757edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|757}} == Theory == 757edo is consistent to the 7-odd-limit, tempering out 4375/4374, 67108864/66976875 and 282475249/281250000. Usi..."
 
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== Theory ==
== Theory ==
757edo is [[consistent]] to the [[7-odd-limit]], [[tempering out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], 4375/4374, [[160083/160000]] and 5764801/5749920 in the [[11-limit]].
757edo is [[consistent]] to the [[7-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], [[160083/160000]] and 5764801/5749920 in the [[11-limit]].


=== Prime harmonics ===
=== Prime harmonics ===
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== 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" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo|1200 -757}}
| {{monzo| 1200 -757 }}
| {{mapping|757 1200}}
| {{mapping| 757 1200 }}
| -0.0917
| -0.0917
| 0.0917
| 0.0917
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|-
|-
| 2.3.5
| 2.3.5
| {{monzo|24 -21 4}}, {{monzo|78 5 -37}}
| {{monzo| 24 -21 4 }}, {{monzo| 78 5 -37 }}
| {{mapping|757 1200 1758}}
| {{mapping| 757 1200 1758 }}
| -0.1295
| -0.1295
| 0.0920
| 0.0920
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| 2.3.5.7
| 2.3.5.7
| 4375/4374, 67108864/66976875, 282475249/281250000
| 4375/4374, 67108864/66976875, 282475249/281250000
| {{mapping|757 1200 1758 2125}}
| {{mapping| 757 1200 1758 2125 }}
| -0.0735
| -0.0735
| 0.1256
| 0.1256
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|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 5632/5625, 4375/4374, 160083/160000, 5764801/5749920
| 4375/4374, 5632/5625, 160083/160000, 5764801/5749920
| {{mapping|757 1200 1758 2125 2619}}
| {{mapping| 757 1200 1758 2125 2619 }}
| -0.0780
| -0.0780
| 0.1127
| 0.1127
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! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Vulture]]
| [[Vulture]]
|}
|}
 
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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

Revision as of 17:09, 10 January 2025

← 756edo 757edo 758edo →
Prime factorization 757 (prime)
Step size 1.5852 ¢ 
Fifth 443\757 (702.246 ¢)
Semitones (A1:m2) 73:56 (115.7 ¢ : 88.77 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

757edo is consistent to the 7-odd-limit. As an equal temperament, it tempers out 4375/4374, 67108864/66976875 and 282475249/281250000. Using the patent val, it tempers out 5632/5625, 160083/160000 and 5764801/5749920 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 757edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.291 +0.476 -0.266 +0.333 -0.369 -0.332 +0.505 -0.533 -0.779 -0.518
Relative (%) +0.0 +18.3 +30.0 -16.8 +21.0 -23.3 -20.9 +31.9 -33.6 -49.2 -32.7
Steps
(reduced) 		757
(0) 		1200
(443) 		1758
(244) 		2125
(611) 		2619
(348) 		2801
(530) 		3094
(66) 		3216
(188) 		3424
(396) 		3677
(649) 		3750
(722)

Subsets and supersets

757edo is the 134th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [1200 -757⟩ [⟨757 1200]] -0.0917 0.0917 5.78
2.3.5 [24 -21 4⟩, [78 5 -37⟩ [⟨757 1200 1758]] -0.1295 0.0920 5.80
2.3.5.7 4375/4374, 67108864/66976875, 282475249/281250000 [⟨757 1200 1758 2125]] -0.0735 0.1256 7.92
2.3.5.7.11 4375/4374, 5632/5625, 160083/160000, 5764801/5749920 [⟨757 1200 1758 2125 2619]] -0.0780 0.1127 7.11

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 300\757 475.561 320/243 Vulture

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

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