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<div style="
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
border: 1px solid #999;
 
margin: 0;
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>
margin-left: 1em;
 
margin-bottom: 0.5em;
produces
padding: 0.5em;
 
background-color: #f0f0f0;
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
min-width: 15em;
 
float: right;
== MOS scalesig ==
max-width: 100%;
{{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}}
overflow: auto;
 
">
== MOS tuning spectrum (AKA, scale tree) ==
{| width="100%" style="border-collapse: collapse;"
 
|+ style="font-weight: bold; text-align: center;" | <table style="width: 100%; margin: 0"><tr><td style="width: 15%; text-align: left; white-space: nowrap; font-size: smaller">4L 1s</td><td style="
{{MOS tuning spectrum
width: 50%; padding-left: 1em; padding-right: 1em; text-align: center; font-size: smaller">5L 1s
| Scale Signature = 1L 1s
</td><td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">6L 1s</td>
| Int Limit = 13
<tr><td style="width: 15%; text-align: left; white-space: nowrap; font-size: smaller">4L 2s</td><td style="width: 50%; padding-left: 1em; padding-right: 1em; text-align: center">5L 2s (2/1-equivalent)</td><td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">6L 2s</td></tr><tr><td style="width: 15%; text-align: left; white-space: nowrap; font-size: smaller">4L 3s</td><td style="
}}
width: 50%; padding-left: 1em; padding-right: 1em; text-align: center; font-size: smaller">5L 3s
 
</td><td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">6L 3s</td></tr></table>
{{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.
|-
|-
| colspan="2" style="text-align:center;" | <pre style="background-color: white; line-height: 1; font-family: monospace; font-size: 1em; padding: 0.1em; margin: 0.1em;">┌╥╥╥┬╥╥┬┐
|'''0-diastep (root)'''
│║║║│║║││
|Perfect 0-diastep
│││││││││
|0
└┴┴┴┴┴┴┴┘</pre>
|0.0¢
|P0ms
|-
|-
| colspan="2" style="text-align:center;" |<b>Scale structure</b>
| rowspan="2" |1-diastep
|Small 1-diastep
|s
|0.0¢ to 171.4¢
|s1ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Step pattern
|Large 1-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |<abbr title="Step pattern of brightest mode">LLLsLLs</abbr>
|L
|171.4¢ to 240.0¢
|L1ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Period (cents)
| rowspan="2" | 2-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |2/1 (1200¢)
|Small 2-diastep
|L + s
|240.0¢ to 342.9¢
|s2ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Bright generator range
|Large 2-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |4\7 (685.7¢) to 3\5 (720¢)
| 2L
|342.9¢ to 480.0¢
|L2ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Dark generator range
| rowspan="2" |'''3-diastep'''
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |2\5 (480¢) to 3\7 (514.3¢)
|'''Small 3-diastep'''
|2L + s
|480.0¢ to 514.3¢
|s3ms
|-
|-
| colspan="2" style="text-align:center;" |<b>TAMNAMS information</b>
|Large 3-diastep
| 3L
|514.3¢ to 720.0¢
| L3ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Name
| rowspan="2" |'''4-diastep'''
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |diatonic
|Small 4-diastep
|2L + 2s
|480.0¢ to 685.7¢
|s4ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Prefix
|'''Large 4-diastep'''
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |dia-
|3L + s
|685.7¢ to 720.0¢
|L4ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Abbrev.
| rowspan="2" |5-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |dia.
|Small 5-diastep
|3L + 2s
|720.0¢ to 857.1¢
|s5ms
|-
|-
| colspan="2" style="text-align:center;" |<b>Related scales</b>
|Large 5-diastep
|4L + s
|857.1¢ to 960.0¢
|L5ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Parent MOS
| rowspan="2" |6-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |2L 3s
|Small 6-diastep
|4L + 2s
|960.0¢ to 1028.6¢
| s6ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Sister MOS
|Large 6-diastep
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |2L 5s
|5L + s
|1028.6¢ to 1200.0¢
|L6ms
|-
|-
| style="text-align:right; padding-right: 0.25em" |Daughter MOSes
|'''7-diastep (octave)'''
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |7L 5s, 5L 7s
|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
|-
|-
| colspan="2" style="text-align:center;" |<b>Simple equal tunings</b>
!Default
!Names
!Bri.
! Rot.
!0
!1
!2
!3
!4
!5
!6
!7
|-
|-
| style="text-align:right; padding-right: 0.25em" | Supersoft (L:s = 4:3)
|<nowiki>5L 2s 6|0</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |15\26 (692.3¢)
|Lydian
|1
|1
|LLLsLLs
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" |Soft (L:s = 3:2)
|<nowiki>5L 2s 5|1</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |11\19 (694.7¢)
|Ionian (major)
|2
|5
|LLsLLLs
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Lg.
|Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" |Semisoft (L:s = 5:3)
|<nowiki>5L 2s 4|2</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |18\31 (696.8¢)
|Mixolydian
|3
|2
|LLsLLsL
|Perf.
|Lg.
| Lg.
|Sm.
|Lg.
|Lg.
|Sm.
|Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" |Basic (L:s = 2:1)
|<nowiki>5L 2s 3|3</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |7\12 (700¢)
|Dorian
|4
|6
|LsLLLsL
|Perf.
|Lg.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
| Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" |Semihard (L:s = 5:2)
|<nowiki>5L 2s 2|4</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |17\29 (703.4¢)
|Aeolian (minor)
|5
|3
|LsLLsLL
|Perf.
|Lg.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" |Hard (L:s = 3:1)
|<nowiki>5L 2s 1|5</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |10\17 (705.9¢)
|Phrygian
|6
|7
|sLLLsLL
|Perf.
|Sm.
| Sm.
|Sm.
|Lg.
|Sm.
|Sm.
|Perf.
|-
|-
| style="text-align:right; padding-right: 0.25em" | Superhard (L:s = 4:1)
|<nowiki>5L 2s 0|6</nowiki>
| style="background-color: white; padding-left: 0.25em; font-weight: bold" |13\22 (709.1¢)
|Locrian
|}</div>
|7
 
|4
 
|sLLsLLL
{{Infobox MOS|Tuning=5729L 2857s|debug=1}}{{Infobox MOS|Tuning=1893L 28934s|debug=1}}{{Infobox MOS|Tuning=360L 192s|debug=1}}{{Infobox MOS|Tuning=79L 43s|debug=1}}
|Perf.
 
