User:Ganaram inukshuk/Sandbox: Difference between revisions

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Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
4,810 edits
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
4,810 edits
Testing out layouts for mode degree tables; cleaned up test code that's no longer needed; organized page
Line 3: Line 3:
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.)


== Test area ==
== Template test area==
 
=== Expanding the mos intro ===
The following pieces of information may be worth adding:
 
* The specific step pattern for the true mos. (The template wiSmall edos (or ed<nowiki><p/q>'s) that support the mos.</nowiki>ll have a link to the page for rotations.)
* Simple edos (or ed<nowiki><p/q>) that support the mos.</nowiki>
* 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) ====
'''''x''L ''y''s<''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2nx+ny'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3nx+ny'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3nx+2ny'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
'''''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2x+y'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3x+y'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3x+2y'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
==== 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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2nx+ny'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3nx+ny'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3nx+2ny'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
'''''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2x+y'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3x+y'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3x+2y'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
==== 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.
 
=== Mos degrees template with new code===
Template to call module without affecting the current template (fill in arguments as needed):
<syntaxhighlight>
{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=
|Step Ratio=
|MOS Prefix=
|Show Abbreviations=
|JI Ratios=
|Notation=
|UDP=
}}
</syntaxhighlight>
Instances of module for testing:
 
{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=5L 2s
|Step Ratio=2/1; 3/1; 3/2
|MOS Prefix=
|Show Abbreviations=1
|Number of Alterations=1
|Notation=Default
|UDP=
|JI Ratios=P3md:4/3; P4md: 3/2
}}
 
{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=5L 4s
|Step Ratio=
|MOS Prefix=
|Show Abbreviations=
|Number of Alterations=
|Notation=
|UDP=
|JI Ratios=
}}
 
{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=4L 3s
|Step Ratio=2/1; 3/1; 3/2
|MOS Prefix=
|Show Abbreviations=1
|Number of Alterations=1
|Notation=Default
|UDP=
|JI Ratios=
M1md: 8/7;
P2md: 77/64, 6/5;
m3md: 14/11;
M3md:11/8;
m4md: 16/11;
M4md: 11/7;
P5md: 5/3;
m6md: 7/4;
}}
 
===Mos degrees template (version 2) mockup ===


===MOS mode degrees===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ Scale degree of 4L 3s
|+Scale degrees of 5L 2s modes (step pattern of LsLLsAs)
! rowspan="2" class="unsortable" | Scale degree
! rowspan="2" |UDP and alterations
! rowspan="2" class="unsortable" | Abbrev.
! rowspan="2" |Rotational Order
! rowspan="2" class="unsortable" | On J
! rowspan="2" |Step pattern
! colspan="2" |11edo (Basic, L:s = 2:1)
! rowspan="2" class="unsortable" |Mode names
! colspan="2" |15edo (Hard, L:s = 3:1)
! colspan="8" class="unsortable" |Scale degree (mosdegree)
! colspan="2" |18edo (Soft, L:s = 3:2)
! Rowspan="2" class="unsortable" | Approx. JI Ratios
|-
|-
! Steps
! class="unsortable" |0
! Cents
! class="unsortable" |1
! Steps
! class="unsortable" |2
! Cents
! class="unsortable" |3
! Steps
! class="unsortable" |4
! Cents
! class="unsortable" |5
! class="unsortable" |6
! class="unsortable" |7
|-
|-
| '''Perfect 0-smistep'''
|<nowiki>2|4 M6md</nowiki>
| P0md
|1
| J
|LsLLsAs
| 0
| Harmonic minor
| 0
|Perf.
| 0
|Maj.
| 0
|Min.
| 0
|Perf.
| 0
|Perf.
| 1/1 (exact), 1/1
|Min.
|Maj.
|Perf.
|-
|-
| Augmented 0-smistep
|<nowiki>0|6 M5md</nowiki>
| A0md
|2
| J&
|sLLsAsL
| 1
|Locrian #6
| 109.1
|Perf.
| 2
|Min.
| 160
|Min.
| 1
|Perf.
| 66.7
|Dim.
|
| Maj.
|Min.
|Perf.
|-
|-
| Diminished 1-smistep
|<nowiki>5|1 A4md</nowiki>
| d1md
|3
| K@@
|LLsAsLs
| 0
|Ionian augmented
| 0
|Perf.
| -1
|Maj.
| -80
|Maj.
| 1
|Perf.
| 66.7
|Aug.
|
| Maj.
|Maj.
|Perf.
|-
|-
| Minor 1-smistep
|<nowiki>3|3 A3md</nowiki>
| m1md
|4
| K@
|LsAsLsL
| 1
|Dorian #4
| 109.1
|Perf.
| 1
|Maj.
| 80
|Min.
| 2
|Aug.
| 133.3
|Perf.
|
|Maj.
|Min.
|Perf.
|-
|-
| Major 1-smistep
|<nowiki>1|5 M2md</nowiki>
| M1md
|5
| K
|sAsLsLL
| 2
|Phrygian dominant
| 218.2
|Perf.
| 3
| Min.
| 240
|Maj.
| 3
| Perf.
| 200
|Perf.
|
|Min.
|Min.
|Perf.
|-
|-
| Augmented 1-smistep
|<nowiki>6|0 A1md</nowiki>
| A1md
|6
| K&
|AsLsLLs
| 3
| Lydian #2
| 327.3
|Perf.
| 5
|Aug.
| 400
|Maj.
| 4
|Aug.
| 266.7
|Perf.
|
|Maj.
|Maj.
|Perf.
|-
|-
| Diminished 2-smistep
|<nowiki>0|6 d3md d6md</nowiki>
| d2md
|7
| L@
|sLsLLsA
| 2
|Locrian b4 bb7
| 218.2
|Perf.
| 2
|Min.
| 160
|Min.
| 4
|Dim.
| 266.7
|Dim.
|
|Min.
|Dim.
|Perf.
|}
 
{| class="wikitable sortable"
|+Scale degrees of 5L 2s modes (step pattern of LLLLsLs)
! rowspan="2" |UDP and alterations
! rowspan="2" |Rotational Order
! rowspan="2" |Step pattern
! colspan="8" class="unsortable" |Scale degree (mosdegree)
|-
|-
| '''Perfect 2-smistep'''
! class="unsortable" |0
| P2md
! class="unsortable" |1
| L
! class="unsortable" |2
| 3
! class="unsortable" |3
| 327.3
! class="unsortable" |4
| 4
! class="unsortable" | 5
| 320
! class="unsortable" |6
| 5
! class="unsortable" |7
| 333.3
|
|-
|-
| Augmented 2-smistep
|<nowiki>6|0 A4md</nowiki>
| A2md
|1
| L&
|LLLLsLs
| 4
|Perf.
| 436.4
|Maj.
| 6
|Maj.
| 480
|Aug.
| 6
|Aug.
| 400
|Maj.
|
|Maj.
|Perf.
|-
|-
| 2× Augmented 2-smistep
|<nowiki>6|0 m6md</nowiki>
| AA2md
|2
| L&&
|LLLsLsL
| 5
|Perf.
| 545.5
|Maj.
| 8
|Maj.
| 640
|Aug.
| 7
|Perf.
| 466.7
|Maj.
|
|Min.
|Perf.
|-
|-
| Diminished 3-smistep
|<nowiki>4|2 m5md</nowiki>
| d3md
|3
| M@@
|LLsLsLL
| 3
|Perf.
| 327.3
|Maj.
| 3
|Maj.
| 240
|Perf.
| 6
| Perf.
| 400
|Min.
|
|Min.
| Perf.
|-
|-
| Minor 3-smistep
|<nowiki>2|4 d4md</nowiki>
| m3md
|4
| M@
|LsLsLLL
| 4
|Perf.
| 436.4
|Maj.
| 5
|Min.
| 400
|Perf.
| 7
|Dim.
| 466.7
|Min.
|
|Min.
|Perf.
|-
|-
| Major 3-smistep
|<nowiki>0|6 d3md</nowiki>
| M3md
|5
| M
|sLsLLLL
| 5
|Perf.
| 545.5
|Min.
| 7
|Min.
| 560
|Dim.
| 8
|Dim.
| 533.3
|Min.
|
| Min.
|Perf.
|-
|-
| Augmented 3-smistep
|<nowiki>5|1 m2md</nowiki>
| A3md
|6
| M&
|LsLLLLs
| 6
|Perf.
| 654.5
|Maj.
| 9
|Min.
| 720
|Perf.
| 9
|Perf.
| 600
|Maj.
|
|Maj.
| Perf.
|-
|-
| Diminished 4-smistep
|<nowiki>3|3 m1md</nowiki>
| d4md
|7
| N@
|sLLLLsL
| 5
|Perf.
| 545.5
| Min.
| 6
|Min.
| 480
|Perf.
| 9
| Perf.
| 600
|Maj.
|
|Min.
|Perf.
|}
 
