472edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| Line 41: | Line 33: | ||
| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095 | | 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095 | ||
| [{{val| 472 748 1096 1325 1633 1747 }}] | | [{{val| 472 748 1096 1325 1633 1747 }}] | ||
| | | −0.0341 | ||
| 0.1365 | | 0.1365 | ||
| 5.37 | | 5.37 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 5-limit temperaments supported by [[118edo|118et]] are not included. | Note: 5-limit temperaments supported by [[118edo|118et]] are not included. | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 82: | Line 68: | ||
|- | |- | ||
| 8 | | 8 | ||
| 196\472<br>(19\472) | | 196\472<br />(19\472) | ||
| 498.31<br>(48.31) | | 498.31<br />(48.31) | ||
| 4/3<br>(36/35) | | 4/3<br />(36/35) | ||
| [[Octant]] | | [[Octant]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
Revision as of 03:49, 16 November 2024
| ← 471edo | 472edo | 473edo → |
Theory
472edo is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma, but the approximation to higher harmonics are much improved. It is a zeta peak integer edo, consistent to the 11-odd-limit or the no-13 29-odd-limit.
In the 7-limit, the equal temperament tempers out 2401/2400, 2460375/2458624, and 30623756184/30517578125; in the 11-limit, 9801/9800, 46656/46585, 117649/117612, and 234375/234256, supporting the maviloid temperament, the bisesqui temperament, and the octant temperament. Using the patent val, it tempers out 729/728, 1575/1573, 2200/2197, 4096/4095, and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.26 | +0.13 | -0.18 | +0.38 | +1.00 | -0.72 | -0.06 | -0.31 | +0.08 | -0.97 |
| Relative (%) | +0.0 | -10.2 | +5.0 | -7.2 | +14.8 | +39.2 | -28.2 | -2.2 | -12.1 | +3.3 | -38.1 | |
| Steps (reduced) |
472 (0) |
748 (276) |
1096 (152) |
1325 (381) |
1633 (217) |
1747 (331) |
1929 (41) |
2005 (117) |
2135 (247) |
2293 (405) |
2338 (450) | |
Subsets and supersets
Since 472 factors into 23 × 59, 472edo has subset edos 2, 4, 8, 59, 118, and 236.
Regular temperament properties
Template:Comma basis begin |- | 2.3.5.7 | 2401/2400, 32805/32768, [8 14 -13⟩ | [⟨472 748 1096 1325]] | +0.0435 | 0.0814 | 3.20 |- | 2.3.5.7.11 | 2401/2400, 9801/9800, 32805/32768, 46656/46585 | [⟨472 748 1096 1325 1633]] | +0.0130 | 0.0950 | 3.74 |- | 2.3.5.7.11.13 | 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095 | [⟨472 748 1096 1325 1633 1747]] | −0.0341 | 0.1365 | 5.37 Template:Comma basis end
Rank-2 temperaments
Note: 5-limit temperaments supported by 118et are not included.
Template:Rank-2 begin
|-
| 1
| 69\472
| 175.42
| 448/405
| Sesquiquartififths
|-
| 1
| 137\472
| 348.31
| 57344/46875
| Subneutral
|-
| 1
| 205\472
| 521.19
| 875/648
| Maviloid
|-
| 2
| 69\472
| 175.42
| 448/405
| Bisesqui
|-
| 8
| 196\472
(19\472)
| 498.31
(48.31)
| 4/3
(36/35)
| Octant
Template:Rank-2 end
Template:Orf