7edf

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7edf

8edf →

Prime factorization	7 (prime)
Step size	100.279 ¢
Octave	12\7edf (1203.35 ¢) (convergent)
Twelfth	19\7edf (1905.31 ¢) (convergent)
Consistency limit	10
Distinct consistency limit	6

7 equal divisions of the perfect fifth (abbreviated 7edf or 7ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 7 equal parts of about 100 ¢ each. Each step represents a frequency ratio of (3/2)^1/7, or the 7th root of 3/2.

Theory

7edf is related to 12edo, but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514 ¢. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves.

Harmonics

Approximation of harmonics in 7edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	+3.35	+3.35	+6.70	+21.51	+6.70	+40.67	+10.05	+6.70	+24.86	-39.87	+10.05	-28.24	+44.02	+24.86	+13.41
	Relative (%)	+3.3	+3.3	+6.7	+21.4	+6.7	+40.6	+10.0	+6.7	+24.8	-39.8	+10.0	-28.2	+43.9	+24.8	+13.4
Steps (reduced)		12 (5)	19 (5)	24 (3)	28 (0)	31 (3)	34 (6)	36 (1)	38 (3)	40 (5)	41 (6)	43 (1)	44 (2)	46 (4)	47 (5)	48 (6)

Subsets and supersets

7edf is the 4th prime edf, after 5edf and before 11edf.

Intervals

#	Cents	Approximate ratios	12edo notation
0	0	exact 1/1	C
1	100.3	18/17, 17/16	C#, Db
2	200.6	9/8	D
3	300.8	19/16, 44/37	D#, Eb
4	401.1	63/50	E
5	501.4	4/3	F
6	601.7	64/45	F#, Gb
7	702.0	exact 3/2	G
8	802.2	100/63	G#, Ab
9	902.5	27/16	A
10	1002.8	16/9	A#, Bb
11	1103.1	17/9	B
12	1203.4	2/1	C
13	1303.6	17/8	C#, Db
14	1403.9	exact 9/4	D

See also

• 12edo – relative edo
• 19edt – relative edt
• 28ed5 – relative ed5
• 31ed6 – relative ed6
• 34ed7 – relative ed7
• 40ed10 – relative ed10
• 43ed12 – relative ed12
• 76ed80 – close to the zeta-optimized tuning for 12edo
• AS18/17 – relative ambitonal sequence