347edo: Difference between revisions
Review |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 44: | Line 36: | ||
| 0.2259 | | 0.2259 | ||
| 6.53 | | 6.53 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 84: | Line 70: | ||
| 104976/78125 | | 104976/78125 | ||
| [[Countermeantone]] | | [[Countermeantone]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
[[Category:Hemimean]] | [[Category:Hemimean]] | ||
[[Category:Sengagen]] | [[Category:Sengagen]] | ||
Revision as of 02:39, 16 November 2024
| ← 346edo | 347edo | 348edo → |
Theory
The equal temperament tempers out [32 -7 -9⟩ (escapade comma) and [54 -37 2⟩ (monzisma), 3136/3125, 420175/419904, and 5250987/5242880 in the 7-limit. It provides an excellent tuning for sengagen, the 99 & 248 temperament tempering out both 3136/3125 and 420175/419904, and the rank-3 hemimean temperament tempering out 3136/3125.
Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. It makes more sense as a 2.3.5.7.13 subgroup temperament, where it tempers out 676/675 and 4096/4095, or as a 2.3.5.7.13.19 subgroup temperament, where it tempers out 1521/1520 and 1729/1728.
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
Template:Comma basis begin |- | 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 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 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 Template:Rank-2 end Template:Orf