User:Ganaram inukshuk/Sandbox: Difference between revisions

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Ganaram inukshuk (talk | contribs)
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m More color testing
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Experimented with a mos mode table with multiple modmos' rotations
Line 5: Line 5:


== Template test area==
== Template test area==
Cell color code test
 
=== Cell color code test===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 12: Line 13:
|-
|-
|Augmented size
|Augmented size
| style="background:#ededb0" | Aug.
| style="background:#ededb0" |Aug.
|-
|-
|Large size
|Large size
| style="background:#ffffe0" | Maj.
| style="background:#ffffe0" |Maj.
|-
|-
|Small size
|Small size
| style="background:#eaeaff" | Min.
| style="background:#eaeaff" |Min.
|-
|-
|Diminished size
|Diminished size
| style="background:#afafe0" | Dim.
| style="background:#afafe0" |Dim.
|}
|}


Line 27: Line 28:
{{MOS mode degrees|Scale Signature=5L 2s}}
{{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=LsLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs|Mode Names=Ionian b6 (Harmonic major); Dorian b5 (Dorian diminished); Phrygian b4; Lydian b3 (Lydian minor); Mixolydian b2; Lydian #2 #5; Locrian bb7}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs|Mode Names=Aeolian ♮6 ♮7 (Melodic minor); Dorian b2; Lydian #5 (Lydian augmented); Lydian b7 (Lydian dominant); Mixolydian b6; Locrian ♮2 (Half-diminished); Locrian bb4 (Altered dominant, super-locrian)}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sLLLLLs|Mode Names=Ionian b2 b3 (Neapolitan major); Lydian #5 #6; Lydian #5 b7; Lydian b6 b7; Locrian ♮2 ♮3 (Major locrian); Locrian ♮2 b4; Locrian bb3 b4}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs|Mode Names=Ionian b6 (Harmonic major); Dorian b5 (Dorian diminished); Phrygian b4; Lydian b3 (Lydian minor); Mixolydian b2; Lydian #2 #5; Locrian bb7}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs|Mode Names=Aeolian ♮6 ♮7 (Melodic minor); Dorian b2; Lydian #5 (Lydian augmented); Lydian b7 (Lydian dominant); Mixolydian b6; Locrian ♮2 (Half-diminished); Locrian bb4 (Altered dominant, super-locrian)}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sLLLLLs|Mode Names=Ionian b2 b3 (Neapolitan major); Lydian #5 #6; Lydian #5 b7; Lydian b6 b7; Locrian ♮2 ♮3 (Major locrian); Locrian ♮2 b4; Locrian bb3 b4}}


{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}
Line 33: Line 36:
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}


