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== Navbox (module-based template) ==
== Navbox (module-based template) ==


{{Navbox|Title=Test title|Is Collapsed=false}}
{{Navbox|Title=Test title|Is Collapsed=false|Header 1=Sample header|Data 1=Sample data}}
=== Navbox MOS ===
 
 
===Navbox MOS===
<div class="wikitable mw-collapsible mw-collapsed" style="overflow:auto">
<div class="wikitable mw-collapsible mw-collapsed" style="overflow:auto">
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>5L 2s (Diatonic)</b></center></div>
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>5L 2s (Diatonic)</b></center></div>
Line 142: Line 144:
</div>
</div>


=== Navbox lumatone ===
===Navbox lumatone===
<div class="wikitable mw-collapsible mw-collapsed" style="overflow:auto">
<div class="wikitable mw-collapsible mw-collapsed" style="overflow:auto">
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>Lumatone mappings</b></center></div>
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>Lumatone mappings</b></center></div>
Line 152: Line 154:
</div>
</div>


== MOS intro ==
 
== MOS intro==
First sentence:
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.
*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.
*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.
*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.
*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.
*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.
*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:
Second sentence:


* Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.


Octave-equivalent relational info:
Octave-equivalent relational info:


* Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
*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.
*Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.


Rothenprop:
Rothenprop:


* Single-period: Scales of this form are always proper because there is only one small step.
*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.
*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===
===Cent ruler ===


<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
<div style="height: 100px; width: 100%; background-color: powderblue; font-size: 0;">
Line 219: Line 222:
</div>
</div>


===MOS characteristics===
=== MOS characteristics===
NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.<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;
Line 306: Line 309:
|Small 1-diastep
|Small 1-diastep
|s
|s
| 0.0¢ to 171.4¢
|0.0¢ to 171.4¢
|s1ms
|s1ms
|-
|-
Line 314: Line 317:
|L1ms
|L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" | 2-diastep
|Small 2-diastep
|Small 2-diastep
|L + s
|L + s
Line 321: Line 324:
|-
|-
|Large 2-diastep
|Large 2-diastep
|2L
| 2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
|L2ms
|L2ms
Line 332: Line 335:
|-
|-
|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 362: Line 365:
|4L + 2s
|4L + 2s
|960.0¢ to 1028.6¢
|960.0¢ to 1028.6¢
|s6ms
| s6ms
|-
|-
|Large 6-diastep
|Large 6-diastep
Line 372: Line 375:
|Perfect 7-diastep
|Perfect 7-diastep
|5L + 2s
|5L + 2s
|1200.0¢
| 1200.0¢
|P7ms
|P7ms
|}
|}
Line 389: Line 392:
! Rot.
! Rot.
!0
!0
! 1
!1
!2
!2
!3
!3
Line 404: Line 407:
|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>
| Ionian (major)
|Ionian (major)
|2
|2
|5
|5
Line 418: Line 421:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 432: Line 435:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 450: Line 453:
|Lg.
|Lg.
|Lg.
|Lg.
| Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 460: Line 463:
|Perf.
|Perf.
|Lg.
|Lg.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 474: Line 477:
|Perf.
|Perf.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 487: Line 490:
|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
Line 499: Line 502:
{| class="wikitable"
{| class="wikitable"
|+
|+
! rowspan="2" | Type
! rowspan="2" |Type
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="4" |Individual steps
! colspan="4" |Individual steps
Line 505: Line 508:
|-
|-
!Start
!Start
! Large step
!Large step
!Small step
!Small step
!End
!End
|-
|-
| Small vis
|Small vis
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌╥╥╥┬╥╥┬┐
|<pre style="line-height: 1; font-family: monospace; font-size: 1em; padding-top: 0.1em; padding-bottom: 0.1em; margin: 0.1em">┌╥╥╥┬╥╥┬┐
│║║║│║║││
│║║║│║║││
Line 572: Line 575:
|}
|}
{| class="wikitable"
{| class="wikitable"
! 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
!Size 3
! Size 3
!Size 4
!Size 4
!Size 5
!Size 5
Line 720: Line 723:


</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 756: Line 759:
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 765: Line 768:
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
Line 773: Line 776:
|
|
|-
|-
| Bright generator
|Bright generator
|3
|3
|360¢
|360¢
|4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 803: Line 806:
|(2x+y)L xs
|(2x+y)L xs
|-
|-
| rowspan="2" | (x+y)L xs
| rowspan="2" |(x+y)L xs
|(2x+y)L (x+y)s
|(2x+y)L (x+y)s
|-
|-
| (x+y)L (2x+y)s
|(x+y)L (2x+y)s
|}
|}




== 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.


Line 825: Line 827:
! 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
!Intervals with 1 size
!Intervals with 1 size
!Nonperfectable intervals
!Nonperfectable intervals
! Bright gen
!Bright gen
!Dark gen
!Dark gen
!Period intervals
!Period intervals
Line 880: Line 882:
|3× Diminished
|3× Diminished
|2× Diminished
|2× Diminished
|3× Diminished
| 3× Diminished
|}
|}
Rationale:
Rationale:
Line 887: Line 889:
**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
Line 898: Line 900:
|-
|-
!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
| Major 1-diastep
|Major 1-diastep
|G
|G
|-
|-
|L + s
|L + s
|2
|2
| -1
| -1
| Minor 2-diastep
|Minor 2-diastep
|Ab
|Ab
|-
|-
Line 933: Line 935:
|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 954: Line 956:
|C
|C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
Line 969: Line 971:
|6
|6
| -1
| -1
| Minor 6-diastep
|Minor 6-diastep
|Eb
|Eb
|-
|-
Line 975: Line 977:
|6
|6
|0
|0
|Major 6-diastep
| Major 6-diastep
|E
|E
|-
|-
Line 1,000: Line 1,002:
!4
!4
!5
!5
!6
! 6
!7
!7
|-
|-
|<nowiki>5L 2s 6|0</nowiki>
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|Lydian
| 1
|1
|1
|1
|LLLsLLs
|LLLsLLs
Line 1,013: Line 1,015:
|0
|0
|0
|0
| 0
|0
|0
|0
|0
|0
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
| Ionian (major)
|Ionian (major)
|2
|2
|5
|5
|LLsLLLs
|LLsLLLs
|0
|0
| 0
|0
|0
|0
| -1
| -1
Line 1,037: Line 1,039:
|LLsLLsL
|LLsLLsL
|0
|0
| 0
|0
|1
|1
| -1
| -1
| 0
|0
|0
|0
| -1
| -1
Line 1,054: Line 1,056:
| -1
| -1
| -1
| -1
| 0
|0
|0
|0
| -1
| -1
Line 1,069: Line 1,071:
| -1
| -1
|0
|0
| -1
| -1
| -1
| -1
|0
|0
Line 1,089: Line 1,091:
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|Locrian
|7
| 7
|4
|4
|sLLsLLL
|sLLsLLL
|0
|0
| -1
| -1
| -1
| -1
| -1
| -1
| -1
| -1
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