Harmonic Series Tunings: 12-tone Simple Harmonic Fragment

Most people who explore various forms of Just Intonation probably try this tuning sooner or later: the first twelve odd numbers interleaved in an octave. A fistfull of superparticulars, all laid out in order. The eight lowest primes. The three lowest odd composites. Even though all twelve step-sizes are different, the overall contrast in step sizes is fairly smooth. It's the same tuning as the 23-limit Exact PLOT, just arrived at by a different theoretical method.

Scale Degree	Ratio	Quotient	Cents	Tuning Table	Rounded Tuning Table	Note Name
1	1:1	1	0.00	29.78	30	C
2	17:16	1.0625	104.96	34.74	35	C#
3	9:8	1.125	203.91	33.69	34	D
4	19:16	1.1875	297.51	27.29	27	D#
5	5:4	1.25	386.31	16.09	16	E
6	21:16	1.3125	470.78	0.56	1	F
7	11:8	1.375	551.32	-18.90	-19	F#
8	23:16	1.4375	628.27	-41.95	-42	G
9	3:2	1.5	701.96	-68.27	-68	G#
10	13:8	1.625	840.53	-29.69	-30	A
11	7:4	1.75	968.83	-1.39	-1	A#
12	15:8	1.875	1088.27	18.05	18	B

Play Tuning bar chart


Largest step size:	138.57 c	(13:12)
Smallest step size:	73.68 c	(24:23)
Number of step sizes:	12

HC = 19.6

2005 by David J. Finnamore
tuning@elvenminstrel.com

Tuning Methods

Harmonic Series Tunings

12-tone Simple Harmonic Fragment