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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]]↓
}}


This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
{{MOS tuning spectrum
| Depth = 3
| Scale Signature= 3L 4s<3/2>
}}


== Test area ==
== 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:


=== Expanding the mos intro ===
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.


==== Including step patterns ====
Octave-equivalent relational info:
'''xL ys''', also called '''mosname''' or '''alt-mosname''', is a moment-of-symmetry scale consisting of x large step(s) and y small step(s), repeating every octave. This scale has a step pattern of step-pattern, or some rotation thereof, and is made using a generator ranging from g1¢ to g2¢, or from d1¢ to d2¢.


'''5L 2s''', also called '''diatonic''', is a [[moment of symmetry]] scale consisting of 5 large steps and 2 small steps, repeating every [[octave]]. This scale has a step pattern of LLLsLLs, or some [[rotation]] thereof, and is made using a [[generator]] ranging from 685.714¢ to 720¢, or from 480¢ to 514.286¢.
*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.


nxL nys, also called mosname or alt-mosname, is a moment-of-symmetry scale consisting of nx large step(s) and ny small step(s), with a period of x large step(s) and y small step(s) that repeats n times every octave, or every p¢. This scale has a step pattern of step-pattern, or some rotation thereof for every period, and is made using a generator ranging from g1¢ to g2¢, or from d1¢ to d2¢.
Rothenprop:


'''3L 6s''', also called '''tcherepnin''', is a [[moment of symmetry]] scale consisting of 3 large steps and 6 small steps, with a [[period]] of 1 large step and 2 small steps that repeats 3 times every [[octave]], or every 400¢. This scale has a step pattern of Lss, or some rotation thereof, for every period, and is made using a [[generator]] ranging from 266.667¢ to 400¢, or from 0¢ to 133.333¢.
*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.


==== Including mos descendant names ====
==Sandbox for proposed templates==
xL ys, also called '''mosname''' or '''alt-mosname''', is a chromatic/enharmonic/subchromatic/nth-descendant of the moment-of-symmetry scale zL ws and consists of x large step(s) and y small step(s), repeating every octave. This scale has a step pattern of step-pattern, or some rotation thereof, and is made using a generator ranging from g1¢ to g2¢, or from d1¢ to d2¢.
===Cent ruler ===


'''5L 7s''', also called '''(hard) diachromatic''' or '''p-chromatic''', is a chromatic scale of the [[moment of symmetry]] scale [[5L 2s]] and consists of 5 large steps and 7 small steps, repeating every [[octave]]. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, and is made using a [[generator]] ranging from 700¢ to 720¢, or from 480¢ to 500¢.  
<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>


=== Mos degrees template with new code===
Template to call module without affecting the current template (fill in arguments as needed):
<syntaxhighlight>
{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=
|Step Ratio=
|MOS Prefix=
|Show Abbreviations=
|JI Ratios=
}}
</syntaxhighlight>
Instances of module for testing:


{{#invoke:MOS_degrees_v2|mos_degrees_frame
<div style="height: 100px; width: 1200px; background-color: powderblue; font-size: 0;">
|Scale Signature=5L 2s
<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>
|Step Ratio=
</div>
|MOS Prefix=
|Show Abbreviations=
|Number of Alterations=
|JI Ratios=
}}


{{#invoke:MOS_degrees_v2|mos_degrees_frame
<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
|Scale Signature=5L 4s
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
|Step Ratio=2
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
|MOS Prefix=
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
|Show Abbreviations=
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 8.333%; background-color: gray;">s</div>
|Number of Alterations=
<div style="display: inline-block; margin: 0px; outline: 1px solid; height: 100px; width: 16.667%; background-color: #eee;">L</div>
|JI Ratios=
<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>