=== MOS mode degrees (other mosses) ===
===Mos mode degrees with rotations of multiple modmosses===
{{MOS mode degrees|Scale Signature=4L 4s}}
{| class="wikitable sortable"
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=AdAdAdAdA}}
! rowspan="2" |UDP
{{MOS mode degrees|Scale Signature=6L 2s}}
! rowspan="2" |Step pattern
! rowspan="2" |Mode names
! colspan="8" | Scale degree (diadegree)
|-
!0
!1
!2
!3
!4
!5
! 6
!7
|-
|<nowiki>6|0</nowiki>
|LLLsLLs
|Lydian
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" | Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>5|1</nowiki>
|LLsLLLs
|Ionian (major)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>4|2</nowiki>
|LLsLLsL
|Mixolydian
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>3|3</nowiki>
|LsLLLsL
|Dorian
| Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" | Min.
|Perf.
|-
|<nowiki>2|4</nowiki>
| LsLLsLL
|Aeolian (minor)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
| Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>1|5</nowiki>
|sLLLsLL
| Phrygian
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
| Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>0|6</nowiki>
|sLLsLLL
|Locrian
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" | Min.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| Perf
|-
|<nowiki>2|4 M6md</nowiki>
| LsLLsAs
|Harmonic minor
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|<nowiki>0|6 M5md</nowiki>
|sLLsAsL
| Locrian #6
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
| style="background:#afafe0" | Dim.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>5|1 A4md</nowiki>
|LLsAsLs
|Ionian augmented
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
| style="background:#ededb0" | Aug.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>3|3 A3md</nowiki>
| LsAsLsL
|Dorian #4
| Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
| style="background:#ededb0" | Aug.
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#eaeaff" | Min.
|Perf.
|-
|<nowiki>1|5 M2md</nowiki>
|sAsLsLL
|Phrygian dominant
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>6|0 A1md</nowiki>
|AsLsLLs
| Lydian #2
|Perf.
| style="background:#ededb0" | Aug.
| style="background:#ffffe0" | Maj.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>0|6 d3md d6md</nowiki>
|sLsLLsA
| Locrian b4 bb7
| Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| Perf.
|-
|<nowiki>5|1 m5md</nowiki>
|LLsLsAs
|Ionian b6 (Harmonic major)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
| Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>3|3 d4md</nowiki>
|LsLsAsL
|Dorian b5 (Dorian diminished)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
| Perf.
|-
|<nowiki>1|5 d3md</nowiki>
| sLsAsLL
|Phrygian b4
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" | Min.
|Perf.
|-
|<nowiki>6|0 m2md</nowiki>
|LsAsLLs
|Lydian b3 (Lydian minor)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|<nowiki>4|2 m1md</nowiki>
|sAsLLsL
|Mixolydian b2
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>6|0 A1md A4md</nowiki>
|AsLLsLs
|Lydian #2 #5
| Perf.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|<nowiki>0|6 d6md</nowiki>
| sLLsLsA
|Locrian bb7
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
|Perf.
|-
|<nowiki>5|1 m2md</nowiki>
| LsLLLLs
|Aeolian ♮6 ♮7 (Melodic minor)
| Perf.
| style="background:#ffffe0" | Maj.
| style="background:#eaeaff" |Min.
| Perf.
| Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>3|3 m1md</nowiki>
| sLLLLsL
|Dorian b2
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" | Min.
| Perf.
| Perf.
| style="background:#ffffe0" | Maj.
| style="background:#eaeaff" |Min.
| Perf.
|-
|<nowiki>6|0 A4md</nowiki>
| LLLLsLs
|Lydian #5 (Lydian augmented)
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" | Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>6|0 m6md</nowiki>
|LLLsLsL
|Lydian b7 (Lydian dominant)
|Perf.
| style="background:#ffffe0" | Maj.
| style="background:#ffffe0" | Maj.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>4|2 m5md</nowiki>
|LLsLsLL
|Mixolydian b6
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
|Perf.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>2|4 d4md</nowiki>
|LsLsLLL
|Locrian ♮2 (Half-diminished)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>0|6 d3md</nowiki>
|sLsLLLL
|Locrian bb4 (Altered dominant, super-locrian)
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" | Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>5|1 m1md m2md</nowiki>
|sLLLLLs
|Ionian b2 b3 (Neapolitan major)
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
|-
|<nowiki>6|0 A4md A5md</nowiki>
|LLLLLss
|Lydian #5 #6
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
|Perf.
|-
|<nowiki>6|0 A4md m6md</nowiki>
|LLLLssL
|Lydian #5 b7
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
| style="background:#ededb0" |Aug.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>6|0 m5md m6md</nowiki>
|LLLssLL
|Lydian b6 b7
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" |Maj.
| style="background:#ededb0" |Aug.
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
| Perf.
|-
|<nowiki>4|2 d4md m5md</nowiki>
|LLssLLL
|Locrian ♮2 ♮3 (Major locrian)
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#ffffe0" | Maj.
|Perf.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>2|4 d3md d4md</nowiki>
|LssLLLL
|Locrian ♮2 b4
|Perf.
| style="background:#ffffe0" |Maj.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|-
|<nowiki>0|6 d2md d3md</nowiki>
|ssLLLLL
|Locrian bb3 b4
|Perf.
| style="background:#eaeaff" |Min.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#afafe0" |Dim.
| style="background:#eaeaff" |Min.
| style="background:#eaeaff" |Min.
|Perf.
|}


===MOS step sizes ===
 
===MOS step sizes===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+3L 4s step sizes
|+3L 4s step sizes
Line 46: Line 482:
! colspan="2" |Hard 3L 4s
! colspan="2" |Hard 3L 4s
(13edo, L:s = 3:1)
(13edo, L:s = 3:1)
! colspan="2" | Soft 3L 4s
! colspan="2" |Soft 3L 4s
(17edo, L:s = 3:2)
(17edo, L:s = 3:2)
! rowspan="2" |Approx. JI ratios
! rowspan="2" |Approx. JI ratios
|-
|-
!Steps
!Steps
! Cents
!Cents
!Steps
!Steps
!Cents
!Cents
Line 60: Line 496:
|2
|2
|240¢
|240¢
| 3
|3
|276.9¢
|276.9¢
| 3
|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
| 92.3¢
|92.3¢
|2
|2
|141.2¢
|141.2¢
Line 78: Line 514:
|3
|3
|360¢
|360¢
| 4
|4
|369.2¢
|369.2¢
|5
| 5
|355.6¢
|355.6¢
|
|
Line 100: Line 536:
'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''equave-equivalent'' moment-of-symmetry scale, containing ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.
'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''equave-equivalent'' moment-of-symmetry scale, containing ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.


====Base wording (for mos descendants)====
==== Base wording (for mos descendants)====
'''''x''L ''y''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''z''L ''w''s<''p/q''>''''','' expanded to ''x'' large steps(s) and ''y'' small step(s) and repeating every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.  
'''''x''L ''y''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''z''L ''w''s<''p/q''>''''','' expanded to ''x'' large steps(s) and ''y'' small step(s) and repeating every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.  


