," and its equave. Sometimes, if one simply wants to talk about step sizes without specifying which is large and small, the notation "5a 2b" is used (which could refer to either [[5L 2s|diatonic]] or [[2L 5s|anti-diatonic]]).


By default, the [[equave]] of a mos ''a''L&nbsp;''b''s is assumed to be [[2/1]]. To specify a non-octave equave, "{{angbr|equave}}" is placed after the signature, e.g. {{mos scalesig|4L 5s<3/1>|link=1}}. Using angle brackets (<code>&#x26;#x27E8;</code> and <code>&#x26;#x27E9;</code>) is recommended; using greater-than and less-than signs ("&#x3C;equave&#x3E;") can also be done, but this can conflict with HTML and other uses of these symbols.
Test


Several naming systems have also been proposed for MOSes, which can be seen at [[MOS naming]].
== 29L 12s, ig. ==


== Equivalent definitions and generalizations ==
{{Infobox MOS|Scale Signature=29L 12s|debug=1}}
A scale is a MOS if and only if it satisfies one of the following equivalent criteria:


# [[Maximum variety]] 2: Ascending by a certain number of steps is equivalent to ascending by one of at most two intervals, and the maximum of two is achieved (i. e. it is not true that ascending by a certain number of steps is always equivalent to ascending by one interval.) For example, in the [[diatonic scale]], ascending by two steps can give you a major third tuned to 400c in 12edo or a minor third tuned to 300c in 12edo, but no other intervals.
{{MOS intro|Scale Signature = 29L 12s}}
# [[Binary]] and has a generator: The scale step comes in exactly two sizes, and the scale is formable from stacking some interval called a generator and octave-reducing.
# Mode of a Christoffel word: The scale can be formed by creating a 2D lattice where the period is on the lattice, then taking pitches by travelling vertically and horizontally from the origin, maintaining as close to the line from the origin to the octave as possible without going above it.


While each characterization has a generalization to scale structures with more step sizes, the generalizations are not equivalent. The concepts of [[Balanced word|balance]] and [[distributional evenness]] provide still different generalizations, although defining MOS through these terms is less helpful. For more information, see [[Mathematics of MOS]].
=== Scale properties ===
{{TAMNAMS use|Scale Signature=29L 12s}}


== History and terminology ==
==== Intervals ====
The term ''MOS'', and the method of scale construction it entails, were invented by [[Erv Wilson]] in 1975. His original paper is archived on Anaphoria.com here: [https://anaphoria.com/mos.pdf ''Moments of Symmetry'']. There is also an introduction by [[Kraig Grady]] here: [https://anaphoria.com/wilsonintroMOS.html ''Introduction to Erv Wilson's Moments of Symmetry''].
{{MOS intervals|Scale Signature=29L 12s}}


Sometimes, scales are defined with respect to a period and an additional "[[equivalence interval]]", considered to be the interval at which pitch classes repeat. MOSes in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called '''Multi-MOSes'''. MOSes in which the equivalence interval is equal to the period are sometimes called '''Strict MOSes'''. MOSes in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.
==== Generator chain ====
{{MOS genchain|Scale Signature=29L 12s}}


With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term [[Distributional evenness|distributionally even scale]], with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as ''well-formed scales'', the term used in the 1989 paper by Norman Carey and David Clampitt<ref>Norman Carey and David Clampitt. "Aspects of Well-Formed Scales", ''Music Theory Spectrum'', Vol. 11, No. 2 (Autumn, 1989), pp. 187-206.</ref>. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilson's concept. They are in a sense the MOS of MOS patterns. This is used to explain the [[Pentatonic|pentatonics]] used in traditional [[Japanese music]], where the 5-tone cycles are derived from a 7-tone MOS, which are not found in the concept of DE.
==== Modes ===
{{MOS mode degrees|Scale Signature=29L 12s}}


