897edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|897}} | {{EDO intro|897}} | ||
==Theory== | |||
897et tempers out [[250047/250000]] in the 7-limit, | 897et tempers out [[250047/250000]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[131072/130977]], 172032/171875, [[5632/5625]], 47265625/47258883, [[3025/3024]], 160083/160000, 102487/102400, [[1771561/1769472]] in the 11-limit. | ||
{{Harmonics in equal|897}} | {{Harmonics in equal|897}} | ||
==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| 474 -299}} | |||
|{{val| 897 1422}} | |||
| -0.1218 | |||
| 0.1218 | |||
| 9.10 | |||
|- | |||
|2.3.5 | |||
|{{monzo| 33 -34 9}}, {{monzo| 70 -9 -24}} | |||
|{{val| 897 1422 2083}} | |||
| -0.1255 | |||
| 0.010 | |||
| 0.75 | |||
|- | |||
|2.3.5.7 | |||
|250047/250000, 67108864/66976875, 28824005/28697814 | |||
|{{val| 897 1422 2083 2518}} | |||
| -0.0706 | |||
| 0.1283 | |||
| 9.59 | |||
|- | |||
|2.3.5.7.11 | |||
|3025/3024, 5632/5625, 160083/160000, 28824005/28697814 | |||
|{{val| 897 1422 2083 2518 3103}} | |||
| -0.0480 | |||
| 0.1234 | |||
| 9.22 | |||
|- | |||
|2.3.5.7.11.13 | |||
|2080/2079, 1001/1000, 3025/3024, 4096/4095, 2058857500/2051893701 | |||
|{{val| 897 1422 2083 2518 3103 3319}} | |||
| -0.0222 | |||
| 0.1265 | |||
| 9.46 | |||
|} | |||
==Music== | ==Music== | ||
* [https://www.youtube.com/watch?v=opR71xbJ-PQ 13|3|23] by Francium | |||
*[https://www.youtube.com/watch?v=opR71xbJ-PQ 13|3|23] by Francium | |||
Revision as of 20:22, 26 March 2023
| ← 896edo | 897edo | 898edo → |
Theory
897et tempers out 250047/250000 in the 7-limit; 100663296/100656875, 2097152/2096325, 131072/130977, 172032/171875, 5632/5625, 47265625/47258883, 3025/3024, 160083/160000, 102487/102400, 1771561/1769472 in the 11-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.386 | +0.308 | -0.264 | -0.566 | -0.147 | -0.394 | -0.643 | -0.608 | -0.523 | +0.122 | +0.488 |
| Relative (%) | +28.9 | +23.0 | -19.7 | -42.3 | -11.0 | -29.4 | -48.1 | -45.4 | -39.1 | +9.1 | +36.5 | |
| Steps (reduced) |
1422 (525) |
2083 (289) |
2518 (724) |
2843 (152) |
3103 (412) |
3319 (628) |
3504 (813) |
3666 (78) |
3810 (222) |
3940 (352) |
4058 (470) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [474 -299⟩ | ⟨897 1422] | -0.1218 | 0.1218 | 9.10 |
| 2.3.5 | [33 -34 9⟩, [70 -9 -24⟩ | ⟨897 1422 2083] | -0.1255 | 0.010 | 0.75 |
| 2.3.5.7 | 250047/250000, 67108864/66976875, 28824005/28697814 | ⟨897 1422 2083 2518] | -0.0706 | 0.1283 | 9.59 |
| 2.3.5.7.11 | 3025/3024, 5632/5625, 160083/160000, 28824005/28697814 | ⟨897 1422 2083 2518 3103] | -0.0480 | 0.1234 | 9.22 |
| 2.3.5.7.11.13 | 2080/2079, 1001/1000, 3025/3024, 4096/4095, 2058857500/2051893701 | ⟨897 1422 2083 2518 3103 3319] | -0.0222 | 0.1265 | 9.46 |
Music
- 13|3|23 by Francium