Bozu's opinions of various edos - Revision history

FloraC: Fix linking

2025-09-11T05:58:04Z

Fix linking

← Older revision		Revision as of 05:58, 11 September 2025
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	I see edo's as fitting into one or more of four different elemental makeups:		I see edo's as fitting into one or more of four different elemental makeups:

	# Augmented. If X is divisible by three, X edo is "[[augmented]] type". The elemental basis of augmented type edo's is [[3edo]].		# Augmented. If X is divisible by three, X edo is "[[augmented (temperament)\|augmented]] type". The elemental basis of augmented type edo's is [[3edo]].
	# Diminished. If X is divisible by four, X edo is "[[diminished]] type". The elemental basis of diminished type edo is [[4edo]].		# Diminished. If X is divisible by four, X edo is "[[diminished (temperament)\|diminished]] type". The elemental basis of diminished type edo is [[4edo]].
	# Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is [[5edo]].		# Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is [[5edo]].
	# Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is [[7edo]].		# Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is [[7edo]].

BudjarnLambeth at 04:37, 9 January 2024

2024-01-09T04:37:46Z

← Older revision		Revision as of 04:37, 9 January 2024
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	I see edo's as fitting into one or more of four different elemental makeups:		I see edo's as fitting into one or more of four different elemental makeups:

	# Augmented. If X is divisible by three, X edo is "augmented type". The elemental basis of augmented type edo's is [[3edo]].		# Augmented. If X is divisible by three, X edo is "[[augmented]] type". The elemental basis of augmented type edo's is [[3edo]].
	# Diminished. If X is divisible by four, X edo is "diminished type". The elemental basis of diminished type edo is [[4edo]].		# Diminished. If X is divisible by four, X edo is "[[diminished]] type". The elemental basis of diminished type edo is [[4edo]].
	# Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is [[5edo]].		# Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is [[5edo]].
	# Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is [[7edo]].		# Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is [[7edo]].
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	[[1edo]] - LOL		[[1edo]] - LOL

	[[2edo]] - 0th order [[diminished]]. Nothing interesting, too constrained.		[[2edo]] - 0th order diminished. Nothing interesting, too constrained.

	[[3edo]] - Elemental [[augmented]] type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.		[[3edo]] - Elemental augmented type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.

	[[4edo]] - Elemental diminished type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.		[[4edo]] - Elemental diminished type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.

BudjarnLambeth: /* Sizes of edo's */

2024-01-09T04:37:17Z

Sizes of edo's

← Older revision		Revision as of 04:37, 9 January 2024
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	== Sizes of edo's ==		== Sizes of edo's ==

	Any X edo X<5 is terribly uninteresting, in my opinion. These offer only drones with very few harmonies. There isn't really enough room to provide any sort of harmonic motion.		Any X edo X<[[5edo\|5]] is terribly uninteresting, in my opinion. These offer only drones with very few harmonies. There isn't really enough room to provide any sort of harmonic motion.

	Any X edo X>=[[5edo\|5]] but X<[[9edo\|9]] is overconstrained. Harmonies are possible, different tonics are possible, but the possibilities are so limited that the differences between melodies are trivial. These tuning sets are what I have been personally calling "drone-like."		Any X edo X>=[[5edo\|5]] but X<[[9edo\|9]] is overconstrained. Harmonies are possible, different tonics are possible, but the possibilities are so limited that the differences between melodies are trivial. These tuning sets are what I have been personally calling "drone-like."

BudjarnLambeth: Added links to dead end page

2024-01-09T04:36:39Z

Added links to dead end page

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Fredg999: Numbered list markup

2023-05-16T01:09:07Z

Numbered list markup

← Older revision		Revision as of 01:09, 16 May 2023
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	I see edo's as fitting into one or more of four different elemental makeups:		I see edo's as fitting into one or more of four different elemental makeups:

	1. Augmented. If X is divisible by three, X edo is "augmented type". The elemental basis of augmented type edo's is 3edo.		# Augmented. If X is divisible by three, X edo is "augmented type". The elemental basis of augmented type edo's is 3edo.
			# Diminished. If X is divisible by four, X edo is "diminished type". The elemental basis of diminished type edo is 4edo.
	2. Diminished. If X is divisible by four, X edo is "diminished type". The elemental basis of diminished type edo is 4edo.		# Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is 5edo.
			# Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.
	3. Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is 5edo.

