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mos intervals text test
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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.)


== Mos intervals ==
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>
The intervals of SCALESIG are named after the number of steps subtended and, apart from the unison (0-step) and octave (STEPCOUNT-step), appear in two varieties or sizes each.{{MOS intervals|Scale Signature=5L 3s}}


== Mos genchain ==
produces
{{MOS genchain|Scale Signature=10L 5s}}{{MOS genchain|Scale Signature=2L 5s}}{{MOS genchain|Scale Signature=5L 2s}}


== 5L 2s modes and modmos modes ==
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 mode degrees|Scale Signature=5L 2s}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LALdLAd}}


== 4L 4s modes and modmos modes ==
== MOS scalesig ==
{{MOS mode degrees|Scale Signature=4L 4s}}{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLLss}}{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLsLs}}
{{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===
===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 46: Line 95:


<div style="height: 100px; width: 1200px; background-color: powderblue; font-size: 0;">
<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 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>


Line 59: Line 108:
</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 172: 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'''
|Small 4-diastep
|Small 4-diastep
| 2L + 2s
|2L + 2s
|480.0¢ to 685.7¢
|480.0¢ to 685.7¢
|s4ms
|s4ms
Line 202: Line 251:
|4L + 2s
|4L + 2s
|960.0¢ to 1028.6¢
|960.0¢ to 1028.6¢
|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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|Perfect 7-diastep
|Perfect 7-diastep
|5L + 2s
|5L + 2s
|1200.0¢
| 1200.0¢
| P7ms
|P7ms
|}
|}


Line 227: Line 276:
!Names
!Names
!Bri.
!Bri.
!Rot.
! Rot.
!0
!0
!1
!1
Line 244: 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 258: Line 307:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 272: Line 321:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 291: Line 340:
|Lg.
|Lg.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 300: Line 349:
|Perf.
|Perf.
|Lg.
|Lg.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 310: Line 359:
|Phrygian
|Phrygian
|6
|6
| 7
|7
|sLLLsLL
|sLLLsLL
|Perf.
|Perf.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
|Sm.
|Sm.
|Sm.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
Line 329: Line 378:
| Sm.
| Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
| Perf.
|Perf.
|}
|}


===KB vis ===
===KB vis===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 414: Line 463:
! 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 560: 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.


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|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
| 276.9¢
|3
|3
|276.9¢
| 3
|211.8¢
|211.8¢
|Hide column if no ratios given
|Hide column if no ratios given
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
Line 613: Line 662:
|
|
|-
|-
| Bright generator
|Bright generator
|3
|3
|360¢
|360¢
|4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 627: 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


===Mos ancestors and descendants ===
===Mos ancestors and descendants===
{| class="wikitable"
{| class="wikitable"
!2nd ancestor
!2nd ancestor
Line 649: 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>
<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>
<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==
== 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 722: Line 728:
|2× Augmented
|2× Augmented
|3× Augmented
|3× Augmented
| 2× Augmented
|2× Augmented
|-
|-
|1
|1
Line 749: Line 755:
|-
|-
| -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
Line 759: Line 765:
|Small minus 2 chromas
|Small minus 2 chromas
|Perfect minus 3 chromas
|Perfect minus 3 chromas
|2× Diminished
|3× Diminished
|2× Diminished
|2× Diminished
| 3× Diminished
| 3× Diminished
|2× Diminished
|3× Diminished
|}
|}
Rationale:
Rationale:
Line 769: Line 775:
**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 780: 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
Line 815: 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 836: Line 842:
|C
|C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
|Minor 5-diastep
|Minor 5-diastep
| Db
|Db
|-
|-
|4L + s
|4L + s
Line 848: Line 854:
|D
|D
|-
|-
| 4L + 2s
|4L + 2s
|6
|6
| -1
| -1
Line 857: Line 863:
|6
|6
|0
|0
|Major 6-diastep
| Major 6-diastep
|E
|E
|-
|-
Line 882: Line 888:
!4
!4
!5
!5
!6
! 6
!7
!7
|-
|-
Line 943: Line 949:
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|Aeolian (minor)
| 5
|5
|3
|3
|LsLLsLL
|LsLLsLL
Line 971: Line 977:
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
|Locrian
|Locrian
|7
| 7
|4
|4
|sLLsLLL
|sLLsLLL
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