619edo: Difference between revisions

Revision as of 13:18, 16 November 2024

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.

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
Error	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)

619edo is the 114th prime EDO.

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	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

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 it is distinct

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

@@ Line 12: / Line 12: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| 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
@@ Line 34: / Line 43: @@
 | 0.0925
 | 4.77
-{{comma basis end}}
+|}
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| 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
@@ Line 44: / Line 60: @@
 | 4/3
 | [[Helmholtz]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is 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