619edo: Difference between revisions
Jump to navigation
Jump to search
ArrowHead294 (talk | contribs) mNo edit summary |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
||
| (5 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 12: | Line 12: | ||
== Regular temperament properties == | == 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]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 18: | Line 27: | ||
| {{mapping|619 981}} | | {{mapping|619 981}} | ||
| 0.0561 | | 0.0561 | ||
| 0.0561 | | +0.0561 | ||
| 2.89 | | 2.89 | ||
|- | |- | ||
| Line 25: | Line 34: | ||
| {{mapping|619 981 1437}} | | {{mapping|619 981 1437}} | ||
| 0.1135 | | 0.1135 | ||
| 0.0932 | | +0.0932 | ||
| 4.81 | | 4.81 | ||
|- | |- | ||
| Line 32: | Line 41: | ||
| {{mapping|619 981 1437 2141}} | | {{mapping|619 981 1437 2141}} | ||
| 0.1395 | | 0.1395 | ||
| 0.0925 | | +0.0925 | ||
| 4.77 | | 4.77 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 43: | Line 59: | ||
| 498.223 | | 498.223 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] | [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] | [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning | * "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] | [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] | [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning | ||
Latest revision as of 13:32, 13 March 2026
| ← 618edo | 619edo | 620edo → |
619 equal divisions of the octave (abbreviated 619edo or 619ed2), also called 619-tone equal temperament (619tet) or 619 equal temperament (619et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 619 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/619, or the 619th root of 2.
Theory
619edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.17.19.23.29.41 subgroup, tempering out 2025/2024, 1089/1088, 3520/3519, 1045/1044, 2755/2754, 71875/71808, 374000/373977 and 1025/1024.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.178 | -0.530 | +0.479 | -0.753 | +0.829 | -0.270 | -0.906 | -0.164 | -0.175 | +0.683 |
| Relative (%) | +0.0 | -9.2 | -27.3 | +24.7 | -38.8 | +42.8 | -13.9 | -46.7 | -8.5 | -9.0 | +35.2 | |
| Steps (reduced) |
619 (0) |
981 (362) |
1437 (199) |
1738 (500) |
2141 (284) |
2291 (434) |
2530 (54) |
2629 (153) |
2800 (324) |
3007 (531) |
3067 (591) | |
Subsets and supersets
619edo is the 114th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-981 619⟩ | [⟨619 981]] | 0.0561 | +0.0561 | 2.89 |
| 2.3.5 | 32805/32768, [-54 -67 69⟩ | [⟨619 981 1437]] | 0.1135 | +0.0932 | 4.81 |
| 2.3.5.11 | 32805/32768, 234375/234256, 314552734375/313456656384 | [⟨619 981 1437 2141]] | 0.1395 | +0.0925 | 4.77 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 257\619 | 498.223 | 4/3 | Helmholtz |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct