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This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)


== Template test area==
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>
Cell color code test
{| class="wikitable"
|+
!Examples
!0
|-
|Augmented size
| style="background:#ededb0" | Aug.
|-
|Large size
| style="background:#ffffe0" | Maj.
|-
|Small size
| style="background:#eaeaff" | Min.
|-
|Diminished size
| style="background:#afafe0" | Dim.
|}


===MOS mode degrees (5L 2s)===
produces
{{MOS mode degrees|Scale Signature=5L 2s}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs|Mode Names=Ionian b6 (Harmonic major); Dorian b5 (Dorian diminished); Phrygian b4; Lydian b3 (Lydian minor); Mixolydian b2; Lydian #2 #5; Locrian bb7}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs|Mode Names=Aeolian ♮6 ♮7 (Melodic minor); Dorian b2; Lydian #5 (Lydian augmented); Lydian b7 (Lydian dominant); Mixolydian b6; Locrian ♮2 (Half-diminished); Locrian bb4 (Altered dominant, super-locrian)}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sLLLLLs|Mode Names=Ionian b2 b3 (Neapolitan major); Lydian #5 #6; Lydian #5 b7; Lydian b6 b7; Locrian ♮2 ♮3 (Major locrian); Locrian ♮2 b4; Locrian bb3 b4}}


{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}
1/1, 50/49, 49/48, 36/35, 28/27, 25/24, 21/20, 16/15, 15/14, 27/25, 49/45, 35/32, 10/9, 28/25, 9/8, 8/7, 7/6, 32/27, 25/21, 6/5, 49/40, 5/4, 32/25, 9/7, 35/27, 21/16, 4/3, 27/20, 49/36, 48/35, 25/18, 7/5, 45/32, 10/7, 36/25, 35/24, 40/27, 3/2, 32/21, 49/32, 14/9, 25/16, 8/5, 45/28, 49/30, 5/3, 42/25, 27/16, 12/7, 7/4, 16/9, 25/14, 9/5, 49/27, 50/27, 28/15, 15/8, 40/21, 48/25, 27/14, 35/18, 49/25, 2/1


{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}
== MOS scalesig ==
{{Infobox|Left Link=Neutral 3rd|Title=Major 3rd|Right Link=Perfect 4th|Data 1='''Interval range information'''|Header 2=Approximate range|Data 2=180{{c}} - 240{{c}}|Header 3=Complement|Data 3=Minor 6th|Data 5='''JI examples'''|Data 6=5/4, 9/7, 81/64|Data 10='''Generated scales'''|Data 11=4L 3s, 4L 7s}}


=== MOS mode degrees (other mosses) ===
== MOS tuning spectrum (AKA, scale tree) ==
{{MOS mode degrees|Scale Signature=4L 4s}}
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=AdAdAdAdA}}
{{MOS mode degrees|Scale Signature=6L 2s}}


===MOS step sizes ===
{{MOS tuning spectrum
{| class="wikitable sortable"
| Scale Signature = 1L 1s
|+3L 4s step sizes
| Int Limit = 13
! rowspan="2" |Interval
}}
! colspan="2" | Basic 3L 4s
(10edo, L:s = 2:1)
! colspan="2" |Hard 3L 4s
(13edo, L:s = 3:1)
! colspan="2" | Soft 3L 4s
(17edo, L:s = 3:2)
! rowspan="2" |Approx. JI ratios
|-
!Steps
! Cents
!Steps
!Cents
!Steps
!Cents
|-
|Large step
|2
|240¢
| 3
|276.9¢
| 3
|211.8¢
| Hide column if no ratios given
|-
| Small step
|1
|120¢
|1
| 92.3¢
|2
|141.2¢
|
|-
|Bright generator
|3
|360¢
| 4
|369.2¢
|5
|355.6¢
|
|}
Notes:


