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This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>
produces
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 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 tuning spectrum (AKA, scale tree) ==
{{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>


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


== Template test area==
<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>


=== Cell color code test===
===MOS intervals (using large/small instead of MmAPd)===
{| class="wikitable"
{| class="wikitable"
|+
|+Intervals of 5L 2s
!Examples
!Interval
!0
!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
|-
|-
|Augmented size
|Large 5-diastep
| style="background:#ededb0" |Aug.
|4L + s
|857.1¢ to 960.0¢
|L5ms
|-
|-
|Large size
| rowspan="2" |6-diastep
| style="background:#ffffe0" |Maj.
|Small 6-diastep
|4L + 2s
|960.0¢ to 1028.6¢
| s6ms
|-
|-
|Small size
|Large 6-diastep
| style="background:#eaeaff" |Min.
|5L + s
|1028.6¢ to 1200.0¢
|L6ms
|-
|-
|Diminished size
|'''7-diastep (octave)'''
| style="background:#afafe0" |Dim.
|Perfect 7-diastep
|5L + 2s
| 1200.0¢
|P7ms
|}
|}


===MOS mode degrees (5L 2s)===
===MOS mode degrees (using large/small instead of MmAPd)===
{{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}}
 
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}
 
===Mos mode degrees with rotations of multiple modmosses===
{| class="wikitable sortable"
{| class="wikitable sortable"
! rowspan="2" |UDP
|+Scale degree qualities of 5L 2s modes
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! rowspan="2" |Step pattern
! rowspan="2" |Mode names
! colspan="8" |Scale degree
! colspan="8" | Scale degree (diadegree)
|-
|-
!Default
!Names
!Bri.
! Rot.
!0
!0
!1
!1
Line 49: Line 283:
!4
!4
!5
!5
! 6
!6
!7
!7
|-
|-
|<nowiki>6|0</nowiki>
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|1
|1
|LLLsLLs
|LLLsLLs
|Lydian
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" | Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|-
|-
|<nowiki>5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
|2
|5
|LLsLLLs
|LLsLLLs
|Ionian (major)
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
|Lg.
| style="background:#ffffe0" |Maj.
| Lg.
|Perf.
|Sm.
|Perf.
|Lg.
| style="background:#ffffe0" |Maj.
|Lg.
| style="background:#ffffe0" |Maj.
|Lg.
|Perf.
|Perf.
|-
|-
|<nowiki>4|2</nowiki>
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|3
|2
|LLsLLsL
|LLsLLsL
|Mixolydian
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
|Lg.
| style="background:#ffffe0" |Maj.
| Lg.
|Perf.
|Sm.
|Perf.
|Lg.
| style="background:#ffffe0" | Maj.
|Lg.
| style="background:#eaeaff" |Min.
|Sm.
|Perf.
|Perf.
|-
|-
|<nowiki>3|3</nowiki>
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|4
|6
|LsLLLsL
|LsLLLsL
|Dorian
|Perf.
|Lg.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
| Perf.
| Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" | Min.
|Perf.
|-
|-
|<nowiki>2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
| LsLLsLL
|Aeolian (minor)
|Aeolian (minor)
|5
|3
|LsLLsLL
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
|Lg.
| style="background:#eaeaff" |Min.
| Sm.
|Perf.
|Sm.
| Perf.
|Lg.
| style="background:#eaeaff" |Min.
|Sm.
| style="background:#eaeaff" |Min.
|Sm.
|Perf.
|Perf.
|-
|-
|<nowiki>1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
|6
|7
|sLLLsLL
|sLLLsLL
| Phrygian
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
|Sm.
| style="background:#eaeaff" |Min.
| Sm.
|Perf.
|Sm.
| Perf.
|Lg.
| style="background:#eaeaff" |Min.
|Sm.
| style="background:#eaeaff" |Min.
|Sm.
|Perf.
|Perf.
|-
|-
|<nowiki>0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|7
|4
|sLLsLLL
|sLLsLLL
|Locrian
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| Sm.
| style="background:#eaeaff" | Min.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Perf.
|Perf.
| style="background:#afafe0" |Dim.
|}
| style="background:#eaeaff" |Min.
 
