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Ganaram inukshuk (talk | contribs)
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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.
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
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.)
==Sandbox for proposed templates==
==Sandbox for proposed templates==
===Cent ruler===


=== MOS characteristics ===
<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
<div style="  display: block;
 
<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;
   background-color: #dddddd;
   column-fill: balance;
   column-fill: balance;
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     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;
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     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 85:
</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
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|L1ms
|L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" | 2-diastep
|Small 2-diastep
|Small 2-diastep
|L + s
|L + s
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|-
|-
|Large 2-diastep
|Large 2-diastep
|2L
| 2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
|L2ms
|L2ms
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| rowspan="2" |'''4-diastep'''
| rowspan="2" |'''4-diastep'''
|Small 4-diastep
|Small 4-diastep
|2L + 2s
| 2L + 2s
|480.0¢ to 685.7¢
|480.0¢ to 685.7¢
|s4ms
|s4ms
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|s6ms
|s6ms
|-
|-
|Large 6-diastep
| Large 6-diastep
|5L + s
|5L + s
|1028.6¢ to 1200.0¢
| 1028.6¢ to 1200.0¢
|L6ms
|L6ms
|-
|-
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|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
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|Phrygian
|Phrygian
|6
|6
|7
| 7
|sLLLsLL
|sLLLsLL
|Perf.
|Perf.
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|Sm.
|Sm.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
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|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
| Perf.
|Sm.
|Perf.
|}
|}


=== KB vis ===
===KB vis ===
{| class="wikitable"
{| class="wikitable"
|+
|+
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! rowspan="2" |Notes
! rowspan="2" |Notes
|-
|-
! Start
!Start
!Large step
!Large step
!Small step
!Small step
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! rowspan="2" |Type
! rowspan="2" |Type
! 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
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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
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|-
|-
!Steps
!Steps
! Cents
!Cents
!Steps
!Steps
!Cents
!Cents
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|3
|3
|276.9¢
|276.9¢
|3
| 3
|211.8¢
|211.8¢
|Hide column if no ratios given
|Hide column if no ratios given
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|
|
|-
|-
|Bright generator
| Bright generator
|3
|3
|360¢
|360¢
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|369.2¢
|369.2¢
|5
|5
| 355.6¢
|355.6¢
|
|
|}
|}
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*JI ratios column only shows if there are any ratios to show
*JI ratios column only shows if there are any ratios to show


===Mos ancestors and descendants===
===Mos ancestors and descendants ===
{| class="wikitable"
{| class="wikitable"
!2nd ancestor
!2nd ancestor
!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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</div>
</div>


== Encoding scheme for module:mos ==
== Encoding scheme for module:mos==


=== Mossteps as a vector of L's and s's ===
===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.


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! 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
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|2× Augmented
|2× Augmented
|3× Augmented
|3× Augmented
|2× Augmented
| 2× Augmented
|-
|-
|1
|1
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|-
|-
| -2
| -2
|Small minus 1 chroma
| Small minus 1 chroma
|Perfect minus 2 chromas
|Perfect minus 2 chromas
|Diminished
| Diminished
|2× Diminished
|2× Diminished
|Diminished
|Diminished
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|Perfect minus 3 chromas
|Perfect minus 3 chromas
|2× Diminished
|2× Diminished
|3× Diminished
| 3× Diminished
|2× Diminished
|2× Diminished
|3× Diminished
|3× Diminished
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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.


Examples of encodings for 5L 2s
Examples of encodings for 5L 2s
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|Gb
|Gb
|-
|-
|L
| L
|1
|1
|0
|0
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| -1
| -1
|Minor 5-diastep
|Minor 5-diastep
|Db
| Db
|-
|-
|4L + s
|4L + s
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|D
|D
|-
|-
|4L + 2s
| 4L + 2s
|6
|6
| -1
| -1
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|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|Aeolian (minor)
|5
| 5
|3
|3
|LsLLsLL
|LsLLsLL
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