User:Xenoindex/Decatonic MV3

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I believe these are all of the strict MV3 scales with ten notes. Unconditional MV3 scales may have any L:M:s ratio. 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. Unconditional sisterhoods may have up to six scales while conditional sisterhoods appear to have up to two scales. The two scales in conditional sisterhoods have their L's and s's swapped.


Here's some stats:

193 Scales Total

12 Unconditional Single-Period

161 Conditional Single-Period

16 Unconditional Multi-Period

4 Conditional Multi-Period


Unconditional

Single-Period

6L 2M 2s: LLMLLsLMLs

6L 2M 2s: LLMLsLMLLs

2L 6M 2s: LMMsMLMsMM

2L 6M 2s: LMMsMMLMsM

2L 2M 6s: LsMsLssMss

2L 2M 6s: LsMssLssMs


4L 4M 2s: LMLMLsMLMs

4L 4M 2s: LMLMsLMLsM

4L 2M 4s: LMsLsLsMLs

4L 2M 4s: LMsLsMLsLs

2L 4M 4s: LMsMLsMsMs

2L 4M 4s: LMsMsMLsMs


Multi-Period

4L 4M 2s: LMLsMLMLsM / LMLMsLMLMs

4L 2M 4s: LsLsMLsLsM / LMsLsLMsLs

2L 4M 4s: LsMsMLsMsM / LMsMsLMsMs


6L 2M 2s: LLsLMLLsLM / LLMLsLLMLs

2L 6M 2s: LMsMMLMsMM / LMMsMLMMsM

2L 2M 6s: LssMsLssMs / LsMssLsMss


4L 4M 2s: LLMsMLLMsM

4L 2M 4s: LLsMsLLsMs

4L 2M 4s: LMLssLMLss

2L 4M 4s: LMssMLMssM


Conditional (MM=Ls)