*Allow option to show the bright generator, dark generator, or no generator.
{{MOS tuning spectrum
*JI ratios column only shows if there are any ratios to show
| Scale Signature= 3L 4s
| Int Limit = 20
| 6/5 = [[Mohaha]] / ptolemy↑
| 5/4 = Mohaha / migration / [[mohajira]]
| 11/8 = Mohaha / mohamaq
| 7/5 = Mohaha / [[neutrominant]]
| 10/7 = [[Hemif]] / [[hemififths]]
| 11/7 = [[Suhajira]]
| 13/8 = Golden suhajira (354.8232¢)
| 5/3 = Suhajira / [[ringo]]
| 12/7 = [[Beatles]]
| 13/5 = Unnamed golden tuning (366.2564¢)
| 7/2 = [[Sephiroth]]
| 9/2 = [[Muggles]]
| 5/1 = [[Magic]]
| 6/1 = [[Würschmidt]]↓
}}


===Expanded MOS intro===
{{MOS tuning spectrum
The following pieces of information may be worth adding:
| Depth = 3
| Scale Signature= 3L 4s<3/2>
}}


*The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
== MOS intro==
*Simple edos (or ed<nowiki><p/q>) that support the mos.</nowiki>
First sentence:
*For mosses with more than 10 notes, that the mos descends from another, TAMNAMS-named mos and how it relates back to that ancestor mos. This requires standardizing the naming scheme for descendant mosses before it can be added.
*Single-period 2/1-equivalent: '''xL ys''' (TAMNAMS name ''tamnams-name''), also called ''other-name'', is an octave-repeating moment of symmetry scale that divides the octave (2/1) into x large and y small steps.
====Base wording (for TAMNAMS-named mosses)====
*Multi-period 2/1-equivalent: '''nxL nys''' (TAMNAMS name ''tamnams-name''), also called ''other-name'', is an octave-repeating moment of symmetry scale that divides the octave (2/1) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
'''''x''L ''y''s<''p/q''>''', also called '''mosname''', is a(n) ''equave-equivalent'' moment-of-symmetry scale, containing ''x'' large steps(s) and ''y'' small step(s) and repeating every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.  
*Single-period 3/1-equivalent: '''3/1-equivalent xL ys''', also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, c cents) into x large and y small steps.
*Multi-period 3/1-equivalent: '''3/1-equivalent nxL nys''', also called ''other-name'', is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
*Single-period 3/2-equivalent: '''3/2-equivalent xL ys''', also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, c cents) into x large and y small steps.
*Multi-period 3/2-equivalent: '''3/2-equivalent nxL nys''', also called ''other-name'', is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
Second sentence:


'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''equave-equivalent'' moment-of-symmetry scale, containing ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.


====Base wording (for mos descendants)====
Octave-equivalent relational info:
'''''x''L ''y''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''z''L ''w''s<''p/q''>''''','' expanded to ''x'' large steps(s) and ''y'' small step(s) and repeating every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.


'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''nz''L ''nw''s''<nowiki><p/q></nowiki>''''', expanded to ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.
*Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
*Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.


====Examples====
Rothenprop:
'''5L 7s''', also called '''(hard) diachromatic''' or '''p-chromatic''', is a chromatic scale of the moment-of-symmetry scale 5L 2s, expanded to 5 large steps and 7 small steps, repeating every octave. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, with a generator that ranges from 700¢ to 720¢, or from 480¢ to 500¢. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo.
===Mbox template test ===
These would be their own templates.


Stub page:
*Single-period: Scales of this form are always proper because there is only one small step.
{{Mbox|type=notice|text=This page is a '''stub'''. You can help the Xenharmonic Wiki by expanding it.}}
*Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.
Page needs cleanup (with example reason):
{{Mbox|type=notice|text=This article may require '''cleanup'''.
Reason: ''page contains advanced concepts.''
You can edit this page to improve it.}}
Page under construction:
{{Mbox|type=notice|text=This article is '''being created or in the process of being rewritten''', and is '''not yet ready for use'''. You are welcome to help with editing this page.}}


==Math symbols test ==
==Sandbox for proposed templates==
===Cent ruler ===


=== Isolated symbols===
<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
<math>T := [ t_1, t_2, ..., t_m ]</math>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<math>S := [ s_1, s_2, ..., s_m ]</math>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<math>P := [ p_1, p_2, ..., p_n ]</math>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 4.166%; background-color: #eee; font-size: 12px">50</div>
</div>


=== Sample text===
Pulled from [[muddle]] page.


Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.
<div style="height: 100px; width: 1200px; background-color: powderblue; font-size: 0;">
<div style="border-bottom: 100px solid #555; border-left: 0px solid transparent; border-right: 30px solid transparent; display: inline-block; height: 0px; width: 33.333%;"></div>
</div>


The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.
<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 8.333%; background-color: gray;">s</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 8.333%; background-color: gray;">s</div>
</div>


==Interval and degree tables==
=== MOS characteristics===
The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.
NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.<div style=" display: block;
{| class="wikitable sortable" style="text-align: left;"
  background-color: #dddddd;
|+<!-- caption -->Intervals of 2L 5s for each mode
  column-fill: balance;
|-
  column-width: auto;
!Mode!!UDP!! align="right" | Rotational order!! align="right" | mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep !!5-mosstep!!6-mosstep!!mosoctave
  column-width: 600px;
|-
  padding: 10px;"><div style="
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
    position: relative;
|-
    background-color: #eee;
|LsssLss ||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
    display: grid;
|-
    break-inside: avoid-column;
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
    padding: 1em;
|-
    ">{{MOS mode degrees|Scale Signature=5L 2s}}
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
</div>
|-
  <div style="
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
    position: relative;
|-
    background-color: #eee;
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
    display: grid;
|-
    break-inside: avoid-column;
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
    padding: 1em;
|}
    ">{{MOS intervals|Scale Signature=5L 2s}}
</div>
  <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">Tamnams suggests the name NAME for this scale, which comes from ORIGIN. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.</div>
  <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">4</div>
  <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">5</div>   <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">6</div>   <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">7</div>   <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">8</div>   <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">9</div>  
</div>


 
===MOS intervals (using large/small instead of MmAPd)===
{| class="wikitable sortable" style="text-align: left;"
{| class="wikitable"
|+Degrees of 2L 5s for each mode
|+Intervals of 5L 2s
!Interval
!Size(s)
!Steps
!Range in cents
!Abbrev.
|-
|-
!Mode!! UDP!! align="right" |Rotational order !! 0-mosdegree !!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|'''0-diastep (root)'''
|-
|Perfect 0-diastep
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major|| major||perfect
|0
|-
|0.0¢
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major||major||perfect||perfect||major||major||perfect
|P0ms
|-
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
| rowspan="2" |1-diastep
|Small 1-diastep
|s
|0.0¢ to 171.4¢
|s1ms
|-
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|Large 1-diastep
|L
|171.4¢ to 240.0¢
|L1ms
|-
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5||perfect||minor||minor||perfect||perfect||minor|| major||perfect
| rowspan="2" | 2-diastep
|Small 2-diastep
|L + s
|240.0¢ to 342.9¢
|s2ms
|-
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1||perfect||minor||minor||perfect||perfect||minor|| minor||perfect
|Large 2-diastep
| 2L
|342.9¢ to 480.0¢
|L2ms
|-
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4||perfect||minor||minor||diminished||perfect||minor ||minor||perfect
| rowspan="2" |'''3-diastep'''
|}
|'''Small 3-diastep'''
Note: don't merge cells on a table with sorting.
|2L + s
{| class="wikitable sortable" style="text-align: left;"
|480.0¢ to 514.3¢
|+Intervals of 2L 5s for each mode (with mode names)
|s3ms
|-
|-
!Mode
|Large 3-diastep
!Mode name!!UDP!! align="right" | Rotational order!! align="right" |mosunison!! 1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
| 3L
|514.3¢ to 720.0¢
| L3ms
|-
|-
|LssLsss
| rowspan="2" |'''4-diastep'''
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|Small 4-diastep
|2L + 2s
|480.0¢ to 685.7¢
|s4ms
|-
|-
|LsssLss
|'''Large 4-diastep'''
|antiphrygian||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|3L + s
|685.7¢ to 720.0¢
|L4ms
|-
|-
|sLssLss
| rowspan="2" |5-diastep
|anti-aeolian||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|Small 5-diastep
|3L + 2s
|720.0¢ to 857.1¢
|s5ms
|-
|-
|sLsssLs
|Large 5-diastep
|antidorian ||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|4L + s
|857.1¢ to 960.0¢
|L5ms
|-
|-
| ssLssLs
| rowspan="2" |6-diastep
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s ||2L+5s
|Small 6-diastep
|4L + 2s
|960.0¢ to 1028.6¢
| s6ms
|-
|-
|ssLsssL
|Large 6-diastep
|anti-ionian||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|5L + s
|1028.6¢ to 1200.0¢
|L6ms
|-
|-
|sssLssL
|'''7-diastep (octave)'''
|antilydian|| 0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|Perfect 7-diastep
|}
|5L + 2s
{| class="wikitable sortable" style="text-align: left;"
| 1200.0¢
|+Degrees of 2L 5s for each mode (with mode names)
|P7ms
|-
!Mode
!Mode name!!UDP!! align="right" | Rotational order !!0-mosdegree!!1-mosdegree!! 2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|LssLsss
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|-
|LsssLss
|antiphrygian||5<nowiki>|</nowiki>1|| align="right" |3
|perfect
|major
|major
|perfect||perfect
|major
|major||perfect
|-
|sLssLss
|anti-aeolian||4<nowiki>|</nowiki>2|| align="right" |6
|perfect||minor
|major
|perfect
|perfect
|major
|major||perfect
|-
|sLsssLs
|antidorian||3<nowiki>|</nowiki>3|| align="right" |2
|perfect
|minor
|major
|perfect
|perfect||minor
|major||perfect
|-
|ssLssLs
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5
|perfect
|minor||minor
|perfect
|perfect
|minor
|major||perfect
|-
|ssLsssL
|anti-ionian||1<nowiki>|</nowiki>5|| align="right" |1
|perfect
|minor
|minor
|perfect
|perfect
|minor||minor||perfect
|-
|sssLssL
|antilydian||0<nowiki>|</nowiki>6|| align="right" |4
|perfect
|minor
|minor||diminished
|perfect
| minor
|minor|| perfect
|}
|}


