Hyperpent and hypopent - Revision history

Jdood: /* Background */ Removed an apostrophe (Edo's --> Edos)

2025-11-19T04:56:16Z

Background: Removed an apostrophe (Edo's --> Edos)

← Older revision		Revision as of 04:56, 19 November 2025
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	"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. Hyperpent is loosely associated with [[superpyth]], but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. Hypopent is loosely associated with [[meantone]], but specifically refers to equal division of the octave that result in any fifth tempered flat.		"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. Hyperpent is loosely associated with [[superpyth]], but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. Hypopent is loosely associated with [[meantone]], but specifically refers to equal division of the octave that result in any fifth tempered flat.

	Large ~~edo's~~ are generally amphipent, meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."		Large edos are generally amphipent, meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."

	== Partial List ==		== Partial List ==

FloraC: Cleanup

2025-11-13T06:54:08Z

Cleanup

← Older revision		Revision as of 06:54, 13 November 2025
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	== Background ==		== Background ==
	"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. ~~The term~~ is loosely associated with "[[~~Superpyth\|superpythagorean~~]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. ~~The term~~ is loosely associated with "[[meantone]]," but specifically refers to equal division of the octave that result in any fifth tempered flat.		"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. Hyperpent is loosely associated with [[superpyth]], but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. Hypopent is loosely associated with [[meantone]], but specifically refers to equal division of the octave that result in any fifth tempered flat.

	Large edo's are generally "amphipent," meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."		Large edo's are generally amphipent, meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."

	== Partial List ==		== Partial List ==

	Anpent (neither hypopent nor hyperpent)		Anpent (neither hypopent nor hyperpent)

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	[[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]]		[[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]]

	== ~~Analysis~~ ==		== Bozu's analysis ==
			If 5edo and 7edo are taken as the smallest hyperpent and hypopent edo's, respectively, other edo tuning systems (let's call it ''X''-edo with ''X'' equal divisions of the octave) can be determined to be hyperpent, hypopent, anpent, or amphipent by addition as follows (with a few exceptions):
			* If ''X'' can be represented as a sum of 5's, Xedo is hyperpent.
			* If ''X'' can be represented as a sum of 7's, Xedo is hypopent.
			* If ''X'' can be represented as a sum of 5's and 7's, with more 5's than 7's, Xedo is hyperpent.
			* If ''X'' can be represented as a sum of 5's and 7's, with more 7's than 5's, or an equal number of 7's and 5's, Xedo is hypopent.
			* If ''X'' cannot be represented as a sum of 5's and 7's, Xedo is anpent.
			* If ''X'' can be represented as a sum of 5's and 7's in multiple ways (for example, 35 can be represented as five sevens or as seven fives), ''X''-edo is amphipent.

	~~If 5edo and 7edo~~ are ~~taken as the smallest hyperpent~~ and ~~hypopent edo's~~, ~~respectively, other edo tuning systems (let's call it "Xedo" with "X" equal divisions of the octave) can be determined to be hyperpent, hypopen, anpent, or~~ amphipent ~~by addition as follows (with a few exceptions):~~		Some exceptions are 37edo and 44edo, which are amphipent, even though 37 cannot be written as multiple sums of 5's and 7's, nor can 44.

	~~If X can be represented as a sum of 5's~~, ~~Xedo is hyperpent.~~

	~~If X can be represented as a sum of 7's, Xedo is hypopent.~~

	~~If X can be represented as a sum of 5's and 7's, with more 5's than 7's, Xedo is hyperpent.~~

	~~If X can be represented as a sum of 5's and 7's, with more 7's than 5's, or an equal number of 7's and 5's, Xedo is hypopent.~~

	~~If X~~ cannot be ~~represented~~ as ~~a sum of 5's and 7's, Xedo is anpent.~~
	~~If X can be represented as a sum~~ of 5's and 7's ~~in multiple ways (for example~~, 35 can ~~be represented as five sevens or as seven fives), Xedo is amphipent~~.

