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

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

12ed5

14ed5 compare 6edo