| style="background:#eaeaff" |Min.
===KB vis===
| Perf
{| class="wikitable"
|+
! rowspan="2" |Type
! rowspan="2" |Visualization
! colspan="4" |Individual steps
! rowspan="2" |Notes
|-
|-
|<nowiki>2|4 M6md</nowiki>
!Start
| LsLLsAs
!Large step
|Harmonic minor
!Small step
|Perf.
!End
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|-
|<nowiki>0|6 M5md</nowiki>
|Small vis
|sLLsAsL
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌╥╥╥┬╥╥┬┐
| Locrian #6
│║║║│║║││
|Perf.
│││││││││
| style="background:#eaeaff" |Min.
└┴┴┴┴┴┴┴┘</pre>
| style="background:#eaeaff" |Min.
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌
|Perf.
│
| style="background:#afafe0" | Dim.
│
| style="background:#ffffe0" |Maj.
└</pre>
| style="background:#eaeaff" |Min.
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">╥
|Perf.
║
│
┴</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.
|-
|-
|<nowiki>5|1 A4md</nowiki>
|Large vis
|LLsAsLs
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
|Ionian augmented
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
|Perf.
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
| style="background:#ffffe0" |Maj.
│░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│
| style="background:#ffffe0" | Maj.
│░░░│░░░│░░░│░░░│░░░│░░░│░░░│░░░│
|Perf.
│░█░│░░░│░░░│░░░│░░░│░░░│░░░│░█░│
| style="background:#ededb0" | Aug.
└───┴───┴───┴───┴───┴───┴───┴───┘</pre>
| style="background:#ffffe0" |Maj.
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌──
| style="background:#ffffe0" |Maj.
│ 
|Perf.
│ 
│ 
│ 
│ 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
|-
|-
|<nowiki>3|3 A3md</nowiki>
!Start
| LsAsLsL
!Size 1
|Dorian #4
!Size 2
| Perf.
! Size 3
| style="background:#ffffe0" |Maj.
!Size 4
| style="background:#eaeaff" |Min.
!Size 5
| style="background:#ededb0" | Aug.
!End
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#eaeaff" | Min.
|Perf.
|-
|-
|<nowiki>1|5 M2md</nowiki>
|Multisize vis (large)
|sAsLsLL
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
|Phrygian dominant
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|Perf.
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
| style="background:#eaeaff" |Min.
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░├─┼─┤░░░░│░░░░░░│
| style="background:#ffffe0" |Maj.
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|Perf.
│░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│
|Perf.
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░├─┴─┤░░░░│░░░░░░│
| style="background:#eaeaff" |Min.
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░│▒▒▒│░░░░│░░░░░░│
| style="background:#eaeaff" |Min.
│░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│
|Perf.
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
|-
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
|<nowiki>6|0 A1md</nowiki>
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
|AsLsLLs
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
| Lydian #2
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘
|Perf.
</pre>
| style="background:#ededb0" | Aug.
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌────
| style="background:#ffffe0" | Maj.
│░░░░
| style="background:#ededb0" |Aug.
│░░░░
|Perf.
│░░░░
| style="background:#ffffe0" |Maj.
│░░░░
| style="background:#ffffe0" |Maj.
│░░░░
|Perf.
│░░░░
|-
│░░░░
|<nowiki>0|6 d3md d6md</nowiki>
│░░░░
|sLsLLsA
│░░░░
| Locrian b4 bb7
│░░░░
| Perf.
│░░░░
| style="background:#eaeaff" |Min.
│░░░░
| style="background:#eaeaff" |Min.
│░░░░
| style="background:#afafe0" |Dim.
└────
| style="background:#afafe0" |Dim.
 