{| class="wikitable sortable"
|+Scale degrees of 5L 2s modes (step pattern of LLLLLss)
! rowspan="2" |UDP and alterations
! rowspan="2" | Rotational Order
! rowspan="2" |Step pattern
! colspan="8" class="unsortable" |Scale degree (mosdegree)
|-
|-
| Minor 4-smistep
! class="unsortable" |0
| m4md
! class="unsortable" | 1
| N
! class="unsortable" |2
| 6
! class="unsortable" |3
| 654.5
! class="unsortable" |4
| 8
! class="unsortable" |5
| 640
! class="unsortable" |6
| 10
! class="unsortable" |7
| 666.7
|
|-
|-
| Major 4-smistep
|<nowiki>6|0 A4md A5md</nowiki>
| M4md
|1
| N&
|LLLLLss
| 7
|Perf.
| 763.6
|Maj.
| 10
|Maj.
| 800
|Aug.
| 11
|Aug.
| 733.3
|Aug.
|
|Maj.
|Perf.
|-
|-
| Augmented 4-smistep
|<nowiki>6|0 A4md m6md</nowiki>
| A4md
|2
| N&&
| LLLLssL
| 8
|Perf.
| 872.7
|Maj.
| 12
|Maj.
| 960
|Aug.
| 12
|Aug.
| 800
|Maj.
|
| Min.
| Perf.
|-
|-
| 2× Diminished 5-smistep
|<nowiki>6|0 m5md m6md</nowiki>
| dd5md
|3
| O@@
|LLLssLL
| 6
|Perf.
| 654.5
| Maj.
| 7
|Maj.
| 560
|Aug.
| 11
| Perf.
| 733.3
|Min.
|
| Min.
|Perf.
|-
|-
| Diminished 5-smistep
|<nowiki>4|2 d4md m5md</nowiki>
| d5md
|4
| O@
|LLssLLL
| 7
|Perf.
| 763.6
|Maj.
| 9
|Maj.
| 720
|Perf.
| 12
| Dim.
| 800
|Min.
|
|Min.
| Perf.
|-
|-
| '''Perfect 5-smistep'''
|<nowiki>2|4 d3md d4md</nowiki>
| P5md
|5
| O
|LssLLLL
| 8
| Perf.
| 872.7
|Maj.
| 11
|Min.
| 880
|Dim.
| 13
|Dim.
| 866.7
|Min.
|
|Min.
|Perf.
|-
|-
| Augmented 5-smistep
|<nowiki>0|6 d2md d3md</nowiki>
| A5md
|6
| O&
| ssLLLLL
| 9
|Perf.
| 981.8
|Min.
| 13
| Dim.
| 1040
| Dim.
| 14
|Dim.
| 933.3
| Min.
|
| Min.
|Perf.
|-
|-
| Diminished 6-smistep
|<nowiki>5|1 m1md m2md</nowiki>
| d6md
|7
| P@
|sLLLLLs
| 8
|Perf.
| 872.7
|Min.
| 10
|Min.
| 800
| Perf.
| 14
| Perf.
| 933.3
|Maj.
|
|Maj.
|-
|Perf.
| Minor 6-smistep
| m6md
| P
| 9
| 981.8
| 12
| 960
| 15
| 1000
|
|-
| Major 6-smistep
| M6md
| P&
| 10
| 1090.9
| 14
| 1120
| 16
| 1066.7
|
|-
| Augmented 6-smistep
| A6md
| P&&
| 11
| 1200
| 16
| 1280
| 17
| 1133.3
|
|-
| Diminished 7-smistep
| d7md
| J@
| 10
| 1090.9
| 13
| 1040
| 17
| 1133.3
|
|-
| '''Perfect 7-smistep'''
| P7md
| J
| 11
| 1200
| 15
| 1200
| 18
| 1200
| 2/1 (exact)
|}
|}


===Step sizes template===
===MOS step sizes ===
{{MOS degrees|Scale Signature=4L 3s}}
{| 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
(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 429: Line 337:
|-
|-
|Large step
|Large step
| 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 449: Line 357:
|3
|3
|360¢
|360¢
|4
| 4
|369.2¢
|369.2¢
|5
|5
Line 460: Line 368:
*JI ratios column only shows if there are any ratios to show
*JI ratios column only shows if there are any ratios to show


