User:Xenoindex/Heptatonic MV3
I believe these are all of the strict MV3 scales with seven 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:
54 Scales Total (incl. chirals)
33 Scales Total (not incl. chirals)
24 Unconditional Scales (incl. chirals)
15 Unconditional Scales (not incl. chirals)
30 Conditional Scales Total (incl. chirals)
18 Conditional Scales Total (not incl. chirals)
28 Conditional (MM=Ls) Scales (incl. chirals)
16 Conditional (MM=Ls) Scales (not incl. chirals)
1 Conditional (MMM=LsL) Scale (not chiral)
1 Conditional (MMM=sLs) Scale (not chiral)
42 Chiral Scales Total (21 pairs)
18 Chiral Unconditional Scales (9 pairs)
24 Chiral Conditional (MM=Ls) Scales (12 pairs)
0 Chiral Conditional (MMM=LsL) Scales
0 Chiral Conditional (MMM=sLs) Scales
12 Achiral Scales Total
6 Achiral Unconditional Scales
4 Achiral Conditional (MM=Ls) Scales
1 Achiral Conditional (MMM=LsL) Scale
1 Achiral Conditional (MMM=sLs) Scale
Unconditional
Single-Period
5L 1M 1s: LLLsLLM / LLLMLLs
1L 5M 1s: LMMsMMM / LMMMsMM
1L 1M 5s: LsssMss / LssMsss
3L 3M 1s:
LMLMLsM / LMLMLMs
3L 1M 3s: LsLsLsM / LMsLsLs
1L 3M 3s: LsMsMsM / LMsMsMs
3L 2M 2s:
LMLsMLs / LMLsLMs
2L 3M 2s: LMsMLsM / LMsLMsM
2L 2M 3s: LsMLsMs / LMsLsMs
4L 2M 1s:
LLMLsLM
4L 1M 2s: LLsLMLs
2L 4M 1s: LMMLMsM
2L 1M 4s: LsMsLss
1L 4M 2s: LMsMMsM
1L 2M 4s: LsMssMs
Multi-Period
(none)
Conditional (MM=Ls)
Single-Period
5-1-1 Family
1L 5M 1s: LMsMMMM / LMMMMsM
1L 5M 1s: LsMMMMM / LMMMMMs
4-2-1 Family
2L 4M 1s: LMMLsMM
1L 4M 2s: LMMsMMs
2L 4M 1s: LMMLMMs
1L 4M 2s: LsMMsMM
4L 2M 1s: LLsLMLM
1L 2M 4s: LsMsMss
4L 2M 1s: LLMLMLs
1L 2M 4s: LssMsMs
3-3-1 Family
3L 3M 1s: LLsLMMM
1L 3M 3s: LsMMMss
3L 3M 1s: LLMMMLs
1L 3M 3s: LssMMMs
3-2-2 Family
2L 3M 2s: LMMsMLs
2L 3M 2s: LMsLsMM
2L 3M 2s: LMMsLsM
2L 3M 2s: LMsMMLs
2L 3M 2s: LsMLsMM / LMMsLMs
2L 3M 2s: LsLsMMM / LMMMsLs
2L 3M 2s: LMLsMMs
2L 3M 2s: LMMLsMs
2L 3M 2s: LLsMMMs
2L 3M 2s: LMMMLss
Multi-Period
(none)
Conditional (MMM=LsL)
2L 4M 1s: LMMMMLs
Conditional (MMM=sLs)
1L 4M 2s: LsMMMMs