==Alternate mos tables==
===MOS mode degrees (using large/small instead of MmAPd)===
{| class="wikitable sortable"
{| class="wikitable sortable"
!Pattern
|+Scale degree qualities of 5L 2s modes
!Number of notes
! colspan="2" |Mode names
!Number of periods
! colspan="2" |Ordering
!Name
! rowspan="2" |Step pattern
! Prefix
! colspan="8" |Scale degree
|-
|-
|[[1L 1s]]
!Default
|2
!Names
!Bri.
! Rot.
!0
!1
!2
!3
!4
!5
!6
!7
|-
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|1
|trivial
|LLLsLLs
|triv-
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|-
|-
|[[1L 1s]]
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|2
|1
|5
|monowood
|LLsLLLs
|monowd-
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Lg.
|Perf.
|-
|-
|[[1L 2s]]
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|3
|1
|antrial
|atri-
|-
|[[2L 1s]]
|3
|1
|trial
|tri-
|-
|[[1L 3s]]
|4
|1
|antetric
|atetra-
|-
|[[2L 2s]]
|4
|2
|2
|biwood
|LLsLLsL
|biwd-
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Sm.
|Perf.
|-
|-
|[[3L 1s]]
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|4
|1
|6
|tetric
|LsLLLsL
|tetra-
|Perf.
|-
|Lg.
|[[1L 4s]]
|Sm.
|5
|Sm.
|1
|Lg.
|pedal
|Lg.
|ped-
|Sm.
|-
| Perf.
|[[2L 3s]]
|5
|1
|pentic
|pent-
|-
|[[3L 2s]]
|5
|1
|antipentic
|apent-
|-
|-
|[[4L 1s]]
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|5
|1
|manual
|manu-
|-
|[[1L 5s]]
|6
|1
|antimachinoid
|amech-
|-
|[[2L 4s]]
|6
|2
|anticitric
|acitro-
|-
|[[3L 3s]]
|6
|3
|3
|triwood
|LsLLsLL
|triwd-
|Perf.
|Lg.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|-
|[[4L 2s]]
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|6
|2
|citric
|citro-
|-
|[[5L 1s]]
| 6
|1
|machinoid
|mech-
|-
|[[1L 6s]]
| 7
|1
|onyx
|on-
|-
|[[2L 5s]]
|7
|7
|1
|sLLLsLL
| antidiatonic
|Perf.
|pel-
|Sm.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|-
|[[3L 4s]]
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|7
|7
|1
|4
|mosh
|sLLsLLL
|mosh-
|Perf.
| Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Perf.
|}
 
