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.
{{ED intro}}
 
== Theory ==
7ed5/2 corresponds to 5.2953…[[edo]]. It is related to the [[semaja]] temperament. Its [[patent val]] tempers out the same 5-limit commas as [[5edo]], but the mapping of 7 and higher prime harmonics differs.
 
=== Harmonics ===
{{Harmonics in equal|7|5|2|columns=11}}
{{Harmonics in equal|7|5|2|columns=12|start=12|collapsed=true|Approximation of harmonics in 7ed5/2 (continued)}}


== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible"
{| class="wikitable center-1 right-2"
|+
|+
!Step
! #
!Interval (¢)
! Cents
!JI approximated
! Approximated ratio
!Simplified ratio
|-
|-
|1
| 1
|226.62
| 227
|34/30
| 17/15
|17/15
|-
|-
|2
| 2
|453.23
| 453
|39/30
| 13/10
|13/10
|-
|-
|3
| 3
|679.85
| 680
|34/23
| 34/23
|
|-
|-
|4
| 4
|906.47
| 906
|66/39
| 11/7
|22/14
|-
|-
|5
| 5
|1133.08
| 1133
|23/12
| 23/12
|
|-
|-
|6
| 6
|1359.70
| 1360
|66/30
| 11/5
|11/5
|-
|-
|7
| 7
|1586.31
| 1586
|5/2
| 5/2
|
|}
|}
The subgroup interpretation used is 5/2.12.23.34.39.51.58.66. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 12*5/2=30.
== Harmonics ==
{{Harmonics in equal
| steps = 7
| num = 5
| denom = 2
}}
{{Harmonics in equal
| steps = 7
| num = 5
| denom = 2
| start = 12
| collapsed = 1
}}
{{todo|expand}}
[[Category:Nonoctave]]

Revision as of 13:54, 27 May 2026

← 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

7 equal divisions of 5/2 (abbreviated 7ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 7 equal parts of about 227 ¢ each. Each step represents a frequency ratio of (5/2)1/7, or the 7th root of 5/2.

Theory

7ed5/2 corresponds to 5.2953…edo. It is related to the semaja temperament. Its patent val tempers out the same 5-limit commas as 5edo, but the mapping of 7 and higher prime harmonics differs.

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 24
Error Absolute (¢) +91.8 -36.5 +70.7 -41.1 +80.6 -18.4 -112.0 +25.9 -58.6 +87.5 +10.5 -63.2
Relative (%) +40.5 -16.1 +31.2 -18.1 +35.6 -8.1 -49.4 +11.4 -25.9 +38.6 +4.6 -27.9
Steps
(reduced) 		20
(6) 		20
(6) 		21
(0) 		21
(0) 		22
(1) 		22
(1) 		22
(1) 		23
(2) 		23
(2) 		24
(3) 		24
(3) 		24
(3)

Intervals

# Cents Approximated ratio
1 227 17/15
2 453 13/10
3 680 34/23
4 906 11/7
5 1133 23/12
6 1360 11/5
7 1586 5/2
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