{{#invoke:MOS_degrees_v2|mos_degrees_frame
=== MOS characteristics===
|Scale Signature=4L 3s
NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.<div style="  display: block;
|Step Ratio=2/1; 3/1; 3/2
  background-color: #dddddd;
|MOS Prefix=
  column-fill: balance;
|Show Abbreviations=1
  column-width: auto;
|Number of Alterations=1
  column-width: 600px;
|JI Ratios=P0md: 1/1;
  padding: 10px;"><div style="
M1md: 8/7;
    position: relative;
P2md: 77/64, 6/5;
    background-color: #eee;
m3md: 14/11;
    display: grid;
M3md:11/8;
    break-inside: avoid-column;
m4md: 16/11;
    padding: 1em;
M4md: 11/7;
    ">{{MOS mode degrees|Scale Signature=5L 2s}}
P5md: 5/3;
</div>
m6md: 7/4;
  <div style="
P7md: 2/1
    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 degrees template (version 2)===
===MOS intervals (using large/small instead of MmAPd)===
{| class="wikitable"
{| class="wikitable"
|+Scale degrees of 5L 2s
|+Intervals of 5L 2s
! rowspan="2" |Scale degree
!Interval
! colspan="2" |Basic 5L 2s
!Size(s)
(12edo, L:s = 2:1)
! colspan="2" |Basic 5L 2s
(12edo, L:s = 2:1)
|-
!Steps
!Cents
!Steps
!Steps
!Cents
!Range in cents
!Abbrev.
|-
|-
|'''Perfect 0-diadegree'''
|'''0-diastep (root)'''
|0
|Perfect 0-diastep
|0
|0
|0
|0
|0.0¢
|P0ms
|-
|-
|Minor 1-diadegree
| rowspan="2" |1-diastep
|1
|Small 1-diastep
|100
|s
|1
|0.0¢ to 171.4¢
|100
|s1ms
|-
|-
|Major 1-diadegree
|Large 1-diastep
|2
|L
|200
|171.4¢ to 240.0¢
|2
|L1ms
|200
|-
|-
|Minor 2-diadegree
| rowspan="2" | 2-diastep
|3
|Small 2-diastep
|300
|L + s
|3
|240.0¢ to 342.9¢
|300
|s2ms
|-
|-
|Major 2-diadegree
|Large 2-diastep
|4
| 2L
|400
|342.9¢ to 480.0¢
|4
|L2ms
|400
|-
|-
|'''Perfect 3-diadegree'''
| rowspan="2" |'''3-diastep'''
|5
|'''Small 3-diastep'''
|500
|2L + s
|5
|480.0¢ to 514.3¢
|500
|s3ms
|-
|-
|Augmented 3-diadegree
|Large 3-diastep
|6
| 3L
|600
|514.3¢ to 720.0¢
|6
| L3ms
|600
|-
|-
|Diminished 4-diadegree
| rowspan="2" |'''4-diastep'''
|6
|Small 4-diastep
|600
|2L + 2s
|6
|480.0¢ to 685.7¢
|600
|s4ms
|-
|-
|'''Perfect 4-diadegree'''
|'''Large 4-diastep'''
|7
|3L + s
|700
|685.7¢ to 720.0¢
|7
|L4ms
|700
|-
|-
|Minor 5-diadegree
| rowspan="2" |5-diastep
|8
|Small 5-diastep
|800
|3L + 2s
|8
|720.0¢ to 857.1¢
|800
|s5ms
|-
|-
|Major 5-diadegree
|Large 5-diastep
|9
|4L + s
|900
|857.1¢ to 960.0¢
|9
|L5ms
|900
|-
|-
|Minor 6-diadegree
| rowspan="2" |6-diastep
|10
|Small 6-diastep
|1000
|4L + 2s
| 10
|960.0¢ to 1028.6¢
|1000
| s6ms
|-
|-
|Major 6-diadegree
|Large 6-diastep
|11
|5L + s
|1100
|1028.6¢ to 1200.0¢
|11
|L6ms
|1100
|-
|-
|'''Perfect 7-diadegree'''
|'''7-diastep (octave)'''
|12
|Perfect 7-diastep
|1200
|5L + 2s
|12
| 1200.0¢
|1200
|P7ms
|}
|}
{| class="wikitable"
 
