Harmonics 7–14: Difference between revisions

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{{Infobox AFDO|steps=7}}
{{Infobox harmonics|7}}
'''7afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''7odo''' ([[otonal division]] of the octave), divides the octave into seven parts of 1/7 each. It is a superset of [[6afdo]] and a subset of [[8afdo]]. As a scale it may be known as [[Harmonic mode|mode 7 of the harmonic series]] or the [[Overtone scale#Over-7 scales|Over-7]] scale. As 7 is a small odd number, 7afdo does not contain a perfect fifth or any reasonable approximation to one in its root position. This makes 7afdo relatively poor for its size at creating traditional tonal music unless rotated.
{{Harmonics intro|7}} As 7 is a small odd number, this scale does not contain a perfect fifth or any reasonable approximation to one in its root position. This makes it relatively poor for its size at creating traditional tonal music unless rotated.


== Intervals ==
== Intervals ==
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* [[Harmd-mix]]
* [[Harmd-mix]]
* [[Oheptad]] – same, but starts with 8/7
* [[Oheptad]] – same, but starts with 8/7
{{Navbox harmonics}}

Revision as of 23:52, 10 October 2026

Harmonics 7–14
Prime factorization 7 (prime)
Dual sharp fifth 11/7 (782.492c)
Dual flat fifth 10/7 (617.488c)

The harmonics 7–14 (also harmonic series segment 7::14 or harmonic series mode 7) are a scale that consists of harmonics 7 through 14 (7:8:9:10:11:12:13:14) and repeats at the octave. Used as a tuning system, it is also called 7afdo. As 7 is a small odd number, this scale does not contain a perfect fifth or any reasonable approximation to one in its root position. This makes it relatively poor for its size at creating traditional tonal music unless rotated.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0 1/1 1.0000 perfect unison
1 231.2 8/7 1.1429 supermajor second
2 435.1 9/7 1.2857 supermajor third
3 617.5 10/7 1.4286 high tritone
4 782.4 11/7 1.5714 undecimal minor sixth
5 933.1 12/7 1.7143 supermajor sixth
6 1071.7 13/7 1.8571 tridecimal submajor seventh
7 1200.0 2/1 2.0000 perfect octave

Scala files

View • Talk • EditOvertone scales 
Small modes 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24
Larger modes 30 • 32 • 36 • 48 • 60 • 128
Families /2: 2 • 4 • 8 • 16 • 32 • 128
/3: 3 • 6 • 9 • 12 • 15 • 18 • 21 • 24
/5: 5 • 10 • 15 • 20 • 25 • 30 • 35 • 60 • 80
/7: 7 • 14 • 21 • 28 • 35 • 56
/11: 11 • 22 • 33
/13: 13 • 26
Related Harmonic series • Subharmonic series • Carlos harmonic scale • Ringer scale • Primodality
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