619edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|619}} == 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 202..."
 
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"
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|619}}
{{ED intro}}


== Theory ==
== Theory ==
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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" |[[Comma list|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! rowspan="2" | Optimal<br />8ve stretch (¢)
|-
! colspan="2" | Tuning error
![[TE error|Absolute]] (¢)
|-
![[TE simple badness|Relative]] (%)
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
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| {{mapping|619 981}}
| {{mapping|619 981}}
| 0.0561
| 0.0561
| 0.0561
| +0.0561
| 2.89
| 2.89
|-
|-
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| {{mapping|619 981 1437}}
| {{mapping|619 981 1437}}
| 0.1135
| 0.1135
| 0.0932
| +0.0932
| 4.81
| 4.81
|-
|-
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| {{mapping|619 981 1437 2141}}
| {{mapping|619 981 1437 2141}}
| 0.1395
| 0.1395
| 0.0925
| +0.0925
| 4.77
| 4.77
|}
|}
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=== 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
|-
|-
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| 498.223
| 498.223
| 4/3
| 4/3
| [[Helmholtz]]
| [[Helmholtz (temperament)|Helmholtz]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<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 ==
; [[Francium]]
* "Would You Like An Egg?" from ''Questions'' (2024) &ndash; [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] &ndash; helmholtz in 619edo tuning

Latest revision as of 13:32, 13 March 2026

← 618edo 619edo 620edo →
Prime factorization 619 (prime)
Step size 1.93861 ¢ 
Fifth 362\619 (701.777 ¢)
Semitones (A1:m2) 58:47 (112.4 ¢ : 91.11 ¢)
Consistency limit 5
Distinct consistency limit 5

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

Approximation of prime harmonics in 619edo
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

Table of rank-2 temperaments by generator
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

Music

Francium
  • "Would You Like An Egg?" from Questions (2024) – Spotify | Bandcamp | YouTube – helmholtz in 619edo tuning
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