Hyperpent and hypopent: Difference between revisions

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== 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 ==

Anpent (neither hypopent nor hyperpent)

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[[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:EDO theory pages]]

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 == 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 ==
 Anpent (neither hypopent nor hyperpent)
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 [[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:EDO theory pages]]