607edo: Difference between revisions

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== Regular temperament properties ==
== 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
| 2.3
Line 55: Line 64:
| 0.1222
| 0.1222
| 6.18
| 6.18
{{comma basis end}}
|}


=== Rank-2 temperaments ===
=== 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
| 1
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| 4/3
| 4/3
| [[Helmholtz]]
| [[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 ==
== Music ==

Revision as of 12:55, 16 November 2024

← 606edo 607edo 608edo →
Prime factorization 607 (prime)
Step size 1.97694 ¢ 
Fifth 355\607 (701.812 ¢)
Semitones (A1:m2) 57:46 (112.7 ¢ : 90.94 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

607edo is consistent to the 9-odd-limit. Using the patent val, the equal temperament tempers out 32805/32768, 420175/419904 and 244140625/243045684 in the 7-limit; 3025/3024, 6250/6237, 32805/32768 and 420175/419904 in the 11-limit. It supports countertertiaschis. Essentially tempered chords available in 607et include baladismic chords and xenismic chords.

Prime harmonics

Approximation of prime harmonics in 607edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.143 -0.811 -0.127 +0.247 -0.330 -0.178 -0.973 +0.391 +0.406 -0.390
Relative (%) +0.0 -7.2 -41.0 -6.4 +12.5 -16.7 -9.0 -49.2 +19.8 +20.6 -19.7
Steps
(reduced) 		607
(0) 		962
(355) 		1409
(195) 		1704
(490) 		2100
(279) 		2246
(425) 		2481
(53) 		2578
(150) 		2746
(318) 		2949
(521) 		3007
(579)

Subsets and supersets

607edo is the 111th prime EDO.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-962 607⟩ [⟨607 962]] 0.0451 0.0451 2.28
2.3.5 32805/32768, [-58 -63 68⟩ [⟨607 962 1409]] 0.1465 0.1481 7.49
2.3.5.7 32805/32768, 420175/419904, 244140625/243045684 [⟨607 962 1409 1704]] 0.1212 0.1355 6.85
2.3.5.7.11 3025/3024, 6250/6237, 32805/32768, 420175/419904 [⟨607 962 1409 1704 2100]] 0.0827 0.1437 7.27
2.3.5.7.11.13 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491 [⟨607 962 1409 1704 2100 2246]] 0.0838 0.1312 6.64
2.3.5.7.11.13.17 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831 [⟨607 962 1409 1704 2100 2246 2481]] 0.0780 0.1222 6.18

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 252\607 498.188 4/3 Helmholtz

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

Music

Francium
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