|+Scale degrees of 5L 2s (with optional columns)
===MOS mode degrees (using large/small instead of MmAPd)===
! rowspan="2" |Scale degree
{| class="wikitable sortable"
! rowspan="2" |Abbrev.
|+Scale degree qualities of 5L 2s modes
! rowspan="2" |On C
! colspan="2" |Mode names
! colspan="2" |Basic 5L 2s
! colspan="2" |Ordering
(12edo, L:s = 2:1)
! rowspan="2" |Step pattern
! rowspan="2" |Approx. JI ratios
! colspan="8" |Scale degree
|-
!Steps
!Cents
|-
|-
|'''Perfect 0-diadegree'''
!Default
|P0md
!Names
|C
!Bri.
|0
! Rot.
|0
!0
|1/1
!1
!2
!3
!4
!5
!6
!7
|-
|-
|Minor 1-diadegree
|<nowiki>5L 2s 6|0</nowiki>
|m1md
|Lydian
|Db
|1
|1
|1
|100
|LLLsLLs
|
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|-
|-
|Major 1-diadegree
|<nowiki>5L 2s 5|1</nowiki>
|M1md
|Ionian (major)
|D
|2
|2
|200
|5
|
|LLsLLLs
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Lg.
|Perf.
|-
|-
|Minor 2-diadegree
|<nowiki>5L 2s 4|2</nowiki>
|m2md
|Mixolydian
|Eb
|3
|3
|300
|2
|
|LLsLLsL
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Sm.
|Perf.
|-
|-
|Major 2-diadegree
|<nowiki>5L 2s 3|3</nowiki>
|M2md
|Dorian
|E
|4
|4
|400
|6
|
|LsLLLsL
|Perf.
|Lg.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
| Perf.
|-
|-
|'''Perfect 3-diadegree'''
|<nowiki>5L 2s 2|4</nowiki>
|P3md
|Aeolian (minor)
|F
|5
|5
|500
|3
|4/3
|LsLLsLL
|Perf.
|Lg.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|-
|Augmented 3-diadegree
|<nowiki>5L 2s 1|5</nowiki>
|A3md
|Phrygian
|F#
|6
|6
|600
|7
|
|sLLLsLL
|-
|Perf.
|Diminished 4-diadegree
|Sm.
|d4md
| Sm.
|Gb
|Sm.
|6
|Lg.
|600
|Sm.
|
|Sm.
|Perf.
|-
|-
|'''Perfect 4-diadegree'''
|<nowiki>5L 2s 0|6</nowiki>
|P4md
|Locrian
|G
|7
|7
|700
|4
|3/2
|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
|-
|-
|Minor 5-diadegree
!Start
|m5md
!Large step
|Ab
!Small step
|8
!End
|800
|
|-
|-
|Major 5-diadegree
|Small vis
|M5md
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌╥╥╥┬╥╥┬┐
|A
│║║║│║║││
|9
│││││││││
|900
└┴┴┴┴┴┴┴┘</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.
|-
|-
|Minor 6-diadegree
|Large vis
|m6md
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
|Bb
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
|10
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
|1000
│░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│
|
│░░░│░░░│░░░│░░░│░░░│░░░│░░░│░░░│
│░█░│░░░│░░░│░░░│░░░│░░░│░░░│░█░│
└───┴───┴───┴───┴───┴───┴───┴───┘</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
|-
|-
|Major 6-diadegree
!Start
|M6md
!Size 1
|B
!Size 2
|11
! Size 3
|1100
!Size 4
|
!Size 5
!End
|-
|-
|'''Perfect 7-diadegree'''
|Multisize vis (large)
|P7md
|<pre style="line-height: 1.1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
|C
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|12
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
|1200
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░├─┼─┤░░░░│░░░░░░│
|2/1
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░├─┴─┤░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░│▒▒▒│░░░░│░░░░░░│
│░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘
</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>
|<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>
|<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>
|<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>
|<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>
|<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>
|<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
|}
|}
===Step sizes template===
 
