View source for 348edo

{{Infobox ET}}
{{ED intro}}

== Theory ==
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]].

In 348edo, the prime harmonics up to 13 map the same way as in [[87edo]], except the 7th harmonic, which is corrected.

=== Odd harmonics ===
{{Harmonics in equal|348}}

=== Subsets and supersets ===
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 ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-	
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.9
| {{monzo| -1103 348 }}
| {{mapping| 348 1103 }}
| +0.0728
| 0.0728
| 2.11
|-
| 2.9.5
| 32805/32768, {{monzo| 7 52 -74 }}
| {{mapping| 348 1103 808 }}
| +0.0639
| 0.0608
| 1.76
|-
| 2.9.5.7
| 32805/32768, 250047/250000, {{monzo| 7 9 -2 -11 }}
| {{mapping| 348 1103 808 977 }}
| +0.0355
| 0.0721
| 2.09
|-
| 2.9.5.7.11
| 9801/9800, 32805/32768, 46656/46585, 151263/151250
| {{mapping| 348 1103 808 977 1204 }}
| +0.0049
| 0.0889
| 2.58
|-
| 2.9.5.7.11.13
| 729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213
| {{mapping| 348 1103 808 977 1204 1288 }}
| −0.0343
| 0.1194
| 3.46
|}