653edo: Difference between revisions

Revision as of 12:35, 16 November 2024

653edo is distinctly consistent to the 21-odd-limit, tempering out [39 -29 3⟩ (tricot comma) and [-20 -24 25⟩ (counterhanson comma) in the 5-limit; 2401/2400, 65625/65536, and [7 -27 13 2⟩ in the 7-limit; 3025/3024, 41503/41472, 496125/495616, and 1953125/1948617 in the 11-limit; 2080/2079, 4459/4455, 6656/6655, 10985/10976, and 170625/170368 in the 13-limit; 1225/1224, 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; 1445/1444, 1521/1520, 1540/1539, 1729/1728, 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

Approximation of prime harmonics in 653edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.036	-0.403	-0.373	-0.016	-0.711	-0.208	+0.190	+0.210	-0.481	-0.166
Error	Relative (%)	+0.0	+1.9	-21.9	-20.3	-0.9	-38.7	-11.3	+10.3	+11.4	-26.2	-9.0
Steps (reduced)		653 (0)	1035 (382)	1516 (210)	1833 (527)	2259 (300)	2416 (457)	2669 (57)	2774 (162)	2954 (342)	3172 (560)	3235 (623)

653edo is the 119th prime edo.

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[1035 -653⟩	[⟨653 1035]]	−0.0113	0.0113	0.61
2.3.5	[39 -29 3⟩, [-20 -24 25⟩	[⟨653 1035 1516]]	+0.0503	0.0875	4.76
2.3.5.7	2401/2400, 65625/65536, [7 -27 13 2⟩	[⟨653 1035 1516 1833]]	+0.0709	0.0838	4.56
2.3.5.7.11	2401/2400, 3025/3024, 65625/65536, 1953125/1948617	[⟨653 1035 1516 1833 2259]]	+0.0576	0.0795	4.33
2.3.5.7.11.13	2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536	[⟨653 1035 1516 1833 2259 2416]]	+0.0801	0.0882	4.80
2.3.5.7.11.13.17	1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976	[⟨653 1035 1516 1833 2259 2416 2669]]	+0.0759	0.0823	4.48
2.3.5.7.11.13.17.19	1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400	[⟨653 1035 1516 1833 2259 2416 2669 2774]]	+0.0608	0.0867	4.72

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	21\653	38.59	45/44	Hemitert
1	42\653	77.18	256/245	Tertiaseptal
1	172/653	316.08	6/5	Counterhanson
1	308/653	566.00	81920/59049	Tricot

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

"Seamless Toggle-Style" from Take Advantage (2024) – Spotify | Bandcamp | YouTube

@@ 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 62: / Line 71: @@
 | 0.0867
 | 4.72
-{{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 90: / Line 106: @@
 | 81920/59049
 | [[Tricot]]
-{{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]]
 * "Seamless Toggle-Style" from ''Take Advantage'' (2024) &ndash; [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] | [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] | [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]