Talk:Maximum variety: Difference between revisions

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== Relationship Between Pairwise-Well-Formed scales and MV3 ==

I wrote this elsewhere at some point, but it would also be good to clarify the relationship between

~~1. Pairwise-Well-Formed scales - those which temper to (strict) MOS in three different ways~~

~~2. Pairwise DE scales - those which temper to DE in three different ways~~

~~3. "Triple Fokker PBs" or "Wakalixes" - which are a Fokker PB in three different ways (I think the current definition of "wakalix," which is from Gene, is even more general)~~

~~4. Scales which have variety exactly equal to 3 for all intervals~~

~~5. Scales which have variety *at most* 3 for all intervals, but for which some can be 1 or 2~~

~~6. Scales which have this generator offset property~~

If memory serves, these are basically all the same thing, modulo the one main quirk regarding if we want *exactly 3* or *at most 3* interval sizes (and similarly with strict MOS / DE in the product words), and with some extra quirkiness with the two scales aabcb and abacaba which are exceptions otherwise. The Zabka paper had some good stuff about all of this.

# Pairwise-Well-Formed scales - those which temper to (strict) MOS in three different ways

# Pairwise DE scales - those which temper to DE in three different ways

# "Triple Fokker PBs" or "Wakalixes" - which are a Fokker PB in three different ways (I think the current definition of "wakalix," which is from Gene, is even more general)

# Scales which have variety exactly equal to 3 for all intervals

# Scales which have variety *at most* 3 for all intervals, but for which some can be 1 or 2

# MV3 scales which also have this generator offset property

If memory serves, these are basically all the same thing, modulo the one main quirk regarding if we want *exactly 3* or *at most 3* interval sizes (and similarly with strict MOS / DE in the product words), and with some extra quirkiness with the two scales aabcb and abacaba which are exceptions otherwise. The Zabka paper had some good stuff about all of this. This is also regarding scale words which are "almost always" MV3 (see note about "Sporadic MV3" scales above.)

== Connections to 5L 2s MODMOSes ==

Hey, Moremajorthanmajor, I think we need to go into the technical specifications as to how 1L 3m 3s with the pattern 4 3 2 3 2 3 2 relates to LsLLsAs and LLsLsAs. It looks like the latter two might also be Metathetic variants of the former, and thus, we need to take stock of the various properties of MV3 scales. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:54, 12 May 2021 (UTC)

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 == Relationship Between Pairwise-Well-Formed scales and MV3 ==
 I wrote this elsewhere at some point, but it would also be good to clarify the relationship between
-. Pairwise-Well-Formed scales - those which temper to (strict) MOS in three different ways
-. Pairwise DE scales - those which temper to DE in three different ways
-. "Triple Fokker PBs" or "Wakalixes" - which are a Fokker PB in three different ways (I think the current definition of "wakalix," which is from Gene, is even more general)
-. Scales which have variety exactly equal to 3 for all intervals
-. Scales which have variety *at most* 3 for all intervals, but for which some can be 1 or 2
-. Scales which have this generator offset property
-If memory serves, these are basically all the same thing, modulo the one main quirk regarding if we want *exactly 3* or *at most 3* interval sizes (and similarly with strict MOS / DE in the product words), and with some extra quirkiness with the two scales aabcb and abacaba which are exceptions otherwise. The Zabka paper had some good stuff about all of this.
+# Pairwise-Well-Formed scales - those which temper to (strict) MOS in three different ways
+# Pairwise DE scales - those which temper to DE in three different ways
+# "Triple Fokker PBs" or "Wakalixes" - which are a Fokker PB in three different ways (I think the current definition of "wakalix," which is from Gene, is even more general)
+# Scales which have variety exactly equal to 3 for all intervals
+# Scales which have variety *at most* 3 for all intervals, but for which some can be 1 or 2
+# MV3 scales which also have this generator offset property
+If memory serves, these are basically all the same thing, modulo the one main quirk regarding if we want *exactly 3* or *at most 3* interval sizes (and similarly with strict MOS / DE in the product words), and with some extra quirkiness with the two scales aabcb and abacaba which are exceptions otherwise. The Zabka paper had some good stuff about all of this. This is also regarding scale words which are "almost always" MV3 (see note about "Sporadic MV3" scales above.)
 == Connections to 5L 2s MODMOSes ==
 Hey, Moremajorthanmajor, I think we need to go into the technical specifications as to how 1L 3m 3s with the pattern 4 3 2 3 2 3 2 relates to LsLLsAs and LLsLsAs.  It looks like the latter two might also be Metathetic variants of the former, and thus, we need to take stock of the various properties of MV3 scales. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:54, 12 May 2021 (UTC)