'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''nz''L ''nw''s''<nowiki><p/q></nowiki>''''', expanded to ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.
'''''nx''L ''ny''s<''p/q''>''', also called '''mosname''', is a(n) ''extension'' scale of the ''equave-equivalent'' moment-of-symmetry scale '''''nz''L ''nw''s''<nowiki><p/q></nowiki>''''', expanded to ''nx'' large steps(s) and ''ny'' small step(s), with a period of ''x'' large step(s) and ''y'' small steps(s) that repeats every ''equave-fraction'', or ''n times'' every ''equave''. Scales of this form have a generalized step pattern of ''step-pattern'' or some rotation thereof. Equal divisions of the ''equave'' that support this scale include ''basic-ed'', ''hard-ed'', and ''soft-ed''. Generating intervals for this scale range from ''g1''¢ to ''g2''¢, or from ''d1''¢ or ''d2''¢.


====Examples====
====Examples ====
'''5L 7s''', also called '''(hard) diachromatic''' or '''p-chromatic''', is a chromatic scale of the moment-of-symmetry scale 5L 2s, expanded to 5 large steps and 7 small steps, repeating every octave. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, with a generator that ranges from 700¢ to 720¢, or from 480¢ to 500¢. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo.  
'''5L 7s''', also called '''(hard) diachromatic''' or '''p-chromatic''', is a chromatic scale of the moment-of-symmetry scale 5L 2s, expanded to 5 large steps and 7 small steps, repeating every octave. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, with a generator that ranges from 700¢ to 720¢, or from 480¢ to 500¢. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo.  
===Mbox template test ===
===Mbox template test===
These would be their own templates.
These would be their own templates.


Line 119: Line 555:
{{Mbox|type=notice|text=This article is '''being created or in the process of being rewritten''', and is '''not yet ready for use'''. You are welcome to help with editing this page.}}
{{Mbox|type=notice|text=This article is '''being created or in the process of being rewritten''', and is '''not yet ready for use'''. You are welcome to help with editing this page.}}


==Math symbols test ==
==Math symbols test==


=== Isolated symbols===
===Isolated symbols===
<math>T := [ t_1, t_2, ..., t_m ]</math>
<math>T := [ t_1, t_2, ..., t_m ]</math>
<math>S := [ s_1, s_2, ..., s_m ]</math>
<math>S := [ s_1, s_2, ..., s_m ]</math>
<math>P := [ p_1, p_2, ..., p_n ]</math>
<math>P := [ p_1, p_2, ..., p_n ]</math>


=== Sample text===
===Sample text===
Pulled from [[muddle]] page.
Pulled from [[muddle]] page.


Line 133: Line 569:
The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.
The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.


==Interval and degree tables==
==Interval and degree tables ==
The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.
The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.
{| class="wikitable sortable" style="text-align: left;"
{| class="wikitable sortable" style="text-align: left;"
|+<!-- caption -->Intervals of 2L 5s for each mode
|+<!-- caption -->Intervals of 2L 5s for each mode
|-
|-
!Mode!!UDP!! align="right" | Rotational order!! align="right" | mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep !!5-mosstep!!6-mosstep!!mosoctave
!Mode!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
|-
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|-
|-
|LsssLss ||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
Line 159: Line 595:
|+Degrees of 2L 5s for each mode
|+Degrees of 2L 5s for each mode
|-
|-
!Mode!! UDP!! align="right" |Rotational order !! 0-mosdegree !!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
!Mode!!UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major|| major||perfect
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|-
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major||major||perfect||perfect||major||major||perfect
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major||major||perfect||perfect||major||major||perfect
Line 169: Line 605:
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|-
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5||perfect||minor||minor||perfect||perfect||minor|| major||perfect
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5||perfect||minor||minor||perfect||perfect||minor||major||perfect
|-
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1||perfect||minor||minor||perfect||perfect||minor|| minor||perfect
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1||perfect||minor||minor||perfect||perfect||minor||minor||perfect
|-
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4||perfect||minor||minor||diminished||perfect||minor ||minor||perfect
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4||perfect||minor||minor||diminished||perfect||minor||minor||perfect
|}
|}
Note: don't merge cells on a table with sorting.
Note: don't merge cells on a table with sorting.
Line 180: Line 616:
|-
|-
!Mode
!Mode
!Mode name!!UDP!! align="right" | Rotational order!! align="right" |mosunison!! 1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
!Mode name!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
|-
|-
|LssLsss
|LssLsss
Line 192: Line 628:
|-
|-
|sLsssLs
|sLsssLs
|antidorian ||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|antidorian||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|-
| ssLssLs
|ssLssLs
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s ||2L+5s
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|-
|ssLsssL
|ssLsssL
Line 201: Line 637:
|-
|-
|sssLssL
|sssLssL
|antilydian|| 0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|antilydian||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|}
|}
{| class="wikitable sortable" style="text-align: left;"
{| class="wikitable sortable" style="text-align: left;"
Line 207: Line 643:
|-
|-
!Mode
!Mode
!Mode name!!UDP!! align="right" | Rotational order !!0-mosdegree!!1-mosdegree!! 2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
!Mode name!!UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|-
|LssLsss
|LssLsss
Line 263: Line 699:
|minor||diminished
|minor||diminished
|perfect
|perfect
| minor
|minor
|minor|| perfect
|minor||perfect
|}
|}