	~~Some exceptions are 37edo and 44edo, which are amphipent, even though 37 cannot be written as multiple sums of 5's and 7's, nor can 44.~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]

FloraC: This is bozu's theory

2025-11-13T06:49:54Z

This is bozu's theory

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-'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2|just fifth]] that is less than a [[81/80|syntonic comma]] sharp.  It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2|just fifth]] that is less than a [[81/80|syntonic comma]] flat. In particular, a hyperpent edo has a fifth ranging from [[3/2]] to [[243/160]] and a hypopent edo has a fifth ranging from [[40/27]] to [[3/2]].
+'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2|just fifth]] that is less than a [[81/80|syntonic comma]] sharp.  It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2|just fifth]] that is less than a [[81/80|syntonic comma]] flat.
 == Background ==
-"Hyperpental" (about 702 to 723c) loosely corresponds to tunings of the [[5L 7s]] sharp chromatic scale (700 to 720 cents) while "hypopental" (about 680-702c) loosely corresponds to tunings of the [[7L 5s]] mellow chromatic scale (686 to 700 cents).
+"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five.  The term is loosely associated with "[[Superpyth|superpythagorean]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. The term is loosely associated with "[[meantone]]," but specifically refers to equal division of the octave that result in any fifth tempered flat.
-Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent." By necessity, these edos have no diatonic fifth, and are a finite set (the largest being 23edo, which is also the largest edo to lack a diatonic scale).
+Large edo's are generally "amphipent," meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."
 == Partial List ==
@@ Line 21: / Line 19: @@
 [[7edo]], [[12edo]], [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]]
 [[Category:Lists of scales]]
 [[Category:EDO theory pages]]

VectorGraphics at 01:35, 13 November 2025

2025-11-13T01:35:17Z

← Older revision		Revision as of 01:35, 13 November 2025
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	Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent." By necessity, these edos have no diatonic fifth, and are a finite set (the largest being 23edo, which is also the largest edo to lack a diatonic scale).		Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent." By necessity, these edos have no diatonic fifth, and are a finite set (the largest being 23edo, which is also the largest edo to lack a diatonic scale).

			Some edos are hypopental but generate [[5L 7s]]. One example is 53edo, which tempers the fifth a fraction of a cent flat.

	== Partial List ==		== Partial List ==

VectorGraphics at 01:34, 13 November 2025

2025-11-13T01:34:11Z

← Older revision		Revision as of 01:34, 13 November 2025
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	== Background ==		== Background ==
	"Hyperpental" is loosely ~~associated with "~~[[~~superpyth~~]]~~," but specifically refers~~ to ~~equal division of the octave that result in any fifth tempered sharp,~~ while "hypopental" is loosely ~~associated with "~~[[~~meantone~~]]~~," but specifically refers~~ to ~~equal division of the octave that result in any fifth tempered flat~~.		"Hyperpental" (about 702 to 723c) loosely corresponds to tunings of the [[5L 7s]] sharp chromatic scale (700 to 720 cents) while "hypopental" (about 680-702c) loosely corresponds to tunings of the [[7L 5s]] mellow chromatic scale (686 to 700 cents).

	Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."		Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent." By necessity, these edos have no diatonic fifth, and are a finite set (the largest being 23edo, which is also the largest edo to lack a diatonic scale).

	== Partial List ==		== Partial List ==

VectorGraphics: removed inaccurate theory

2025-11-13T01:29:43Z

removed inaccurate theory

← Older revision		Revision as of 01:29, 13 November 2025
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	'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] flat.		'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] flat. In particular, a hyperpent edo has a fifth ranging from [[3/2]] to [[243/160]] and a hypopent edo has a fifth ranging from [[40/27]] to [[3/2]].

	== Background ==		== Background ==
	"~~Hyper-~~" ~~is the Greek prefix for high or above and "pent" is Greek for five. The term~~ is loosely associated with "[[~~Superpyth\|superpythagorean~~]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "~~hypo-~~" ~~is the Greek prefix for low or below and "pent" is Greek for five. The term~~ is loosely associated with "[[meantone]]," but specifically refers to equal division of the octave that result in any fifth tempered flat.		"Hyperpental" is loosely associated with "[[superpyth]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypopental" is loosely associated with "[[meantone]]," but specifically refers to equal division of the octave that result in any fifth tempered flat.

	~~Large edo's are generally "amphipent," meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat.~~ Some ~~edo's~~ may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."		Some edos may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."

