7980edo: Difference between revisions
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{{ED intro}} | |||
== Theory == | |||
It is a very strong 5-limit system, tempering out [[Kirnberger's atom]] ({{monzo|161 -84 -12}}) and the [[satanic comma]] ({{monzo|1054 665}}), as well as {{monzo|73 77 -84}} and {{monzo|234 -7 -96}}. | |||
In the 7-limit, it tempers out the [[euzenius comma]] (78125000/78121827), the [[akjaysma]] (140737488355328/140710042265625), and {{monzo|-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|inline=1|review|comment=Are the 7-limit and 11-limit descriptions musically relevant?}} | |||
{{Harmonics in equal|7980}} | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
[[Category:Atomic]] | |||
[[Category:Satanic]] | [[Category:Satanic]] | ||
Latest revision as of 19:36, 30 June 2026
| ← 7979edo | 7980edo | 7981edo → |
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 21/7980, 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? |
| 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) | |