Harmonics 14–28

The harmonics 14–28 (also harmonic series segment 14::28 or harmonic series mode 14) are a scale that consists of harmonics 14 through 28 (14:15:…:28) and repeats at the octave. Used as a tuning system, it is also called 14afdo.

Harmonics 14–28

Prime factorization	2 × 7
Fifth	21/14 (701.955c)

Theory

The esoteric Factor 9 grid scale is a mode of this scale starting on the 11th step from the tonic, of which 12 or 13 notes were conveniently selected for "A = 432 Hz" conspiracy purposes. It contains supraminor and supermajor triads above the root.

Intervals

#	Cents	Ratio	Decimal	Interval name	Audio
0	0.0	1/1	1.0000	perfect unison
1	119.4	15/14	1.0714	septimal diatonic semitone
2	231.2	8/7	1.1429	supermajor second
3	336.1	17/14	1.2149	septendecimal supraminor third
4	435.1	9/7	1.2857	supermajor third
5	528.7	19/14	1.3571	hendrix fourth
6	617.5	10/7	1.4286	high tritone
7	702.0	3/2	1.5000	just perfect fifth
8	782.4	11/7	1.5714	undecimal minor sixth
9	859.4	23/14	1.6428	vicesimotertial neutral sixth
10	933.1	12/7	1.7143	supermajor sixth
11	1003.8	25/14	1.7857	(septimal) middle minor seventh
12	1071.7	13/7	1.8571	tridecimal submajor seventh
13	1137.0	27/14	1.9286	septimal major seventh
14	1200.0	2/1	2.0000	perfect octave

Factor 9 grid can be obtained if the scale is rotated to start at 12/7 instead of 1/1.

Scales

• 14:15:18:19:21:22:26:28 Apex^{[idiosyncratic term]}
• 14:16:18:21:24:28 septimal minor pentatonic