7edt

← 6edt

7edt

8edt →

Prime factorization	7 (prime)
Step size	271.708 ¢
Octave	4\7edt (1086.83 ¢)
Consistency limit	3
Distinct consistency limit	3

7 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 7edt or 7ed3), is a nonoctave tuning system that divides the interval of 3/1 into 7 equal parts of about 272 ¢ each. Each step represents a frequency ratio of 3^1/7, or the 7th root of 3.

Theory

Since one step of 7edt approximates a 7/6 subminor third (4.84 ¢ sharp) quite nicely, three steps are almost exactly 8/5 (tempering out 1728/1715, the orwellisma), and four steps are very nearly 15/8 (tempering out 2430/2401, the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some 7-limit harmony, along with some elements of the 11-limit, such as the 11/8 major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.

Due to the proximity of the step size with 7/6, 7edt supports orwell temperament. One step of 7edt is almost identical to 12\53, the 53edo orwell generator, at about 271.698 cents. 7edt is also a good tuning for Electra temperament, with two steps of 7edt being a close approximation to 15/11.

Harmonics

Approximation of harmonics in 7edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	-113	+0	+45	-69	-113	-108	-68	+0	+89	-76	+45	-93	+50	-69	+91
	Relative (%)	-41.7	+0.0	+16.7	-25.5	-41.7	-39.9	-25.0	+0.0	+32.9	-27.9	+16.7	-34.3	+18.5	-25.5	+33.4
Steps (reduced)		4 (4)	7 (0)	9 (2)	10 (3)	11 (4)	12 (5)	13 (6)	14 (0)	15 (1)	15 (1)	16 (2)	16 (2)	17 (3)	17 (3)	18 (4)

Subsets and supersets

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

Intervals

#	Cents	Hekts	Approximate ratios	Electra notation (J = 1/1)
0	0	0	1/1	J
1	272	186	7/6	K
2	543	371	11/8, 15/11	L
3	815	557	8/5	M
4	1087	743	15/8	N
5	1359	929	11/5	O
6	1630	1114	18/7	P
7	1902	1300	3/1	J