===KB vis===
{| class="wikitable"
|+
! rowspan="2" |Type
! rowspan="2" |Visualization
! colspan="4" |Individual steps
! rowspan="2" |Notes
|-
|-
|[[4L 3s]]
!Start
|7
!Large step
|1
!Small step
|smitonic
!End
|smi-
|-
|-
|[[5L 2s]]
|Small vis
|7
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌╥╥╥┬╥╥┬┐
|1
│║║║│║║││
|diatonic
│││││││││
|''none''
└┴┴┴┴┴┴┴┘</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌
│
│
└</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">╥
║
│
┴</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬
│
│
┴</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┐
│
│
┘</pre>
|Not enough room for note names.
|-
|-
|[[6L 1s]]
|Large vis
|7
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
| 1
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
|arch(a)eotonic
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
|arch-
│░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│
│░░░│░░░│░░░│░░░│░░░│░░░│░░░│░░░│
│░█░│░░░│░░░│░░░│░░░│░░░│░░░│░█░│
└───┴───┴───┴───┴───┴───┴───┴───┘</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌──
│ 
│ 
│ 
│ 
│ X
└──</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─
│ │
│ │
└┬┘
│ 
│ X
─┴──</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">─┬──
│
│
│
│ 
│ X
─┴──</pre>
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">─┐
│
│
│
│
│
─┘</pre>
|Black squares indicate notes one equave apart.
Contains shading characters, meant for spacing.
|}
{| class="wikitable"
! rowspan="2" |Type
! rowspan="2" |Visualization
! colspan="7" |Individual steps
! rowspan="2" | Notes
|-
|-
|[[1L 7s]]
!Start
|8
!Size 1
|1
!Size 2
|antipine
! Size 3
|apine-
!Size 4
!Size 5
!End
|-
|-
|[[2L 6s]]
|Multisize vis (large)
| 8
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
|2
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|antiekic
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|anek-
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░├─┼─┤░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░├─┴─┤░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░│▒▒▒│░░░░│░░░░░░│
│░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌────
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
└────
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">────┬──
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
────┴──
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
├───┤░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
├─┴─┤░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
├─┼─┤░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
└─┼─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────
 
</pre>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">──┐
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
──┘
 
</pre>
| X's are placeholders for note names.
Naturals only, as there is not enough room for accidentals.
 
May not display correctly on some devices.
 
Testing with unintrusive filler characters
|}
 
===TAMNAMS use===
<blockquote>''This article assumes [[TAMNAMS]] conventions for naming scale degrees, intervals, and step ratios.''</blockquote>Names for the [[Degree|scale degrees]] of ''x''L ''y''s, the position of the scales tones, are called '''mosdegrees''', or '''''prefix''degrees'''. Its [[Interval|intervals]], the pitch difference between any two tones, are based on the number of large and small steps between them and are called '''mossteps''', or '''''prefix''steps'''. Both mosdegrees and mossteps use ''0-indexed'' numbering, as opposed to using ''1-indexed ordinals'', such as mos-1st instead of 0-mosstep. The use of 1-indexed ordinal names is discouraged for nondiatonic MOS scales.
 
===JI ratio intro===
For general ratios: '''m/n''', also called '''interval-name''', is a p-limit just intonation ratio of exactly/about r¢.
 
For harmonics: '''m/1''', also called '''interval-name''', is a just intonation ration that represents the mth harmonic of exactly/about r¢.
 
===MOS step sizes===
{| class="wikitable sortable"
|+3L 4s step sizes
! rowspan="2" |Interval
! colspan="2" | Basic 3L 4s
(10edo, L:s = 2:1)
! colspan="2" |Hard 3L 4s
(13edo, L:s = 3:1)
! colspan="2" |Soft 3L 4s
(17edo, L:s = 3:2)
! rowspan="2" |Approx. JI ratios
|-
|-
|[[3L 5s]]
!Steps
| 8
!Cents
|1
!Steps
|checkertonic
!Cents
|check-
!Steps
!Cents
|-
|-
|[[4L 4s]]
|Large step
|8
| 2
|4
| 240¢
|tetrawood; diminished
|3
|tetwd-
| 276.9¢
|3
|211.8¢
|Hide column if no ratios given
|-
|-
|[[5L 3s]]
|Small step
|8
| 1
|120¢
|1
|1
|oneirotonic
|92.3¢
|neiro-
|-
|[[6L 2s]]
|8
|2
|2
|ekic
|141.2¢
|ek-
|
|-
|-
|[[7L 1s]]
|Bright generator
|8
|1
|pine
|pine-
|-
|[[1L 8s]]
|9
|1
|antisubneutralic
|ablu-
|-
|[[2L 7s]]
|9
| 1
|balzano
|bal- /bæl/
|-
|[[3L 6s]]
|9
|3
|3
|tcherepnin
|360¢
|cher-
|4
|369.2¢
| 5
|355.6¢
|
|}
Notes:
 
