7980edo

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7980edo

7981edo →

Prime factorization	22 × 3 × 5 × 7 × 19
Step size	0.150376 ¢
Fifth	4668\7980 (701.955 ¢) (→ 389\665)
Semitones (A1:m2)	756:600 (113.7 ¢ : 90.23 ¢)
Consistency limit	9
Distinct consistency limit	9

7980 equal divisions of the octave (abbreviated 7980edo or 7980ed2), also called 7980-tone equal temperament (7980tet) or 7980 equal temperament (7980et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7980 equal parts of about 0.15 ¢ each. Each step represents a frequency ratio of 2^1/7980, or the 7980th root of 2.

Theory

It is a very strong 5-limit system, tempering out Kirnberger's atom ([161 -84 -12⟩) and the satanic comma ([1054 665⟩), as well as [73 77 -84⟩ and [234 -7 -96⟩.

In the 7-limit, it tempers out the euzenius comma (78125000/78121827), the akjaysma (140737488355328/140710042265625), and [-17 50 1 -23⟩.

In the 11-limit, using the patent val, it tempers out the kalisma (9801/9800), 47265625/47258883, 39630026842637/39627113103360, and 163470238547968/163443018796875.

Todo: review Are the 7-limit and 11-limit descriptions musically relevant?

Approximation of prime harmonics in 7980edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0001	+0.0021	+0.0463	-0.0397	+0.0738	+0.0070	-0.0694	-0.0037	+0.0469	-0.0732
	Relative (%)	+0.0	-0.1	+1.4	+30.8	-26.4	+49.1	+4.7	-46.2	-2.4	+31.2	-48.7
Steps (reduced)		7980 (0)	12648 (4668)	18529 (2569)	22403 (6443)	27606 (3666)	29530 (5590)	32618 (698)	33898 (1978)	36098 (4178)	38767 (6847)	39534 (7614)