| style="background:#eaeaff" |Min.
</pre>
| style="background:#afafe0" |Dim.
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">────┬──
| Perf.
░░░░│░░
|-
░░░░│░░
|<nowiki>5|1 m5md</nowiki>
░░░░│░░
|LLsLsAs
░░░░│░░
|Ionian b6 (Harmonic major)
░░░░│░░
|Perf.
░░░░│░░
| style="background:#ffffe0" |Maj.
░░░░│░░
| style="background:#ffffe0" | Maj.
░░░░│░░
| Perf.
░░░░│░░
|Perf.
░░░░│░░
| style="background:#eaeaff" |Min.
░░░░│░░
| style="background:#ffffe0" |Maj.
░░░░│░░
|Perf.
░░░░│░░
|-
────┴──
|<nowiki>3|3 d4md</nowiki>
 
|LsLsAsL
</pre>
|Dorian b5 (Dorian diminished)
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
|Perf.
│▓▓▓│░░
| style="background:#ffffe0" |Maj.
│▓▓▓│░░
| style="background:#eaeaff" |Min.
│▓▓▓│░░
|Perf.
│▓▓▓│░░
| style="background:#afafe0" |Dim.
│▓▓▓│░░
| style="background:#ffffe0" |Maj.
│▓▓▓│░░
| style="background:#eaeaff" |Min.
│▓▓▓│░░
| Perf.
│▓▓▓│░░
|-
└─┬─┘░░
|<nowiki>1|5 d3md</nowiki>
░░│░░░░
| sLsAsLL
░░│░░░░
|Phrygian b4
░░│░░░░
|Perf.
░░│░░░░
| style="background:#eaeaff" |Min.
──┴────
| style="background:#eaeaff" |Min.
 
| style="background:#afafe0" |Dim.
</pre>
|Perf.
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬───┬──
| style="background:#eaeaff" |Min.
│▓▓▓│░░
| style="background:#eaeaff" | Min.
│▓▓▓│░░
|Perf.
│▓▓▓│░░
|-
│▓▓▓│░░
|<nowiki>6|0 m2md</nowiki>
├───┤░░
|LsAsLLs
│▓▓▓│░░
|Lydian b3 (Lydian minor)
│▓▓▓│░░
|Perf.
│▓▓▓│░░
| style="background:#ffffe0" |Maj.
└─┬─┘░░
| style="background:#eaeaff" |Min.
░░│░░░░
| style="background:#ededb0" |Aug.
░░│░░░░
|Perf.
░░│░░░░
| style="background:#ffffe0" |Maj.
░░│░░░░
| style="background:#ffffe0" | Maj.
──┴────
|Perf.
 
|-
</pre>
|<nowiki>4|2 m1md</nowiki>
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
|sAsLLsL
│▓│▓│░░
|Mixolydian b2
│▓│▓│░░
|Perf.
│▓│▓│░░
| style="background:#eaeaff" |Min.
│▓│▓│░░
| style="background:#ffffe0" |Maj.
├─┴─┤░░
|Perf.
│▓▓▓│░░
|Perf.
│▓▓▓│░░
| style="background:#ffffe0" |Maj.
│▓▓▓│░░
| style="background:#eaeaff" |Min.
└─┬─┘░░
|Perf.
░░│░░░░
|-
░░│░░░░
|<nowiki>6|0 A1md A4md</nowiki>
░░│░░░░
|AsLLsLs
░░│░░░░
|Lydian #2 #5
──┴────
| Perf.
 
| style="background:#ededb0" |Aug.
</pre>
| style="background:#ffffe0" |Maj.
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┬─┬─┬──
| style="background:#ededb0" |Aug.
│▓│▓│░░
| style="background:#ededb0" |Aug.
│▓│▓│░░
| style="background:#ffffe0" |Maj.
│▓│▓│░░
| style="background:#ffffe0" | Maj.
│▓│▓│░░
|Perf.
├─┼─┤░░
|-
│▓│▓│░░
|<nowiki>0|6 d6md</nowiki>
│▓│▓│░░
| sLLsLsA
│▓│▓│░░
|Locrian bb7
└─┼─┘░░
|Perf.
░░│░░░░
| style="background:#eaeaff" |Min.
░░│░░░░
| style="background:#eaeaff" |Min.
░░│░░░░
|Perf.
░░│░░░░
| style="background:#afafe0" |Dim.
──┴────
| style="background:#eaeaff" |Min.
 