Single-Period

1L 8M 1s: LMMMsMMMMM / LMMMMMsMMM


1L 8M 1s: LMMsMMMMMM / LMMMMMMsMM


1L 8M 1s: LMsMMMMMMM / LMMMMMMMsM


1L 8M 1s: LsMMMMMMMM / LMMMMMMMMs


7L 2M 1s: LLLsLLMLLM

1L 2M 7s: LssMssMsss


7L 2M 1s: LLLMLLsLLM

1L 2M 7s: LssMsssMss


7L 2M 1s: LLLMLLMLLs

1L 2M 7s: LsssMssMss


7L 2M 1s: LLLLsLLLMM

1L 2M 7s: LsssMMssss


7L 2M 1s: LLLLMMLLLs

1L 2M 7s: LssssMMsss


3L 6M 1s: LMMLMMLsMM

1L 6M 3s: LMMsMMsMMs


3L 6M 1s: LMMLMMLMsM

1L 6M 3s: LMsMMsMMsM


3L 6M 1s: LMMLMMLMMs

1L 6M 3s: LsMMsMMsMM


3L 6M 1s: LMLsMLMMMM

1L 6M 3s: LMsMMMMsMs


3L 6M 1s: LMLMsLMMMM

1L 6M 3s: LsMMMMsMsM


3L 6M 1s: LMLMMMMLsM

1L 6M 3s: LMsMsMMMMs


3L 6M 1s: LMLMMMMLMs

1L 6M 3s: LsMsMMMMsM


3L 6M 1s: LLsLMMMMMM

1L 6M 3s: LsMMMMMMss


3L 6M 1s: LLMMMMMMLs

1L 6M 3s: LssMMMMMMs


2L 6M 2s: LMMsMMLsMM / LMMsLMMsMM


2L 6M 2s: LMMMsMMLsM

2L 6M 2s: LMMsLMsMMM


2L 6M 2s: LMMMsMMLMs

2L 6M 2s: LMMsMLsMMM


2L 6M 2s: LMMMsMLsMM

2L 6M 2s: LMMsMMMLMs


2L 6M 2s: LMsMLMsMMM / LMMMsMLMsM


2L 6M 2s: LMMMsMLMMs

2L 6M 2s: LMsMMLsMMM


2L 6M 2s: LMMMsLsMMM

2L 6M 2s: LMMMsMMMLs


2L 6M 2s: LMMMsLMsMM

2L 6M 2s: LMMsMMMLsM


2L 6M 2s: LMMMsLMMsM

2L 6M 2s: LMsMMMLsMM


2L 6M 2s: LMMMMsMMLs

2L 6M 2s: LMMsLsMMMM


2L 6M 2s: LMsLMsMMMM / LMMMMsMLsM


2L 6M 2s: LMMMMsMLMs

2L 6M 2s: LMsMLsMMMM


2L 6M 2s: LMMMMsLsMM

2L 6M 2s: LMMsMMMMLs


2L 6M 2s: LMMMMsLMsM

2L 6M 2s: LMsMMMMLsM


2L 6M 2s: LsMMLsMMMM / LMMMMsLMMs


2L 6M 2s: LMMMMMsMLs

2L 6M 2s: LMsLsMMMMM


2L 6M 2s: LMMMMMsLsM

2L 6M 2s: LMsMMMMMLs


2L 6M 2s: LsMLsMMMMM / LMMMMMsLMs


2L 6M 2s: LsLsMMMMMM / LMMMMMMsLs


2L 6M 2s: LMMMLsMMMs


2L 6M 2s: LMMLsMMMMs

2L 6M 2s: LMMMMLsMMs


2L 6M 2s: LMLsMMMMMs

2L 6M 2s: LMMMMMLsMs


2L 6M 2s: LLsMMMMMMs

2L 6M 2s: LMMMMMMLss


5L 4M 1s: LLsLMLMMLM

1L 4M 5s: LsMsMMsMss


5L 4M 1s: LLMMMLMLLs

1L 4M 5s: LssMMMsMss


5L 4M 1s: LLMMMLLsLM

1L 4M 5s: LsMssMMMss


5L 4M 1s: LLMMLMLsLM

1L 4M 5s: LsMssMMsMs


5L 4M 1s: LLMMLLsLMM

1L 4M 5s: LsMMssMMss


5L 4M 1s: LLMMLLMMLs

1L 4M 5s: LssMMssMMs


5L 4M 1s: LLMLsLMLMM

1L 4M 5s: LsMsMMssMs


5L 4M 1s: LLMLsLLMMM

1L 4M 5s: LssMMMssMs


5L 4M 1s: LLMLMMMLLs

1L 4M 5s: LssMsMMMss


5L 4M 1s: LLMLMMLMLs

1L 4M 5s: LssMsMMsMs


5L 2M 3s: LLsLsLMMLs

3L 2M 5s: LsLsMMsLss


5L 2M 3s: LLsLMMLsLs

3L 2M 5s: LsLssLsMMs


4L 2M 4s: LMsLsLsLsM

4L 2M 4s: LMsMLsLsLs


4L 2M 4s: LsLsLsMLsM / LMsLMsLsLs


4L 2M 4s: LsLsLsLsMM / LMMsLsLsLs


4L 4M 2s: LMLsMLMMLs

2L 4M 4s: LMsMMsLsMs


4L 4M 2s: LMLsLMMLsM

2L 4M 4s: LMsMsLsMMs


4L 4M 2s: LMLsLMMLMs

2L 4M 4s: LsMMsMLsMs


4L 4M 2s: LMLMsLMMLs

2L 4M 4s: LsMMsLsMsM


3L 4M 3s: LMsLsMLMsM

3L 4M 3s: LMsMLMsMLs


3L 4M 3s: LMsMLsMLsM / LMsLMsLMsM


3L 4M 3s: LMMsMLsMLs

3L 4M 3s: LMsLMsLsMM


3L 4M 3s: LMsLsLMsMM / LMMsMLsLsM


3L 4M 3s: LMMsMLsLMs

3L 4M 3s: LMsLsMLsMM


3L 4M 3s: LMMsMLMsLs

3L 4M 3s: LMsMLsLsMM


3L 4M 3s: LMMsLsMLsM

3L 4M 3s: LMsLMsMMLs


3L 4M 3s: LMMsLsMLMs

3L 4M 3s: LMsMLsMMLs


3L 4M 3s: LMMsLsLsMM

3L 4M 3s: LMMsMMLsLs


3L 4M 3s: LMMsLsLMsM

3L 4M 3s: LMsMMLsLsM


3L 4M 3s: LMMsLMsMLs

3L 4M 3s: LMsLsMMLsM


3L 4M 3s: LMMsLMsLsM

3L 4M 3s: LMsMMLsMLs


3L 4M 3s: LsMLsMLsMM / LMMsLMsLMs


3L 4M 3s: LsLsMMLsMM / LMMsLMMsLs


3L 4M 3s: LMMMsMLsLs

3L 4M 3s: LMsLsLsMMM


3L 4M 3s: LMsLsMMMLs / LMMMsLsMLs


3L 4M 3s: LMMMsLsLsM

3L 4M 3s: LMsMMMLsLs


3L 4M 3s: LMMMsLsLMs

3L 4M 3s: LsLsMLsMMM


3L 4M 3s: LMMMsLMsLs

3L 4M 3s: LsLsMMMLsM


3L 4M 3s: LsLsLsMMMM / LMMMMsLsLs


Multi-Period

2L 6M 2s: LsMMMLsMMM / LMMMsLMMMs


Conditional (Not MM=Ls)

Single-Period

(none)


Multi-Period

4L 4M 2s: LMMLsLMMLs

2L 4M 4s: LsMMsLsMMs


Conditional (MMM=sLs)

1L 7M 2s: LsMMMMMMMs


Conditional (MMM=LsL)

2L 7M 1s: LMMMMMMMLs

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