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TES: The largest network of teachers in the world

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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