Harmonics 13–26: Difference between revisions

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{{Infobox AFDO|steps=13}}
{{Infobox harmonics|13}}
'''13afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''13odo''' ([[otonal division]] of the octave), divides the octave into thirteen parts of 1/13 each. It is a superset of [[12afdo]] and a subset of [[14afdo]]. As a scale it may be known as [[Harmonic mode|mode 13 of the harmonic series]] or the [[Overtone scale#Over-n%20scales|Over-13]] scale. Due to being odd, it does not contain a perfect fifth above the root.
{{Harmonics intro|13}} Due to being odd, it does not contain a perfect fifth above the root.
== Intervals ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
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| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}
|}
{{Navbox harmonics}}

Latest revision as of 00:08, 11 October 2026

Harmonics 13–26
Prime factorization 13 (prime)
Dual sharp fifth 20/13 (745.786c)
Dual flat fifth 19/13 (656.985c)

The harmonics 13–26 (also harmonic series segment 13::26 or harmonic series mode 13) are a scale that consists of harmonics 13 through 26 (13:14:…:26) and repeats at the octave. Used as a tuning system, it is also called 13afdo. Due to being odd, it does not contain a perfect fifth above the root.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0.00 1/1 1.0000 perfect unison
1 128.30 14/13 1.0769 tridecimal supraminor second
2 247.74 15/13 1.1538 subminor third
3 359.47 16/13 1.23077 (greater) tridecimal neutral third
4 464.42 17/13 1.3077 septendecimal subfourth
5 563.38 18/13 1.3846 tridecimal augmented fourth
6 656.99 19/13 1.4615 undevicesimal subfifth
7 745.79 20/13 1.53846 tridecimal semitenth
8 830.25 21/13 1.61539 tridecimal supraminor sixth
9 910.79 22/13 1.69231 tridecimal major sixth
10 987.75 23/13 1.76923 vicesimotertial minor seventh
11 1061.43 24/13 1.84615 tridecimal neutral seventh
12 1132.09 25/13 1.92308 lesser tridecimal diminished octave
13 1200.0 2/1 2.0000 perfect octave
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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