As for using MOS scales in practice for making music, the period and equivalence interval are often taken to be the octave, but an additional parameter is required for defining a scale: the ''step ratio'', which is the ratio of the small step (usually denoted ''s'') to the large step (usually denoted ''L''). This is usually written as ''L''/''s'', however, using ''s''/''L'' has the advantage of avoiding division by zero in the trivial case where {{nowrap|''s'' {{=}} 0}}. Different step ratios can produce very varied sounding scales (and very varied corresponding potential temperament interpretations) for a given MOS pattern and period, so it's useful to consider a spectrum of simple step ratios for tunings. The [[TAMNAMS#Step ratio spectrum|TAMNAMS]] system has names for both specific ratios and ranges of ratios.
=== Scale tree ===
 
{{MOS tuning spectrum|Scale Signature=29L 12s}}
== Step ratio spectrum ==
The melodic sound of a MOS is not just affected by the tuning of its intervals, but by the sizes of its steps. MOSes with ''L'' more similar to ''s'' sound smoother and more mellow. MOSes with ''L'' much larger than ''s'' sound jagged and dramatic. The ''step ratio'', the ratio between the sizes of ''L'' and ''s'', is thus important to the sound of the scale.
 
An in-depth analysis of this can be found at [[Step ratio]].
 
== Properties ==
 
=== Basic properties ===
 
* For every MOS scale with an [[octave]] period (which is usually the [[octave]]), if ''x''-[[edo]] is the [[collapsed]] tuning (where the small step vanishes) and ''y''-[[edo]] is the [[equalized]] tuning (where the large (''L'') step and small (''s'') step are the same size), then by definition it is an {{nowrap|''x''L (''y'' &minus; ''x'')s}} MOS scale, and the [[basic]] tuning where {{nowrap|''L'' {{=}} 2''s''}} is thus {{nowrap|(''x'' + ''y'')}}-[[edo]]. This is also true if the period is 1\''p'', that is, 1 step of ''p''-[[edo]], which implies that ''x'' and ''y'' are divisible by ''p'', though note that in that case (if {{nowrap|''p'' &gt; 1}}) you are considering a "multiperiod" MOS scale.
* More generally, whenever ''px''-[[edo]] and ''py''-[[edo]] are used to define two [[Val|vals]] (usually but not necessarily through taking the [[Patent val|patent vals]]) while simultaneously also being used to define the {{nowrap|''px''L (''py'' &minus; ''px'')s}} MOS scale (where ''p'' is the number of periods per octave), then the ''px'' & ''py'' temperament corresponds to that MOS scale, and adding ''x'' and/or ''y'' corresponds to tuning closer to ''x''-[[edo]] and/or ''y''-[[edo]] respectively. (Optionally, see the below more precise statement for the mathematically-inclined.)
* For the mathematically-inclined, we can say that whenever we consider a MOS with ''X''/''p'' notes per period in the [[collapsed]] tuning and ''Y''/''p'' notes per period in the [[equalized]] tuning and ''p'' periods per [[Octave stretching|tempered octave]] (or more generally tempered [[equave]]), and whenever we want to associate that MOS with the {{nowrap|''X'' &amp; ''Y''}} rank 2 temperament'''*''', we can say that any {{w|natural number|natural}}-coefficient {{w|linear combination}} of vals {{val|''X'' ...}} and {{val|''Y'' ...}} (where {{nowrap|''X'' &lt; ''Y''}}) corresponds uniquely to a tuning of the {{nowrap|''X'' &amp; ''Y''}} rank 2 temperament between ''X''-[[ET]] and ''Y''-[[ET]] (inclusive) iff {{nowrap|gcd(''a'', ''b'') {{=}} 1}}, because if {{nowrap|''k'' {{=}} gcd(''a'', ''b'') &gt; 1}} then the val {{nowrap|''a''{{val| ''X'' ...}} + ''b''{{val| ''Y'' ...}}}} has a common factor ''k'' in all of its terms, meaning it is guaranteed to be [[contorted]]. The tuning corresponding to the [[wikipedia:Rational number|rational]] ''a''/''b'' is technically only unique up to (discarding of) [[octave stretching]] (or more generally [[equave]]-tempering).
 