{{MOS degrees|Scale Signature=4L 3s}}
===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"
{| class="wikitable sortable"
|+3L 4s step sizes
|+3L 4s step sizes
! rowspan="2" |Interval
! rowspan="2" |Interval
! colspan="2" |Basic 3L 4s
! colspan="2" | Basic 3L 4s
(10edo, L:s = 2:1)
(10edo, L:s = 2:1)
! colspan="2" |Hard 3L 4s
! colspan="2" |Hard 3L 4s
Line 300: Line 646:
|Large step
|Large step
| 2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 321: Line 667:
|4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 330: 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


===Mbox template test===
===Mos ancestors and descendants===
These would be their own templates.
{| 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
|}


Stub page:
{{Mbox|type=notice|text=This page is a '''stub'''. You can help the Xenharmonic Wiki by expanding it.}}
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==
== Encoding scheme for module:mos==


===Isolated symbols ===
=== Mossteps as a vector of L's and s's===
<math>T := [ t_1, t_2, ..., t_m ]</math>
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.
<math>S := [ s_1, s_2, ..., s_m ]</math>
<math>P := [ p_1, p_2, ..., p_n ]</math>


===Sample text===
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 }.
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.
Through this, the "original size" of the interval can always be deduced.


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.
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"
==Interval and degree tables==
|+Encoding scheme
The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.
! rowspan="2" |Value
{| class="wikitable sortable" style="text-align: left;"
! colspan="2" |Encoded
|+<!-- caption -->Intervals of 2L 5s for each mode
! colspan="4" | Decoded
|-
|-
!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'''
|'''Perfect'''
|'''Major'''
|'''Perfect'''
|'''Augmented'''
|'''Perfect'''
|-
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
| -1
|'''Small'''
|Perfect minus 1 chroma
|'''Minor'''
|'''Diminished'''
|'''Perfect'''
|Diminished
|-
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
| -2
|Small minus 1 chroma
|Perfect minus 2 chromas
|Diminished
|2× Diminished
|Diminished
|2× Diminished
|-
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
| -3
|-
|Small minus 2 chromas
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s|| L+3s||L+4s||L+5s||2L+5s
|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.


