475edo: Difference between revisions
Review |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 37: | Line 29: | ||
| 0.0935 | | 0.0935 | ||
| 3.70 | | 3.70 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 55: | Line 41: | ||
|- | |- | ||
| 5 | | 5 | ||
| 329\475<br>(44\475) | | 329\475<br />(44\475) | ||
| 831.16<br>(111.16) | | 831.16<br />(111.16) | ||
| 160/99<br>(16/15) | | 160/99<br />(16/15) | ||
| [[Quintosec]] | | [[Quintosec]] | ||
|- | |- | ||
| 19 | | 19 | ||
| 197\475<br>(3\475) | | 197\475<br />(3\475) | ||
| 497.68<br>(7.58) | | 497.68<br />(7.58) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Enneadecal]] (475d) | | [[Enneadecal]] (475d) | ||
{{rank-2 end}} | |||
{{orf}} | |||
Revision as of 01:54, 16 November 2024
| ← 474edo | 475edo | 476edo → |
Theory
475edo is only consistent to the 5-odd-limit. The equal temperament tempers out [-14 -19 19⟩ (enneadeca) and [47 -15 -10⟩ (quintosec comma) in the 5-limit. In the 7-limit, the 475d val supports enneadecal and the patent val supports cotoneum.
It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 2376/2375, 3250/3249, 11132/11115, 11979/11960, 14300/14283 and 42757/42750.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.36 | +0.21 | -1.25 | -0.58 | +0.74 | +1.15 | +0.59 | +0.78 | +1.16 | -0.61 |
| Relative (%) | +0.0 | +14.3 | +8.4 | -49.4 | -23.0 | +29.1 | +45.5 | +23.4 | +30.8 | +45.9 | -24.3 | |
| Steps (reduced) |
475 (0) |
753 (278) |
1103 (153) |
1333 (383) |
1643 (218) |
1758 (333) |
1942 (42) |
2018 (118) |
2149 (249) |
2308 (408) |
2353 (453) | |
Subsets and supersets
Since 475 factors into 52 × 19, 475edo has subset edos 5, 19, 25, and 95. 950edo, which doubles it, gives a good correction to the harmonic 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [753 -475⟩ | [⟨475 753]] | -0.1138 | 0.1138 | 4.50 |- | 2.3.5 | [-14 -19 19⟩, [47 -15 -10⟩ | [⟨475 753 1103]] | -0.1064 | 0.0935 | 3.70 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 157\475
| 396.63
| 98304/78125
| Squarschmidt
|-
| 5
| 329\475
(44\475)
| 831.16
(111.16)
| 160/99
(16/15)
| Quintosec
|-
| 19
| 197\475
(3\475)
| 497.68
(7.58)
| 4/3
(225/224)
| Enneadecal (475d)
Template:Rank-2 end
Template:Orf