: The period of this temperament is {{nowrap|1\gcd(''X'', ''Y'')}}, and the rational ''a''/''b'' is very closely related to the [[step ratio]] of the corresponding MOS scale, because {{nowrap|1{{val| ''X'' ...}} + 0{{val| ''Y'' ...}}}} is the {{nowrap|''L'' {{=}} 1|''s'' {{=}} 0}} tuning while {{nowrap|0{{val| ''X'' ...}} + 1{{val| ''Y'' ...}}}} is the {{nowrap|''L'' {{=}} 1|''s'' {{=}} 1}} tuning and {{nowrap|1{{val| ''X'' ...}} + 1{{val| ''Y'' ...}}}} is the {{nowrap|''L'' {{=}} 2|''s'' {{=}} 1}} tuning, so that {{nowrap|''L'' {{=}} ''a'' + ''b''}} and {{nowrap|''s'' {{=}} ''b''}} and therefore:
 
: {{nowrap|1/([[step ratio]]) {{=}} ''s''/''L''}} {{nowrap|{{=}} ''b''/(''a'' + ''b'')}} implying {{nowrap|[[step ratio]] {{=}} (''a'' + ''b'')/''b'' &ge; 1}} for [[wikipedia:Natural number|natural]] ''a'' and ''b'', where if {{nowrap|''b'' {{=}} 0}} then the step ratio is infinite, corresponding to the [[collapsed]] tuning.<ref group="note">It is '''important to note''' that the correspondence to the {{nowrap|''X'' &amp; ''Y''}} rank 2 temperament only works in all cases if we allow the temperament to be [[contorted]] on its [[subgroup]]; alternatively, it works if we exclude cases where {{nowrap|''X'' &amp; ''Y''}} describe a contorted temperament on the subgroup given. An example is the {{nowrap|5 &amp; 19}} temperament is contorted in the [[5-limit]] (having a generator of a semifourth, corresponding to [[5L 14s]]), so we either need to consider the temperament itself to be contorted (generated by something lacking an interpretation in the subgroup given, two of which yielding a meantone-tempered [[~]][[4/3]]) or we exclude it because of its contortion.</ref>
 
* Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L&nbsp;''b''s are {{nowrap|(''a'' + ''b'')L ''a''s}} (generated by generators of soft-of-basic ''a''L&nbsp;''b''s) and {{nowrap|''a''L (''a'' + ''b'')s}} (generated by generators of hard-of-basic ''a''L''&nbsp;b''s).
* Every MOS scale (with a specified [[equave]] ''&#x190;''&#x200A;), excluding {{nowrap|''a''L ''a''s{{angbr|''&#x190;''&#x200A;}}}}, has a ''parent MOS''. If {{nowrap|''a'' &gt; ''b''}}, the parent of ''a''L&nbsp;''b''s is {{nowrap|''b''L (''a'' &minus; ''b'')s}}; if {{nowrap|''a'' &lt; ''b''}}, the parent of ''a''L&nbsp;''b''s is {{nowrap|''a''L (''b'' &minus; ''a'')s}}.
 
=== Advanced discussion ===
See:
 
* [[Mathematics of MOS]], a more formal definition and a discussion of the mathematical properties.
** [[Recursive structure of MOS scales]], a description of how MOS scales are recursive and how one scale can be converted into a related scale.
** [[MOS scale family tree]], a tree initially described by Erv Wilson that organizes scales by parent-and-child relationship, which also helps illustrate mos recursion.
* [[Generator ranges of MOS]], organized by number of scale steps and quantity of L/s steps.
* [[MOS diagrams]], visualizations of the MOS process.
* [http://x31eq.com/temper/method.html How to Find Linear Temperaments], by [[Graham Breed]]
 
== Variations ==
 
* [[MODMOS scales]] are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of {{nowrap|L &minus; s}}, the "chroma".
* [[Muddle|Muddles]] are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.
* [[MOS cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.
* [[Operations on MOSes]]
 