Line 273: Line 709:
!Number of periods
!Number of periods
!Name
!Name
! Prefix
!Prefix
|-
|-
|[[1L 1s]]
|[[1L 1s]]
Line 366: Line 802:
|-
|-
|[[5L 1s]]
|[[5L 1s]]
| 6
|6
|1
|1
|machinoid
|machinoid
Line 372: Line 808:
|-
|-
|[[1L 6s]]
|[[1L 6s]]
| 7
|7
|1
|1
|onyx
|onyx
Line 380: Line 816:
|7
|7
|1
|1
| antidiatonic
|antidiatonic
|pel-
|pel-
|-
|-
Line 403: Line 839:
|[[6L 1s]]
|[[6L 1s]]
|7
|7
| 1
|1
|arch(a)eotonic
|arch(a)eotonic
|arch-
|arch-
Line 414: Line 850:
|-
|-
|[[2L 6s]]
|[[2L 6s]]
| 8
|8
|2
|2
|antiekic
|antiekic
Line 420: Line 856:
|-
|-
|[[3L 5s]]
|[[3L 5s]]
| 8
|8
|1
|1
|checkertonic
|checkertonic
Line 457: Line 893:
|[[2L 7s]]
|[[2L 7s]]
|9
|9
| 1
|1
|balzano
|balzano
|bal- /bæl/
|bal- /bæl/
Line 476: Line 912:
|9
|9
|1
|1
| semiquartal
|semiquartal
|cthon-
|cthon-
|-
|-
Line 500: Line 936:
|10
|10
|1
|1
| antisinatonic
|antisinatonic
|asina-
|asina-
|-
|-
Line 513: Line 949:
|1
|1
|sephiroid
|sephiroid
| seph-
|seph-
|-
|-
|[[4L 6s]]
|[[4L 6s]]
Line 525: Line 961:
|5
|5
|pentawood
|pentawood
| penwd-
|penwd-
|-
|-
|[[6L 4s]]
|[[6L 4s]]
Line 552: Line 988:
|}
|}


== Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)==
==Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)==
{| class="wikitable"
{| class="wikitable"
! colspan="6" |Generator
! colspan="6" |Generator
Line 570: Line 1,006:
|600.000
|600.000
|600.000
|600.000
| 1
|1
|1
|1
|1.000
|1.000
Line 584: Line 1,020:
|545.455
|545.455
|6
|6
| 5
|5
| 1.200
|1.200
| rowspan="3" |2L 5s range (includes 2L 7s and 7L 2s)
| rowspan="3" |2L 5s range (includes 2L 7s and 7L 2s)
|-
|-
Line 598: Line 1,034:
|5
|5
|4
|4
| 1.250
|1.250
|-
|-
|
|
Line 605: Line 1,041:
|
|
|
|
| 9\16
|9\16
|675.000
|675.000
|525.000
|525.000
Line 658: Line 1,094:
|705.882
|705.882
|494.118
|494.118
| 10
|10
|7
|7
| 1.429
|1.429
|-
|-
|
|
Line 760: Line 1,196:
|9
|9
|5
|5
| 1.800
|1.800
|-
|-
|
|
Line 808: Line 1,244:
|847.059
|847.059
|352.941
|352.941
| 12
|12
|5
|5
| 2.400
|2.400
|-
|-
|
|
Line 956: Line 1,392:
|
|
|6\7
|6\7
| 1028.571
|1028.571
|171.429
|171.429
| 6
|6
| 1
|1
|6.000
|6.000
|-
|-
Line 983: Line 1,419:
!1st ancestor
!1st ancestor
!Mos
!Mos
! 1st descendants
!1st descendants
!2nd descendants
!2nd descendants
|-
|-
Line 992: Line 1,428:
|xL (2x+y)s
|xL (2x+y)s
|-
|-
| (2x+y)L xs
|(2x+y)L xs
|-
|-
| rowspan="2" |(x+y)L xs
| rowspan="2" |(x+y)L xs

Revision as of 08:09, 22 November 2023


This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)

Template test area

Cell color code test

Examples 0
Augmented size Aug.
Large size Maj.
Small size Min.
Diminished size Dim.

