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== MOS tunings==
== MOS tunings==
{| class="wikitable sortable right-all left-1 left-2 mw-collapsible"
{{{{#ifeq: 1 |1|subst:|}}#invoke: MOS_tunings| mos_tunings
|+ style="font-size: 105%; white-space: nowrap;" | Simple Tunings of 5L 3s
| Scale Signature=5L 3s
! rowspan="2" class="unsortable" | Scale degree
| MOS Prefix=
! rowspan="2" class="unsortable" | Abbrev.
| MOS Abbrev=
! colspan="2" | Basic (2:1)<br />[[13edo]]
| Collapsed=
! colspan="2" | Hard (3:1)<br />[[18edo]]
| Step Ratios=
! colspan="2" | Soft (3:2)<br />[[21edo]]
| JI Ratios=
! rowspan="2" class="unsortable" | Approx.<br />Ratios
}}
|-
! Steps
! Cents
! Steps
! Cents
! Steps
! Cents
|-
| Perfect 0-oneirodegree || P0oneid || 0\13 || 0.0 || 0\18 || 0.0 || 0\21 || 0.0|| style="text-align: left;" | [[1/1]]
|-
| Minor 1-oneirodegree || m1oneid || 1\13 || 92.3 || 1\18 || 66.7 || 2\21 || 114.3|| style="text-align: left;" | [[16/15]], [[19/18]], [[20/19]], [[25/24]]
|-
| Major 1-oneirodegree || M1oneid || 2\13 || 184.6 || 3\18 || 200.0 || 3\21 || 171.4|| style="text-align: left;" | [[9/8]], [[10/9]], [[11/10]]
|-
| Minor 2-oneirodegree || m2oneid || 3\13 || 276.9 || 4\18 || 266.7 || 5\21 || 285.7|| style="text-align: left;" | [[19/16]], [[22/19]], [[32/27]]
|-
| Major 2-oneirodegree || M2oneid || 4\13 || 369.2 || 6\18 || 400.0 || 6\21 || 342.9|| style="text-align: left;" | [[5/4]], [[11/9]], [[27/22]]
|-
| Diminished 3-oneirodegree || d3oneid || 4\13 || 369.2 || 5\18 || 333.3 || 7\21 || 400.0|| style="text-align: left;" | [[5/4]], [[11/9]], [[27/22]]
|-
| Perfect 3-oneirodegree || P3oneid || 5\13 || 461.5 || 7\18 || 466.7 || 8\21 || 457.1|| style="text-align: left;" | [[25/19]], [[33/25]]
|-
| Minor 4-oneirodegree || m4oneid || 6\13 || 553.8 || 8\18 || 533.3 || 10\21 || 571.4|| style="text-align: left;" | [[11/8]], [[15/11]], [[25/18]]
|-
| Major 4-oneirodegree || M4oneid || 7\13 || 646.2 || 10\18 || 666.7 || 11\21 || 628.6|| style="text-align: left;" | [[16/11]], [[22/15]], [[36/25]]
|-
| Perfect 5-oneirodegree || P5oneid || 8\13 || 738.5 || 11\18 || 733.3 || 13\21 || 742.9|| style="text-align: left;" | [[38/25]]
|-
| Augmented 5-oneirodegree || A5oneid || 9\13 || 830.8 || 13\18 || 866.7 || 14\21 || 800.0|| style="text-align: left;" | [[8/5]], [[18/11]]
|-
| Minor 6-oneirodegree || m6oneid || 9\13 || 830.8 || 12\18 || 800.0 || 15\21 || 857.1|| style="text-align: left;" | [[8/5]], [[18/11]]
|-
| Major 6-oneirodegree || M6oneid || 10\13 || 923.1 || 14\18 || 933.3 || 16\21 || 914.3|| style="text-align: left;" | [[19/11]], [[27/16]], [[32/19]]
|-
| Minor 7-oneirodegree || m7oneid || 11\13 || 1015.4 || 15\18 || 1000.0 || 18\21 || 1028.6|| style="text-align: left;" | [[9/5]], [[16/9]], [[20/11]]
|-
| Major 7-oneirodegree || M7oneid || 12\13 || 1107.7 || 17\18 || 1133.3 || 19\21 || 1085.7|| style="text-align: left;" | [[15/8]], [[19/10]], [[36/19]]
|-
| Perfect 8-oneirodegree || P8oneid || 13\13 || 1200.0 || 18\18 || 1200.0 || 21\21 || 1200.0|| style="text-align: left;" | [[2/1]]
|}
<span style="font-size: 0.75em;">Ratios shown are within the 2.3.5.11.19 subgroup. Not all notable ratios may be shown, and other interpretations are possible.</span>


