13ed5/2: Difference between revisions

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"Jub" is equivalent to jubilic
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!#
!#
!Cents
!Cents
!Jubilic[8] notation
|-
|-
|0
|0
|0.000
|0.000
|C
|-
|-
|1
|1
|122.024
|122.024
|C#, Db
|-
|-
|2
|2
|244.048
|244.048
|D
|-
|-
|3
|3
|366.072
|366.072
|D#, Eb
|-
|-
|4
|4
|488.096
|488.096
|E
|-
|-
|5
|5
|610.120
|610.120
|F
|-
|-
|6
|6
|732.144
|732.144
|F#, Gb
|-
|-
|7
|7
|854.168
|854.168
|G
|-
|-
|8
|8
|976.192
|976.192
|H
|-
|-
|9
|9
|1098.216
|1098.216
|H#, Ab
|-
|-
|10
|10
|1220.240
|1220.240
|A
|-
|-
|11
|11
|1342.264
|1342.264
|A#, Bb
|-
|-
|12
|12
|1464.288
|1464.288
|B
|-
|-
|13
|13
|1586.312
|1586.312
|C
|}
|}

Revision as of 06:49, 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

Like 10edo, 13ed5/2 tempers out 50/49 in the no-threes 7-limit, supporting 5/2-equivalent jubilic temperament with a generator of ~7/5.


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 Jubilic[8] notation
0 0.000 C
1 122.024 C#, Db
2 244.048 D
3 366.072 D#, Eb
4 488.096 E
5 610.120 F
6 732.144 F#, Gb
7 854.168 G
8 976.192 H
9 1098.216 H#, Ab
10 1220.240 A
11 1342.264 A#, Bb
12 1464.288 B
13 1586.312 C