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. | 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]]. | 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). | 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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; 100 and beyond | ; 100 and beyond | ||
* [[116ed5|116]], [[139ed5|139]], [[256ed5|256]] | * [[116ed5|116]], [[139ed5|139]], [[175ed5|175]], [[256ed5|256]] | ||
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* [http://www.nonoctave.com/tuning/fifth_harmonic.html| Nonoctave.com: tuning: equal division of the fifth harmonic] | * [http://www.nonoctave.com/tuning/fifth_harmonic.html| Nonoctave.com: tuning: equal division of the fifth harmonic] | ||
[[Category:Ed5| ]] <!-- main article --> | [[Category:Ed5's| ]] | ||
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[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[Category:Pentave]] | [[Category:Pentave]] | ||
{{Todo|add sound example}} | {{Todo|add sound example}} | ||