23ed5/3: Difference between revisions

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'''23ED5/3''' is the [[EdVI|equal division of the just major sixth]] into 23 parts of 38.4504 [[cent|cents]] each, corresponding to 31.2091 [[edo]]. It is very closely related to the [[Marvel temperaments|slender temperament]].
{{Infobox ET}}
'''23ed5/3''' is the [[Ed5/3|equal division of the just major sixth]] into 23 parts of 38.4504 [[cent]]s each, corresponding to 31.2091[[edo]]. It is very closely related to the [[Marvel temperaments #Slender|slender temperament]].


[[Category:EdVI]]
== Harmonics ==
{{Harmonics in equal|23|5|3}}
{{Harmonics in equal|23|5|3|collapsed=1|start=12}}
 
== Intervals ==
{| class="wikitable"
|+
!Degrees
! colspan="2" |Hexadecatonic
!Cents
|-
|1
| colspan="2" |D
|38.4504
|-
|2
|D#/Eb
|Dp/E\\
|76.9008
|-
|3
| colspan="2" |E
|115.3511
|-
|4
| colspan="2" |F
|153.8015
|-
|5
|F#/Gb~0b
|Fp/G\\~0\\
|192.2519
|-
|6
| colspan="2" |G~0
|230.7023
|-
|7
| colspan="2" |1
|269.15235
|-
|8
|1#/2b
|1p/2\\
|307.603
|-
|9
| colspan="2" |2
|346.0534
|-
|10
| colspan="2" |3
|384.5038
|-
|11
|3#/4(b)
|3p\4(//)
|422.9542
|-
|12
|4(#)/5b
|4(p)/5\\
|461.40455
|-
|13
| colspan="2" |5
|499.8549
|-
|14
| colspan="2" |6
|538.3053
|-
|15
|6#/7b
|6p/7\\
|576.7557
|-
|16
| colspan="2" |7
|615.2061
|-
|17
| colspan="2" |8
|653.6564
|-
|18
|8#/9b
|8p/9\\
|692.1068
|-
|19
| colspan="2" |9
|730.5572
|-
|20
| colspan="2" |A
|769.0076
|-
|21
|A#/Bb
|Ap\B\\
|807.45795
|-
|22
| colspan="2" |B
|845.9083
|-
|23
| colspan="2" |C
|884.3587
|}
 
{{todo|expand}}
[[Category:Nonoctave]]
[[Category:Nonoctave]]

Latest revision as of 22:19, 21 December 2024

← 22ed5/3 23ed5/3 24ed5/3 →
Prime factorization 23 (prime)
Step size 38.4504 ¢ 
Octave 31\23ed5/3 (1191.96 ¢)
Twelfth 49\23ed5/3 (1884.07 ¢)
Consistency limit 5
Distinct consistency limit 5

23ed5/3 is the equal division of the just major sixth into 23 parts of 38.4504 cents each, corresponding to 31.2091edo. It is very closely related to the slender temperament.

Harmonics

Approximation of harmonics in 23ed5/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -8.0 -17.9 -16.1 -17.9 +12.5 +14.8 +14.3 +2.7 +12.5 +1.3 +4.5
Relative (%) -20.9 -46.5 -41.8 -46.5 +32.6 +38.5 +37.3 +7.0 +32.6 +3.4 +11.7
Steps
(reduced) 		31
(8) 		49
(3) 		62
(16) 		72
(3) 		81
(12) 		88
(19) 		94
(2) 		99
(7) 		104
(12) 		108
(16) 		112
(20)
Approximation of harmonics in 23ed5/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -18.7 +6.8 +2.7 +6.3 +16.7 -5.4 +16.4 +4.5 -3.1 -6.7 -6.8
Relative (%) -48.7 +17.6 +7.0 +16.4 +43.4 -13.9 +42.6 +11.7 -8.0 -17.5 -17.6
Steps
(reduced) 		115
(0) 		119
(4) 		122
(7) 		125
(10) 		128
(13) 		130
(15) 		133
(18) 		135
(20) 		137
(22) 		139
(1) 		141
(3)

Intervals

Degrees Hexadecatonic Cents
1 D 38.4504
2 D#/Eb Dp/E\\ 76.9008
3 E 115.3511
4 F 153.8015
5 F#/Gb~0b Fp/G\\~0\\ 192.2519
6 G~0 230.7023
7 1 269.15235
8 1#/2b 1p/2\\ 307.603
9 2 346.0534
10 3 384.5038
11 3#/4(b) 3p\4(//) 422.9542
12 4(#)/5b 4(p)/5\\ 461.40455
13 5 499.8549
14 6 538.3053
15 6#/7b 6p/7\\ 576.7557
16 7 615.2061
17 8 653.6564
18 8#/9b 8p/9\\ 692.1068
19 9 730.5572
20 A 769.0076
21 A#/Bb Ap\B\\ 807.45795
22 B 845.9083
23 C 884.3587
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