	4. Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.

	If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.		If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.

Moremajorthanmajor: /* Supercomma */

2023-05-15T23:41:37Z

Supercomma

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Fredg999 category edits: Categories

2023-01-20T22:22:30Z

Bozu at 18:14, 27 July 2020

2020-07-27T18:14:19Z

← Older revision		Revision as of 18:14, 27 July 2020
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	== List of edo's ==		== List of edo's ==

	Drone-like		==== Drone-like ====

	1edo - LOL		1edo - LOL

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	8edo - kind of a cool diminished scale, but it suffers from the same problems as other drone-like edo's, in terms of options and constraints.		8edo - kind of a cool diminished scale, but it suffers from the same problems as other drone-like edo's, in terms of options and constraints.

	Chromatic-like		==== Chromatic-like ====

	9edo - 3rd order augmented scale. I want to like this tuning, but I can't see any value in it beyond noodling.		9edo - 3rd order augmented scale. I want to like this tuning, but I can't see any value in it beyond noodling.

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	30edo - Hyperpent. Augmented. Meh, too many seemingly useless intervals.		30edo - Hyperpent. Augmented. Meh, too many seemingly useless intervals.

			==== Supercomma ====
	31edo - This is sort of the gold standard of meantone tuning. Composite hypopent. Great thirds and fifths and everything else used to make western-esque music, and also some really nifty other spicier options. Very user-friendly. If you start with 12edo and go to 19edo and like it, this would be the obvious next recommendation. My only complaint here is that we are starting to get into the territory of having too many notes to easily perform on a guitar or standard black-and-white-key two row keyboard. Going with subsets at this point is beneficial, but those provide new challenges.		31edo - This is sort of the gold standard of meantone tuning. Composite hypopent. Great thirds and fifths and everything else used to make western-esque music, and also some really nifty other spicier options. Very user-friendly. If you start with 12edo and go to 19edo and like it, this would be the obvious next recommendation. My only complaint here is that we are starting to get into the territory of having too many notes to easily perform on a guitar or standard black-and-white-key two row keyboard. Going with subsets at this point is beneficial, but those provide new challenges.

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	53edo - Generally the stopping point. If you are comfortable with >50 tones, then this tuning offers almost everything you will need. If not, stick with 31edo or something smaller.		53edo - Generally the stopping point. If you are comfortable with >50 tones, then this tuning offers almost everything you will need. If not, stick with 31edo or something smaller.

	Subcomma		==== Subcomma ====

	59edo - Seems to have some interesting options, but it's a lot of notes, and other neighbouring edo's can do some more versatile things.		59edo - Seems to have some interesting options, but it's a lot of notes, and other neighbouring edo's can do some more versatile things.

Bozu at 18:13, 27 July 2020

2020-07-27T18:13:08Z

← Older revision		Revision as of 18:13, 27 July 2020
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	4. Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.		4. Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.

	If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A<B or A=B). With larger edo's, there is the possibility of a hybrid tuning with both hyperpent and hypopent characteristics, when X can be expressed as X = 5A + 7B and also as X = 5C + 7D, where either A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.		If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.

	There are also a couple of cases in which X edo has no relation to any of these elements. One special case is 2edo, which I classify as 0th order diminished type. The other cases are 11edo, 13edo, and 23edo, which are not divisible by 3, 4, 5, nor 7, and cannot be expressed as 5A + 7B with any non-negative integers A and B.		There are also a couple of cases in which X edo has no relation to any of these elements. One special case is 2edo, which I classify as 0th order diminished type. The other cases are 11edo, 13edo, and 23edo, which are not divisible by 3, 4, 5, nor 7, and cannot be expressed as 5A + 7B with any non-negative integers A and B.

	Thus...		Thus...


	== Sizes of edo's ==		== Sizes of edo's ==

Bozu: Undo revision 47959 by Bozu (talk)

2020-07-27T18:12:40Z

Undo revision 47959 by Bozu (talk)

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← Older revision		Revision as of 22:22, 20 January 2023
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	87edo - 29edo with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this.		87edo - 29edo with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this.

			[[Category:Impression]]