=== 5L 3s only ===
===5L 3s only===
{{MOS tunings|Scale Signature=5L 3s}}
{{MOS tunings|Scale Signature=5L 3s}}


Line 85: Line 44:
{{MOS tunings|Scale Signature=5L 3s|Step Ratios=Hard-of-basic}}
{{MOS tunings|Scale Signature=5L 3s|Step Ratios=Hard-of-basic}}


=== 6-note mosses ===
===6-note mosses===


{{MOS tunings|Scale Signature=1L 5s}}
{{MOS tunings|Scale Signature=1L 5s}}
Line 97: Line 56:
{{MOS tunings|Scale Signature=5L 1s}}
{{MOS tunings|Scale Signature=5L 1s}}


=== 7-note mosses ===
===7-note mosses===


{{MOS tunings|Scale Signature=1L 6s}}
{{MOS tunings|Scale Signature=1L 6s}}
Line 111: Line 70:
{{MOS tunings|Scale Signature=6L 1s}}
{{MOS tunings|Scale Signature=6L 1s}}


=== 8-note mosses ===
===8-note mosses===


{{MOS tunings|Scale Signature=1L 7s}}
{{MOS tunings|Scale Signature=1L 7s}}
Line 127: Line 86:
{{MOS tunings|Scale Signature=7L 1s}}
{{MOS tunings|Scale Signature=7L 1s}}


=== 9-note mosses ===
===9-note mosses===


{{MOS tunings|Scale Signature=1L 8s}}
{{MOS tunings|Scale Signature=1L 8s}}
Line 145: Line 104:
{{MOS tunings|Scale Signature=8L 1s}}
{{MOS tunings|Scale Signature=8L 1s}}


=== 10-note mosses ===
=== 10-note mosses===


{{MOS tunings|Scale Signature=1L 9s}}
{{MOS tunings|Scale Signature=1L 9s}}
Line 165: Line 124:
{{MOS tunings|Scale Signature=9L 1s}}
{{MOS tunings|Scale Signature=9L 1s}}


=== Misc ===
===Misc ===


{{MOS tunings|Scale Signature=8L 3s <3/1>|Step Ratios=17/12; 10/7; 7/5|JI Ratios=Int Limit: 25; Tenney Height: 8}}
{{MOS tunings|Scale Signature=8L 3s <3/1>|Step Ratios=17/12; 10/7; 7/5|JI Ratios=Int Limit: 25; Tenney Height: 8}}
{{MOS tunings|Scale Signature=9L 4s <7/2>|Step Ratios=Central Spectrum|JI Ratios=NONE}}
{{MOS tunings|Scale Signature=9L 4s <7/2>|Step Ratios=Central Spectrum|JI Ratios=NONE}}


==Name==
==Name==
Line 195: Line 155:
{{Template:TAMNAMS name|6L 1s}}
{{Template:TAMNAMS name|6L 1s}}


=== 8-note mosses===
===8-note mosses===
{{Template:TAMNAMS name|1L 7s}}
{{Template:TAMNAMS name|1L 7s}}


Line 227: Line 187:
{{Template:TAMNAMS name|8L 1s}}
{{Template:TAMNAMS name|8L 1s}}


=== 10-note mosses===
===10-note mosses===
{{Template:TAMNAMS name|1L 9s}}
{{Template:TAMNAMS name|1L 9s}}


Line 247: Line 207:


==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 360: Line 320:
</div>
</div>