*Allow option to show the bright generator, dark generator, or no generator.
*JI ratios column only shows if there are any ratios to show
 
===Mos ancestors and descendants===
{| class="wikitable"
!2nd ancestor
!1st ancestor
!Mos
!1st descendants
!2nd descendants
|-
|-
|[[4L 5s]]
| rowspan="4" |uL vs
|9
| rowspan="4" |zL ws
|1
| rowspan="4" |xL ys
|gramitonic
| rowspan="2" |xL (x+y)s
|gram-
|xL (2x+y)s
|-
|-
|[[5L 4s]]
|(2x+y)L xs
|9
|1
| semiquartal
|cthon-
|-
|-
|[[6L 3s]]
| rowspan="2" |(x+y)L xs
|9
|(2x+y)L (x+y)s
|3
|hyrulic
|hyru-
|-
|-
|[[7L 2s]]
|(x+y)L (2x+y)s
|9
|}
|1
 
|superdiatonic
 
|arm-
== Encoding scheme for module:mos==
|-
 
|[[8L 1s]]
=== Mossteps as a vector of L's and s's===
|9
For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.
|1
 
|subneutralic
Alterations by adding a chroma always adds one L and subtracts one s (or subtracts one L and adds one s, if lowering by a chroma), so the sum of L's and s's, even if one of the quantities is negative, will always denote what ''k''-mosstep that interval is. EG, raising "LLLsL" by a chroma produces the vector { 5, 0 }, and raising it by another chroma produces the vector { 6, -1 }.
|blu-
 
Through this, the "original size" of the interval can always be deduced.
 
EG, the vector { 6, -2 } is given, assuming a mos of 5L 2s. Adding 6 and -2 shows that the interval is a 4-mosstep. Taking the brightest mode of 5L 2s (LLLsLLs) and truncating it to the first 4 steps (LLLs), the corresponding vector is { 3, 1 }. This is the vector to compare to. Subtracting the given vector from the comparison vector ( as { 6-3, -2-1 }) produces the vector { 3, -3 }, meaning that { 6, -2 } is the large 4-mosstep raised by 3 chromas. (A shortcut can be employed by simply subtracting only the L-values.) The decoding scheme below shows how the "large 4-mosstep plus 3 chromas" can be decoded into more familiar terms. In this example, since the large 4-mosstep is the perfect bright generator, adding 3 chromas makes it triply augmented.
{| class="wikitable"
|+Encoding scheme
! rowspan="2" |Value
! colspan="2" |Encoded
! colspan="4" | Decoded
|-
|-
|[[1L 9s]]
!Intervals with 2 sizes
|10
!Intervals with 1 size
|1
!Nonperfectable intervals
| antisinatonic
!Bright gen
|asina-
!Dark gen
!Period intervals
|-
|-
|[[2L 8s]]
|10
|2
|2
|jaric
|Large plus 2 chromas
|jara-
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|-
|-
|[[3L 7s]]
|10
|1
|1
|sephiroid
|Large plus 1 chroma
| seph-
|Perfect plus 1 chroma
|Augmented
|Augmented
|2× Augmented
|Augmented
|-
|-
|[[4L 6s]]
|0
|10
|'''Large'''
|2
|'''Perfect'''
|lime
|'''Major'''
|lime-
|'''Perfect'''
|-
|'''Augmented'''
|[[5L 5s]]
|'''Perfect'''
|10
|5
|pentawood
| penwd-
|-
|[[6L 4s]]
|10
|2
|lemon
|lem-
|-
|-
|[[7L 3s]]
| -1
|10
|'''Small'''
|1
|Perfect minus 1 chroma
|dicoid /'daɪkɔɪd/
|'''Minor'''
|dico-
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
|-
|[[8L 2s]]
| -2
|10
|Small minus 1 chroma
|2
|Perfect minus 2 chromas
|taric
|Diminished
|tara-
|2× Diminished
|Diminished
|2× Diminished
|-
|-
|[[9L 1s]]
| -3
|10
|Small minus 2 chromas
|1
|Perfect minus 3 chromas
|sinatonic
|2× Diminished
|sina-
|3× Diminished
|2× Diminished
| 3× Diminished
|}
|}
Rationale:
*Vectors of L's and s's can always be translated back to the original ''k''-mosstep, no matter how many chromas were added. The "unmodified" vector (the large ''k''-mosstep, or perfect ''k''-mosstep for period intervals) can be compared with the mosstep vector to produce the number of chromas.
**Alterations by entire large steps or small steps is considered interval arithmetic.


== Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)==
* Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.
 
Examples of encodings for 5L 2s
{| class="wikitable"
{| class="wikitable"
! colspan="6" |Generator
|+Interval encodings for 5L 2s
!Bright gen.
! rowspan="2" |Interval in mossteps
!Dark gen.
! colspan="2" |Encoding
!L
! rowspan="2" |Decoding
!s
! rowspan="2" |Standard notation in the key of F
!L/s
!Ranges of mosses
|-
|-
|1\2
!Mossteps
|
! Chroma
|
|
|
|
|600.000
|600.000
| 1
|1
|1.000
|
|-
|-
|
|0
|
|0
|
| 0
|
|Perfect 0-diastep
|
| F
|6\11
|654.545
|545.455
|6
| 5
| 1.200
| rowspan="3" |2L 5s range (includes 2L 7s and 7L 2s)
|-
|-
|
|s
|
|1
|
| -1
|
|Minor 1-diastep
|5\9
|Gb
|
|666.667
|533.333
|5
|4
| 1.250
|-
|-
|
| L
|
|1
|
|0
|
|Major 1-diastep
|
|G
| 9\16
|675.000
|525.000
|9
|7
|1.286
|-
|-
|
|L + s
|
|2
|
| -1
|4\7
|Minor 2-diastep
|
|Ab
|
|685.714
|514.286
|4
|3
|1.333
|Basic 2L 3s
|-
|
|
|
|
|
|11\19
|694.737
|505.263
|11
|8
|1.375
| rowspan="3" |5L 2s range (includes 7L 5s and 5L 7s)
|-
|-
|
|2L
|
|
|
|7\12
|
|700.000
|500.000
|7
|5
|1.400
|-
|
|
|
|
|
|10\17
|705.882
|494.118
| 10
|7
| 1.429
|-
|
|
|3\5
|
|
|
|720.000
|480.000
|3
|2
|2
|1.500
|0
|Basic 2L 1s
|Major 2-diastep
|A
|-
|-
|
|2L + s
|
|
|
|
|11\18
|733.333
|466.667
|11
|7
|1.571
| rowspan="3" |5L 3s range
|-
|
|
|
|
|8\13
|
|738.462
|461.538
|8
|5
|1.600
|-
|
|
|
|
|
|13\21
|742.857
|457.143
|13
|8
|1.625
|-
|
|
|
|5\8
|
|
|750.000
|450.000
|5
|3
|3
|1.667
| -1
|Basic 3L 2s
| Perfect 3-diastep
|Bb
|-
|-
|
|3L
|
| 3
|
|0
|
|Augmented 3-diastep
|
|B
|12\19
|757.895
|442.105
|12
|7
|1.714
| rowspan="3" |3L 5s range
|-
|-
|
|2L + 2s
|
|
|
|7\11
|
|763.636
|436.364
|7
|4
|4
|1.750
| -1
|Diminished 4-diastep
|Cb
|-
|-
|
|3L + s
|
|
|
|
|9\14
|771.429
|428.571
|9
|5
| 1.800
|-
|
|2\3
|
|
|
|
|800.000
|400.000
|2
|1
|2.000
|Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
|-
|
|
|
|
|
|9\13
|830.769
|369.231
|9
|4
|4
|2.250
|0
| rowspan="3" |3L 4s range (includes 3L 7s and 7L 3s)
|Perfect 4-diastep
|C
|-
|-
|
| 3L + 2s
|
|
|
|7\10
|
|840.000
|360.000
|7
|3
|2.333
|-
|
|
|
|
|
|12\17
|847.059
|352.941
| 12
|5
|5
| 2.400
| -1
|Minor 5-diastep
|Db
|-
