Hyperpent and hypopent: Difference between revisions
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'''Hyperpent''' or hyperpental edo is an equal division of the octave which has a just fifth that is less than a 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. | ||
== Background == | == Background == | ||
"Hyper-" is the Greek prefix for high or above and "pent" is Greek for five. The term is loosely associated with "superpythagorean," but specifically refers to equal division of the octave that result in any fifth tempered sharp. | "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 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. | 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. | ||
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Anpent (neither hypopent nor hyperpent) | Anpent (neither hypopent nor hyperpent) | ||
2edo | [[2edo]], [[3edo]], [[4edo]], [[6edo]], [[8edo]], [[9edo]], [[11edo]], [[13edo]], [[16edo]], [[18edo]], [[23edo]] | ||
3edo | |||
4edo | |||
6edo | |||
8edo | |||
9edo | |||
11edo | |||
13edo | |||
16edo | |||
18edo | |||
23edo | |||
Hyperpent | Hyperpent | ||
5edo | [[5edo]] ,[[10edo]], [[15edo]], [[17edo]], [[20edo]], [[22edo]], [[25edo]], [[27edo]], [[29edo]], [[30edo]], [[32edo]], [[34edo]], [[39edo]], [[41edo]], [[46edo]] | ||
10edo | |||
15edo | |||
17edo | |||
20edo | |||
22edo | |||
25edo | |||
27edo | |||
29edo | |||
30edo | |||
32edo | |||
34edo | |||
39edo | |||
41edo | |||
46edo | |||
Hypopent | Hypopent | ||
7edo | [[7edo]], [[12edo]] [[14edo]], [[19edo]], [[21edo]], [[24edo]], [[26edo]], [[28edo]], [[31edo]], [[33edo]], [[36edo]], [[38edo]], [[43edo]] | ||
12edo | |||
14edo | |||
19edo | |||
21edo | |||
24edo | |||
26edo | |||
28edo | |||
31edo | |||
33edo | |||
36edo | |||
38edo | |||
43edo | |||
Amphipent (both hyperpent and hypopent) | Amphipent (both hyperpent and hypopent) | ||
35edo | [[35edo]], [[37edo]], [[40edo]], [[42edo]], [[44edo]], [[45edo]], [[47edo]] | ||
37edo | |||
40edo | |||
42edo | |||
44edo | |||
45edo | |||
47edo | |||
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If X can be represented as a sum of 5's, Xedo is hyperpent. | 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 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 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 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 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. | 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. | 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. | ||