10ed5/3: Difference between revisions

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{{Stub}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}}


== Intervals ==
== Intervals ==
{{Interval table}}
{| class="wikitable mw-collapsible"
|+
!Step
!Interval (¢)
!JI approximated
!Simplified ratios
|-
|1
|88.44
|81/77
|
|-
|2
|176.87
|10/9, 11/10
|
|-
|3
|265.31
|7/6, 29/25
|
|-
|4
|353.74
|11/9, 29/24, 36/29
|
|-
|5
|442.18
|9/7
|
|-
|6
|530.62
|15/11, 40/29
|
|-
|7
|619.05
|10/7, 63/44
|
|-
|8
|707.49
|6/4, 44/29
|3/2
|-
|9
|795.92
|16/10, 11/7, 46/29
|8/5
|-
|10
|884.36
|5/3, 42/25
|
|-
|11
|972.80
|7/4, 44/25
|
|-
|12
|1061.23
|11/6, 54/29
|
|-
|13
|1149.67
|29/15
|
|-
|14
|1238.10
|66/32
|33/16
|-
|15
|1326.54
|15/7
|
|-
|16
|1414.97
|9/4, 16/7, 25/11
|
|-
|17
|1503.41
|24/10
|12/5
|-
|18
|1591.85
|10/4, 63/25
|5/2
|-
|19
|1680.28
|16/6, 29/11, 66/25
|8/3
|-
|20
|1768.72
|11/4, 28/10
|14/5
|}
The subgroup interpretation used is 5/3.4.6.7.9.10.11.29. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 9*5/3=15, 15*5/3=25.


== Harmonics ==
== Harmonics ==
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| collapsed = 1
| collapsed = 1
}}
}}
{{stub}}

Latest revision as of 07:48, 17 December 2024

← 9ed5/3 10ed5/3 11ed5/3 →
Prime factorization 2 × 5
Step size 88.4359 ¢ 
Octave 14\10ed5/3 (1238.1 ¢) (→ 7\5ed5/3)
Twelfth 22\10ed5/3 (1945.59 ¢) (→ 11\5ed5/3)
Consistency limit 3
Distinct consistency limit 3

10 equal divisions of 5/3 (abbreviated 10ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 10 equal parts of about 88.4 ¢ each. Each step represents a frequency ratio of (5/3)1/10, or the 10th root of 5/3.

Intervals

Step Interval (¢) JI approximated Simplified ratios
1 88.44 81/77
2 176.87 10/9, 11/10
3 265.31 7/6, 29/25
4 353.74 11/9, 29/24, 36/29
5 442.18 9/7
6 530.62 15/11, 40/29
7 619.05 10/7, 63/44
8 707.49 6/4, 44/29 3/2
9 795.92 16/10, 11/7, 46/29 8/5
10 884.36 5/3, 42/25
11 972.80 7/4, 44/25
12 1061.23 11/6, 54/29
13 1149.67 29/15
14 1238.10 66/32 33/16
15 1326.54 15/7
16 1414.97 9/4, 16/7, 25/11
17 1503.41 24/10 12/5
18 1591.85 10/4, 63/25 5/2
19 1680.28 16/6, 29/11, 66/25 8/3
20 1768.72 11/4, 28/10 14/5

The subgroup interpretation used is 5/3.4.6.7.9.10.11.29. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 9*5/3=15, 15*5/3=25.

Harmonics

Approximation of harmonics in 10ed5/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +38.1 +43.6 -12.2 +43.6 -6.7 -8.3 +25.9 -1.2 -6.7 +5.2 +31.4
Relative (%) +43.1 +49.3 -13.8 +49.3 -7.6 -9.3 +29.3 -1.3 -7.6 +5.8 +35.5
Steps
(reduced) 		14
(4) 		22
(2) 		27
(7) 		32
(2) 		35
(5) 		38
(8) 		41
(1) 		43
(3) 		45
(5) 		47
(7) 		49
(9)
Approximation of harmonics in 10ed5/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -18.7 +29.8 -1.2 -24.5 -41.0 +36.9 +31.8 +31.4 +35.4 +43.3 -33.7
Relative (%) -21.2 +33.7 -1.3 -27.7 -46.3 +41.8 +35.9 +35.5 +40.0 +48.9 -38.1
Steps
(reduced) 		50
(0) 		52
(2) 		53
(3) 		54
(4) 		55
(5) 		57
(7) 		58
(8) 		59
(9) 		60
(0) 		61
(1) 		61
(1)


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