===Mbox template test===
===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<nowiki><p/q>) that support the mos.</nowiki>
*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)====
'''''x''L ''y''s<''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2nx+ny'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3nx+ny'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3nx+2ny'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
'''''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2x+y'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3x+y'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3x+2y'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
====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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2nx+ny'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3nx+ny'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3nx+2ny'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
'''''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 step pattern of ''step-pattern'' or some rotation thereof, with a generator that ranges from ''g1''¢ to ''g2''¢ or from ''d1''¢ or ''d2''¢. Equal divisions of the ''equave'' that support this scale's step pattern include (''2x+y'')ed''<nowiki><p/q></nowiki>'' (L = 2 and s = 1), (''3x+y'')''ed<nowiki><p/q></nowiki>'' (L = 3 and s = 1), and (''3x+2y'')ed''<nowiki><p/q></nowiki>'' (L = 3 and s = 2)''.''
 
====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.
These would be their own templates.


Line 472: Line 398:
{{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 491: Line 417:
|+<!-- 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 505: Line 431:
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|-
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s|| L+3s||L+4s||L+5s||2L+5s
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|}
|}


Line 512: Line 438:
|+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
|-
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
Line 522: Line 448:
|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 533: Line 459:
|-
|-
!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
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L|| L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|-
|-
|LsssLss
|LsssLss
Line 545: Line 471:
|-
|-
|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 554: Line 480:
|-
|-
|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 560: Line 486:
|-
|-
!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 616: Line 542:
|minor||diminished
|minor||diminished
|perfect
|perfect
|minor
| minor
|minor||perfect
|minor|| perfect
|}
|}


