User:Xenoindex/Octotonic MV3

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. 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:

57 Scales Total

0 Unconditional Single-Period

55 Conditional Single-Period

0 Unconditional Multi-Period

2 Conditional Multi-Period

Unconditional

NONE

Conditional (MM=Ls)

Single-Period

1L 6M 1s: LMMsMMMM / LMMMMsMM

1L 6M 1s: LMsMMMMM / LMMMMMsM

1L 6M 1s: LsMMMMMM / LMMMMMMs

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

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

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

3L 2M 3s: LMsLsLsM

3L 2M 3s: LMsMLsLs

3L 2M 3s: LsLsMLsM / LMsLMsLs

3L 2M 3s: LsLsLsMM / LMMsLsLs

Multi-Period

2L 4M 2s: LsMMLsMM / LMMsLMMs

Conditional (MMM=sLs)

1L 5M 2s: LsMMMMMs

Conditional (MMM=LsL)

2L 5M 1s: LMMMMMLs