| style="background:#afafe0" |Dim.
</pre>
|Perf.
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">──┐
|-
░░│
|<nowiki>5|1 m2md</nowiki>
░░│
| LsLLLLs
░░│
|Aeolian ♮6 ♮7 (Melodic minor)
░░│
| Perf.
░░│
| style="background:#ffffe0" | Maj.
░░│
| style="background:#eaeaff" |Min.
░░│
| Perf.
░░│
| Perf.
░░│
| style="background:#ffffe0" |Maj.
░░│
| style="background:#ffffe0" |Maj.
░░│
|Perf.
░░│
|-
░░│
|<nowiki>3|3 m1md</nowiki>
──┘
| sLLLLsL
 
|Dorian b2
</pre>
|Perf.
| X's are placeholders for note names.
| style="background:#eaeaff" |Min.
Naturals only, as there is not enough room for accidentals.
| style="background:#eaeaff" | Min.
 
| Perf.
May not display correctly on some devices.
| Perf.
 
| style="background:#ffffe0" | Maj.
Testing with unintrusive filler characters
| style="background:#eaeaff" |Min.
| Perf.
|-
|<nowiki>6|0 A4md</nowiki>
| LLLLsLs
|Lydian #5 (Lydian augmented)
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" | Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>6|0 m6md</nowiki>
|LLLsLsL
|Lydian b7 (Lydian dominant)
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#ffffe0" | Maj.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>4|2 m5md</nowiki>
|LLsLsLL
|Mixolydian b6
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>2|4 d4md</nowiki>
|LsLsLLL
|Locrian ♮2 (Half-diminished)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>0|6 d3md</nowiki>
|sLsLLLL
|Locrian bb4 (Altered dominant, super-locrian)
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" | Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>5|1 m1md m2md</nowiki>
|sLLLLLs
|Ionian b2 b3 (Neapolitan major)
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|<nowiki>6|0 A4md A5md</nowiki>
|LLLLLss
|Lydian #5 #6
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>6|0 A4md m6md</nowiki>
|LLLLssL
|Lydian #5 b7
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>6|0 m5md m6md</nowiki>
|LLLssLL
|Lydian b6 b7
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| Perf.
|-
|<nowiki>4|2 d4md m5md</nowiki>
|LLssLLL
|Locrian ♮2 ♮3 (Major locrian)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>2|4 d3md d4md</nowiki>
|LssLLLL
|Locrian ♮2 b4
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>0|6 d2md d3md</nowiki>
|ssLLLLL
|Locrian bb3 b4
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|}
|}


===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===
===MOS step sizes===
Line 494: Line 645:
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 503: Line 654:
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
Line 525: Line 676:
*JI ratios column only shows if there are any ratios to show
*JI ratios column only shows if there are any ratios to show


===Expanded MOS intro===
===Mos ancestors and descendants===
The following pieces of information may be worth adding:
{| 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
|}


*Distinguishing between TAMNAMS names from other, noteworthy non-TAMNAMS names. Equave-agnostic names can be treated as TAMNAMS name for appropriate mosses (EG, 4L 1s).
*The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
*Simple edos (or ed<nowiki><p/q>) that support the mos.</nowiki>
*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.
====Base wording (for TAMNAMS-named mosses)====
'''''x''L ''y''s<''p/q''>''' (TAMNAMS name '''''tamnams-name''''', 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''¢.


'''''nx''L ''ny''s<''p/q''>''' (TAMNAMS name '''''tamnams-name''''', 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''¢.
== Encoding scheme for module:mos==


==== Base wording (for mos descendants)====
=== Mossteps as a vector of L's and s's===
'''''x''L ''y''s<''p/q''>''' (TAMNAMS name '''''tamnams-name''''', 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''¢.  
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.


