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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.)


== Math symbols test ==
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>


=== Isolated symbols ===
produces
<math>T := [ t_1, t_2, ..., t_m ]</math>
<math>S := [ s_1, s_2, ..., s_m ]</math>
<math>P := [ p_1, p_2, ..., p_n ]</math>


=== Sample text ===
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
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.
== 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}}


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.
== MOS tuning spectrum (AKA, scale tree) ==


== Interval and degree tables ==
{{MOS tuning spectrum
| Scale Signature = 1L 1s
| Int Limit = 13
}}
 
{{MOS tuning spectrum
| 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]]↓
}}
 
{{MOS tuning spectrum
| Depth = 3
| Scale Signature= 3L 4s<3/2>
}}
 
== MOS intro==
First sentence:
*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.
*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.
*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:
 
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.
 
Octave-equivalent relational info:
 
*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.
 
Rothenprop:
 
*Single-period: Scales of this form are always proper because there is only one small step.
*Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.
 
==Sandbox for proposed templates==
===Cent ruler ===
 
<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: 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 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>
 
 
<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>
 
<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>
 
=== MOS characteristics===
NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.<div style="  display: block;
  background-color: #dddddd;
  column-fill: balance;
  column-width: auto;
  column-width: 600px;
  padding: 10px;"><div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    padding: 1em;
    ">{{MOS mode degrees|Scale Signature=5L 2s}}
</div>
  <div style="
    position: relative;
    background-color: #eee;
    display: grid;
    break-inside: avoid-column;
    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"
|+Intervals of 5L 2s
!Interval
!Size(s)
!Steps
!Range in cents
!Abbrev.
|-
|'''0-diastep (root)'''
|Perfect 0-diastep
|0
|0.0¢
|P0ms
|-
| rowspan="2" |1-diastep
|Small 1-diastep
|s
|0.0¢ to 171.4¢
|s1ms
|-
|Large 1-diastep
|L
|171.4¢ to 240.0¢
|L1ms
|-
| rowspan="2" | 2-diastep
|Small 2-diastep
|L + s
|240.0¢ to 342.9¢
|s2ms
|-
|Large 2-diastep
| 2L
|342.9¢ to 480.0¢
|L2ms
|-
| rowspan="2" |'''3-diastep'''
|'''Small 3-diastep'''
|2L + s
|480.0¢ to 514.3¢
|s3ms
|-
|Large 3-diastep
| 3L
|514.3¢ to 720.0¢
| L3ms
|-
| rowspan="2" |'''4-diastep'''
|Small 4-diastep
|2L + 2s
|480.0¢ to 685.7¢
|s4ms
|-
|'''Large 4-diastep'''
|3L + s
|685.7¢ to 720.0¢
|L4ms
|-
| rowspan="2" |5-diastep
|Small 5-diastep
|3L + 2s
|720.0¢ to 857.1¢
|s5ms
|-
|Large 5-diastep
|4L + s
|857.1¢ to 960.0¢
|L5ms
|-
| rowspan="2" |6-diastep
|Small 6-diastep
|4L + 2s
|960.0¢ to 1028.6¢
| s6ms
|-
|Large 6-diastep
|5L + s
|1028.6¢ to 1200.0¢
|L6ms
|-
|'''7-diastep (octave)'''
|Perfect 7-diastep
|5L + 2s
| 1200.0¢
|P7ms
|}
 
===MOS mode degrees (using large/small instead of MmAPd)===
{| class="wikitable sortable"
|+Scale degree qualities of 5L 2s modes
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree
|-
!Default
!Names
!Bri.
! Rot.
!0
!1
!2
!3
!4
!5
!6
!7
|-
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|LLLsLLs
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|-
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|5
|LLsLLLs
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Lg.
|Perf.
|-
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|2
|LLsLLsL
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Sm.
|Perf.
|-
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|6
|LsLLLsL
|Perf.
|Lg.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
| Perf.
|-
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|3
|LsLLsLL
|Perf.
|Lg.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|7
|sLLLsLL
|Perf.
|Sm.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|7
|4
|sLLsLLL
|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
|-
!Start
!Large step
!Small step
!End
|-
|Small vis
|<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>
|<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.
|-
|Large vis
|<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; 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
|-
!Start
!Size 1
!Size 2
! Size 3
!Size 4
!Size 5
!End
|-
|Multisize vis (large)
|<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">┌────
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">────┬──
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
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──┴────
 
