ED5: Difference between revisions

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The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.

One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics|primes]] [[2/1|2]] and [[3/1|3]]. In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5|equal divisions of 11/5]] and [[ed11/7|equal divisions of 11/7]], although this trades consonance for smaller size.

One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics|primes]] [[2/1|2]] and [[3/1|3]] and using subgroups like 5.7.11.13.17... In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5|equal divisions of 11/5]] and [[ed11/7|equal divisions of 11/7]], although this trades consonance for smaller size.

The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).

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 The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.
-One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics|primes]] [[2/1|2]] and [[3/1|3]]. In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5|equal divisions of 11/5]] and [[ed11/7|equal divisions of 11/7]], although this trades consonance for smaller size.
+One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics|primes]] [[2/1|2]] and [[3/1|3]] and using subgroups like 5.7.11.13.17... In this approach, [[5:7:11]] could be seen as analogous to the [[3:5:7]] chord of [[Bohlen-Pierce]]. If 5/1 is seen as too large of an equave, Other equivalences that could be used for such no-2's no-3's music include [[ed11/5|equal divisions of 11/5]] and [[ed11/7|equal divisions of 11/7]], although this trades consonance for smaller size.
 The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-5's", full on zeta).