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m More color testing
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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
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Sandbox"