Harmonics 5–10

Harmonics 5–10

Prime factorization	5 (prime)
Dual sharp fifth	8/5 (813.686c)
Dual flat fifth	7/5 (582.512c)

The harmonics 5–10 (also harmonic series segment 5::10 or harmonic series mode 5) are a scale that consists of harmonics 5 through 10 (5:6:7:8:9:10) and repeats at the octave. Used as a tuning system, it is also called 5afdo. As 5 is a small odd number, this scale does not contain a perfect fifth or any reasonable approximation to it over the root, and it is relatively poor for its size at creating traditional tonal music compared to harmonics 4–8 and harmonics 6–12 (again only if over the root, the modes have more to offer).

Intervals

#	Cents	Ratio	Decimal	Interval name	Audio
0	0	1/1	1.0000	perfect unison
1	315.6	6/5	1.2000	just minor third
2	582.5	7/5	1.40000	narrow tritone
3	813.7	8/5	1.6000	just minor sixth
4	1017.6	9/5	1.8000	just minor seventh
5	1200.0	2/1	2.0000	perfect octave

Scala files

This file starts with 8/5.

! otonalpentad.scl
!
The otonal pentad as a wakalix
! Fokblock([28/27, 21/20, 16/15], [2, 3, 0]) = Fokblock([36/35, 21/20, 16/15], [2, 3, 0])
! = Fokblock([21/20, 36/35, 28/27], [3, 0, 0])
5
!
9/8
5/4
3/2
7/4
2/1

See also

• 4:5:6:7:9 – this scale as a chord