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.
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.




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== Conditional (MM=Ls) ==
== Conditional (MM=Ls) ==


'''1L 2M 5s'''
'''<u>6-1-1 Family</u>'''


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


LsssMMss / LssMMsss


'''1L 6M 1s:''' LMsMMMMM / LMMMMMsM


'''1L 4M 3s'''


LsMMsMsM / LMsMsMMs
'''1L 6M 1s:''' LsMMMMMM / LMMMMMMs


LsMsMMsM / LMsMMsMs


LssMMMMs / LsMMMMss
'''<u>5-2-1 Family</u>'''


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


'''1L 6M 1s'''
'''1L 2M 5s:''' LsMssMss


LMMsMMMM / LMMMMsMM


LMsMMMMM / LMMMMMsM


LsMMMMMM / LMMMMMMs
'''5L 2M 1s:''' LLMLLMLs


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


'''2L 4M 2s'''


LLsMMMMs


LMLsMMMs
'''5L 2M 1s:''' LLLsLLMM


LMMLsMMs
'''1L 2M 5s:''' LssMMsss


LMMMLsMs


LMMMMLss


LMMsLsMM
'''5L 2M 1s:''' LLLMMLLs


LMMsMMLs
'''1L 2M 5s:''' LsssMMss


LMsLMsMM / LMMsMLsM


LMsLsMMM / LMMMsLsM


LMsMLsMM / LMMsLMsM
'''<u>4-3-1 Family</u>'''


LMsMMLsM / LMMsMLMs
'''3L 4M 1s:''' LMLsMLMM


LMsMMMLs / LMMMsMLs
'''1L 4M 3s:''' LMsMMsMs


LsLsMMMM / LMMMMsLs


LsMLsMMM / LMMMsLMs


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


'''3L 2M 3s'''
'''1L 4M 3s:''' LsMMsMsM


LMsLsLsM


LMsMLsLs


LsLsLsMM / LMMsLsLs
'''3L 4M 1s:''' LMLMMLsM


LsLsMLsM / LMsLMsLs
'''1L 4M 3s:''' LMsMsMMs




'''3L 4M 1s'''


LLsLMMMM / LLMMMMLs
'''3L 4M 1s:''' LMLMMLMs


LMLMsLMM / LMLMMLsM
'''1L 4M 3s:''' LsMsMMsM


LMLsMLMM / LMLMMLMs




'''5L 2M 1s'''
'''3L 4M 1s:''' LLsLMMMM


LLLsLLMM / LLLMMLLs
'''1L 4M 3s:''' LsMMMMss


LLMLLsLM / LLMLLMLs
 
 
'''3L 4M 1s:''' LLMMMMLs
 
'''1L 4M 3s:''' LssMMMMs
 
 
 
'''<u>4-2-2 Family</u>'''
 
'''2L 4M 2s:''' LMsLMsMM / LMMsMLsM
 
 
'''2L 4M 2s:''' LMMsMLMs
 
'''2L 4M 2s:''' LMsMLsMM
 
 
 
'''2L 4M 2s:''' LMMsLsMM
 
'''2L 4M 2s:''' LMMsMMLs
 
 
 
'''2L 4M 2s:''' LMMsLMsM
 
'''2L 4M 2s:''' LMsMMLsM
 
 
 
'''2L 4M 2s:''' LMMMsMLs
 
'''2L 4M 2s:''' LMsLsMMM
 
 
 
'''2L 4M 2s:''' LMMMsLsM
 
'''2L 4M 2s:''' LMsMMMLs
 
 
 
'''2L 4M 2s:''' LsMLsMMM / LMMMsLMs
 
 
'''2L 4M 2s:''' LsLsMMMM / LMMMMsLs
 
 
'''2L 4M 2s:''' LMMLsMMs
 
 
 
'''2L 4M 2s:''' LMLsMMMs
 
'''2L 4M 2s:''' LMMMLsMs
 
 
 
'''2L 4M 2s:''' LLsMMMMs
 
'''2L 4M 2s:''' LMMMMLss
 
 
 
'''<u>3-3-2 Family</u>'''
 
'''3L 2M 3s:''' LMsLsLsM
 
'''3L 2M 3s:''' LMsMLsLs
 
 
 
'''3L 2M 3s:''' LsLsMLsM / LMsLMsLs
 
 
'''3L 2M 3s:''' LsLsLsMM / LMMsLsLs




== Conditional (MMM=sLs) ==
== Conditional (MMM=sLs) ==


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




== Conditional (MMM=LsL) ==
== Conditional (MMM=LsL) ==


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

Revision as of 20:52, 18 October 2021

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.


Here's some stats:

55 Scales Total (incl. chirals)

33 Scales Total (not incl. chirals)


0 Unconditional Scales (incl. chirals)

0 Unconditional Scales (not incl. chirals)


53 Conditional (MM=Ls) Scales (incl. chirals)

31 Conditional (MM=Ls) Scales (not incl. chirals)


1 Conditional (MMM=sLs) Scale (not chiral)

1 Conditional (MMM=LsL) Scale (not chiral)


44 Chiral Scales Total (22 pairs)

11 Achiral Scales Total


Unconditional

NONE


Conditional (MM=Ls)

6-1-1 Family

1L 6M 1s: LMMsMMMM / LMMMMsMM


1L 6M 1s: LMsMMMMM / LMMMMMsM


1L 6M 1s: LsMMMMMM / LMMMMMMs


5-2-1 Family

5L 2M 1s: LLMLLsLM

1L 2M 5s: LsMssMss


5L 2M 1s: LLMLLMLs

1L 2M 5s: LssMssMs


5L 2M 1s: LLLsLLMM

1L 2M 5s: LssMMsss


5L 2M 1s: LLLMMLLs

1L 2M 5s: LsssMMss


4-3-1 Family

3L 4M 1s: LMLsMLMM

1L 4M 3s: LMsMMsMs


3L 4M 1s: LMLMsLMM

1L 4M 3s: LsMMsMsM


3L 4M 1s: LMLMMLsM

1L 4M 3s: LMsMsMMs


3L 4M 1s: LMLMMLMs

1L 4M 3s: LsMsMMsM


3L 4M 1s: LLsLMMMM

1L 4M 3s: LsMMMMss


3L 4M 1s: LLMMMMLs

1L 4M 3s: LssMMMMs


4-2-2 Family

2L 4M 2s: LMsLMsMM / LMMsMLsM


2L 4M 2s: LMMsMLMs

2L 4M 2s: LMsMLsMM


2L 4M 2s: LMMsLsMM

2L 4M 2s: LMMsMMLs


2L 4M 2s: LMMsLMsM

2L 4M 2s: LMsMMLsM


2L 4M 2s: LMMMsMLs

2L 4M 2s: LMsLsMMM


2L 4M 2s: LMMMsLsM

2L 4M 2s: LMsMMMLs


2L 4M 2s: LsMLsMMM / LMMMsLMs


2L 4M 2s: LsLsMMMM / LMMMMsLs


2L 4M 2s: LMMLsMMs


2L 4M 2s: LMLsMMMs

2L 4M 2s: LMMMLsMs


2L 4M 2s: LLsMMMMs

2L 4M 2s: LMMMMLss


3-3-2 Family

3L 2M 3s: LMsLsLsM

3L 2M 3s: LMsMLsLs


3L 2M 3s: LsLsMLsM / LMsLMsLs


3L 2M 3s: LsLsLsMM / LMMsLsLs


Conditional (MMM=sLs)

1L 5M 2s: LsMMMMMs


Conditional (MMM=LsL)

2L 5M 1s: LMMMMMLs

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