|-
|
|4L + s
|
|
|5\7
|
|
|857.143
|342.857
|5
|5
|2
|0
|2.500
|Major 5-diastep
|Basic 3L 1s
|D
|-
|-
|
|4L + 2s
|
|6
|
| -1
|
|Minor 6-diastep
|
|Eb
|13\18
|866.667
|333.333
|13
|5
|2.600
| rowspan="3" |4L 3s range
|-
|-
|
|5L + s
|
|6
|
|0
|
| Major 6-diastep
|8\11
|E
|
|872.727
|327.273
|8
|3
|2.667
|-
|-
|
|5L + 2s
|
|
|
|
|11\15
|880.000
|320.000
|11
|4
|2.750
|-
|
|
|3\4
|
|
|
|900.000
|300.000
|3
|1
|3.000
|Basic 1L 2s
|-
|
|
|
|
|
|10\13
|923.077
|276.923
|10
|3
|3.333
| rowspan="3" |Range of 1L 4s (includes 4L 5s and 5L 4s)
|-
|
|
|
|
|7\9
|
|933.333
|266.667
|7
|7
|2
|0
|3.500
|Perfect 7-diastep
|F
|}
{| class="wikitable sortable"
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
|-
|-
|
!Default
|
!Names
|
!Bri.
|
!Rot.
|
!0
|11\14
!1
|942.857
!2
|257.143
!3
|11
!4
|3
!5
|3.667
! 6
!7
|-
|-
|
|<nowiki>5L 2s 6|0</nowiki>
|
|Lydian
|
|1
|4\5
|
|
|960.000
|240.000
|4
|1
|1
|4.000
|LLLsLLs
|Basic 1L 4s
|0
|0
|0
|0
|0
|0
|0
|0
|-
|-
|
|<nowiki>5L 2s 5|1</nowiki>
|
|Ionian (major)
|
|
|
|9\11
|981.818
|218.182
|9
|2
|2
|4.500
| rowspan="3" |Range of 4L 1s (includes 5L 1s and 1L 5s)
|-
|
|
|
|
|5\6
|
|1000.000
|200.000
|5
|5
|1
|LLsLLLs
|5.000
|0
|0
|0
| -1
|0
|0
|0
|0
|-
|-
|
|<nowiki>5L 2s 4|2</nowiki>
|
|Mixolydian
|
|3
|
|2
|
|LLsLLsL
|6\7
|0
| 1028.571
|0
|171.429
| 6
| 1
|6.000
|-
|1\1
|
|
|
|
|
|1200.000
|0.000
|1
|1
| -1
|0
|0
| -1
|0
|0
|→ inf
|
|}
==Module and template sandbox==
===Mos ancestors and descendants===
{| class="wikitable"
!2nd ancestor
!1st ancestor
!Mos
! 1st descendants
!2nd descendants
|-
|-
| rowspan="4" |uL vs
|<nowiki>5L 2s 3|3</nowiki>
| rowspan="4" |zL ws
|Dorian
| rowspan="4" |xL ys
|4
| rowspan="2" |xL (x+y)s
|6
|xL (2x+y)s
|LsLLLsL
|0
|0
| -1
| -1
|0
|0
| -1
|0
|-
|-
| (2x+y)L xs
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|3
|LsLLsLL
|0
|0
| -1
| -1
|0
| -1
| -1
|0
|-
|-
| rowspan="2" |(x+y)L xs
|<nowiki>5L 2s 1|5</nowiki>
|(2x+y)L (x+y)s
|Phrygian
|6
|7
|sLLLsLL
|0
| -1
| -1
| -1
|0
| -1
| -1
|0
|-
|-
|(x+y)L (2x+y)s
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
| 7
|4
|sLLsLLL
|0
| -1
| -1
| -1
| -1
| -1
| -1
|0
|}
|}
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