253edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 401 -253 }} | | {{monzo| 401 -253 }} | ||
| {{mapping| 253 401 }} | | {{mapping| 253 401 }} | ||
| | | −0.007 | ||
| 0.007 | | 0.007 | ||
| 0.14 | | 0.14 | ||
| Line 63: | Line 55: | ||
| 0.295 | | 0.295 | ||
| 6.22 | | 6.22 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 97: | Line 83: | ||
| 7/5 | | 7/5 | ||
| [[Cotritone]] | | [[Cotritone]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||
Revision as of 04:49, 16 November 2024
| ← 252edo | 253edo | 254edo → |
(semiconvergent)
Theory
253edo is consistent to the 17-odd-limit, approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. The equal temperament tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides the optimal patent val for the tertiaschis temperament, and a good tuning for the sesquiquartififths temperament in the higher limits.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.02 | -2.12 | -1.24 | -1.12 | -1.00 | -0.61 | +1.30 | -2.19 | -0.33 | -1.95 |
| Relative (%) | +0.0 | +0.4 | -44.8 | -26.1 | -23.6 | -21.1 | -12.8 | +27.4 | -46.1 | -6.9 | -41.2 | |
| Steps (reduced) |
253 (0) |
401 (148) |
587 (81) |
710 (204) |
875 (116) |
936 (177) |
1034 (22) |
1075 (63) |
1144 (132) |
1229 (217) |
1253 (241) | |
Subsets and supersets
253 = 11 × 23, and has subset edos 11edo and 23edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [401 -253⟩ | [⟨253 401]] | −0.007 | 0.007 | 0.14 |- | 2.3.5 | 32805/32768, [-4 -37 27⟩ | [⟨253 401 587]] | +0.300 | 0.435 | 9.16 |- | 2.3.5.7 | 2401/2400, 32805/32768, 390625/387072 | [⟨253 401 587 710]] | +0.335 | 0.381 | 8.03 |- | 2.3.5.7.11 | 385/384, 1375/1372, 4000/3993, 19712/19683 | [⟨253 401 587 710 875]] | +0.333 | 0.341 | 7.19 |- | 2.3.5.7.11.13 | 325/324, 385/384, 1375/1372, 1575/1573, 2200/2197 | [⟨253 401 587 710 875 936]] | +0.323 | 0.312 | 6.58 |- | 2.3.5.7.11.13.17 | 325/324, 375/374, 385/384, 595/594, 1275/1274, 2200/2197 | [⟨253 401 587 710 875 936 1034]] | +0.298 | 0.295 | 6.22 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 35\253 | 166.01 | 11/10 | Tertiaschis |- | 1 | 37\253 | 175.49 | 448/405 | Sesquiquartififths |- | 1 | 105\253 | 498.02 | 4/3 | Helmholtz |- | 1 | 123\253 | 583.40 | 7/5 | Cotritone Template:Rank-2 end Template:Orf
Scales
- 63 32 63 63 32: One of many pentic scales available
- 43 43 19 43 43 43 19: Helmholtz[7]
- 41 41 24 41 41 41 24: Meantone[7]
- 35 35 35 35 35 35 35 8: Porcupine[8]
- 33 33 33 11 33 33 33 33 11: "The Hendecapliqued superdiatonic of the Icositriphony"
- 31 31 31 18 31 31 31 31 18: Mavila[9]
- 26 26 15 26 26 26 15 26 26 26 15: Sensi[11]
- 20 20 20 11 20 20 20 20 11 20 20 20 20 11: Ketradektriatoh scale