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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.)


== Test ==
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>
NOTE: to make the table caption have a border like that of a header cell... just make it another header cell!
 
{| class="wikitable mw-collapsible"
produces
! colspan="3" | Generator chain of 5L 3s&nbsp;
 
|-
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
! Bright gens !! Scale Degree !! Abbrev.
 
|-
== MOS scalesig ==
| 12 || Augmented 4-oneirodegree || A4oneid
{{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}}
|-
 
| 11 || Augmented 1-oneirodegree || A1oneid
== MOS tuning spectrum (AKA, scale tree) ==
|-
 
| 10 || Augmented 6-oneirodegree || A6oneid
{{MOS tuning spectrum
|-
| Scale Signature = 1L 1s
| 9 || Augmented 3-oneirodegree || A3oneid
| Int Limit = 13
|-
}}
| 8 || Augmented 0-oneirodegree || A0oneid
 
|-
{{MOS tuning spectrum
| 7 || Augmented 5-oneirodegree || A5oneid
| Scale Signature= 3L 4s
|-
| Int Limit = 20
| 6 || Major 2-oneirodegree || M2oneid
| 6/5 = [[Mohaha]] / ptolemy↑
|-
| 5/4 = Mohaha / migration / [[mohajira]]
| 5 || Major 7-oneirodegree || M7oneid
| 11/8 = Mohaha / mohamaq
|-
| 7/5 = Mohaha / [[neutrominant]]
| 4 || Major 4-oneirodegree || M4oneid
| 10/7 = [[Hemif]] / [[hemififths]]
|-
| 11/7 = [[Suhajira]]
| 3 || Major 1-oneirodegree || M1oneid
| 13/8 = Golden suhajira (354.8232¢)
|-
| 5/3 = Suhajira / [[ringo]]
| 2 || Major 6-oneirodegree || M6oneid
| 12/7 = [[Beatles]]
|-
| 13/5 = Unnamed golden tuning (366.2564¢)
| 1 || Perfect 3-oneirodegree || P3oneid
| 7/2 = [[Sephiroth]]
|-
| 9/2 = [[Muggles]]
| 0 || Perfect 0-oneirodegree<br>Perfect 8-oneirodegree || P0oneid<br>P8oneid
| 5/1 = [[Magic]]
|-
| 6/1 = [[Würschmidt]]↓
| -1 || Perfect 5-oneirodegree || P5oneid
}}
|-
 
| -2 || Minor 2-oneirodegree || m2oneid
{{MOS tuning spectrum
|-
| Depth = 3
| -3 || Minor 7-oneirodegree || m7oneid
| Scale Signature= 3L 4s<3/2>
|-
}}
| -4 || Minor 4-oneirodegree || m4oneid
 
|-
== MOS intro==
| -5 || Minor 1-oneirodegree || m1oneid
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.
| -6 || Minor 6-oneirodegree || m6oneid
*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.
| -7 || Diminished 3-oneirodegree || d3oneid
*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.
| -8 || Diminished 8-oneirodegree || d8oneid
*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:
| -9 || Diminished 5-oneirodegree || d5oneid
 
|-
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.
| -10 || Diminished 2-oneirodegree || d2oneid
 
|-
Octave-equivalent relational info:
| -11 || Diminished 7-oneirodegree || d7oneid
|-
| -12 || Diminished 4-oneirodegree || d4oneid
|-
|}


{{MOS scale properties|Scale Signature=5L 3s}}
*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.


== 5L 2s modes and modmos modes==
Rothenprop:
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=cscscsscscss}}
{{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 ==
*Single-period: Scales of this form are always proper because there is only one small step.
{{MOS mode degrees|Scale Signature=4L 4s}}
*Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLLss}}
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLsLs}}


