419edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|419}}. ==Theory== 419et tempers out 32805/32768, 29360128/29296875, 1959552/1953125, 420175/419904 and 2100875/2097152 in the 7-limit and 3..." |
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419edo is the 81th [[prime edo]]. | 419edo is the 81th [[prime edo]]. | ||
{{Harmonics in equal|419}} | {{Harmonics in equal|419}} | ||
==Regular temperament properties== | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo| -664 419}} | |||
|{{val| 419 664}} | |||
| +0.0897 | |||
| 0.0897 | |||
| 25.69 | |||
|- | |||
|2.3.5 | |||
|32805/32768, {{monzo| 41 43 -47}} | |||
|{{val| 419 664 973}} | |||
| +0.0137 | |||
| 0.1301 | |||
| 37.26 | |||
|- | |||
|2.3.5.7 | |||
|32805/32768, 420175/419904, 1959552/1953125 | |||
|{{val| 419 664 973 1176}} | |||
| +0.0821 | |||
| 0.1635 | |||
| 46.83 | |||
|- | |||
|2.3.5.7.11 | |||
|441/440, 200704/200475, 160083/160000, 472392/471625 | |||
|{{val| 419 664 973 1176 1450}} | |||
| -0.0168 | |||
| 0.2460 | |||
| 70.45 | |||
|- | |||
|} | |||
==Scales== | ==Scales== | ||
*[[Sextilififths13]] | *[[Sextilififths13]] | ||
Revision as of 18:07, 26 March 2023
| ← 418edo | 419edo | 420edo → |
Theory
419et tempers out 32805/32768, 29360128/29296875, 1959552/1953125, 420175/419904 and 2100875/2097152 in the 7-limit and 35156250/35153041, 25165824/25109315, 26214400/26198073, 4000/3993, 1366875/1362944, 759375/758912, 21437500/21434787, 2359296/2358125, 472392/471625, 369140625/369098752, 200704/200475, 441/440, 43046721/43025920, 17537553/17500000, 422576/421875, 160083/160000, 199297406/199290375, 244515348/244140625 and 67110351/67108864 in the 11-limit. It supports the sextilififths temperament. 419edo is the 81th prime edo.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.28 | +0.32 | -0.81 | +1.43 | -1.39 | +1.01 | +0.34 | -1.07 | -1.41 | +0.55 |
| Relative (%) | +0.0 | -9.9 | +11.2 | -28.2 | +49.8 | -48.4 | +35.3 | +11.8 | -37.2 | -49.4 | +19.2 | |
| Steps (reduced) |
419 (0) |
664 (245) |
973 (135) |
1176 (338) |
1450 (193) |
1550 (293) |
1713 (37) |
1780 (104) |
1895 (219) |
2035 (359) |
2076 (400) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-664 419⟩ | ⟨419 664] | +0.0897 | 0.0897 | 25.69 |
| 2.3.5 | 32805/32768, [41 43 -47⟩ | ⟨419 664 973] | +0.0137 | 0.1301 | 37.26 |
| 2.3.5.7 | 32805/32768, 420175/419904, 1959552/1953125 | ⟨419 664 973 1176] | +0.0821 | 0.1635 | 46.83 |
| 2.3.5.7.11 | 441/440, 200704/200475, 160083/160000, 472392/471625 | ⟨419 664 973 1176 1450] | -0.0168 | 0.2460 | 70.45 |