'''''nx''L ''ny''s<''p/q''>''' (TAMNAMS name '''''tamnams-name''''', 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''¢.
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 }.


====Examples ====
Through this, the "original size" of the interval can always be deduced.
'''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:
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.
{{Mbox|type=notice|text=This page is a '''stub'''. You can help the Xenharmonic Wiki by expanding it.}}
{| class="wikitable"
Page needs cleanup (with example reason):
|+Encoding scheme
{{Mbox|type=notice|text=This article may require '''cleanup'''.
! rowspan="2" |Value
Reason: ''page contains advanced concepts.''
! colspan="2" |Encoded
You can edit this page to improve it.}}
! colspan="4" | Decoded
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==
 
===Isolated symbols===
<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===
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.
 
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.
 
==Interval and degree tables ==
The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.
{| class="wikitable sortable" style="text-align: left;"
|+<!-- caption -->Intervals of 2L 5s for each mode
|-
|-
!Mode!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
!Intervals with 2 sizes
!Intervals with 1 size
!Nonperfectable intervals
!Bright gen
!Dark gen
!Period intervals
|-
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|2
|Large plus 2 chromas
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|-
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|1
|Large plus 1 chroma
|Perfect plus 1 chroma
|Augmented
|Augmented
|2× Augmented
|Augmented
|-
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|0
|-
|'''Large'''
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|'''Perfect'''
|'''Major'''
|'''Perfect'''
|'''Augmented'''
|'''Perfect'''
|-
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
| -1
|'''Small'''
|Perfect minus 1 chroma
|'''Minor'''
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
| -2
|Small minus 1 chroma
|Perfect minus 2 chromas
|Diminished
|2× Diminished
|Diminished
|2× Diminished
|-
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
| -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.