===MOS intervals (using large/small instead of MmAPd) ===
===MOS intervals (using large/small instead of MmAPd)===
{| class="wikitable"
{| class="wikitable"
|+Intervals of 5L 2s
|+Intervals of 5L 2s
!Interval
!Interval
!Size(s)
!Size(s)
! Steps
!Steps
!Range in cents
!Range in cents
!Abbrev.
!Abbrev.
Line 376: Line 336:
|-
|-
| rowspan="2" |1-diastep
| rowspan="2" |1-diastep
| Small 1-diastep
|Small 1-diastep
|s
|s
|0.0¢ to 171.4¢
| 0.0¢ to 171.4¢
| s1ms
|s1ms
|-
|-
| Large 1-diastep
|Large 1-diastep
|L
|L
|171.4¢ to 240.0¢
| 171.4¢ to 240.0¢
|L1ms
| L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" |2-diastep
Line 390: Line 350:
|L + s
|L + s
|240.0¢ to 342.9¢
|240.0¢ to 342.9¢
|s2ms
| s2ms
|-
|-
|Large 2-diastep
|Large 2-diastep
Line 410: Line 370:
| 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 416: Line 376:
|'''Large 4-diastep'''
|'''Large 4-diastep'''
|3L + s
|3L + s
|685.7¢ to 720.0¢
| 685.7¢ to 720.0¢
| L4ms
|L4ms
|-
|-
| 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¢
Line 428: Line 388:
|4L + s
|4L + s
|857.1¢ to 960.0¢
|857.1¢ to 960.0¢
| L5ms
|L5ms
|-
|-
| rowspan="2" |6-diastep
| rowspan="2" |6-diastep
|Small 6-diastep
|Small 6-diastep
|4L + 2s
|4L + 2s
|960.0¢ to 1028.6¢
| 960.0¢ to 1028.6¢
|s6ms
|s6ms
|-
|-
Line 439: Line 399:
|5L + s
|5L + s
|1028.6¢ to 1200.0¢
|1028.6¢ to 1200.0¢
| L6ms
|L6ms
|-
|-
|'''7-diastep (octave)'''
|'''7-diastep (octave)'''
Line 445: Line 405:
|5L + 2s
|5L + 2s
|1200.0¢
|1200.0¢
|P7ms
| P7ms
|}
|}


===MOS mode degrees (using large/small instead of MmAPd) ===
===MOS mode degrees (using large/small instead of MmAPd)===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+Scale degree qualities of 5L 2s modes
|+Scale degree qualities of 5L 2s modes
! colspan="2" |Mode names
! colspan="2" |Mode names
! colspan="2" |Ordering
! colspan="2" |Ordering
! rowspan="2" | Step pattern
! rowspan="2" |Step pattern
! colspan="8" |Scale degree
! colspan="8" |Scale degree
|-
|-
!Default
!Default
! Names
!Names
!Bri.
!Bri.
!Rot.
!Rot.
!0
! 0
!1
!1
!2
!2
!3
! 3
!4
!4
!5
! 5
!6
! 6
!7
!7
|-
|-
Line 472: Line 432:
|Lydian
|Lydian
|1
|1
| 1
|1
|LLLsLLs
|LLLsLLs
|Perf.
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
Line 484: Line 444:
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
| Ionian (major)
|Ionian (major)
|2
|2
|5
|5
Line 492: Line 452:
|Lg.
|Lg.
|Sm.
|Sm.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 4|2</nowiki>
|<nowiki>5L 2s 4|2</nowiki>
| Mixolydian
|Mixolydian
| 3
| 3
|2
|2
|LLsLLsL
|LLsLLsL
|Perf.
|Perf.
|Lg.
| Lg.
|Lg.
|Lg.
|Sm.
|Sm.
Line 509: Line 469:
|Lg.
|Lg.
|Sm.
|Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 3|3</nowiki>
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|Dorian
|4
|4
|6
| 6
|LsLLLsL
| LsLLLsL
|Perf.
| Perf.
|Lg.
| Lg.
|Sm.
|Sm.
|Sm.
|Sm.
|Lg.
|Lg.
|Lg.
|Lg.
|Sm.
| Sm.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
| Aeolian (minor)
|5
|5
|3
| 3
|LsLLsLL
|LsLLsLL
| Perf.
|Perf.
|Lg.
|Lg.
|Sm.
|Sm.
Line 536: Line 496:
|Lg.
|Lg.
|Sm.
|Sm.
|Sm.
| Sm.
|Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
| Phrygian
|6
| 6
|7
|7
|sLLLsLL
| sLLLsLL
|Perf.
|Perf.
|Sm.
|Sm.
Line 549: Line 509:
|Sm.
|Sm.
|Lg.
|Lg.
| Sm.
|Sm.
|Sm.
|Sm.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
Line 573: Line 533:
! rowspan="2" |Type
! rowspan="2" |Type
! 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
|<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 602: Line 562:
│
│
┘</pre>
┘</pre>
| Not enough room for note names.
|Not enough room for note names.
|-
|-
|Large vis
|Large vis
Line 645: Line 605:
{| 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
Line 792: Line 752:


</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 811: Line 771:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+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 829: Line 789:
|Large step
|Large step
|2
|2
| 240¢
|240¢
|3
|3
|276.9¢
|276.9¢
Line 839: Line 799:
|1
|1
|120¢
|120¢
| 1
|1
| 92.3¢
|92.3¢
|2
|2
|141.2¢
|141.2¢
|
|
|-
|-
| Bright generator
|Bright generator
|3
|3
|360¢
|360¢
|4
|4
| 369.2¢
|369.2¢
|5
|5
|355.6¢
|355.6¢
Line 859: Line 819:
*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
!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
| rowspan="2" |xL (x+y)s
| rowspan="2" |xL (x+y)s
Line 925: Line 885:
</div>
</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 946: Line 906:
!Bright gen
!Bright gen
!Dark gen
!Dark gen
!Period intervals
! Period intervals
|-
|-
|2
|2
|Large plus 2 chromas
|Large plus 2 chromas
|Perfect plus 2 chromas
|Perfect plus 2 chromas
| 2× Augmented
|2× Augmented
|2× Augmented
|3× Augmented
|2× Augmented
|2× Augmented
|3× Augmented
| 2× Augmented
|-
|-
|1
|1
Line 974: Line 934:
| -1
| -1
|'''Small'''
|'''Small'''
| Perfect minus 1 chroma
|Perfect minus 1 chroma
|'''Minor'''
|'''Minor'''
|'''Diminished'''
|'''Diminished'''
Line 1,001: Line 961:
**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 1,008: Line 968:
! rowspan="2" |Interval in mossteps
! rowspan="2" |Interval in mossteps
! colspan="2" |Encoding
! colspan="2" |Encoding
! rowspan="2" | Decoding
! rowspan="2" |Decoding
! rowspan="2" |Standard notation in the key of F
! rowspan="2" |Standard notation in the key of F
|-
|-
!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 1,050: Line 1,010:
|Bb
|Bb
|-
|-
|3L
| 3L
|3
| 3
|0
|0
|Augmented 3-diastep
|Augmented 3-diastep
Line 1,059: Line 1,019:
|4
|4
| -1
| -1
|Diminished 4-diastep
| Diminished 4-diastep
|Cb
|Cb
|-
|-
|3L + s
|3L + s
| 4
|4
|0
| 0
|Perfect 4-diastep
|Perfect 4-diastep
|C
| C
|-
|-
|3L + 2s
| 3L + 2s
|5
|5
| -1
| -1
|Minor 5-diastep
|Minor 5-diastep
|Db
|Db
|-
|-
|4L + s
| 4L + s
|5
|5
|0
|0
Line 1,083: Line 1,043:
|6
|6
| -1
| -1
|Minor 6-diastep
| Minor 6-diastep
|Eb
|Eb
|-
|-
Line 1,093: Line 1,053:
|-
|-
|5L + 2s
|5L + 2s
|7
| 7
|0
|0
|Perfect 7-diastep
|Perfect 7-diastep
Line 1,101: Line 1,061:
! colspan="2" |Mode names
! colspan="2" |Mode names
! colspan="2" |Ordering
! colspan="2" |Ordering
! rowspan="2" |Step pattern
! rowspan="2" | Step pattern
! colspan="8" |Scale degree (encoded)
! colspan="8" |Scale degree (encoded)
|-
|-
!Default
!Default
!Names
! Names
!Bri.
!Bri.
!Rot.
!Rot.
Line 1,120: Line 1,080:
|Lydian
|Lydian
|1
|1
| 1
|1
|LLLsLLs
| LLLsLLs
|0
|0
|0
|0
|0
Line 1,130: Line 1,089:
|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
| -1
|0
|  -1
|0
|0
|0
|0
Line 1,154: Line 1,114:
|1
|1
| -1
| -1
| 0
|0
|0
|0
| -1
| -1
|0
| 0
|-
|-
|<nowiki>5L 2s 3|3</nowiki>
|<nowiki>5L 2s 3|3</nowiki>
Line 1,165: Line 1,125:
|LsLLLsL
|LsLLLsL
|0
|0
|0
| 0
| -1
| -1
| -1
| -1
Line 1,171: Line 1,131:
|0
|0
| -1
| -1
|0
| 0
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 1,178: Line 1,138:
|3
|3
|LsLLsLL
|LsLLsLL
|0
| 0
|0
|0
| -1
| -1
| -1
| -1
|0
| 0
| -1
| -1
| -1
| -1
|0
|0
Line 1,197: Line 1,157:
| -1
| -1
|0
|0
| -1
| -1
| -1
| -1
|0
|0
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|sLLsLLL
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