MOS mode degrees (5L 2s)

Scale degrees of the modes of 5L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.
Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.
Scale degrees of the modes of 5L 2s (LLsLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m5md 1 LLsLsAs Perf. Maj. Maj. Perf. Perf. Min. Maj. Perf.
3|3 d4md 2 LsLsAsL Perf. Maj. Min. Perf. Dim. Maj. Min. Perf.
1|5 d3md 3 sLsAsLL Perf. Min. Min. Dim. Perf. Min. Min. Perf.
6|0 m2md 4 LsAsLLs Perf. Maj. Min. Aug. Perf. Maj. Maj. Perf.
4|2 m1md 5 sAsLLsL Perf. Min. Maj. Perf. Perf. Maj. Min. Perf.
6|0 A1md A4md 6 AsLLsLs Perf. Aug. Maj. Aug. Aug. Maj. Maj. Perf.
0|6 d6md 7 sLLsLsA Perf. Min. Min. Perf. Dim. Min. Dim. Perf.
Scale degrees of the modes of 5L 2s (LsLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m2md
3|3 M6md 		1 LsLLLLs Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md
1|5 M5md 		2 sLLLLsL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
6|0 A4md 3 LLLLsLs Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md
4|2 A3md 		4 LLLsLsL Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md
2|4 M2md 		5 LLsLsLL Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md
0|6 M1md 		6 LsLsLLL Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md 7 sLsLLLL Perf. Min. Min. Dim. Dim. Min. Min. Perf.
Scale degrees of the modes of 5L 2s (sLLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m1md m2md
1|5 M5md M6md 		1 sLLLLLs Perf. Min. Min. Perf. Perf. Maj. Maj. Perf.
6|0 A4md A5md 2 LLLLLss Perf. Maj. Maj. Aug. Aug. Aug. Maj. Perf.
6|0 A4md m6md
4|2 A3md A4md 		3 LLLLssL Perf. Maj. Maj. Aug. Aug. Maj. Min. Perf.
6|0 m5md m6md
2|4 M2md A3md 		4 LLLssLL Perf. Maj. Maj. Aug. Perf. Min. Min. Perf.
4|2 d4md m5md
0|6 M1md M2md 		5 LLssLLL Perf. Maj. Maj. Perf. Dim. Min. Min. Perf.
2|4 d3md d4md
0|6 M1md d3md 		6 LssLLLL Perf. Maj. Min. Dim. Dim. Min. Min. Perf.
0|6 d2md d3md 7 ssLLLLL Perf. Min. Dim. Dim. Dim. Min. Min. Perf.


Scale degrees of the modes of 5L 2s (LLLLLLd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 A4md A5md A6md 1 LLLLLLd Perf. Maj. Maj. Aug. Aug. Aug. Aug. Perf.
6|0 A4md A5md m6md
4|2 A3md A4md A5md 		2 LLLLLdL Perf. Maj. Maj. Aug. Aug. Aug. Min. Perf.
6|0 A4md m5md m6md
2|4 M2md A3md A4md 		3 LLLLdLL Perf. Maj. Maj. Aug. Aug. Min. Min. Perf.
6|0 d4md m5md m6md
0|6 M1md M2md A3md 		4 LLLdLLL Perf. Maj. Maj. Aug. Dim. Min. Min. Perf.
4|2 d3md d4md m5md
0|6 M1md M2md d3md 		5 LLdLLLL Perf. Maj. Maj. Dim. Dim. Min. Min. Perf.
2|4 d2md d3md d4md
0|6 M1md d2md d3md 		6 LdLLLLL Perf. Maj. Dim. Dim. Dim. Min. Min. Perf.
0|6 d1md d2md d3md 7 dLLLLLL Perf. Dim. Dim. Dim. Dim. Min. Min. Perf.


Scale degrees of the modes of 5L 2s (AAdAdAd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 A1md AA2md AA4md A6md 1 AAdAdAd Perf. Aug. 2× Aug. Aug. 2× Aug. Maj. Aug. Perf.
6|0 A1md m2md d4md d6md
0|6 A1md A3md M5md d6md 		2 AdAdAdA Perf. Aug. Min. Aug. Dim. Maj. Dim. Perf.
0|6 d1md dd3md dd5md d6md 3 dAdAdAA Perf. Dim. Min. 2× Dim. Dim. 2× Dim. Dim. Perf.
6|0 A1md m2md d4md A6md
0|6 A1md A3md M5md A6md 		4 AdAdAAd Perf. Aug. Min. Aug. Dim. Maj. Aug. Perf.
3|3 d1md dd3md d4md d6md
0|6 d1md dd3md M5md d6md 		5 dAdAAdA Perf. Dim. Min. 2× Dim. Dim. Maj. Dim. Perf.
6|0 A1md m2md AA4md A6md
3|3 A1md A3md AA4md A6md 		6 AdAAdAd Perf. Aug. Min. Aug. 2× Aug. Maj. Aug. Perf.
6|0 d1md m2md d4md d6md
0|6 d1md A3md M5md d6md 		7 dAAdAdA Perf. Dim. Min. Aug. Dim. Maj. Dim. Perf.

