347edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories |
+regular temperament properties |
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{{EDO intro|347}} | {{EDO intro|347}} | ||
== Theory == | |||
The equal temperament [[tempering out|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both, and the planar [[hemimean]] temperament tempering out 3136/3125. | The equal temperament [[tempering out|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both, and the planar [[hemimean]] temperament tempering out 3136/3125. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
347edo is the 69th [[prime edo]]. | 347edo is the 69th [[prime edo]]. | ||
== 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|550 -347}} | |||
|{{mapping|347 550}} | |||
| -0.0197 | |||
| 0.0197 | |||
| 0.57 | |||
|- | |||
|2.3.5 | |||
|{{monzo|32 -7 -9}}, {{monzo|-22 30 -11}} | |||
|{{mapping|347 550 806}} | |||
| -0.1576 | |||
| 0.1956 | |||
| 5.66 | |||
|- | |||
|2.3.5.7 | |||
|3136/3125, 420175/419904, 5250987/5242880 | |||
|{{mapping|347 550 806 974}} | |||
| -0.0713 | |||
| 0.2259 | |||
| 6.53 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced)* | |||
! Cents<br>(reduced)* | |||
! Associated<br>Ratio* | |||
! Temperaments | |||
|- | |||
|1 | |||
|7\347 | |||
|24.21 | |||
|686/675 | |||
|[[Sengagen]] | |||
|- | |||
|1 | |||
|16\347 | |||
|55.33 | |||
|16875/16384 | |||
|[[Escapade]] | |||
|- | |||
|1 | |||
|69\347 | |||
|238.62 | |||
|147/128 | |||
|[[Tokko]] | |||
|- | |||
|1 | |||
|72\347 | |||
|248.99 | |||
|{{monzo|-26 18 -1}} | |||
|[[Monzismic]] | |||
|- | |||
|1 | |||
|146\347 | |||
|504.90 | |||
|104976/78125 | |||
|[[Countermeantone]] | |||
|} | |||
[[Category:Hemimean]] | [[Category:Hemimean]] | ||
[[Category:Sengagen]] | [[Category:Sengagen]] | ||
Revision as of 11:26, 8 December 2023
| ← 346edo | 347edo | 348edo → |
Theory
The equal temperament tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides an excellent tuning for sengagen, the 99 & 248 temperament tempering out both, and the planar hemimean temperament tempering out 3136/3125.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.06 | +1.01 | -0.53 | -1.46 | -0.18 | -1.21 | -0.11 | +1.12 | +0.97 | -0.37 |
| Relative (%) | +0.0 | +1.8 | +29.1 | -15.2 | -42.3 | -5.3 | -35.0 | -3.1 | +32.4 | +28.1 | -10.6 | |
| Steps (reduced) |
347 (0) |
550 (203) |
806 (112) |
974 (280) |
1200 (159) |
1284 (243) |
1418 (30) |
1474 (86) |
1570 (182) |
1686 (298) |
1719 (331) | |
Subsets and supersets
347edo is the 69th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [550 -347⟩ | [⟨347 550]] | -0.0197 | 0.0197 | 0.57 |
| 2.3.5 | [32 -7 -9⟩, [-22 30 -11⟩ | [⟨347 550 806]] | -0.1576 | 0.1956 | 5.66 |
| 2.3.5.7 | 3136/3125, 420175/419904, 5250987/5242880 | [⟨347 550 806 974]] | -0.0713 | 0.2259 | 6.53 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced)* |
Cents (reduced)* |
Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 7\347 | 24.21 | 686/675 | Sengagen |
| 1 | 16\347 | 55.33 | 16875/16384 | Escapade |
| 1 | 69\347 | 238.62 | 147/128 | Tokko |
| 1 | 72\347 | 248.99 | [-26 18 -1⟩ | Monzismic |
| 1 | 146\347 | 504.90 | 104976/78125 | Countermeantone |