14edf: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 14 equal parts''' (14EDF) is related to [[24edo|24 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 50.1396 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.
{{ED intro}}
 
14EDF is related to [[24edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.


Lookalikes: [[24edo]], [[38edt]]
Lookalikes: [[24edo]], [[38edt]]


==Harmonics==
== Harmonics ==
{{Harmonics in equal|14|3|2|intervals=prime}}
{{Harmonics in equal|14|3|2|intervals=prime}}
{{Harmonics in equal|14|3|2|start=12|collapsed=1|intervals=prime}}
{{Harmonics in equal|14|3|2|start=12|collapsed=1|intervals=prime}}


==Intervals==
== Intervals ==
{{todo|complete table|text=add column with note names, JI approximations and/or comments on practical uses}}
{{todo|complete table|text=add column with note names, JI approximations, and/or comments on practical uses}}
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+ Intervals of 14edf
|+ style="font-size: 105%;" | Intervals of 14edf
!Degree
|-
!Cents
! Degree
! Cents
|-
|-
|0
| 0
|0
| 0
|-
|-
|1
| 1
|50.1396
| 50.1396
|-
|-
|2
| 2
|100.2793
| 100.2793
|-
|-
|3
| 3
|150.4189
| 150.4189
|-
|-
|4
| 4
|200.5586
| 200.5586
|-
|-
|5
| 5
|250.6982
| 250.6982
|-
|-
|6
| 6
|300.8379
| 300.8379
|-
|-
|7
| 7
|350.9775
| 350.9775
|-
|-
|8
| 8
|401.1171
| 401.1171
|-
|-
|9
| 9
|451.2568
| 451.2568
|-
|-
|10
| 10
|501.3964
| 501.3964
|-
|-
|11
| 11
|551.536
| 551.536
|-
|-
|12
| 12
|601.6757
| 601.6757
|-
|-
|13
| 13
|651.8154
| 651.8154
|-
|-
|14
| 14
|701.955
| 701.955
|-
|-
|15
| 15
|752.0946
| 752.0946
|-
|-
|16
| 16
|802.2343
| 802.2343
|-
|-
|17
| 17
|852.3739
| 852.3739
|-
|-
|18
| 18
|902.5136
| 902.5136
|-
|-
|19
| 19
|952.6532
| 952.6532
|-
|-
|20
| 20
|1002.7929
| 1002.7929
|-
|-
|21
| 21
|1052.9235
| 1052.9235
|-
|-
|22
| 22
|1103.0721
| 1103.0721
|-
|-
|23
| 23
|1153.2118
| 1153.2118
|-
|-
|24
| 24
|1203.3514
| 1203.3514
|-
|-
|25
| 25
|1253.4911
| 1253.4911
|-
|-
|26
| 26
|1303.6307
| 1303.6307
|-
|-
|27
| 27
|1353.7704
| 1353.7704
|-
|-
|28
| 28
|1403.91
| 1403.91
|}
|}




{{stub}}
{{stub}}
[[Category:Edonoi]]

Revision as of 17:03, 21 January 2025

← 13edf 14edf 15edf →
Prime factorization 2 × 7
Step size 50.1396 ¢ 
Octave 24\14edf (1203.35 ¢) (→ 12\7edf)
Twelfth 38\14edf (1905.31 ¢) (→ 19\7edf)
Consistency limit 6
Distinct consistency limit 6

14 equal divisions of the perfect fifth (abbreviated 14edf or 14ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 14 equal parts of about 50.1 ¢ each. Each step represents a frequency ratio of (3/2)1/14, or the 14th root of 3/2.

14EDF is related to 24edo, but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.

Lookalikes: 24edo, 38edt

Harmonics

Approximation of prime harmonics in 14edf
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +3.4 +3.4 +21.5 -9.5 +10.3 +21.9 +8.7 +16.7 -13.2 -13.4 +21.6
Relative (%) +6.7 +6.7 +42.9 -18.9 +20.5 +43.7 +17.4 +33.4 -26.3 -26.7 +43.0
Steps
(reduced) 		24
(10) 		38
(10) 		56
(0) 		67
(11) 		83
(13) 		89
(5) 		98
(0) 		102
(4) 		108
(10) 		116
(4) 		119
(7)
Approximation of prime harmonics in 14edf
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +16.1 -11.2 +6.6 +3.1 -4.4 +10.5 +2.9 -9.1 -9.2 -7.1 +6.5
Relative (%) +32.1 -22.3 +13.2 +6.1 -8.7 +21.0 +5.9 -18.1 -18.3 -14.2 +13.1
Steps
(reduced) 		125
(13) 		128
(2) 		130
(4) 		133
(7) 		137
(11) 		141
(1) 		142
(2) 		145
(5) 		147
(7) 		148
(8) 		151
(11)

Intervals

Intervals of 14edf
Degree Cents
0 0
1 50.1396
2 100.2793
3 150.4189
4 200.5586
5 250.6982
6 300.8379
7 350.9775
8 401.1171
9 451.2568
10 501.3964
11 551.536
12 601.6757
13 651.8154
14 701.955
15 752.0946
16 802.2343
17 852.3739
18 902.5136
19 952.6532
20 1002.7929
21 1052.9235
22 1103.0721
23 1153.2118
24 1203.3514
25 1253.4911
26 1303.6307
27 1353.7704
28 1403.91


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