Mos mode degrees with rotations of multiple modmosses

UDP Step pattern Mode names Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 LLLsLLs Lydian Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 LLsLLLs Ionian (major) Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 LLsLLsL Mixolydian Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 LsLLLsL Dorian Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 LsLLsLL Aeolian (minor) Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 sLLLsLL Phrygian Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 sLLsLLL Locrian Perf. Min. Min. Perf. Dim. Min. Min. Perf
2|4 M6md LsLLsAs Harmonic minor Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md sLLsAsL Locrian #6 Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md LLsAsLs Ionian augmented Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md LsAsLsL Dorian #4 Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md sAsLsLL Phrygian dominant Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md AsLsLLs Lydian #2 Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md sLsLLsA Locrian b4 bb7 Perf. Min. Min. Dim. Dim. Min. Dim. Perf.
5|1 m5md LLsLsAs Ionian b6 (Harmonic major) Perf. Maj. Maj. Perf. Perf. Min. Maj. Perf.
3|3 d4md LsLsAsL Dorian b5 (Dorian diminished) Perf. Maj. Min. Perf. Dim. Maj. Min. Perf.
1|5 d3md sLsAsLL Phrygian b4 Perf. Min. Min. Dim. Perf. Min. Min. Perf.
6|0 m2md LsAsLLs Lydian b3 (Lydian minor) Perf. Maj. Min. Aug. Perf. Maj. Maj. Perf.
4|2 m1md sAsLLsL Mixolydian b2 Perf. Min. Maj. Perf. Perf. Maj. Min. Perf.
6|0 A1md A4md AsLLsLs Lydian #2 #5 Perf. Aug. Maj. Aug. Aug. Maj. Maj. Perf.
0|6 d6md sLLsLsA Locrian bb7 Perf. Min. Min. Perf. Dim. Min. Dim. Perf.
5|1 m2md LsLLLLs Aeolian ♮6 ♮7 (Melodic minor) Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md sLLLLsL Dorian b2 Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
6|0 A4md LLLLsLs Lydian #5 (Lydian augmented) Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md LLLsLsL Lydian b7 (Lydian dominant) Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md LLsLsLL Mixolydian b6 Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md LsLsLLL Locrian ♮2 (Half-diminished) Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md sLsLLLL Locrian bb4 (Altered dominant, super-locrian) Perf. Min. Min. Dim. Dim. Min. Min. Perf.
5|1 m1md m2md sLLLLLs Ionian b2 b3 (Neapolitan major) Perf. Min. Min. Perf. Perf. Maj. Maj. Perf.
6|0 A4md A5md LLLLLss Lydian #5 #6 Perf. Maj. Maj. Aug. Aug. Aug. Maj. Perf.
6|0 A4md m6md LLLLssL Lydian #5 b7 Perf. Maj. Maj. Aug. Aug. Maj. Min. Perf.
6|0 m5md m6md LLLssLL Lydian b6 b7 Perf. Maj. Maj. Aug. Perf. Min. Min. Perf.
4|2 d4md m5md LLssLLL Locrian ♮2 ♮3 (Major locrian) Perf. Maj. Maj. Perf. Dim. Min. Min. Perf.
2|4 d3md d4md LssLLLL Locrian ♮2 b4 Perf. Maj. Min. Dim. Dim. Min. Min. Perf.
0|6 d2md d3md ssLLLLL Locrian bb3 b4 Perf. Min. Dim. Dim. Dim. Min. Min. Perf.


MOS step sizes

3L 4s step sizes
Interval Basic 3L 4s

(10edo, L:s = 2:1)

Hard 3L 4s

(13edo, L:s = 3:1)

Soft 3L 4s

(17edo, L:s = 3:2)

Approx. JI ratios
Steps Cents Steps Cents Steps Cents
Large step 2 240¢ 3 276.9¢ 3 211.8¢ Hide column if no ratios given
Small step 1 120¢ 1 92.3¢ 2 141.2¢
Bright generator 3 360¢ 4 369.2¢ 5 355.6¢

Notes:

  • Allow option to show the bright generator, dark generator, or no generator.
  • JI ratios column only shows if there are any ratios to show

Expanded MOS intro

The following pieces of information may be worth adding:

  • The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
  • Simple edos (or ed<p/q>) that support the mos.
  • For mosses with more than 10 notes, that the mos descends from another, TAMNAMS-named mos and how it relates back to that ancestor mos. This requires standardizing the naming scheme for descendant mosses before it can be added.