Line 626: Line 552:
!Number of periods
!Number of periods
!Name
!Name
!Prefix
! Prefix
|-
|-
|[[1L 1s]]
|[[1L 1s]]
| 2
|2
|1
|1
|trivial
|trivial
Line 635: Line 561:
|-
|-
|[[1L 1s]]
|[[1L 1s]]
| 2
|2
|1
|1
|monowood
|monowood
Line 641: Line 567:
|-
|-
|[[1L 2s]]
|[[1L 2s]]
| 3
|3
|1
|1
|antrial
|antrial
Line 647: Line 573:
|-
|-
|[[2L 1s]]
|[[2L 1s]]
| 3
|3
|1
|1
|trial
|trial
Line 653: Line 579:
|-
|-
|[[1L 3s]]
|[[1L 3s]]
| 4
|4
|1
|1
|antetric
|antetric
Line 659: Line 585:
|-
|-
|[[2L 2s]]
|[[2L 2s]]
| 4
|4
|2
|2
|biwood
|biwood
Line 665: Line 591:
|-
|-
|[[3L 1s]]
|[[3L 1s]]
| 4
|4
|1
|1
|tetric
|tetric
Line 671: Line 597:
|-
|-
|[[1L 4s]]
|[[1L 4s]]
| 5
|5
|1
|1
|pedal
|pedal
Line 677: Line 603:
|-
|-
|[[2L 3s]]
|[[2L 3s]]
| 5
|5
|1
|1
|pentic
|pentic
Line 683: Line 609:
|-
|-
|[[3L 2s]]
|[[3L 2s]]
| 5
|5
|1
|1
|antipentic
|antipentic
Line 689: Line 615:
|-
|-
|[[4L 1s]]
|[[4L 1s]]
| 5
|5
|1
|1
|manual
|manual
Line 695: Line 621:
|-
|-
|[[1L 5s]]
|[[1L 5s]]
| 6
|6
|1
|1
|antimachinoid
|antimachinoid
Line 701: Line 627:
|-
|-
|[[2L 4s]]
|[[2L 4s]]
| 6
|6
|2
|2
|anticitric
|anticitric
Line 707: Line 633:
|-
|-
|[[3L 3s]]
|[[3L 3s]]
| 6
|6
|3
|3
|triwood
|triwood
Line 713: Line 639:
|-
|-
|[[4L 2s]]
|[[4L 2s]]
| 6
|6
|2
|2
|citric
|citric
Line 731: Line 657:
|-
|-
|[[2L 5s]]
|[[2L 5s]]
| 7
|7
|1
|1
|antidiatonic
| antidiatonic
|pel-
|pel-
|-
|-
|[[3L 4s]]
|[[3L 4s]]
| 7
|7
|1
|1
|mosh
|mosh
Line 743: Line 669:
|-
|-
|[[4L 3s]]
|[[4L 3s]]
| 7
|7
|1
|1
|smitonic
|smitonic
Line 749: Line 675:
|-
|-
|[[5L 2s]]
|[[5L 2s]]
| 7
|7
|1
|1
|diatonic
|diatonic
Line 755: Line 681:
|-
|-
|[[6L 1s]]
|[[6L 1s]]
| 7
|7
|1
| 1
|arch(a)eotonic
|arch(a)eotonic
|arch-
|arch-
|-
|-
|[[1L 7s]]
|[[1L 7s]]
| 8
|8
|1
|1
|antipine
|antipine
Line 779: Line 705:
|-
|-
|[[4L 4s]]
|[[4L 4s]]
| 8
|8
|4
|4
|tetrawood; diminished
|tetrawood; diminished
Line 785: Line 711:
|-
|-
|[[5L 3s]]
|[[5L 3s]]
| 8
|8
|1
|1
|oneirotonic
|oneirotonic
Line 791: Line 717:
|-
|-
|[[6L 2s]]
|[[6L 2s]]
| 8
|8
|2
|2
|ekic
|ekic
Line 797: Line 723:
|-
|-
|[[7L 1s]]
|[[7L 1s]]
| 8
|8
|1
|1
|pine
|pine
Line 803: Line 729:
|-
|-
|[[1L 8s]]
|[[1L 8s]]
| 9
|9
|1
|1
|antisubneutralic
|antisubneutralic
Line 809: Line 735:
|-
|-
|[[2L 7s]]
|[[2L 7s]]
| 9
|9
|1
| 1
|balzano
|balzano
|bal- /bæl/
|bal- /bæl/
|-
|-
|[[3L 6s]]
|[[3L 6s]]
| 9
|9
|3
|3
|tcherepnin
|tcherepnin
Line 821: Line 747:
|-
|-
|[[4L 5s]]
|[[4L 5s]]
| 9
|9
|1
|1
|gramitonic
|gramitonic
Line 827: Line 753:
|-
|-
|[[5L 4s]]
|[[5L 4s]]
| 9
|9
|1
|1
|semiquartal
| semiquartal
|cthon-
|cthon-
|-
|-
|[[6L 3s]]
|[[6L 3s]]
| 9
|9
|3
|3
|hyrulic
|hyrulic
Line 839: Line 765:
|-
|-
|[[7L 2s]]
|[[7L 2s]]
| 9
|9
|1
|1
|superdiatonic
|superdiatonic
Line 845: Line 771:
|-
|-
|[[8L 1s]]
|[[8L 1s]]
| 9
|9
|1
|1
|subneutralic
|subneutralic
Line 851: Line 777:
|-
|-
|[[1L 9s]]
|[[1L 9s]]
| 10
|10
|1
|1
|antisinatonic
| antisinatonic
|asina-
|asina-
|-
|-
|[[2L 8s]]
|[[2L 8s]]
| 10
|10
|2
|2
|jaric
|jaric
Line 863: Line 789:
|-
|-
|[[3L 7s]]
|[[3L 7s]]
| 10
|10
|1
|1
|sephiroid
|sephiroid
|seph-
| seph-
|-
|-
|[[4L 6s]]
|[[4L 6s]]
| 10
|10
|2
|2
|lime
|lime
Line 875: Line 801:
|-
|-
|[[5L 5s]]
|[[5L 5s]]
| 10
|10
|5
|5
|pentawood
|pentawood
|penwd-
| penwd-
|-
|-
|[[6L 4s]]
|[[6L 4s]]
| 10
|10
|2
|2
|lemon
|lemon
Line 887: Line 813:
|-
|-
|[[7L 3s]]
|[[7L 3s]]
| 10
|10
|1
|1
|dicoid /'daɪkɔɪd/
|dicoid /'daɪkɔɪd/
Line 893: Line 819:
|-
|-
|[[8L 2s]]
|[[8L 2s]]
| 10
|10
|2
|2
|taric
|taric
Line 899: Line 825:
|-
|-
|[[9L 1s]]
|[[9L 1s]]
| 10
|10
|1
|1
|sinatonic
|sinatonic
Line 905: Line 831:
|}
|}


