Talk:Maximum variety - Revision history

Mike Battaglia at 00:16, 28 May 2022

2022-05-28T00:16:41Z

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	: [[User:Xenoindex/MV3 Lists\|This]] may be of interest to anyone interested in MV3 who hasn't seen it yet, basically I bruteforce found and listed all the MV3 up to 14 tones. May come in handy, let me know if anyone finds any mistakes. --[[User:Xenoindex\|Xenoindex]] ([[User talk:Xenoindex\|talk]]) 08:31, 24 May 2022 (UTC)		: [[User:Xenoindex/MV3 Lists\|This]] may be of interest to anyone interested in MV3 who hasn't seen it yet, basically I bruteforce found and listed all the MV3 up to 14 tones. May come in handy, let me know if anyone finds any mistakes. --[[User:Xenoindex\|Xenoindex]] ([[User talk:Xenoindex\|talk]]) 08:31, 24 May 2022 (UTC)

			:: Good stuff! It would be good to see if every scale is generated in this way from two alternating generators. I think if memory serves they all are except for scales of the form "aabcb" and "abacaba". Some of these aren't "pairwise well-formed" but only "pairwise DE" scales and I was quite surprised to see that even these apparently tend to be generated from two alternating generators, just in different interval classes. [[User:Mike Battaglia\|Mike Battaglia]] ([[User talk:Mike Battaglia\|talk]]) 00:16, 28 May 2022 (UTC)

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

Xenoindex: I got MV3 lists

2022-05-24T08:31:19Z

I got MV3 lists

← Older revision		Revision as of 08:31, 24 May 2022
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	It would be a good idea to clarify which of these theorems hold for only General MV3 scale words and which hold for every possible MV3 scale. FWIW I think this problem actually goes way way back to Keenan Pepper's original version of this page (which originated from some tuning-math and IRC discussions at least 10 years ago), so I'll ask him about it. Also kudos to Inthar for a lot of great work on this. [[User:Mike Battaglia\|Mike Battaglia]] ([[User talk:Mike Battaglia\|talk]]) 00:24, 24 May 2022 (UTC)		It would be a good idea to clarify which of these theorems hold for only General MV3 scale words and which hold for every possible MV3 scale. FWIW I think this problem actually goes way way back to Keenan Pepper's original version of this page (which originated from some tuning-math and IRC discussions at least 10 years ago), so I'll ask him about it. Also kudos to Inthar for a lot of great work on this. [[User:Mike Battaglia\|Mike Battaglia]] ([[User talk:Mike Battaglia\|talk]]) 00:24, 24 May 2022 (UTC)

			: [[User:Xenoindex/MV3 Lists\|This]] may be of interest to anyone interested in MV3 who hasn't seen it yet, basically I bruteforce found and listed all the MV3 up to 14 tones. May come in handy, let me know if anyone finds any mistakes. --[[User:Xenoindex\|Xenoindex]] ([[User talk:Xenoindex\|talk]]) 08:31, 24 May 2022 (UTC)

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

Mike Battaglia: signature

2022-05-24T00:24:01Z

signature

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	There is another important set of MV3 scales you can get by taking just one generator and iterating it to a number of scale steps that is NOT an MOS (like meantone[6]), but from initial inspection I do think that these tends of scales actually will be General MV3 scales.		There is another important set of MV3 scales you can get by taking just one generator and iterating it to a number of scale steps that is NOT an MOS (like meantone[6]), but from initial inspection I do think that these tends of scales actually will be General MV3 scales.

	It would be a good idea to clarify which of these theorems hold for only General MV3 scale words and which hold for every possible MV3 scale. FWIW I think this problem actually goes way way back to Keenan Pepper's original version of this page (which originated from some tuning-math and IRC discussions at least 10 years ago), so I'll ask him about it. Also kudos to Inthar for a lot of great work on this.		It would be a good idea to clarify which of these theorems hold for only General MV3 scale words and which hold for every possible MV3 scale. FWIW I think this problem actually goes way way back to Keenan Pepper's original version of this page (which originated from some tuning-math and IRC discussions at least 10 years ago), so I'll ask him about it. Also kudos to Inthar for a lot of great work on this. [[User:Mike Battaglia\|Mike Battaglia]] ([[User talk:Mike Battaglia\|talk]]) 00:24, 24 May 2022 (UTC)

	== Relationship Between Pairwise-Well-Formed scales and MV3 ==		== Relationship Between Pairwise-Well-Formed scales and MV3 ==
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	# MV3 scales which also have this generator offset property		# 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.)		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.) [[User:Mike Battaglia\|Mike Battaglia]] ([[User talk:Mike Battaglia\|talk]]) 00:24, 24 May 2022 (UTC)

	== Connections to 5L 2s MODMOSes ==		== 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)		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)

Mike Battaglia: /* Relationship Between Pairwise-Well-Formed scales and MV3 */

2022-05-23T23:57:21Z

Relationship Between Pairwise-Well-Formed scales and MV3

← Older revision		Revision as of 23:57, 23 May 2022
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	== Relationship Between Pairwise-Well-Formed scales and MV3 ==		== 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		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 ==		== 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)		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)

Mike Battaglia: sporadic MV3 scales and relationship between different types of MV3 scales

2022-05-23T23:56:35Z

sporadic MV3 scales and relationship between different types of MV3 scales

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 == 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)

Aura: /* Connections to 5L 2s MODMOSes */ new section

2021-05-12T19:54:46Z

Connections to 5L 2s MODMOSes: new section

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	{{WSArchiveLink}}		{{WSArchiveLink}}

			== 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)

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:39Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
(No difference)

WikispacesArchive>Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-10-01T18:01:16Z

Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' <span style="color:#800000">''...

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	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

	~~<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

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	~~== needs a lot of work ==~~
	~~any way we could get some diagrams here? too many leaps of thought and disconnected points. seems within grasp but really unclear.~~

	~~- '''cmloegcmluin''' January 16, 2016, 12:28:26 PM UTC-0800~~
	~~----~~

Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-09-20T07:00:50Z

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	= ARCHIVED WIKISPACES DISCUSSION BELOW =		= ARCHIVED WIKISPACES DISCUSSION BELOW =
	'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''		'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''

			<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.

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Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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== needs a lot of work ==
any way we could get some diagrams here? too many leaps of thought and disconnected points. seems within grasp but really unclear.

- '''cmloegcmluin''' January 16, 2016, 12:28:26 PM UTC-0800
----