Base wording (for TAMNAMS-named mosses)

xL ys<p/q>, also called mosname, is a(n) equave-equivalent moment-of-symmetry scale, containing x large steps(s) and y small step(s) and repeating every equave. Scales of this form have a generalized step pattern of step-pattern or some rotation thereof. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generating intervals for this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

nxL nys<p/q>, also called mosname, is a(n) equave-equivalent moment-of-symmetry scale, containing nx large steps(s) and ny small step(s), with a period of x large step(s) and y small steps(s) that repeats every equave-fraction, or n times every equave. Scales of this form have a generalized step pattern of step-pattern or some rotation thereof. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generating intervals for this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

Base wording (for mos descendants)

xL ys<p/q>, also called mosname, is a(n) extension scale of the equave-equivalent moment-of-symmetry scale zL ws<p/q>, expanded to x large steps(s) and y small step(s) and repeating every equave. Scales of this form have a generalized step pattern of step-pattern or some rotation thereof. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generating intervals for this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

nxL nys<p/q>, also called mosname, is a(n) extension scale of the equave-equivalent moment-of-symmetry scale nzL nws<p/q>, expanded to nx large steps(s) and ny small step(s), with a period of x large step(s) and y small steps(s) that repeats every equave-fraction, or n times every equave. Scales of this form have a generalized step pattern of step-pattern or some rotation thereof. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generating intervals for this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

Examples

5L 7s, also called (hard) diachromatic or p-chromatic, is a chromatic scale of the moment-of-symmetry scale 5L 2s, expanded to 5 large steps and 7 small steps, repeating every octave. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, with a generator that ranges from 700¢ to 720¢, or from 480¢ to 500¢. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo.

Mbox template test

These would be their own templates.

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Math symbols test

Isolated symbols

[math]\displaystyle{ T := [ t_1, t_2, ..., t_m ] }[/math] [math]\displaystyle{ S := [ s_1, s_2, ..., s_m ] }[/math] [math]\displaystyle{ P := [ p_1, p_2, ..., p_n ] }[/math]

Sample text

Pulled from muddle page.

Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.

Interval and degree tables

The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.

Intervals of 2L 5s for each mode
Mode UDP Rotational order mosunison 1-mosstep 2-mosstep 3-mosstep 4-mosstep 5-mosstep 6-mosstep mosoctave
LssLsss 6|0 0 0 L L+s L+2s 2L+2s 2L+3s 2L+4s 2L+5s
LsssLss 5|1 3 0 L L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLssLss 4|2 6 0 s L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLsssLs 3|3 2 0 s L+s L+2s L+3s L+4s 2L+4s 2L+5s
ssLssLs 2|4 5 0 s 2s L+2s L+3s L+4s 2L+4s 2L+5s
ssLsssL 1|5 1 0 s 2s L+2s L+3s L+4s L+5s 2L+5s
sssLssL 0|6 4 0 s 2s 3s L+3s L+4s L+5s 2L+5s


Degrees of 2L 5s for each mode
Mode UDP Rotational order 0-mosdegree 1-mosdegree 2-mosdegree 3-mosdegree 4-mosdegree 5-mosdegree 6-mosdegree 7-mosdegree
LssLsss 6|0 0 perfect major major perfect augmented major major perfect
LsssLss 5|1 3 perfect major major perfect perfect major major perfect
sLssLss 4|2 6 perfect minor major perfect perfect major major perfect
sLsssLs 3|3 2 perfect minor major perfect perfect minor major perfect
ssLssLs 2|4 5 perfect minor minor perfect perfect minor major perfect
ssLsssL 1|5 1 perfect minor minor perfect perfect minor minor perfect
sssLssL 0|6 4 perfect minor minor diminished perfect minor minor perfect

Note: don't merge cells on a table with sorting.

Intervals of 2L 5s for each mode (with mode names)
Mode Mode name UDP Rotational order mosunison 1-mosstep 2-mosstep 3-mosstep 4-mosstep 5-mosstep 6-mosstep mosoctave
LssLsss antilocrian 6|0 0 0 L L+s L+2s 2L+2s 2L+3s 2L+4s 2L+5s
LsssLss antiphrygian 5|1 3 0 L L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLssLss anti-aeolian 4|2 6 0 s L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLsssLs antidorian 3|3 2 0 s L+s L+2s L+3s L+4s 2L+4s 2L+5s
ssLssLs antimixolydian 2|4 5 0 s 2s L+2s L+3s L+4s 2L+4s 2L+5s
ssLsssL anti-ionian 1|5 1 0 s 2s L+2s L+3s L+4s L+5s 2L+5s
sssLssL antilydian 0|6 4 0 s 2s 3s L+3s L+4s L+5s 2L+5s
Degrees of 2L 5s for each mode (with mode names)
Mode Mode name UDP Rotational order 0-mosdegree 1-mosdegree 2-mosdegree 3-mosdegree 4-mosdegree 5-mosdegree 6-mosdegree 7-mosdegree
LssLsss antilocrian 6|0 0 perfect major major perfect augmented major major perfect
LsssLss antiphrygian 5|1 3 perfect major major perfect perfect major major perfect
sLssLss anti-aeolian 4|2 6 perfect minor major perfect perfect major major perfect
sLsssLs antidorian 3|3 2 perfect minor major perfect perfect minor major perfect
ssLssLs antimixolydian 2|4 5 perfect minor minor perfect perfect minor major perfect
ssLsssL anti-ionian 1|5 1 perfect minor minor perfect perfect minor minor perfect
sssLssL antilydian 0|6 4 perfect minor minor diminished perfect minor minor perfect