== Listen ==
This is an algorithmically generated recording of every MOS scale that has 14 or fewer notes for a total of 91 scales being showcased here. Each MOS scale played has its simplest step ratio (large step is 2 small step is 1) and therefore is inside the smallest EDO that can support it. Each MOS scale is also in its brightest mode. And rhythmically, each scale is being played with its respective MOS rhythm. Note that changing the mode or step ratio of any of these MOSes may dramatically alter the sound and therefore this recording is not thoroughly representative of each MOS but rather a small taste.
[[File:Every-MOS-Scale-With-14-Or-Fewer-Notes.mp3|left|800x800px]]
{{clear}}
 
== See also ==
 
* [[Diamond-mos notation]], a microtonal [[notation]] system focused on MOS scales
* [[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]]
* [[MOS rhythm]]
* [[:Category:MOS scales]], the category including all MOS-related articles on this wiki
* Gallery of MOS patterns
** [[Gallery of MOS patterns|1&#x2013;32 units]]
** [[User:Contribution/Gallery of MOS patterns (33 - 64 units)|33&#x2013;64 units]]
** [[User:Contribution/Gallery of MOS patterns (65 - 96 units)|65&#x2013;96 units]]
** [[User:Contribution/Gallery of MOS patterns (97 - 112 units)|97&#x2013;112 units]]
** [[User:Contribution/Gallery of MOS patterns (113 - 128 units)|113&#x2013;128 units]]
 
== Notes ==
<references group="note" />
 
== References ==
<references /><!--Sort order in category: this page shows above A-->
 
{{Infobox ET}}

Latest revision as of 20:36, 10 August 2026


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Iθ″ + bθ′ + mgL sin(θ) = 0

702

fafshdtharsgdasjdkhajsgdh

Test

29L 12s, ig.

↖ 28L 11s ↑ 29L 11s 30L 11s ↗
← 28L 12s 29L 12s 30L 12s →
↙ 28L 13s ↓ 29L 13s 30L 13s ↘
Scale structure
Step pattern ...41 steps...
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 24\41 to 17\29 (702.4 ¢ to 703.4 ¢)
Dark 12\29 to 17\41 (496.6 ¢ to 497.6 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 7:3 to 5:2
Related MOS scales
Parent 12L 17s
Sister 12L 29s
Daughters 41L 29s, 29L 41s
Neutralized 17L 24s
2-Flought 70L 12s, 29L 53s
Equal tunings
Equalized (L:s = 1:1) 24\41 (702.4 ¢)
Supersoft (L:s = 4:3) 89\152 (702.6 ¢)
Soft (L:s = 3:2) 65\111 (702.7 ¢)
Semisoft (L:s = 5:3) 106\181 (702.8 ¢)
Basic (L:s = 2:1) 41\70 (702.9 ¢)
Semihard (L:s = 5:2) 99\169 (703.0 ¢)
Hard (L:s = 3:1) 58\99 (703.0 ¢)
Superhard (L:s = 4:1) 75\128 (703.1 ¢)
Collapsed (L:s = 1:0) 17\29 (703.4 ¢)
View • Talk • Edit

