727edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Francium (talk | contribs)
4,816 edits
m please put the table below the contents part, plus doing a selected intervals table for just one interval is questionable
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"
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|727}}
{{ED intro}}


== Theory ==
== Theory ==
Line 13: Line 13:
== 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|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 error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| -1152 727}}
| {{monzo| -1152 727}}
| {{mapping|727 1152}}
| {{mapping|727 1152}}
| 0.1394
| +0.1394
| 0.1394
| 0.1394
| 8.45
| 8.45
Line 32: Line 33:
| {{monzo| 8 14 -13}}, {{monzo| -96 43 12}}
| {{monzo| 8 14 -13}}, {{monzo| -96 43 12}}
| {{mapping|727 1152 1688}}
| {{mapping|727 1152 1688}}
| 0.1028
| +0.1028
| 0.1250
| 0.1250
| 7.57
| 7.57
Line 39: Line 40:
| 703125/702464, 5250987/5242880, 43046721/42875000
| 703125/702464, 5250987/5242880, 43046721/42875000
| {{mapping|727 1152 1688 2041}}
| {{mapping|727 1152 1688 2041}}
| 0.0693
| +0.0693
| 0.1229
| 0.1229
| 7.45
| 7.45
Line 46: Line 47:
| 24057/24010, 160083/160000, 137781/137500, 496125/495616
| 24057/24010, 160083/160000, 137781/137500, 496125/495616
| {{mapping|727 1152 1688 2041 2515}}
| {{mapping|727 1152 1688 2041 2515}}
| 0.0561
| +0.0561
| 0.1130
| 0.1130
| 6.84
| 6.84
Line 53: Line 54:
| 729/728, 1716/1715, 78975/78848, 34398/34375, 160083/160000
| 729/728, 1716/1715, 78975/78848, 34398/34375, 160083/160000
| {{mapping|727 1152 1688 2041 2515 2690}}
| {{mapping|727 1152 1688 2041 2515 2690}}
| 0.0631
| +0.0631
| 0.1043
| 0.1043
| 6.32
| 6.32
Line 60: Line 61:
=== 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
|-
|-
Line 73: Line 75:
| [[Parakleismic]]
| [[Parakleismic]]
|}
|}
<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 />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
== Music ==
; [[Francium]]
* "Rent A Person" from ''I Want To'' (2025) – [https://open.spotify.com/track/6ow6ZzkLpaCkOOJ7qAhjjq Spotify] | [https://francium223.bandcamp.com/track/rent-a-person Bandcamp] | [https://www.youtube.com/watch?v=bvWCK2sggks YouTube]
* "Take the SQUEEPS" from ''Things to Scream at People'' (2025) – [https://open.spotify.com/track/5lOj1lUVhEwR7T7RoPsgbH Spotify] | [https://francium223.bandcamp.com/track/take-the-squeeps Bandcamp] | [https://www.youtube.com/watch?v=8kVuEk2GWG8 YouTube]

Latest revision as of 13:31, 13 March 2026

← 726edo 727edo 728edo →
Prime factorization 727 (prime)
Step size 1.65062 ¢ 
Fifth 425\727 (701.513 ¢)
Semitones (A1:m2) 67:56 (110.6 ¢ : 92.43 ¢)
Consistency limit 7
Distinct consistency limit 7

727 equal divisions of the octave (abbreviated 727edo or 727ed2), also called 727-tone equal temperament (727tet) or 727 equal temperament (727et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 727 equal parts of about 1.65 ¢ each. Each step represents a frequency ratio of 21/727, or the 727th root of 2.

Theory

727edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 24057/24010, 160083/160000, 137781/137500 and 496125/495616 in the 11-limit; 729/728, 1716/1715, 78975/78848, 34398/34375 and 160083/160000 in the 13-limit. It supports exodia.

Odd harmonics

Approximation of odd harmonics in 727edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.442 -0.069 +0.087 +0.767 -0.011 -0.363 -0.511 +0.684 -0.402 -0.354 +0.611
Relative (%) -26.8 -4.2 +5.3 +46.5 -0.7 -22.0 -30.9 +41.5 -24.3 -21.5 +37.0
Steps
(reduced) 		1152
(425) 		1688
(234) 		2041
(587) 		2305
(124) 		2515
(334) 		2690
(509) 		2840
(659) 		2972
(64) 		3088
(180) 		3193
(285) 		3289
(381)

Subsets and supersets

727edo is the 129th prime EDO.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-1152 727⟩ [⟨727 1152]] +0.1394 0.1394 8.45
2.3.5 [8 14 -13⟩, [-96 43 12⟩ [⟨727 1152 1688]] +0.1028 0.1250 7.57
2.3.5.7 703125/702464, 5250987/5242880, 43046721/42875000 [⟨727 1152 1688 2041]] +0.0693 0.1229 7.45
2.3.5.7.11 24057/24010, 160083/160000, 137781/137500, 496125/495616 [⟨727 1152 1688 2041 2515]] +0.0561 0.1130 6.84
2.3.5.7.11.13 729/728, 1716/1715, 78975/78848, 34398/34375, 160083/160000 [⟨727 1152 1688 2041 2515 2690]] +0.0631 0.1043 6.32

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 191\727 315.268 6/5 Parakleismic

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

Music

Francium
Retrieved from "https://en.xen.wiki/index.php?title=727edo&oldid=225786"