13ed5/2: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''13ed5/2''' is the equal division of the [[5/2]] interval into 13 parts of 122.024 [[cent]]s each. It roughly corresponds to [[10edo]].
== Theory ==
13ed5/2 tempers out [[50/49]] in the no-threes 7-limit, [[support]]ing 5/2-equivalent jubilismic temperament (named "jub" by [[User:CompactStar|CompactStar]]).
{{Harmonics in equal|13|5|2}}
== Intervals ==
{|class="wikitable article-table"
|-
!#
!Cents
|-
|0
|0.000
|-
|1
|122.024
|-
|2
|244.048
|-
|3
|366.072
|-
|4
|488.096
|-
|5
|610.120
|-
|6
|732.144
|-
|7
|854.168
|-
|8
|976.192
|-
|9
|1098.216
|-
|10
|1220.240
|-
|11
|1342.264
|-
|12
|1464.288
|-
|13
|1586.312
|}

Revision as of 01:58, 24 June 2023

← 12ed5/2 13ed5/2 14ed5/2 →
Prime factorization 13 (prime)
Step size 122.024 ¢ 
Octave 10\13ed5/2 (1220.24 ¢)
(semiconvergent)
Twelfth 16\13ed5/2 (1952.39 ¢)
Consistency limit 5
Distinct consistency limit 5

13ed5/2 is the equal division of the 5/2 interval into 13 parts of 122.024 cents each. It roughly corresponds to 10edo.

Theory

13ed5/2 tempers out 50/49 in the no-threes 7-limit, supporting 5/2-equivalent jubilismic temperament (named "jub" by CompactStar).

Approximation of harmonics in 13ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +20.2 +50.4 +40.5 +20.2 -51.4 +47.8 +60.7 -21.2 +40.5 -2.5 -31.1
Relative (%) +16.6 +41.3 +33.2 +16.6 -42.1 +39.2 +49.8 -17.3 +33.2 -2.0 -25.5
Steps
(reduced) 		10
(10) 		16
(3) 		20
(7) 		23
(10) 		25
(12) 		28
(2) 		30
(4) 		31
(5) 		33
(7) 		34
(8) 		35
(9)

Intervals

# Cents
0 0.000
1 122.024
2 244.048
3 366.072
4 488.096
5 610.120
6 732.144
7 854.168
8 976.192
9 1098.216
10 1220.240
11 1342.264
12 1464.288
13 1586.312
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