29L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 29 large steps and 12 small steps, repeating every octave. 29L 12s is related to 5L 2s, expanding it by 34 tones. Generators that produce this scale range from 702.4 ¢ to 703.4 ¢, or from 496.6 ¢ to 497.6 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 29L 12s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 29.3 ¢
Major 1-mosstep M1ms L 29.3 ¢ to 41.4 ¢
2-mosstep Minor 2-mosstep m2ms L + s 41.4 ¢ to 58.5 ¢
Major 2-mosstep M2ms 2L 58.5 ¢ to 82.8 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 82.8 ¢ to 87.8 ¢
Major 3-mosstep M3ms 3L 87.8 ¢ to 124.1 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 82.8 ¢ to 117.1 ¢
Major 4-mosstep M4ms 3L + s 117.1 ¢ to 124.1 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 124.1 ¢ to 146.3 ¢
Major 5-mosstep M5ms 4L + s 146.3 ¢ to 165.5 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 165.5 ¢ to 175.6 ¢
Major 6-mosstep M6ms 5L + s 175.6 ¢ to 206.9 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 165.5 ¢ to 204.9 ¢
Major 7-mosstep M7ms 5L + 2s 204.9 ¢ to 206.9 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 206.9 ¢ to 234.1 ¢
Major 8-mosstep M8ms 6L + 2s 234.1 ¢ to 248.3 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 248.3 ¢ to 263.4 ¢
Major 9-mosstep M9ms 7L + 2s 263.4 ¢ to 289.7 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 289.7 ¢ to 292.7 ¢
Major 10-mosstep M10ms 8L + 2s 292.7 ¢ to 331.0 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 289.7 ¢ to 322.0 ¢
Major 11-mosstep M11ms 8L + 3s 322.0 ¢ to 331.0 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 331.0 ¢ to 351.2 ¢
Major 12-mosstep M12ms 9L + 3s 351.2 ¢ to 372.4 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 372.4 ¢ to 380.5 ¢
Major 13-mosstep M13ms 10L + 3s 380.5 ¢ to 413.8 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 372.4 ¢ to 409.8 ¢
Major 14-mosstep M14ms 10L + 4s 409.8 ¢ to 413.8 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 413.8 ¢ to 439.0 ¢
Major 15-mosstep M15ms 11L + 4s 439.0 ¢ to 455.2 ¢
16-mosstep Minor 16-mosstep m16ms 11L + 5s 455.2 ¢ to 468.3 ¢
Major 16-mosstep M16ms 12L + 4s 468.3 ¢ to 496.6 ¢
17-mosstep Perfect 17-mosstep P17ms 12L + 5s 496.6 ¢ to 497.6 ¢
Augmented 17-mosstep A17ms 13L + 4s 497.6 ¢ to 537.9 ¢
18-mosstep Minor 18-mosstep m18ms 12L + 6s 496.6 ¢ to 526.8 ¢
Major 18-mosstep M18ms 13L + 5s 526.8 ¢ to 537.9 ¢
19-mosstep Minor 19-mosstep m19ms 13L + 6s 537.9 ¢ to 556.1 ¢
