1051edo: Difference between revisions
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→Regular temperament properties: plz note 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. It doesn't seem to be supporting edson in any obvious way, either |
→Theory: plz note that subgroup is part of RTT perspective. |
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{{EDO intro|1051}} | {{EDO intro|1051}} | ||
== Theory == | == Theory == | ||
1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit. | 1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup. | ||
===Odd harmonics=== | Assume the [[patent val]], 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|1051}} | {{Harmonics in equal|1051}} | ||
===Subsets and supersets=== | |||
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic | === Subsets and supersets === | ||
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
Revision as of 08:23, 8 May 2023
| ← 1050edo | 1051edo | 1052edo → |
Theory
1051edo only has a consistency limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.
Assume the patent val, 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.233 | -0.396 | +0.537 | +0.467 | +0.157 | -0.185 | -0.162 | +0.087 | +0.489 | -0.372 | -0.301 |
| Relative (%) | +20.4 | -34.6 | +47.0 | +40.9 | +13.7 | -16.2 | -14.2 | +7.7 | +42.8 | -32.6 | -26.4 | |
| Steps (reduced) |
1666 (615) |
2440 (338) |
2951 (849) |
3332 (179) |
3636 (483) |
3889 (736) |
4106 (953) |
4296 (92) |
4465 (261) |
4616 (412) |
4754 (550) | |
Subsets and supersets
1051edo is the 177th prime edo. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1666 -1051⟩ | ⟨1051 1666] | -0.0736 | 0.0736 | 6.45 |
| 2.3.5 | [-68 18 17⟩, [-26 -29 31⟩ | ⟨1051 1666 2440] (1051) | +0.0077 | 0.1298 | 11.4 |
| 2.3.5 | [40 7 -22⟩, [63 -50 7⟩ | ⟨1051 1666 2441] (1051c) | -0.1562 | 0.1313 | 11.5 |