337edo: Difference between revisions
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== 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 | ||
|- | |- | ||
| Line 46: | Line 47: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 71: | Line 73: | ||
| [[Sqrtphi]] (337, 11-limit) | | [[Sqrtphi]] (337, 11-limit) | ||
|} | |} | ||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "The End Of A Good Day" from ''Mysteries'' (2023) | * "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] | [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] | [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 01:08, 16 November 2024
| ← 336edo | 337edo | 338edo → |
Theory
337edo is consistent to the 9-odd-limit, but the error of harmonic 5 is quite large. If the harmonic is used at all, it tends very flat. The equal temperament tempers out 16875/16807, 420175/419904, and 5250987/5242880 in the 7-limit. It supports tokko and sqrtphi.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.47 | -1.74 | -0.28 | -0.94 | +0.61 | -0.17 | +1.35 | -1.69 | +1.60 | -0.75 | -1.57 |
| Relative (%) | -13.2 | -49.0 | -7.9 | -26.5 | +17.2 | -4.8 | +37.8 | -47.5 | +44.8 | -21.1 | -44.0 | |
| Steps (reduced) |
534 (197) |
782 (108) |
946 (272) |
1068 (57) |
1166 (155) |
1247 (236) |
1317 (306) |
1377 (29) |
1432 (84) |
1480 (132) |
1524 (176) | |
Subsets and supersets
337edo is the 68th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-534 337⟩ | [⟨337 534]] | 0.1487 | 0.1487 | 4.18 |
| 2.3.5 | 15625/15552, [-88 57 -1⟩ | [⟨337 534 782]] | 0.3495 | 0.3089 | 8.67 |
| 2.3.5.7 | 15625/15552, 16875/16807, 7381125/7340032 | [⟨337 534 782 946]] | 0.2870 | 0.2886 | 8.10 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 67\337 | 238.58 | 147/128 | Tokko |
| 1 | 89\337 | 316.91 | 6/5 | Hanson |
| 1 | 117\337 | 416.62 | 14/11 | Sqrtphi (337, 11-limit) |