Major 19-mosstep M19ms 14L + 5s 556.1 ¢ to 579.3 ¢
20-mosstep Minor 20-mosstep m20ms 14L + 6s 579.3 ¢ to 585.4 ¢
Major 20-mosstep M20ms 15L + 5s 585.4 ¢ to 620.7 ¢
21-mosstep Minor 21-mosstep m21ms 14L + 7s 579.3 ¢ to 614.6 ¢
Major 21-mosstep M21ms 15L + 6s 614.6 ¢ to 620.7 ¢
22-mosstep Minor 22-mosstep m22ms 15L + 7s 620.7 ¢ to 643.9 ¢
Major 22-mosstep M22ms 16L + 6s 643.9 ¢ to 662.1 ¢
23-mosstep Minor 23-mosstep m23ms 16L + 7s 662.1 ¢ to 673.2 ¢
Major 23-mosstep M23ms 17L + 6s 673.2 ¢ to 703.4 ¢
24-mosstep Diminished 24-mosstep d24ms 16L + 8s 662.1 ¢ to 702.4 ¢
Perfect 24-mosstep P24ms 17L + 7s 702.4 ¢ to 703.4 ¢
25-mosstep Minor 25-mosstep m25ms 17L + 8s 703.4 ¢ to 731.7 ¢
Major 25-mosstep M25ms 18L + 7s 731.7 ¢ to 744.8 ¢
26-mosstep Minor 26-mosstep m26ms 18L + 8s 744.8 ¢ to 761.0 ¢
Major 26-mosstep M26ms 19L + 7s 761.0 ¢ to 786.2 ¢
27-mosstep Minor 27-mosstep m27ms 19L + 8s 786.2 ¢ to 790.2 ¢
Major 27-mosstep M27ms 20L + 7s 790.2 ¢ to 827.6 ¢
28-mosstep Minor 28-mosstep m28ms 19L + 9s 786.2 ¢ to 819.5 ¢
Major 28-mosstep M28ms 20L + 8s 819.5 ¢ to 827.6 ¢
29-mosstep Minor 29-mosstep m29ms 20L + 9s 827.6 ¢ to 848.8 ¢
Major 29-mosstep M29ms 21L + 8s 848.8 ¢ to 869.0 ¢
30-mosstep Minor 30-mosstep m30ms 21L + 9s 869.0 ¢ to 878.0 ¢
Major 30-mosstep M30ms 22L + 8s 878.0 ¢ to 910.3 ¢
31-mosstep Minor 31-mosstep m31ms 21L + 10s 869.0 ¢ to 907.3 ¢
Major 31-mosstep M31ms 22L + 9s 907.3 ¢ to 910.3 ¢
32-mosstep Minor 32-mosstep m32ms 22L + 10s 910.3 ¢ to 936.6 ¢
Major 32-mosstep M32ms 23L + 9s 936.6 ¢ to 951.7 ¢
33-mosstep Minor 33-mosstep m33ms 23L + 10s 951.7 ¢ to 965.9 ¢
Major 33-mosstep M33ms 24L + 9s 965.9 ¢ to 993.1 ¢
34-mosstep Minor 34-mosstep m34ms 24L + 10s 993.1 ¢ to 995.1 ¢
Major 34-mosstep M34ms 25L + 9s 995.1 ¢ to 1034.5 ¢
35-mosstep Minor 35-mosstep m35ms 24L + 11s 993.1 ¢ to 1024.4 ¢
Major 35-mosstep M35ms 25L + 10s 1024.4 ¢ to 1034.5 ¢
36-mosstep Minor 36-mosstep m36ms 25L + 11s 1034.5 ¢ to 1053.7 ¢
Major 36-mosstep M36ms 26L + 10s 1053.7 ¢ to 1075.9 ¢
37-mosstep Minor 37-mosstep m37ms 26L + 11s 1075.9 ¢ to 1082.9 ¢
Major 37-mosstep M37ms 27L + 10s 1082.9 ¢ to 1117.2 ¢
38-mosstep Minor 38-mosstep m38ms 26L + 12s 1075.9 ¢ to 1112.2 ¢
Major 38-mosstep M38ms 27L + 11s 1112.2 ¢ to 1117.2 ¢
39-mosstep Minor 39-mosstep m39ms 27L + 12s 1117.2 ¢ to 1141.5 ¢
Major 39-mosstep M39ms 28L + 11s 1141.5 ¢ to 1158.6 ¢
40-mosstep Minor 40-mosstep m40ms 28L + 12s 1158.6 ¢ to 1170.7 ¢
Major 40-mosstep M40ms 29L + 11s 1170.7 ¢ to 1200.0 ¢
41-mosstep Perfect 41-mosstep P41ms 29L + 12s 1200.0 ¢