| Sm.
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
|Sm.
 
| Sm.
==Infobox testing ==
|Sm.
 
|Sm.
Testing out several mos infoboxes (plus some obscenely large mosses).
|Sm.
==Sandbox for proposed templates==
|Perf.
{{Mbox|type=notice|text='''This article or section contains multiple [[:Category:Pages_with_idiosyncratic_terms|idiosyncratic terms]].''' Such terms are used by a small group of people or a single person and are not regularly used within the community.}}
|}


===KB vis===
===KB vis===
Line 103: Line 393:
! rowspan="2" |Notes
! rowspan="2" |Notes
|-
|-
! Start
!Start
!Large step
!Large step
!Small step
!Small step
Line 174: Line 464:
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="7" |Individual steps
! colspan="7" |Individual steps
! rowspan="2" |Notes
! rowspan="2" | Notes
|-
|-
! Start
!Start
!Size 1
!Size 1
!Size 2
!Size 2
!Size 3
! Size 3
!Size 4
!Size 4
!Size 5
!Size 5
Line 319: Line 609:


</pre>
</pre>
|X's are placeholders for note names.
| X's are placeholders for note names.
Naturals only, as there is not enough room for accidentals.
Naturals only, as there is not enough room for accidentals.


Line 335: Line 625:
For harmonics: '''m/1''', also called '''interval-name''', is a just intonation ration that represents the mth harmonic 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===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+3L 4s step sizes
|+3L 4s step sizes
Line 348: Line 638:
|-
|-
!Steps
!Steps
! Cents
!Cents
!Steps
!Steps
!Cents
!Cents
Line 355: Line 645:
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 364: Line 654:
|-
|-
|Small step
|Small step
|1
| 1
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!1st ancestor
!1st ancestor
!Mos
!Mos
! 1st descendants
!1st descendants
! 2nd descendants
!2nd descendants
|-
|-
| rowspan="4" |uL vs
| rowspan="4" |uL vs
| rowspan="4" |zL ws
| rowspan="4" |zL ws
| rowspan="4" |xL ys
| rowspan="4" |xL ys
| rowspan="2" | xL (x+y)s
| rowspan="2" |xL (x+y)s
|xL (2x+y)s
|xL (2x+y)s
|-
|-
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|}
|}


===Navbox MOS===
<div class="wikitable mw-collapsible" style="overflow:auto">
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>[[MOS scale|Moment-of-symmetry scales]]</b></center></div>
<table class="mw-collapsible-content nowraplinks" style="width: 100%; margin:0em">
<tr style="display: table-row">
<td style="width:15%; text-align:right; background-color:#eaecf0;">6- to 10-note mosses</td>
<td style="width:85%; text-align:left;">1L 5s (selenite) {{!}} 2L 4s ( {{!}} 3L 3s {{!}} 4L 2 {{!}} 5L 1s</td>
</tr>


<tr>
== Encoding scheme for module:mos==
<td style="width:15%; text-align:right; background-color:#eaecf0;">Monolarge family</td>
<td>1L 5s (selenite) {{!}} 1L 6s (onyx) {{!}} 1L 7s (spinel) {{!}} 1L 8s (agate) {{!}} 1L 9s (olivine)</td>
</tr>


<tr>
=== Mossteps as a vector of L's and s's===
<td style="width:15%; text-align:right; background-color:#eaecf0;">Diatonic mos family</td>
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.
<td style="width:85%; text-align:left; padding:0; margin:0;">


<table class="nowraplinks" style="width:100%; margin:0em">
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 }.
<tr>
<td style="width:15%; text-align:right; background-color:#eaecf0;">Parent mos</td>
<td style="width:85%; text-align:left;">5L 2s (diatonic)</td>
</tr>


<tr>
Through this, the "original size" of the interval can always be deduced.
<td style="width: 15%; text-align: right; background-color:#eaecf0;">Chromatic scales</td>
<td style="width: 85%; text-align: left;">7L 5s (soft diatonic chromatic) {{!}} 5L 7s (hard diatonic chromatic)</td>
</tr>


<tr>
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.
<td style="width: 15%; text-align: right; background-color:#eaecf0;">Enharmonic scales</td>
{| class="wikitable"
<td style="width: 85%; text-align: left;">7L 12s (soft diatonic enharmonic) {{!}} 12L 7s (hyposoft diatonic enharmonic) {{!}} 12L 5s (hypohard diatonic enharmonic) {{!}} 5L 12s (hard diatonic enharmonic)</td>
|+Encoding scheme
</tr>
! 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:


<tr>
*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.
<td style="width: 15%; text-align: right; background-color:#eaecf0;">Subchromatic scales</td>
**Alterations by entire large steps or small steps is considered interval arithmetic.
<td style="width: 85%; text-align: left;">7L 19s and 19L 7s {{!}} 19L 12s and 12L 19s {{!}} 12L 17s and 17L 12s {{!}} 17L 5s and 5L 17s</td>
</tr>
</table></td>
</tr>
</table>


</div>
* 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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