Xenharmonic Wiki

User:Ganaram inukshuk/Sandbox: Difference between revisions

← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
mNo edit summary
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
No edit summary
 
(101 intermediate revisions by the same user not shown)
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.)


== Name ==
<pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre>


=== 6-note mosses ===
produces
{{User:Ganaram inukshuk/Template:TAMNAMS name|1L 5s}}


{{User:Ganaram inukshuk/Template:TAMNAMS name|2L 4s}}
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


{{User:Ganaram inukshuk/Template:TAMNAMS name|3L 3s}}
== 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}}


{{User:Ganaram inukshuk/Template:TAMNAMS name|4L 2s}}
== MOS tuning spectrum (AKA, scale tree) ==


{{User:Ganaram inukshuk/Template:TAMNAMS name|5L 1s}}
{{MOS tuning spectrum
| Scale Signature = 1L 1s
| Int Limit = 13
}}


=== 7-note mosses ===
{{MOS tuning spectrum
{{User:Ganaram inukshuk/Template:TAMNAMS name|1L 6s}}
| 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]]↓
}}


{{User:Ganaram inukshuk/Template:TAMNAMS name|2L 5s}}
{{MOS tuning spectrum
| Depth = 3
| Scale Signature= 3L 4s<3/2>
}}


{{User:Ganaram inukshuk/Template:TAMNAMS name|3L 4s}}
== 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:


{{User:Ganaram inukshuk/Template:TAMNAMS name|4L 3s}}
*Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.


{{User:Ganaram inukshuk/Template:TAMNAMS name|5L 2s}}
Octave-equivalent relational info:


{{User:Ganaram inukshuk/Template:TAMNAMS name|6L 1s}}
*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.


=== 8-note mosses ===
Rothenprop:
{{User:Ganaram inukshuk/Template:TAMNAMS name|1L 7s}}


{{User:Ganaram inukshuk/Template:TAMNAMS name|2L 6s}}
*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.


{{User:Ganaram inukshuk/Template:TAMNAMS name|3L 5s}}
==Sandbox for proposed templates==
 
===Cent ruler ===
{{User:Ganaram inukshuk/Template:TAMNAMS name|4L 4s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|5L 3s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|6L 2s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|7L 1s}}
 
=== 9-note mosses ===
{{User:Ganaram inukshuk/Template:TAMNAMS name|1L 8s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|2L 7s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|3L 6s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|4L 5s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|5L 4s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|6L 3s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|7L 2s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|8L 1s}}
 
=== 10-note mosses ===
{{User:Ganaram inukshuk/Template:TAMNAMS name|1L 9s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|2L 8s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|3L 7s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|4L 6s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|5L 5s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|6L 4s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|7L 3s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|8L 2s}}
 
{{User:Ganaram inukshuk/Template:TAMNAMS name|9L 1s}}
 
{{MOS scale properties|Scale Signature=5L 3s}}
 
==5L 2s modes and modmos modes==
{{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==
{{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}}
 
== Sandbox for proposed templates==
===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 243: Line 212:
| 2L
| 2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
| L2ms
|L2ms
|-
|-
| rowspan="2" |'''3-diastep'''
| rowspan="2" |'''3-diastep'''
Line 252: 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 268: Line 237:
|-
|-
| 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
|-
|-
|Large 5-diastep
|Large 5-diastep
Line 282: 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
Line 292: Line 261:
|Perfect 7-diastep
|Perfect 7-diastep
|5L + 2s
|5L + 2s
|1200.0¢
| 1200.0¢
|P7ms
|P7ms
|}
|}
Line 305: Line 274:
|-
|-
!Default
!Default
! Names
!Names
!Bri.
!Bri.
! Rot.
! Rot.
Line 329: Line 298:
|Lg.
|Lg.
|Lg.
|Lg.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
Line 338: Line 307:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 352: Line 321:
|Perf.
|Perf.
|Lg.
|Lg.
|Lg.
| Lg.
|Sm.
|Sm.
|Lg.
|Lg.
Line 371: Line 340:
|Lg.
|Lg.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 380: Line 349:
|Perf.
|Perf.
|Lg.
|Lg.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 394: Line 363:
|Perf.
|Perf.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Lg.
|Lg.
Line 407: Line 376:
|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
|Sm.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
Line 495: 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 640: 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 660: 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 668: Line 637:
! rowspan="2" |Approx. JI ratios
! rowspan="2" |Approx. JI ratios
|-
|-
! Steps
!Steps
!Cents
!Cents
!Steps
!Steps
!Cents
!Cents
!Steps
!Steps
! Cents
!Cents
|-
|-
|Large step
|Large step
|2
| 2
|240¢
| 240¢
|3
|3
|276.9¢
| 276.9¢
|3
|3
|211.8¢
|211.8¢
Line 685: Line 654:
|-
|-
|Small step
|Small step
|1
| 1
|120¢
|120¢
|1
|1
|92.3¢
|92.3¢
|2
|2
| 141.2¢
|141.2¢
|
|
|-
|-
Line 698: Line 667:
|4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 712: 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
Line 723: Line 692:
|(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
|-
|-
Line 729: 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 787: 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 797: Line 723:
|-
|-
|2
|2
| Large plus 2 chromas
|Large plus 2 chromas
|Perfect plus 2 chromas
|Perfect plus 2 chromas
|2× Augmented
|2× Augmented
Line 820: Line 746:
|'''Perfect'''
|'''Perfect'''
|-
|-
| -1
| -1
|'''Small'''
|'''Small'''
|Perfect minus 1 chroma
|Perfect minus 1 chroma
Line 837: Line 763:
|-
|-
| -3
| -3
| Small minus 2 chromas
|Small minus 2 chromas
|Perfect minus 3 chromas
|Perfect minus 3 chromas
|2× Diminished
|2× Diminished
|3× Diminished
|3× Diminished
|2× Diminished
|2× Diminished
|3× Diminished
| 3× Diminished
|}
|}
Rationale:
Rationale:
Line 849: 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 860: 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 895: 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 916: Line 842:
|C
|C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
Line 937: Line 863:
|6
|6
|0
|0
|Major 6-diastep
| Major 6-diastep
|E
|E
|-
|-
Line 962: Line 888:
!4
!4
!5
!5
!6
! 6
!7
!7
|-
|-
Line 1,051: 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"