User:Xenoindex/Octotonic MV3: Difference between revisions

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I believe these are all of the strict MV3 scales with eight notes. There are no unconditional eight note MV3 scales that may have any L:M:s ratio and still be strict MV3, note that this means that there exist hardnesses (such as 5:2:1) with no possible strict MV3 scales with eight notes. Conditional MV3 scales have a condition specified in the section header that the L:M:s ratio needs to satisfy in order for the scale to be strict MV3. Lines with two scales separated with a slash are lexicographically left and right chiral scales respectively, lines with only one scale are therefore achiral. All scales are written in their brightest mode. Scales are grouped into ~~families and~~ sisterhoods however, conditional sisterhoods appear to only have up to two sisters unlike unconditional sisterhoods which may have up to six. The two scales in conditional sisterhoods have their L's and s's swapped.

I believe these are all of the strict MV3 scales with eight notes. There are no unconditional eight note MV3 scales that may have any L:M:s ratio and still be strict MV3, note that this means that there exist hardnesses (such as 5:2:1) with no possible strict MV3 scales with eight notes. Conditional MV3 scales have a condition specified in the section header that the L:M:s ratio needs to satisfy in order for the scale to be strict MV3. Lines with two scales separated with a slash are lexicographically left and right chiral scales respectively, lines with only one scale are therefore achiral. All scales are written in their brightest mode. Scales are grouped into sisterhoods however, conditional sisterhoods appear to only have up to two sisters unlike unconditional sisterhoods which may have up to six. The two scales in conditional sisterhoods have their L's and s's swapped.

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== Conditional (MM=Ls) ==

~~'''~~6-~~1-1 Family~~~~'''~~

=== Single-Period ===

'''1L 6M 1s:''' LMMsMMMM / LMMMMsMM

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~~'''5-2-1 Family'''~~

'''5L 2M 1s:''' LLMLLsLM

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~~'''4-3-1 Family'''~~

'''3L 4M 1s:''' LMLsMLMM

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~~'''4-2-2 Family'''~~

'''2L 4M 2s:''' LMsLMsMM / LMMsMLsM

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~~'''3-3-2 Family'''~~

'''3L 2M 3s:''' LMsLsLsM

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'''3L 2M 3s:''' LsLsLsMM / LMMsLsLs

=== Multi-Period ===

'''2L 4M 2s:''' LsMMLsMM / LMMsLMMs

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-I believe these are all of the strict MV3 scales with eight notes. There are no unconditional eight note MV3 scales that may have any L:M:s ratio and still be strict MV3, note that this means that there exist hardnesses (such as 5:2:1) with no possible strict MV3 scales with eight notes. Conditional MV3 scales have a condition specified in the section header that the L:M:s ratio needs to satisfy in order for the scale to be strict MV3. Lines with two scales separated with a slash are lexicographically left and right chiral scales respectively, lines with only one scale are therefore achiral. All scales are written in their brightest mode. Scales are grouped into families and sisterhoods however, conditional sisterhoods appear to only have up to two sisters unlike unconditional sisterhoods which may have up to six. The two scales in conditional sisterhoods have their L's and s's swapped.
+I believe these are all of the strict MV3 scales with eight notes. There are no unconditional eight note MV3 scales that may have any L:M:s ratio and still be strict MV3, note that this means that there exist hardnesses (such as 5:2:1) with no possible strict MV3 scales with eight notes. Conditional MV3 scales have a condition specified in the section header that the L:M:s ratio needs to satisfy in order for the scale to be strict MV3. Lines with two scales separated with a slash are lexicographically left and right chiral scales respectively, lines with only one scale are therefore achiral. All scales are written in their brightest mode. Scales are grouped into sisterhoods however, conditional sisterhoods appear to only have up to two sisters unlike unconditional sisterhoods which may have up to six. The two scales in conditional sisterhoods have their L's and s's swapped.
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 == Conditional (MM=Ls) ==
-'''<u>6-1-1 Family</u>'''
+=== <u>Single-Period</u> ===
 '''1L 6M 1s:''' LMMsMMMM / LMMMMsMM
@@ Line 48: / Line 48: @@
-'''<u>5-2-1 Family</u>'''
 '''5L 2M 1s:''' LLMLLsLM
@@ Line 73: / Line 72: @@
-'''<u>4-3-1 Family</u>'''
 '''3L 4M 1s:''' LMLsMLMM
@@ Line 111: / Line 108: @@
-'''<u>4-2-2 Family</u>'''
 '''2L 4M 2s:''' LMsLMsMM / LMMsMLsM
@@ Line 168: / Line 163: @@
-'''<u>3-3-2 Family</u>'''
 '''3L 2M 3s:''' LMsLsLsM
@@ Line 181: / Line 174: @@
 '''3L 2M 3s:''' LsLsLsMM / LMMsLsLs
+=== <u>Multi-Period</u> ===
+'''2L 4M 2s:''' LsMMLsMM / LMMsLMMs