Generator chain

Generator chain of 29L 12s
Bright gens Scale degree Abbrev.
69 Augmented 16-mosdegree A16md
68 Augmented 33-mosdegree A33md
67 Augmented 9-mosdegree A9md
66 Augmented 26-mosdegree A26md
65 Augmented 2-mosdegree A2md
64 Augmented 19-mosdegree A19md
63 Augmented 36-mosdegree A36md
62 Augmented 12-mosdegree A12md
61 Augmented 29-mosdegree A29md
60 Augmented 5-mosdegree A5md
59 Augmented 22-mosdegree A22md
58 Augmented 39-mosdegree A39md
57 Augmented 15-mosdegree A15md
56 Augmented 32-mosdegree A32md
55 Augmented 8-mosdegree A8md
54 Augmented 25-mosdegree A25md
53 Augmented 1-mosdegree A1md
52 Augmented 18-mosdegree A18md
51 Augmented 35-mosdegree A35md
50 Augmented 11-mosdegree A11md
49 Augmented 28-mosdegree A28md
48 Augmented 4-mosdegree A4md
47 Augmented 21-mosdegree A21md
46 Augmented 38-mosdegree A38md
45 Augmented 14-mosdegree A14md
44 Augmented 31-mosdegree A31md
43 Augmented 7-mosdegree A7md
42 Augmented 24-mosdegree A24md
41 Augmented 0-mosdegree A0md
40 Augmented 17-mosdegree A17md
39 Major 34-mosdegree M34md
38 Major 10-mosdegree M10md
37 Major 27-mosdegree M27md
36 Major 3-mosdegree M3md
35 Major 20-mosdegree M20md
34 Major 37-mosdegree M37md
33 Major 13-mosdegree M13md
32 Major 30-mosdegree M30md
31 Major 6-mosdegree M6md
30 Major 23-mosdegree M23md
29 Major 40-mosdegree M40md
28 Major 16-mosdegree M16md
27 Major 33-mosdegree M33md
26 Major 9-mosdegree M9md
25 Major 26-mosdegree M26md
24 Major 2-mosdegree M2md
23 Major 19-mosdegree M19md
22 Major 36-mosdegree M36md
21 Major 12-mosdegree M12md
20 Major 29-mosdegree M29md
19 Major 5-mosdegree M5md
18 Major 22-mosdegree M22md
17 Major 39-mosdegree M39md
16 Major 15-mosdegree M15md
15 Major 32-mosdegree M32md
14 Major 8-mosdegree M8md
13 Major 25-mosdegree M25md
12 Major 1-mosdegree M1md
11 Major 18-mosdegree M18md
10 Major 35-mosdegree M35md
9 Major 11-mosdegree M11md
8 Major 28-mosdegree M28md
7 Major 4-mosdegree M4md
6 Major 21-mosdegree M21md
5 Major 38-mosdegree M38md
4 Major 14-mosdegree M14md
3 Major 31-mosdegree M31md
2 Major 7-mosdegree M7md
1 Perfect 24-mosdegree P24md
0 Perfect 0-mosdegree
Perfect 41-mosdegree		 P0md
P41md
−1 Perfect 17-mosdegree P17md
−2 Minor 34-mosdegree m34md
−3 Minor 10-mosdegree m10md
−4 Minor 27-mosdegree m27md
−5 Minor 3-mosdegree m3md
−6 Minor 20-mosdegree m20md
−7 Minor 37-mosdegree m37md
−8 Minor 13-mosdegree m13md
−9 Minor 30-mosdegree m30md
−10 Minor 6-mosdegree m6md
−11 Minor 23-mosdegree m23md
−12 Minor 40-mosdegree m40md
−13 Minor 16-mosdegree m16md
−14 Minor 33-mosdegree m33md
−15 Minor 9-mosdegree m9md
−16 Minor 26-mosdegree m26md
−17 Minor 2-mosdegree m2md
−18 Minor 19-mosdegree m19md
−19 Minor 36-mosdegree m36md
−20 Minor 12-mosdegree m12md
−21 Minor 29-mosdegree m29md
−22 Minor 5-mosdegree m5md
−23 Minor 22-mosdegree m22md
−24 Minor 39-mosdegree m39md
−25 Minor 15-mosdegree m15md
−26 Minor 32-mosdegree m32md
−27 Minor 8-mosdegree m8md
−28 Minor 25-mosdegree m25md
−29 Minor 1-mosdegree m1md
−30 Minor 18-mosdegree m18md
−31 Minor 35-mosdegree m35md
−32 Minor 11-mosdegree m11md
−33 Minor 28-mosdegree m28md
−34 Minor 4-mosdegree m4md
−35 Minor 21-mosdegree m21md
−36 Minor 38-mosdegree m38md
−37 Minor 14-mosdegree m14md
−38 Minor 31-mosdegree m31md
−39 Minor 7-mosdegree m7md
−40 Diminished 24-mosdegree d24md
−41 Diminished 41-mosdegree d41md
−42 Diminished 17-mosdegree d17md
−43 Diminished 34-mosdegree d34md
−44 Diminished 10-mosdegree d10md
−45 Diminished 27-mosdegree d27md
−46 Diminished 3-mosdegree d3md
−47 Diminished 20-mosdegree d20md
−48 Diminished 37-mosdegree d37md
−49 Diminished 13-mosdegree d13md
−50 Diminished 30-mosdegree d30md
−51 Diminished 6-mosdegree d6md
−52 Diminished 23-mosdegree d23md
−53 Diminished 40-mosdegree d40md
−54 Diminished 16-mosdegree d16md
−55 Diminished 33-mosdegree d33md
−56 Diminished 9-mosdegree d9md
−57 Diminished 26-mosdegree d26md
−58 Diminished 2-mosdegree d2md
−59 Diminished 19-mosdegree d19md
−60 Diminished 36-mosdegree d36md
−61 Diminished 12-mosdegree d12md
−62 Diminished 29-mosdegree d29md
−63 Diminished 5-mosdegree d5md
−64 Diminished 22-mosdegree d22md
−65 Diminished 39-mosdegree d39md
−66 Diminished 15-mosdegree d15md
−67 Diminished 32-mosdegree d32md
−68 Diminished 8-mosdegree d8md
−69 Diminished 25-mosdegree d25md

