Prime Limit Otonal Tunings: 23-limit Full

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A. Rational Tunings

· Prime Limit

· 5-limit Full

· 5-limit Exact

· 7-limit Full

· 7-limit Exact

· 11-limit Full

· 11-limit Exact

· 13-limit Full

· 13-limit Exact

· 17-limit Full

· 17-limit Exact

· 19-limit Full

· 19-limit Exact

· 23-limit Full

· 23-limit Exact

· Harmonic Series

· Simple Skip-sets

· Saturated Ratios

· Tetrachords

· Septimal Chromatic

· Hexanies

B. Equal Temperaments

· Octave Repeating

· Non-octave Repeating

· 88c

C. Non-Equal, Non-Rational

· Golden Horagramic

· Lucy Tuning™

· 2pi Roots

This is the only case in which the Full version of a PLOT tuning has a higher HC than the Exact version.

Scale Degree	Num	:	Den	Quotient	Cents	Tuning Table	Rounded Tuning Table	Note Name
1	1	:	1	1	0.00	4.63	5	C
2	17	:	16	1.0625	104.96	9.58	10	C#
3	9	:	8	1.125	203.91	8.54	9	D
4	19	:	16	1.1875	297.51	2.14	2	D#
5	5	:	4	1.25	386.31	-9.06	-9	E
6	11	:	8	1.375	551.32	55.94	56	F
7	23	:	16	1.4375	628.27	32.90	33	F#
8	3	:	2	1.5	701.96	6.58	7	G
9	25	:	16	1.5625	772.63	-22.75	-23	G#
10	13	:	8	1.625	840.53	-54.85	-55	A
11	7	:	4	1.75	968.83	-26.55	-27	A#
12	15	:	8	1.875	1088.27	-7.11	-7	B

Play Tuning bar chart

Largest step size:	165.00 c	(11:10)
Smallest step size:	67.90 c	(26:25)
Number of step sizes:	12

Odd limit 25
HC = 21.2

Consists of:
	3 (2)	5 (2)	7	11	13	17	19	23
Squares	3²	5²

Totals	4	4	1	1	1	1	1	1

2004 by David J. Finnamore
tuning@elvenminstrel.com