{| class="wikitable sortable" style="text-align: left;"
* 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.
|+Degrees of 2L 5s for each mode
|-
!Mode!! UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major ||major||perfect||perfect||major||major||perfect
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|-
|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==
Examples of encodings for 5L 2s
{| class="wikitable sortable"
{| class="wikitable"
!Pattern
|+Interval encodings for 5L 2s
!Number of notes
! rowspan="2" |Interval in mossteps
!Number of periods
! colspan="2" |Encoding
!Name
! rowspan="2" |Decoding
!Prefix
! rowspan="2" |Standard notation in the key of F
|-
|-
|[[1L 1s]]
!Mossteps
| 2
! Chroma
|1
|trivial
|triv-
|-
|-
|[[1L 1s]]
|0
| 2
|0
|1
| 0
|monowood
|Perfect 0-diastep
|monowd-
| F
|-
|-
|[[1L 2s]]
|s
| 3
|1
|1
|antrial
| -1
|atri-
|Minor 1-diastep
|Gb
|-
|-
|[[2L 1s]]
| L
| 3
|1
|1
|trial
|0
|tri-
|Major 1-diastep
|G
|-
|-
|[[1L 3s]]
|L + s
| 4
|1
|antetric
|atetra-
|-
|[[2L 2s]]
| 4
|2
|2
|biwood
| -1
|biwd-
|Minor 2-diastep
|-
|Ab
|[[3L 1s]]
| 4
|1
|tetric
|tetra-
|-
|[[1L 4s]]
| 5
|1
|pedal
|ped-
|-
|[[2L 3s]]
| 5
|1
|pentic
|pent-
|-
|[[3L 2s]]
| 5
|1
|antipentic
|apent-
|-
|[[4L 1s]]
| 5
|1
|manual
|manu-
|-
|[[1L 5s]]
| 6
|1
|antimachinoid
|amech-
|-
|-
|[[2L 4s]]
|2L
| 6
|2
|2
|anticitric
|0
|acitro-
|Major 2-diastep
|A
|-
|-
|[[3L 3s]]
|2L + s
| 6
|3
|3
|triwood
| -1
|triwd-
| Perfect 3-diastep
|Bb
|-
|-
|[[4L 2s]]
|3L
| 6
| 3
|2
|0
|citric
|Augmented 3-diastep
|citro-
|B
|-
|-
|[[5L 1s]]
|2L + 2s
| 6
|4
|1
| -1
|machinoid
|Diminished 4-diastep
|mech-
|Cb
|-
|-
|[[1L 6s]]
|3L + s
| 7
|1
|onyx
|on-
|-
|[[2L 5s]]
| 7
|1
|antidiatonic
|pel-
|-
|[[3L 4s]]
| 7
|1
|mosh
|mosh-
|-
|[[4L 3s]]
| 7
|1
|smitonic
|smi-
|-
|[[5L 2s]]
| 7
|1
|diatonic
|''none''
|-
|[[6L 1s]]
| 7
|1
|arch(a)eotonic
|arch-
|-
|[[1L 7s]]
| 8
|1
|antipine
|apine-
|-
|[[2L 6s]]
| 8
|2
|antiekic
|anek-
|-
|[[3L 5s]]
| 8
|1
|checkertonic
|check-
|-
|[[4L 4s]]
| 8
|4
|4
|tetrawood; diminished
|0
|tetwd-
|Perfect 4-diastep
|C
|-
|-
|[[5L 3s]]
| 3L + 2s
| 8
|5
|1
| -1
|oneirotonic
|Minor 5-diastep
|neiro-
|Db
|-
|-
|[[6L 2s]]
|4L + s
| 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
|0
|penwd-
|Major 5-diastep
|D
|-
|-
|[[6L 4s]]
|4L + 2s
| 10
|6
|2
| -1
|lemon
|Minor 6-diastep
|lem-
|Eb
|-
|-
|[[7L 3s]]
|5L + s
| 10
|6
|1
|0
|dicoid /'daɪkɔɪd/
| Major 6-diastep
|dico-
|E
|-
|-
|[[8L 2s]]
|5L + 2s
| 10
|7
|2
|0
|taric
|Perfect 7-diastep
|tara-
|F
|}
{| class="wikitable sortable"
! colspan="2" |Mode names
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
|-
|-
|[[9L 1s]]
!Default
| 10
!Names
|1
!Bri.
|sinatonic
!Rot.
|sina-
!0
|}
!1
 
!2
==Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)==
!3
{| class="wikitable"
!4
! colspan="6" |Generator
!5
!Bright gen.
! 6
! Dark gen.
!7
! L
!s
!L/s
!Ranges of mosses
|-
|-
|1\2
|<nowiki>5L 2s 6|0</nowiki>
|
|Lydian
|
|
|
|
|600.000
|600.000
|1
|1
|1
|1
|1.000
|LLLsLLs
|
|0
|-
|0
|
|0
|
|0
|
|0
|
|0
|
|0
|6\11
|0
|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
|-
|-
|
|<nowiki>5L 2s 5|1</nowiki>
|
|Ionian (major)
|
|
|
|10\17
|705.882
|494.118
|10
|7
|1.429
|-
|
|
|3\5
|
|
|
|720.000
|480.000
|3
|2
|2
|1.500
|Basic 2L 1s
|-
|
|
|
|
|
|11\18
|733.333
|466.667
|11
|7
|1.571
| rowspan="3" |5L 3s range
|-
|
|
|
|
|8\13
|
|738.462
|461.538
|8
|5
|5
|1.600
|LLsLLLs
|0
|0
|0
| -1
|0
|0
|0
|0
|-
|-
|
|<nowiki>5L 2s 4|2</nowiki>
|
|Mixolydian
|
|
|
|13\21
|742.857
|457.143
|13
|8
|1.625
|-
|
|
|
|5\8
|
|
|750.000
|450.000
|5
|3
|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
|2
|LLsLLsL
|0
|0
|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
|5
|2.400
|-
|
|
|
|5\7
|
|
|857.143
|342.857
|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
|}
|}
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