User:Ganaram inukshuk/Sandbox: Difference between revisions
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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.) | ||
== | <pre>{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}</pre> | ||
produces | |||
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 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}} | |||
''' | |||
''' | |||
''' | |||
== 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 == | == 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 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 306: | Line 195: | ||
|Small 1-diastep | |Small 1-diastep | ||
|s | |s | ||
| 0.0¢ to 171.4¢ | |0.0¢ to 171.4¢ | ||
|s1ms | |s1ms | ||
|- | |- | ||
| Line 314: | Line 203: | ||
|L1ms | |L1ms | ||
|- | |- | ||
| rowspan="2" |2-diastep | | rowspan="2" | 2-diastep | ||
|Small 2-diastep | |Small 2-diastep | ||
|L + s | |L + s | ||
| Line 321: | Line 210: | ||
|- | |- | ||
|Large 2-diastep | |Large 2-diastep | ||
|2L | | 2L | ||
|342.9¢ to 480.0¢ | |342.9¢ to 480.0¢ | ||
|L2ms | |L2ms | ||
| Line 332: | 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 362: | Line 251: | ||
|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 261: | ||
|Perfect 7-diastep | |Perfect 7-diastep | ||
|5L + 2s | |5L + 2s | ||
|1200.0¢ | | 1200.0¢ | ||
|P7ms | |P7ms | ||
|} | |} | ||
| Line 389: | Line 278: | ||
! Rot. | ! Rot. | ||
!0 | !0 | ||
! 1 | !1 | ||
!2 | !2 | ||
!3 | !3 | ||
| Line 404: | Line 293: | ||
|Perf. | |Perf. | ||
|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 307: | ||
|Perf. | |Perf. | ||
|Lg. | |Lg. | ||
|Lg. | | Lg. | ||
|Sm. | |Sm. | ||
|Lg. | |Lg. | ||
| Line 432: | Line 321: | ||
|Perf. | |Perf. | ||
|Lg. | |Lg. | ||
|Lg. | | Lg. | ||
|Sm. | |Sm. | ||
|Lg. | |Lg. | ||
| Line 450: | Line 339: | ||
|Lg. | |Lg. | ||
|Lg. | |Lg. | ||
| Sm. | |Sm. | ||
|Perf. | | Perf. | ||
|- | |- | ||
|<nowiki>5L 2s 2|4</nowiki> | |<nowiki>5L 2s 2|4</nowiki> | ||
| Line 460: | Line 349: | ||
|Perf. | |Perf. | ||
|Lg. | |Lg. | ||
|Sm. | | Sm. | ||
|Sm. | |Sm. | ||
|Lg. | |Lg. | ||
| Line 474: | Line 363: | ||
|Perf. | |Perf. | ||
|Sm. | |Sm. | ||
|Sm. | | Sm. | ||
|Sm. | |Sm. | ||
|Lg. | |Lg. | ||
| Line 487: | Line 376: | ||
|sLLsLLL | |sLLsLLL | ||
|Perf. | |Perf. | ||
| Sm. | |||
|Sm. | |Sm. | ||
| Sm. | |||
|Sm. | |||
|Sm. | |Sm. | ||
|Sm. | |Sm. | ||
| Line 499: | Line 388: | ||
{| 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 394: | ||
|- | |- | ||
!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 461: | ||
|} | |} | ||
{| 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 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 756: | Line 645: | ||
|- | |- | ||
|Large step | |Large step | ||
|2 | | 2 | ||
|240¢ | | 240¢ | ||
|3 | |3 | ||
|276.9¢ | | 276.9¢ | ||
|3 | |3 | ||
|211.8¢ | |211.8¢ | ||
| Line 765: | Line 654: | ||
|- | |- | ||
|Small step | |Small step | ||
|1 | | 1 | ||
|120¢ | |120¢ | ||
|1 | |1 | ||
| Line 773: | Line 662: | ||
| | | | ||
|- | |- | ||
| Bright generator | |Bright generator | ||
|3 | |3 | ||
|360¢ | |360¢ | ||
|4 | |4 | ||
|369.2¢ | |369.2¢ | ||
|5 | | 5 | ||
|355.6¢ | |355.6¢ | ||
| | | | ||
| Line 803: | 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 | ||
|- | |- | ||
| (x+y)L (2x+y)s | |(x+y)L (2x+y)s | ||
|} | |} | ||
== 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 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 | ||
!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 768: | ||
|3× Diminished | |3× Diminished | ||
|2× Diminished | |2× Diminished | ||
|3× Diminished | | 3× Diminished | ||
|} | |} | ||
Rationale: | Rationale: | ||
| Line 887: | 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 898: | 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 | ||
| Major 1-diastep | |Major 1-diastep | ||
|G | |G | ||
|- | |- | ||
|L + s | |L + s | ||
|2 | |2 | ||
| | | -1 | ||
| Minor 2-diastep | |Minor 2-diastep | ||
|Ab | |Ab | ||
|- | |- | ||
| Line 933: | 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 954: | Line 842: | ||
|C | |C | ||
|- | |- | ||
|3L + 2s | | 3L + 2s | ||
|5 | |5 | ||
| -1 | | -1 | ||
| Line 969: | Line 857: | ||
|6 | |6 | ||
| -1 | | -1 | ||
| Minor 6-diastep | |Minor 6-diastep | ||
|Eb | |Eb | ||
|- | |- | ||
| Line 975: | Line 863: | ||
|6 | |6 | ||
|0 | |0 | ||
|Major 6-diastep | | Major 6-diastep | ||
|E | |E | ||
|- | |- | ||
| Line 1,000: | Line 888: | ||
!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 901: | ||
|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 925: | ||
|LLsLLsL | |LLsLLsL | ||
|0 | |0 | ||
| 0 | |0 | ||
|1 | |1 | ||
| -1 | | -1 | ||
| 0 | |0 | ||
|0 | |0 | ||
| -1 | | -1 | ||
| Line 1,054: | Line 942: | ||
| -1 | | -1 | ||
| -1 | | -1 | ||
| 0 | |0 | ||
|0 | |0 | ||
| -1 | | -1 | ||
| Line 1,069: | Line 957: | ||
| -1 | | -1 | ||
|0 | |0 | ||
| | | -1 | ||
| -1 | | -1 | ||
|0 | |0 | ||
| Line 1,089: | Line 977: | ||
|<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 | ||