= Modes

Scale degrees of the modes of 29L 12s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
40|0 1 LLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
39|1 25 LLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
38|2 8 LLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
37|3 32 LLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
36|4 15 LLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
35|5 39 LLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
34|6 22 LLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
33|7 5 LLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf.
32|8 29 LLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf.
31|9 12 LLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf.
30|10 36 LLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf.
29|11 19 LLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf.
28|12 2 LLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
27|13 26 LLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
26|14 9 LLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
25|15 33 LLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
24|16 16 LLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsL Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
23|17 40 LsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
22|18 23 LsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf.
21|19 6 LsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf.
20|20 30 LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf.
19|21 13 LsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf.
18|22 37 LsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf.
17|23 20 LsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf.
16|24 3 LsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
15|25 27 LsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
14|26 10 LsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
13|27 34 LsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
12|28 17 LsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLL Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
11|29 41 sLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLL Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
10|30 24 sLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLL Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf.
9|31 7 sLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf.
8|32 31 sLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf.
7|33 14 sLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf.
6|34 38 sLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf.
5|35 21 sLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf.
4|36 4 sLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
3|37 28 sLLsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
2|38 11 sLLsLLLsLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
1|39 35 sLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|40 18 sLLsLLsLLLsLLsLLLsLLsLLsLLLsLLsLLLsLLsLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 29L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
24\41 702.439 497.561 1:1 1.000 Equalized 29L 12s
137\234 702.564 497.436 6:5 1.200
113\193 702.591 497.409 5:4 1.250
202\345 702.609 497.391 9:7 1.286
89\152 702.632 497.368 4:3 1.333 Supersoft 29L 12s
243\415 702.651 497.349 11:8 1.375
154\263 702.662 497.338 7:5 1.400
219\374 702.674 497.326 10:7 1.429
65\111 702.703 497.297 3:2 1.500 Soft 29L 12s
236\403 702.730 497.270 11:7 1.571
171\292 702.740 497.260 8:5 1.600
277\473 702.748 497.252 13:8 1.625
106\181 702.762 497.238 5:3 1.667 Semisoft 29L 12s
253\432 702.778 497.222 12:7 1.714
147\251 702.789 497.211 7:4 1.750
188\321 702.804 497.196 9:5 1.800
41\70 702.857 497.143 2:1 2.000 Basic 29L 12s
Scales with tunings softer than this are proper
181\309 702.913 497.087 9:4 2.250
140\239 702.929 497.071 7:3 2.333
239\408 702.941 497.059 12:5 2.400
99\169 702.959 497.041 5:2 2.500 Semihard 29L 12s
256\437 702.975 497.025 13:5 2.600
157\268 702.985 497.015 8:3 2.667
215\367 702.997 497.003 11:4 2.750
58\99 703.030 496.970 3:1 3.000 Hard 29L 12s
191\326 703.067 496.933 10:3 3.333
133\227 703.084 496.916 7:2 3.500
208\355 703.099 496.901 11:3 3.667
75\128 703.125 496.875 4:1 4.000 Superhard 29L 12s
167\285 703.158 496.842 9:2 4.500
92\157 703.185 496.815 5:1 5.000
109\186 703.226 496.774 6:1 6.000
17\29 703.448 496.552 1:0 → ∞ Collapsed 29L 12s
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