7ed5/2: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.
'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.
== Intervals ==
{{Interval table}}
== Harmonics ==
{{Harmonics in equal
| steps = 7
| num = 5
| denom = 2
}}
{{Harmonics in equal
| steps = 7
| num = 5
| denom = 2
| start = 12
| collapsed = 1
}}


[[Category:Ed5/2]]
[[Category:Ed5/2]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]

Revision as of 08:45, 4 October 2024

← 6ed5/2 7ed5/2 8ed5/2 →
Prime factorization 7 (prime)
Step size 226.616 ¢ 
Octave 5\7ed5/2 (1133.08 ¢)
Twelfth 8\7ed5/2 (1812.93 ¢)
Consistency limit 3
Distinct consistency limit 3

7ED5/2 is the equal division of the 5/2 interval into 7 parts of 226.6162 cents each, corresponding to 5.2953 EDO. It is related to the semaja temperament. Its patent val tempers out the same 5-limit commas as 5EDO, but mapping of 7 and higher prime harmonics differs to 5EDO.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 226.6 9/8, 10/9
2 453.2 4/3, 14/11, 17/13, 19/15
3 679.8 3/2
4 906.5 5/3, 19/11
5 1133.1 15/8, 19/10, 21/11
6 1359.7 9/4, 11/5, 20/9
7 1586.3 5/2, 17/7

Harmonics

Approximation of harmonics in 7ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -66.9 -89.0 +92.8 -66.9 +70.7 +30.4 +25.9 +48.6 +92.8 -72.2 +3.8
Relative (%) -29.5 -39.3 +40.9 -29.5 +31.2 +13.4 +11.4 +21.4 +40.9 -31.9 +1.7
Steps
(reduced)
5
(5)
8
(1)
11
(4)
12
(5)
14
(0)
15
(1)
16
(2)
17
(3)
18
(4)
18
(4)
19
(5)
Approximation of harmonics in 7ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +91.8 -36.5 +70.7 -41.1 +80.6 -18.4 -112.0 +25.9 -58.6 +87.5 +10.5
Relative (%) +40.5 -16.1 +31.2 -18.1 +35.6 -8.1 -49.4 +11.4 -25.9 +38.6 +4.6
Steps
(reduced)
20
(6)
20
(6)
21
(0)
21
(0)
22
(1)
22
(1)
22
(1)
23
(2)
23
(2)
24
(3)
24
(3)