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
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|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">──┐
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──┘
 
</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
|-
!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.
*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
|-
| rowspan="4" |uL vs
| rowspan="4" |zL ws
| rowspan="4" |xL ys
| rowspan="2" |xL (x+y)s
|xL (2x+y)s
|-
|(2x+y)L xs
|-
| rowspan="2" |(x+y)L xs
|(2x+y)L (x+y)s
|-
|(x+y)L (2x+y)s
|}
 
 
== Encoding scheme for module:mos==
 
=== Mossteps as a vector of L's and s's===
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.
 
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 }.
 
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
|-
!Intervals with 2 sizes
!Intervals with 1 size
!Nonperfectable intervals
!Bright gen
!Dark gen
!Period intervals
|-
|2
|Large plus 2 chromas
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|-
|1
|Large plus 1 chroma
|Perfect plus 1 chroma
|Augmented
|Augmented
|2× Augmented
|Augmented
|-
|0
|'''Large'''
|'''Perfect'''
|'''Major'''
|'''Perfect'''
|'''Augmented'''
|'''Perfect'''
|-
| -1
|'''Small'''
|Perfect minus 1 chroma
|'''Minor'''
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
| -2
|Small minus 1 chroma
|Perfect minus 2 chromas
|Diminished
|2× Diminished
|Diminished
|2× Diminished
|-
| -3
|Small minus 2 chromas
|Perfect minus 3 chromas
|2× Diminished
|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.
 
* 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"
|+Interval encodings for 5L 2s
! rowspan="2" |Interval in mossteps
! colspan="2" |Encoding
! rowspan="2" |Decoding
! rowspan="2" |Standard notation in the key of F
|-
!Mossteps
! Chroma
|-
|0
|0
| 0
|Perfect 0-diastep
| F
|-
|s
|1
|  -1
|Minor 1-diastep
|Gb
|-
| L
|1
|0
|Major 1-diastep
|G
|-
|L + s
|2
| -1
|Minor 2-diastep
|Ab
|-
|2L
|2
|0
|Major 2-diastep
|A
|-
|2L + s
|3
| -1
| Perfect 3-diastep
|Bb
|-
|3L
| 3
|0
|Augmented 3-diastep
|B
|-
|2L + 2s
|4
| -1
|Diminished 4-diastep
|Cb
|-
|3L + s
|4
|0
|Perfect 4-diastep
|C
|-
| 3L + 2s
|5
| -1
|Minor 5-diastep
|Db
|-
|4L + s
|5
|0
|Major 5-diastep
|D
|-
|4L + 2s
|6
| -1
|Minor 6-diastep
|Eb
|-
|5L + s
|6
|0
| Major 6-diastep
|E
|-
|5L + 2s
|7
|0
|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
!1
!2
!3
!4
!5
! 6
!7
|-
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|LLLsLLs
|0
|0
|0
|0
|0
|0
|0
|0
|-
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|5
|LLsLLLs
|0
|0
|0
| -1
|0
|0
|0
|0
|-
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|2
|LLsLLsL
|0
|0
|1
| -1
|0
|0
| -1
|0
|-
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|6
|LsLLLsL
|0
|0
| -1
| -1
|0
|0
| -1
|0
|-
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|5
|3
|LsLLsLL
|0
|0
| -1
| -1
|0
| -1
| -1
|0
|-
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|7
|sLLLsLL
|0
| -1
| -1
| -1
|0
| -1
| -1
|0
|-
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
| 7
|4
|sLLsLLL
|0
| -1
| -1
| -1
| -1
| -1
| -1
|0
|}
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