==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
!Bright gen.
!Bright gen.
! Dark gen.
!Dark gen.
! L
!L
!s
!s
!L/s
!L/s
Line 923: Line 849:
|600.000
|600.000
|600.000
|600.000
|1
| 1
|1
|1
|1.000
|1.000
Line 937: Line 863:
|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 951: Line 877:
|5
|5
|4
|4
|1.250
| 1.250
|-
|-
|
|
Line 958: Line 884:
|
|
|
|
|9\16
| 9\16
| 675.000
|675.000
|525.000
|525.000
|9
|9
Line 1,011: Line 937:
|705.882
|705.882
|494.118
|494.118
|10
| 10
|7
|7
|1.429
| 1.429
|-
|-
|
|
Line 1,113: Line 1,039:
|9
|9
|5
|5
|1.800
| 1.800
|-
|-
|
|
Line 1,138: Line 1,064:
|9
|9
|4
|4
| 2.250
|2.250
| rowspan="3" |3L 4s range (includes 3L 7s and 7L 3s)
| rowspan="3" |3L 4s range (includes 3L 7s and 7L 3s)
|-
|-
Line 1,161: Line 1,087:
|847.059
|847.059
|352.941
|352.941
|12
| 12
|5
|5
|2.400
| 2.400
|-
|-
|
|
Line 1,288: Line 1,214:
|9
|9
|2
|2
| 4.500
|4.500
| rowspan="3" |Range of 4L 1s (includes 5L 1s and 1L 5s)
| rowspan="3" |Range of 4L 1s (includes 5L 1s and 1L 5s)
|-
|-
Line 1,309: Line 1,235:
|
|
|6\7
|6\7
|1028.571
| 1028.571
|171.429
|171.429
|6
| 6
|1
| 1
|6.000
|6.000
|-
|-
Line 1,336: Line 1,262:
!1st ancestor
!1st ancestor
!Mos
!Mos
!1st descendants
! 1st descendants
!2nd descendants
!2nd descendants
|-
|-
Line 1,345: Line 1,271:
|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 08:03, 19 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

MOS mode degrees

Scale degrees of 5L 2s modes (step pattern of LsLLsAs)
UDP and alterations Rotational Order Step pattern Mode names Scale degree (mosdegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Harmonic minor Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Locrian #6 Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Ionian augmented Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Dorian #4 Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Phrygian dominant Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Lydian #2 Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Locrian b4 bb7 Perf. Min. Min. Dim. Dim. Min. Dim. Perf.
Scale degrees of 5L 2s modes (step pattern of LLLLsLs)
UDP and alterations Rotational Order Step pattern Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 A4md 1 LLLLsLs Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md 2 LLLsLsL Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md 3 LLsLsLL Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md 4 LsLsLLL Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md 5 sLsLLLL Perf. Min. Min. Dim. Dim. Min. Min. Perf.
5|1 m2md 6 LsLLLLs Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md 7 sLLLLsL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
Scale degrees of 5L 2s modes (step pattern of LLLLLss)
UDP and alterations Rotational Order Step pattern Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 A4md A5md 1 LLLLLss Perf. Maj. Maj. Aug. Aug. Aug. Maj. Perf.
6|0 A4md m6md 2 LLLLssL Perf. Maj. Maj. Aug. Aug. Maj. Min. Perf.
6|0 m5md m6md 3 LLLssLL Perf. Maj. Maj. Aug. Perf. Min. Min. Perf.
4|2 d4md m5md 4 LLssLLL Perf. Maj. Maj. Perf. Dim. Min. Min. Perf.
2|4 d3md d4md 5 LssLLLL Perf. Maj. Min. Dim. Dim. Min. Min. Perf.
0|6 d2md d3md 6 ssLLLLL Perf. Min. Dim. Dim. Dim. Min. Min. Perf.
5|1 m1md m2md 7 sLLLLLs Perf. Min. Min. Perf. Perf. Maj. Maj. 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 step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2nx+ny)ed<p/q> (L = 2 and s = 1), (3nx+ny)ed<p/q> (L = 3 and s = 1), and (3nx+2ny)ed<p/q> (L = 3 and s = 2).

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 step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2x+y)ed<p/q> (L = 2 and s = 1), (3x+y)ed<p/q> (L = 3 and s = 1), and (3x+2y)ed<p/q> (L = 3 and s = 2).

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 step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2nx+ny)ed<p/q> (L = 2 and s = 1), (3nx+ny)ed<p/q> (L = 3 and s = 1), and (3nx+2ny)ed<p/q> (L = 3 and s = 2).

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 step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2x+y)ed<p/q> (L = 2 and s = 1), (3x+y)ed<p/q> (L = 3 and s = 1), and (3x+2y)ed<p/q> (L = 3 and s = 2).

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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