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Division of the Fifth Harmonic (5/1) into n equal parts


The fifth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see 17ed5). However, perhaps the more common reason to use these scales 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-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

3ed5 orwell generator (with octaves)
4ed5 meantone generator (with octaves)
5ed5 thuja generator (with octaves)
6ed5 uncle generator (with octaves)
7ed5
8ed5
10ed5
11ed5
12ed5
13ed5
14ed5 compare 6edo
15ed5
16ed5 compare 7edo
17ed5
18ed5
19ed5 compare Bohlen-Pierce
20ed5 (Hieronymus Tuning)
21ed5 compare 9edo
22ed5
23ed5 compare 10edo
24ed5
25ed5 (Stockhausen, McLaren)
26ed5
27ed5
28ed5 compare 12edo
29ed5
30ed5 compare 13edo
31ed5
32ed5 compare 14edo
33ed5
34ed5
35ed5 compare 15edo
36ed5
37ed5 compare 16edo
38ed5 compare 26edt
39ed5

Pentave Reduced Harmonics
Pentave Reduced Subharmonics

http://www.nonoctave.com/tuning/fifth_harmonic.html