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Fleshed out rationale for encoding scheme to be used for module:mos. It's all based on vectors of L's and s's.
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Line 1: Line 1:
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
<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==
==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 ===
=== MOS characteristics===
<div style="  display: block;
NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.<div style="  display: block;
   background-color: #dddddd;
   background-color: #dddddd;
   column-fill: balance;
   column-fill: balance;
   column-width: auto;
   column-width: auto;
   column-width: 600px;
   column-width: 600px;
   padding: 10px;">
   padding: 10px;"><div style="
  <div style="
     position: relative;
     position: relative;
     background-color: #eee;
     background-color: #eee;
Line 15: Line 120:
     break-inside: avoid-column;
     break-inside: avoid-column;
     padding: 1em;
     padding: 1em;
     ">{{MOS mode degrees|Scale Signature=5L 2s}}</div>
     ">{{MOS mode degrees|Scale Signature=5L 2s}}
</div>
   <div style="
   <div style="
     position: relative;
     position: relative;
Line 22: Line 128:
     break-inside: avoid-column;
     break-inside: avoid-column;
     padding: 1em;
     padding: 1em;
     ">{{MOS intervals|Scale Signature=5L 2s}}</div>
     ">{{MOS intervals|Scale Signature=5L 2s}}
</div>
   <div style="
   <div style="
     position: relative;
     position: relative;
Line 70: Line 177:
</div>
</div>


===MOS intervals (using large/small instead of MmAPd) ===
===MOS intervals (using large/small instead of MmAPd)===
{| class="wikitable"
{| class="wikitable"
|+Intervals of 5L 2s
|+Intervals of 5L 2s
Line 96: Line 203:
|L1ms
|L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" | 2-diastep
|Small 2-diastep
|Small 2-diastep
|L + s
|L + s
Line 103: Line 210:
|-
|-
|Large 2-diastep
|Large 2-diastep
|2L
| 2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
|L2ms
|L2ms
Line 114: Line 221:
|-
|-
|Large 3-diastep
|Large 3-diastep
|3L
| 3L
|514.3¢ to 720.0¢
|514.3¢ to 720.0¢
|L3ms
| L3ms
|-
|-
| rowspan="2" |'''4-diastep'''
| rowspan="2" |'''4-diastep'''
Line 144: Line 251:
|4L + 2s
|4L + 2s
|960.0¢ to 1028.6¢
|960.0¢ to 1028.6¢
|s6ms
| s6ms
|-
|-
|Large 6-diastep
|Large 6-diastep
Line 154: Line 261:
|Perfect 7-diastep
|Perfect 7-diastep
|5L + 2s
|5L + 2s
|1200.0¢
| 1200.0¢
|P7ms
|P7ms
|}
|}


=== MOS mode degrees (using large/small instead of MmAPd) ===
===MOS mode degrees (using large/small instead of MmAPd)===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+Scale degree qualities of 5L 2s modes
|+Scale degree qualities of 5L 2s modes
Line 169: Line 276:
!Names
!Names
!Bri.
!Bri.
!Rot.
! Rot.
!0
!0
!1
!1
Line 186: Line 293:
|Perf.
|Perf.
|Lg.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
Line 200: Line 307:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 214: Line 321:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 233: Line 340:
|Lg.
|Lg.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 242: Line 349:
|Perf.
|Perf.
|Lg.
|Lg.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 256: Line 363:
|Perf.
|Perf.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 269: Line 376:
|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
Line 278: Line 385:
|}
|}


=== KB vis ===
===KB vis===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 286: Line 393:
! rowspan="2" |Notes
! rowspan="2" |Notes
|-
|-
! Start
!Start
!Large step
!Large step
!Small step
!Small step
Line 357: 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 502: 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 518: 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 531: Line 638:
|-
|-
!Steps
!Steps
! Cents
!Cents
!Steps
!Steps
!Cents
!Cents
Line 538: Line 645:
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 547: Line 654:
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
Line 560: Line 667:
|4
|4
|369.2¢
|369.2¢
|5
| 5
| 355.6¢
|355.6¢
|
|
|}
|}
Line 574: Line 681:
!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
|-
|-
Line 591: Line 698:
|}
|}


===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>
<td style="width:85%; text-align:left; padding:0; margin:0;">
 
<table class="nowraplinks" style="width:100%; margin:0em">
<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>
<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>
<td style="width: 15%; text-align: right; background-color:#eaecf0;">Enharmonic scales</td>
<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>
</tr>
 
<tr>
<td style="width: 15%; text-align: right; background-color:#eaecf0;">Subchromatic scales</td>
<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>
 
== Encoding scheme for module:mos ==
 
=== Mossteps as a vector of L's and s's ===
For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.
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.


Line 649: Line 713:
! rowspan="2" |Value
! rowspan="2" |Value
! colspan="2" |Encoded
! colspan="2" |Encoded
! colspan="4" |Decoded
! colspan="4" | Decoded
|-
|-
!Intervals with 2 sizes
!Intervals with 2 sizes
Line 704: Line 768:
|3× Diminished
|3× Diminished
|2× Diminished
|2× Diminished
|3× Diminished
| 3× Diminished
|}
|}
Rationale:
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.
*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.
**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.
* 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.
Line 722: Line 786:
|-
|-
!Mossteps
!Mossteps
!Chroma
! Chroma
|-
|-
|0
|0
|0
|0
|0
| 0
|Perfect 0-diastep
|Perfect 0-diastep
|F
| F
|-
|-
|s
|s
|1
|1
| -1
| -1
|Minor 1-diastep
|Minor 1-diastep
|Gb
|Gb
|-
|-
|L
| L
|1
|1
|0
|0
Line 757: Line 821:
|3
|3
| -1
| -1
|Perfect 3-diastep
| Perfect 3-diastep
|Bb
|Bb
|-
|-
|3L
|3L
|3
| 3
|0
|0
|Augmented 3-diastep
|Augmented 3-diastep
Line 778: Line 842:
|C
|C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
Line 799: Line 863:
|6
|6
|0
|0
|Major 6-diastep
| Major 6-diastep
|E
|E
|-
|-
Line 824: Line 888:
!4
!4
!5
!5
!6
! 6
!7
!7
|-
|-
Line 913: Line 977:
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|Locrian
|7
| 7
|4
|4
|sLLsLLL
|sLLsLLL
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Sandbox"