{| class="wikitable sortable" style="text-align: left;"
Examples of encodings for 5L 2s
|+Degrees of 2L 5s for each mode
{| 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
|-
|-
!Mode!!UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
!Mossteps
! Chroma
|-
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|0
|0
| 0
|Perfect 0-diastep
| F
|-
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major||major||perfect||perfect||major||major||perfect
|s
|1
| -1
|Minor 1-diastep
|Gb
|-
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
| L
|1
|0
|Major 1-diastep
|G
|-
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|L + s
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5||perfect||minor||minor||perfect||perfect||minor||major||perfect
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1||perfect||minor||minor||perfect||perfect||minor||minor||perfect
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4||perfect||minor||minor||diminished||perfect||minor||minor||perfect
|}
Note: don't merge cells on a table with sorting.
{| class="wikitable sortable" style="text-align: left;"
|+Intervals of 2L 5s for each mode (with mode names)
|-
!Mode
!Mode name!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
|-
|LssLsss
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|-
|LsssLss
|antiphrygian||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|sLssLss
|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
|-
|sLsssLs
|antidorian||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLssLs
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLsssL
|anti-ionian||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|-
|sssLssL
|antilydian||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|}
{| class="wikitable sortable" style="text-align: left;"
|+Degrees of 2L 5s for each mode (with mode names)
|-
!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==
{| class="wikitable sortable"
!Pattern
!Number of notes
!Number of periods
!Name
!Prefix
|-
|[[1L 1s]]
|2
|2
|1
| -1
|trivial
|Minor 2-diastep
|triv-
|Ab
|-
|-
|[[1L 1s]]
|2L
|2
|2
|1
|0
|monowood
|Major 2-diastep
|monowd-
|A
|-
|-
|[[1L 2s]]
|2L + s
|3
|3
|1
| -1
|antrial
| Perfect 3-diastep
|atri-
|Bb
|-
|-
|[[2L 1s]]
|3L
|3
| 3
|1
|0
|trial
|Augmented 3-diastep
|tri-
|B
|-
|-
|[[1L 3s]]
|2L + 2s
|4
|4
|1
| -1
|antetric
|Diminished 4-diastep
|atetra-
|Cb
|-
|-
|[[2L 2s]]
|3L + s
|4
|4
|2
|0
|biwood
|Perfect 4-diastep
|biwd-
|C
|-
|[[3L 1s]]
|4
|1
|tetric
|tetra-
|-
|-
|[[1L 4s]]
| 3L + 2s
|5
|5
|1
| -1
|pedal
|Minor 5-diastep
|ped-
|Db
|-
|-
|[[2L 3s]]
|4L + s
|5
|5
|1
|0
|pentic
|Major 5-diastep
|pent-
|D
|-
|-
|[[3L 2s]]
|4L + 2s
|5
|1
|antipentic
|apent-
|-
|[[4L 1s]]
|5
|1
|manual
|manu-
|-
|[[1L 5s]]
|6
|6
|1
| -1
|antimachinoid
|Minor 6-diastep
|amech-
|Eb
|-
|-
|[[2L 4s]]
|5L + s
|6
|6
|2
|0
|anticitric
| Major 6-diastep
|acitro-
|E
|-
|[[3L 3s]]
|6
|3
|triwood
|triwd-
|-
|[[4L 2s]]
|6
|2
|citric
|citro-
|-
|[[5L 1s]]
|6
|1
|machinoid
|mech-
|-
|-
|[[1L 6s]]
|5L + 2s
|7
|7
|1
|0
|onyx
|Perfect 7-diastep
|on-
|F
|}
{| class="wikitable sortable"
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
|-
|-
|[[2L 5s]]
!Default
|7
!Names
|1
!Bri.
|antidiatonic
!Rot.
|pel-
!0
!1
!2
!3
!4
!5
! 6
!7
|-
|-
|[[3L 4s]]
|<nowiki>5L 2s 6|0</nowiki>
|7
|Lydian
|1
|mosh
|mosh-
|-
|[[4L 3s]]
|7
|1
|1
|smitonic
|smi-
|-
|[[5L 2s]]
|7
|1
|1
|diatonic
|LLLsLLs
|''none''
|0
|0
|0
|0
|0
|0
|0
|0
|-
|-
|[[6L 1s]]
|<nowiki>5L 2s 5|1</nowiki>
|7
|Ionian (major)
|1
|arch(a)eotonic
|arch-
|-
|[[1L 7s]]
|8
|1
|antipine
|apine-
|-
|[[2L 6s]]
|8
|2
|2
|antiekic
|anek-
|-
|[[3L 5s]]
|8
|1
|checkertonic
|check-
|-
|[[4L 4s]]
|8
|4
|tetrawood; diminished
|tetwd-
|-
|[[5L 3s]]
|8
|1
|oneirotonic
|neiro-
|-
|[[6L 2s]]
|8
|2
|ekic
|ek-
|-
|[[7L 1s]]
|8
|1
|pine
|pine-
|-
|[[1L 8s]]
|9
|1
|antisubneutralic
|ablu-
|-
|[[2L 7s]]
|9
|1
|balzano
|bal- /bæl/
|-
|[[3L 6s]]
|9
|3
|tcherepnin
|cher-
|-
|[[4L 5s]]
|9
|1
|gramitonic
|gram-
|-
|[[5L 4s]]
|9
|1
|semiquartal
|cthon-
|-
|[[6L 3s]]
|9
|3
|hyrulic
|hyru-
|-
|[[7L 2s]]
|9
|1
|superdiatonic
|arm-
|-
|[[8L 1s]]
|9
|1
|subneutralic
|blu-
|-
|[[1L 9s]]
|10
|1
|antisinatonic
|asina-
|-
|[[2L 8s]]
|10
|2
|jaric
|jara-
|-
|[[3L 7s]]
|10
|1
|sephiroid
|seph-
|-
|[[4L 6s]]
|10
|2
|lime
|lime-
|-
|[[5L 5s]]
|10
|5
|5
|pentawood
|LLsLLLs
|penwd-
|0
|0
|0
| -1
|0
|0
|0
|0
|-
|-
|[[6L 4s]]
|<nowiki>5L 2s 4|2</nowiki>
|10
|Mixolydian
|2
|lemon
|lem-
|-
|[[7L 3s]]
|10
|1
|dicoid /'daɪkɔɪd/
|dico-
|-
|[[8L 2s]]
|10
|2
|taric
|tara-
|-
|[[9L 1s]]
|10
|1
|sinatonic
|sina-
|}
 
==Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)==
{| class="wikitable"
! colspan="6" |Generator
!Bright gen.
!Dark gen.
!L
!s
!L/s
!Ranges of mosses
|-
|1\2
|
|
|
|
|
|600.000
|600.000
|1
|1
|1.000
|
|-
|
|
|
|
|
|6\11
|654.545
|545.455
|6
|5
|1.200
| rowspan="3" |2L 5s range (includes 2L 7s and 7L 2s)
|-
|
|
|
|
|5\9
|
|666.667
|533.333
|5
|4
|1.250
|-
|
|
|
|
|
|9\16
|675.000
|525.000
|9
|7
|1.286
|-
|
|
|
|4\7
|
|
|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)
|-
|
|
|
|
|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
|3
|2
|2
|1.500
|LLsLLsL
|Basic 2L 1s
|0
|-
|0
|
|
|
|
|
|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
|1.667
|Basic 3L 2s
|-
|
|
|
|
|
|12\19
|757.895
|442.105
|12
|7
|1.714
| rowspan="3" |3L 5s range
|-
|
|
|
|
|7\11
|
|763.636
|436.364
|7
|4
|1.750
|-
|
|
|
|
|
|9\14
|771.429
|428.571
|9
|5
|1.800
|-
|
|2\3
|
|
|
|
|800.000
|400.000
|2
|1
|1
|2.000
| -1
|Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
|0
|0
| -1
|0
|-
|-
|
|<nowiki>5L 2s 3|3</nowiki>
|
|Dorian
|
|
|
|9\13
|830.769
|369.231
|9
|4
|4
|2.250
|6
| rowspan="3" |3L 4s range (includes 3L 7s and 7L 3s)
|LsLLLsL
|0
|0
| -1
| -1
|0
|0
| -1
|0
|-
|-
|
|<nowiki>5L 2s 2|4</nowiki>
|
|Aeolian (minor)
|
|
|7\10
|
|840.000
|360.000
|7
|3
|2.333
|-
|
|
|
|
|
|12\17
|847.059
|352.941
|12
|5
|2.400
|-
|
|
|
|5\7
|
|
|857.143
|342.857
|5
|5
|2
|2.500
|Basic 3L 1s
|-
|
|
|
|
|
|13\18
|866.667
|333.333
|13
|5
|2.600
| rowspan="3" |4L 3s range
|-
|
|
|
|
|8\11
|
|872.727
|327.273
|8
|3
|3
|2.667
|LsLLsLL
|0
|0
| -1
| -1
|0
| -1
| -1
|0
|-
|-
|
|<nowiki>5L 2s 1|5</nowiki>
|
|Phrygian
|
|6
|
|
|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
|sLLLsLL
|3.500
|0
| -1
| -1
| -1
|0
| -1
| -1
|0
|-
|-
|
|<nowiki>5L 2s 0|6</nowiki>
|
|Locrian
|
| 7
|
|
|11\14
|942.857
|257.143
|11
|3
|3.667
|-
|
|
|
|4\5
|
|
|960.000
|240.000
|4
|4
|1
|sLLsLLL
|4.000
|0
|Basic 1L 4s
| -1
|-
| -1
|
| -1
|
| -1
|
| -1
|
| -1
|
|9\11
|981.818
|218.182
|9
|2
|4.500
| rowspan="3" |Range of 4L 1s (includes 5L 1s and 1L 5s)
|-
|
|
|
|
|5\6
|
|1000.000
|200.000
|5
|1
|5.000
|-
|
|
|
|
|
|6\7
|1028.571
|171.429
|6
|1
|6.000
|-
|1\1
|
|
|
|
|
|1200.000
|0.000
|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
| 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
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Sandbox"