Alternate mos tables

Pattern Number of notes Number of periods Name Prefix
1L 1s 2 1 trivial triv-
1L 1s 2 1 monowood monowd-
1L 2s 3 1 antrial atri-
2L 1s 3 1 trial tri-
1L 3s 4 1 antetric atetra-
2L 2s 4 2 biwood biwd-
3L 1s 4 1 tetric tetra-
1L 4s 5 1 pedal ped-
2L 3s 5 1 pentic pent-
3L 2s 5 1 antipentic apent-
4L 1s 5 1 manual manu-
1L 5s 6 1 antimachinoid amech-
2L 4s 6 2 anticitric acitro-
3L 3s 6 3 triwood triwd-
4L 2s 6 2 citric citro-
5L 1s 6 1 machinoid mech-
1L 6s 7 1 onyx on-
2L 5s 7 1 antidiatonic pel-
3L 4s 7 1 mosh mosh-
4L 3s 7 1 smitonic smi-
5L 2s 7 1 diatonic none
6L 1s 7 1 arch(a)eotonic arch-
1L 7s 8 1 antipine apine-
2L 6s 8 2 antiekic anek-
3L 5s 8 1 checkertonic check-
4L 4s 8 4 tetrawood; diminished tetwd-
5L 3s 8 1 oneirotonic neiro-
6L 2s 8 2 ekic ek-
7L 1s 8 1 pine pine-
1L 8s 9 1 antisubneutralic ablu-
2L 7s 9 1 balzano bal- /bæl/
3L 6s 9 3 tcherepnin cher-
4L 5s 9 1 gramitonic gram-
5L 4s 9 1 semiquartal cthon-
6L 3s 9 3 hyrulic hyru-
7L 2s 9 1 superdiatonic arm-
8L 1s 9 1 subneutralic blu-
1L 9s 10 1 antisinatonic asina-
2L 8s 10 2 jaric jara-
3L 7s 10 1 sephiroid seph-
4L 6s 10 2 lime lime-
5L 5s 10 5 pentawood penwd-
6L 4s 10 2 lemon lem-
7L 3s 10 1 dicoid /'daɪkɔɪd/ dico-
8L 2s 10 2 taric tara-
9L 1s 10 1 sinatonic sina-

Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)

Generator Bright gen. Dark gen. L s L/s Ranges of mosses
1\2 600.000 600.000 1 1 1.000
6\11 654.545 545.455 6 5 1.200 2L 5s range (includes 2L 7s and 7L 2s)
5\9 666.667 533.333 5 4 1.250
9\16 675.000 525.000 9 7 1.286
4\7 685.714 514.286 4 3 1.333 Basic 2L 3s
11\19 694.737 505.263 11 8 1.375 5L 2s range (includes 7L 5s and 5L 7s)
7\12 700.000 500.000 7 5 1.400
10\17 705.882 494.118 10 7 1.429
3\5 720.000 480.000 3 2 1.500 Basic 2L 1s
11\18 733.333 466.667 11 7 1.571 5L 3s range
8\13 738.462 461.538 8 5 1.600
13\21 742.857 457.143 13 8 1.625
5\8 750.000 450.000 5 3 1.667 Basic 3L 2s
12\19 757.895 442.105 12 7 1.714 3L 5s range
7\11 763.636 436.364 7 4 1.750
9\14 771.429 428.571 9 5 1.800
2\3 800.000 400.000 2 1 2.000 Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
9\13 830.769 369.231 9 4 2.250 3L 4s range (includes 3L 7s and 7L 3s)
7\10 840.000 360.000 7 3 2.333
12\17 847.059 352.941 12 5 2.400
5\7 857.143 342.857 5 2 2.500 Basic 3L 1s
13\18 866.667 333.333 13 5 2.600 4L 3s range
8\11 872.727 327.273 8 3 2.667
11\15 880.000 320.000 11 4 2.750
3\4 900.000 300.000 3 1 3.000 Basic 1L 2s
10\13 923.077 276.923 10 3 3.333 Range of 1L 4s (includes 4L 5s and 5L 4s)
7\9 933.333 266.667 7 2 3.500
11\14 942.857 257.143 11 3 3.667
4\5 960.000 240.000 4 1 4.000 Basic 1L 4s
9\11 981.818 218.182 9 2 4.500 Range of 4L 1s (includes 5L 1s and 1L 5s)
5\6 1000.000 200.000 5 1 5.000
6\7 1028.571 171.429 6 1 6.000
1\1 1200.000 0.000 1 0 → inf

Module and template sandbox

Mos ancestors and descendants

2nd ancestor 1st ancestor Mos 1st descendants 2nd descendants
uL vs zL ws xL ys xL (x+y)s xL (2x+y)s
(2x+y)L xs
(x+y)L xs (2x+y)L (x+y)s
(x+y)L (2x+y)s
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