607edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|607}}
{{ED intro}}


== Theory ==
== Theory ==
607edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|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 [[support]]s [[countertertiaschis]]. [[Essentially tempered chords]] available in 607et include [[baladismic chords]] and [[xenismic chords]].
607edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|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 [[support]]s [[countertertiaschis]]. [[Essentially tempered chord]]s available in 607et include [[baladismic chords]] and [[xenismic chords]].


=== Prime harmonics ===
=== Prime harmonics ===
Line 10: Line 10:
=== Subsets and supersets ===
=== Subsets and supersets ===
607edo is the 111th [[prime EDO]].
607edo is the 111th [[prime EDO]].
== Intervals ==
{{Main|Table of 607edo intervals}}


== 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
| {{monzo|-962 607}}
| {{monzo|-962 607}}
| {{mapping|607 962}}
| {{mapping|607 962}}
| 0.0451
| +0.0451
| 0.0451
| 0.0451
| 2.28
| 2.28
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| 32805/32768, {{monzo|-58 -63 68}}
| 32805/32768, {{monzo|-58 -63 68}}
| {{mapping|607 962 1409}}
| {{mapping|607 962 1409}}
| 0.1465
| +0.1465
| 0.1481
| 0.1481
| 7.49
| 7.49
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| 32805/32768, 420175/419904, 244140625/243045684
| 32805/32768, 420175/419904, 244140625/243045684
| {{mapping|607 962 1409 1704}}
| {{mapping|607 962 1409 1704}}
| 0.1212
| +0.1212
| 0.1355
| 0.1355
| 6.85
| 6.85
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| 3025/3024, 6250/6237, 32805/32768, 420175/419904
| 3025/3024, 6250/6237, 32805/32768, 420175/419904
| {{mapping|607 962 1409 1704 2100}}
| {{mapping|607 962 1409 1704 2100}}
| 0.0827
| +0.0827
| 0.1437
| 0.1437
| 7.27
| 7.27
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| 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491
| 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491
| {{mapping|607 962 1409 1704 2100 2246}}
| {{mapping|607 962 1409 1704 2100 2246}}
| 0.0838
| +0.0838
| 0.1312
| 0.1312
| 6.64
| 6.64
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| 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
| 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
| {{mapping|607 962 1409 1704 2100 2246 2481}}
| {{mapping|607 962 1409 1704 2100 2246 2481}}
| 0.0780
| +0.0780
| 0.1222
| 0.1222
| 6.18
| 6.18
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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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| 498.188
| 498.188
| 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
<nowiki>*</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 ==
; [[Francium]]
; [[Francium]]
* "Complete Edition" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3U1YP47z0bmKZ76DzXEDTG Spotify] | [https://francium223.bandcamp.com/track/complete-edition Bandcamp] | [https://www.youtube.com/watch?v=PTpp4HPi98A YouTube] – countertertiaschis[15] in 607edo tuning
* "Complete Edition" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3U1YP47z0bmKZ76DzXEDTG Spotify] | [https://francium223.bandcamp.com/track/complete-edition Bandcamp] | [https://www.youtube.com/watch?v=PTpp4HPi98A YouTube] – in Countertertiaschis[15], 607edo tuning
* "TAKE THE NIGHT WITH YOU" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3xjT48PIa0OjNL7yTBWwVF Spotify] | [https://francium223.bandcamp.com/track/take-the-night-with-you Bandcamp] | [https://www.youtube.com/watch?v=5fzzB753wfM YouTube]
* "Sweep Away" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3W9U6apb2cfKHtUXsmILDE Spotify] | [https://francium223.bandcamp.com/track/sweep-away Bandcamp] | [https://www.youtube.com/watch?v=5Q-aQnStoaA YouTube]
* "In the Field of Vodka" from ''Scoop'' (2024) – [https://open.spotify.com/track/79JeaYC5nBpz4fG6pPgkEe Spotify] | [https://francium223.bandcamp.com/track/in-the-field-of-vodka Bandcamp] | [https://www.youtube.com/watch?v=j_tkNX986sU YouTube]
* "The Cereal Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/7rO4vqdT05EV324fiXGPXI Spotify] | [https://francium223.bandcamp.com/track/the-cereal-egg Bandcamp] | [https://www.youtube.com/watch?v=-mkzaimrst4 YouTube]
 
[[Category:Listen]]

Latest revision as of 13:32, 13 March 2026

← 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

607 equal divisions of the octave (abbreviated 607edo or 607ed2), also called 607-tone equal temperament (607tet) or 607 equal temperament (607et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 607 equal parts of about 1.98 ¢ each. Each step represents a frequency ratio of 21/607, or the 607th root of 2.

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.

Intervals

Main article: Table of 607edo intervals

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 distinct

Music

Francium
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