348edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|348}} == Theory == 348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgrou..." |
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== Theory == | == Theory == | ||
348et is consistent to the 7-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgroup temperament. Using the patent val, it tempers out | 348et is [[consistent]] to the [[7-odd-limit]], but the error of the [[harmonic]] [[3/1|3]] is quite large, commending itself as a 2.9.5.7.11.13 [[subgroup]] temperament. | ||
Using the [[patent val]], it tempers out [[2401/2400]], [[15625/15552]], [[390625/388962]] and 156250000/155649627 and in the 7-limit. It [[support]]s [[quadritikleismic]] and [[subneutral]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
348 factors into 2<sup>2</sup> × 3 × 29, | Since 348 factors into 2<sup>2</sup> × 3 × 29, 348edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 29, 58, 87, 116, and 174 }}. [[696edo]], which doubles 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" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|-1103 348}} | | {{monzo| -1103 348 }} | ||
|{{mapping|348 1103}} | | {{mapping| 348 1103 }} | ||
| +0.0728 | | +0.0728 | ||
| 0.0728 | | 0.0728 | ||
| 2.11 | | 2.11 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|32805/32768, {{monzo|52 | | 32805/32768, {{monzo| 7 52 -74 }} | ||
|{{mapping|348 1103 808}} | | {{mapping| 348 1103 808 }} | ||
| +0.0639 | | +0.0639 | ||
| 0.0608 | | 0.0608 | ||
|1.76 | | 1.76 | ||
|- | |- | ||
|2.9.5.7 | | 2.9.5.7 | ||
|32805/32768, 250047/250000, | | 32805/32768, 250047/250000, {{monzo| 7 9 -2 -11 }} | ||
|{{mapping|348 1103 808 977}} | | {{mapping| 348 1103 808 977 }} | ||
| +0.0355 | | +0.0355 | ||
| 0.0721 | | 0.0721 | ||
| 2.09 | | 2.09 | ||
|- | |- | ||
|2.9.5.7.11 | | 2.9.5.7.11 | ||
|9801/9800, 32805/32768, 46656/46585, | | 9801/9800, 32805/32768, 46656/46585, 151263/151250 | ||
|{{mapping|348 1103 808 977 1204}} | | {{mapping| 348 1103 808 977 1204 }} | ||
| +0.0049 | | +0.0049 | ||
| 0.0889 | | 0.0889 | ||
| 2.58 | | 2.58 | ||
|- | |- | ||
|2.9.5.7.11.13 | | 2.9.5.7.11.13 | ||
|729/728, 1575/1573, | | 729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213 | ||
|{{mapping|348 1103 808 977 1204 1288}} | | {{mapping| 348 1103 808 977 1204 1288 }} | ||
| -0.0343 | | -0.0343 | ||
| 0.1194 | | 0.1194 | ||
| 3.46 | | 3.46 | ||
|} | |} | ||