==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 121: 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 208: Line 195:
|Small 1-diastep
|Small 1-diastep
|s
|s
| 0.0¢ to 171.4¢
|0.0¢ to 171.4¢
|s1ms
|s1ms
|-
|-
Line 216: Line 203:
|L1ms
|L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" | 2-diastep
|Small 2-diastep
|Small 2-diastep
|L + s
|L + s
Line 223: Line 210:
|-
|-
|Large 2-diastep
|Large 2-diastep
|2L
| 2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
|L2ms
|L2ms
Line 234: 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 245: Line 232:
|-
|-
|'''Large 4-diastep'''
|'''Large 4-diastep'''
| 3L + s
|3L + s
|685.7¢ to 720.0¢
|685.7¢ to 720.0¢
|L4ms
|L4ms
Line 251: Line 238:
| rowspan="2" |5-diastep
| rowspan="2" |5-diastep
|Small 5-diastep
|Small 5-diastep
| 3L + 2s
|3L + 2s
|720.0¢ to 857.1¢
|720.0¢ to 857.1¢
|s5ms
|s5ms
Line 264: 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¢
Line 274: Line 261:
|Perfect 7-diastep
|Perfect 7-diastep
|5L + 2s
|5L + 2s
|1200.0¢
| 1200.0¢
|P7ms
|P7ms
|}
|}
Line 289: Line 276:
!Names
!Names
!Bri.
!Bri.
!Rot.
! Rot.
!0
!0
!1
!1
Line 306: 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 320: Line 307:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 4|2</nowiki>
|<nowiki>5L 2s 4|2</nowiki>
Line 334: Line 321:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 353: Line 340:
|Lg.
|Lg.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 362: Line 349:
|Perf.
|Perf.
|Lg.
|Lg.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
|Sm.
|Sm.
|Sm.
|Sm.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
Line 376: Line 363:
|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 389: Line 376:
|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Perf.
|Perf.
Line 404: Line 391:
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="4" |Individual steps
! colspan="4" |Individual steps
! rowspan="2" | Notes
! rowspan="2" |Notes
|-
|-
!Start
!Start
!Large step
!Large step
!Small step
!Small step
! End
!End
|-
|-
|Small vis
|Small vis
Line 477: 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 622: 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 642: Line 629:
|+3L 4s step sizes
|+3L 4s step sizes
! rowspan="2" |Interval
! rowspan="2" |Interval
! colspan="2" |Basic 3L 4s
! colspan="2" | Basic 3L 4s
(10edo, L:s = 2:1)
(10edo, L:s = 2:1)
! colspan="2" |Hard 3L 4s
! colspan="2" |Hard 3L 4s
Line 658: Line 645:
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 667: Line 654:
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
| 92.3¢
|92.3¢
|2
|2
| 141.2¢
|141.2¢
|
|
|-
|-
Line 680: Line 667:
|4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 711: 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===
Line 769: 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 802: Line 746:
|'''Perfect'''
|'''Perfect'''
|-
|-
| -1
| -1
|'''Small'''
|'''Small'''
|Perfect minus 1 chroma
|Perfect minus 1 chroma
Line 824: 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.


Examples of encodings for 5L 2s
Examples of encodings for 5L 2s
Line 842: 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 877: Line 821:
|3
|3
| -1
| -1
|Perfect 3-diastep
| Perfect 3-diastep
|Bb
|Bb
|-
|-
Line 887: Line 831:
|-
|-
|2L + 2s
|2L + 2s
| 4
|4
| -1
| -1
|Diminished 4-diastep
|Diminished 4-diastep
Line 898: Line 842:
|C
|C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
Line 918: Line 862:
|5L + s
|5L + s
|6
|6
| 0
|0
|Major 6-diastep
| Major 6-diastep
|E
|E
|-
|-
Line 944: Line 888:
!4
!4
!5
!5
!6
! 6
!7
!7
|-
|-
Line 953: Line 897:
|LLLsLLs
|LLLsLLs
|0
|0
| 0
|0
| 0
|0
|0
|0
|0
|0
Line 967: Line 911:
|LLsLLLs
|LLsLLLs
|0
|0
| 0
|0
| 0
|0
| -1
| -1
|0
|0
Line 981: Line 925:
|LLsLLsL
|LLsLLsL
|0
|0
| 0
|0
| 1
|1
| -1
| -1
|0
|0
Line 993: Line 937:
|4
|4
|6
|6
| LsLLLsL
|LsLLLsL
|0
|0
|0
|0
Line 1,012: Line 956:
| -1
| -1
| -1
| -1
| 0
|0
| -1
| -1
| -1
| -1
Line 1,018: Line 962:
|-
|-
|<nowiki>5L 2s 1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
| Phrygian
|Phrygian
| 6
|6
|7
|7
|sLLLsLL
|sLLLsLL
Line 1,033: 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"