4973edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} It is a very strong [[7-limit]] system: it tempers out the [[unnoticeable comma]] {{monzo| 1 -15 -18 23 }} and supports a number of [[very high accuracy temperaments|very high accuracy 7-limit rank-3 temperaments]]. In the 5-limit it [[support]]s [[whoosh]], the [[441edo|441]] & [[730edo|730]] temperament. It is a [[zeta peak integer edo]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|4973|prec=4}} | |||
[[Category:Zeta|####]] <!-- 4-digit number --> | |||
[[Category:Zeta]] | |||
Latest revision as of 06:54, 20 February 2025
| ← 4972edo | 4973edo | 4974edo → |
4973 equal divisions of the octave (abbreviated 4973edo or 4973ed2), also called 4973-tone equal temperament (4973tet) or 4973 equal temperament (4973et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4973 equal parts of about 0.241 ¢ each. Each step represents a frequency ratio of 21/4973, or the 4973rd root of 2. It is a very strong 7-limit system: it tempers out the unnoticeable comma [1 -15 -18 23⟩ and supports a number of very high accuracy 7-limit rank-3 temperaments. In the 5-limit it supports whoosh, the 441 & 730 temperament. It is a zeta peak integer edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0045 | +0.0124 | +0.0058 | +0.0595 | -0.0692 | +0.0114 | +0.0136 | +0.0788 | +0.0629 | -0.0527 |
| Relative (%) | +0.0 | -1.9 | +5.2 | +2.4 | +24.7 | -28.7 | +4.7 | +5.6 | +32.6 | +26.1 | -21.8 | |
| Steps (reduced) |
4973 (0) |
7882 (2909) |
11547 (1601) |
13961 (4015) |
17204 (2285) |
18402 (3483) |
20327 (435) |
21125 (1233) |
22496 (2604) |
24159 (4267) |
24637 (4745) | |