	== Partial List ==		== Partial List ==
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	[[7edo]], [[12edo]], [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]]		[[7edo]], [[12edo]], [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]]

	~~Amphipent (both hyperpent and hypopent)~~

	~~[[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]]~~

	~~== Analysis ==~~

	If 5edo and 7edo are taken as the smallest hyperpent and hypopent edo's, respectively, other edo tuning systems (let's call it "Xedo" with "X" equal divisions of the octave) can be determined to be hyperpent, hypopen, anpent, or amphipent by addition as follows (with a few exceptions):

	~~If X can be represented as a sum of 5's, Xedo is hyperpent.~~

	~~If X can be represented as a sum of 7's, Xedo is hypopent.~~

	~~If X can be represented as a sum of 5's and 7's, with more 5's than 7's, Xedo is hyperpent.~~

	~~If X can be represented as a sum of 5's and 7's, with more 7's than 5's, or an equal number of 7's and 5's, Xedo is hypopent.~~

	~~If X cannot be represented as a sum of 5's and 7's, Xedo is anpent.~~
	~~If X can be represented as a sum of 5's and 7's in multiple ways (for example, 35 can be represented as five sevens or as seven fives), Xedo is amphipent.~~

	~~Some exceptions are 37edo and 44edo, which are amphipent, even though 37 cannot be written as multiple sums of 5's and 7's, nor can 44.~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]

Lériendil: /* Partial List */

2024-09-27T20:17:02Z

Partial List

← Older revision		Revision as of 20:17, 27 September 2024
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	Hyperpent		Hyperpent

	[[5edo]] ,[[10edo]], [[15edo]], [[17edo]], [[20edo]], [[22edo]], [[25edo]], [[27edo]], [[29edo]], [[30edo]], [[32edo]], [[34edo]], [[39edo]], [[41edo]], [[46edo]]		[[5edo]], [[10edo]], [[15edo]], [[17edo]], [[20edo]], [[22edo]], [[25edo]], [[27edo]], [[29edo]], [[30edo]], [[32edo]], [[34edo]], [[39edo]], [[41edo]], [[46edo]]

	Hypopent		Hypopent

	[[7edo]], [[12edo]] [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]]		[[7edo]], [[12edo]], [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]]

	Amphipent (both hyperpent and hypopent)		Amphipent (both hyperpent and hypopent)

Lériendil at 19:32, 27 September 2024

2024-09-27T19:32:11Z

← Older revision		Revision as of 19:32, 27 September 2024
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	[[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]]		[[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]]


	== Analysis ==		== Analysis ==

Lériendil at 19:32, 27 September 2024

2024-09-27T19:32:01Z

← Older revision		Revision as of 19:32, 27 September 2024
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	'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] flat.		'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] flat.


	== Background ==		== Background ==

Lériendil: combined content from hypopent

2024-09-27T19:31:55Z

combined content from hypopent

← Older revision		Revision as of 19:31, 27 September 2024
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	'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by [[hypopent]] or hypopental edo tuning systems.		'''Hyperpent''' or hyperpental edo is an [[equal division of the octave]] which has a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] sharp. It is juxtaposed by '''hypopent''' or hypopental edo tuning systems, which have a [[3/2\|just fifth]] that is less than a [[81/80\|syntonic comma]] flat.


	== Background ==		== Background ==
			"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. The term is loosely associated with "[[Superpyth\|superpythagorean]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp, while "hypo-" is the Greek prefix for low or below and "pent" is Greek for five. The term is loosely associated with "[[meantone]]," but specifically refers to equal division of the octave that result in any fifth tempered flat.

	"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. The term is loosely associated with "[[Superpyth\|superpythagorean]]," but specifically refers to equal division of the octave that result in any fifth tempered sharp.		Large edo's are generally "amphipent," meaning both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent, and are refered to as "anpent."

	Large edo's are generally both hyperpent and hypopent, because they contain multiple representations of the fifth that may be sharp and flat. Some edo's may contain no intervals in the span of a just fifth plus or minus a [[syntonic comma]], and thus are neither hyperpent nor hypopent.


	== Partial List ==		== Partial List ==