43edt: Difference between revisions

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'''[[Edt|Division of the third harmonic]] into 43 equal parts''' (43EDT) is related to [[27edo|27 EDO]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the [[9-odd-limit|10-integer-limit]].
=43 EDT=
=43 EDT=


This tuning is related to [[27edo|27edo]] having compressed octaves of 1194.251 cents, a small but significant deviation. This is particularly relevant because 27edo is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).
This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).


However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13edt]] is not. The 4L+5s MOS has L=7 s=3.
However, in addition to its rich octave-based harmony, the 43EDT is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13EDT]] is not. The 4L+5s MOS has L=7 s=3.


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Degrees
! | degrees
! | Cents
! | cents value
! | corresponding <br>JI intervals
|-
|-
| | 1
| | 1
| | 44.232
| | 44.232
| | 40/39, 39/38
|-
|-
| | 2
| | 2
| | 88.463
| | 88.463
| | [[20/19]]
|-
|-
| | 3
| | 3
| | 132.695
| | 132.695
| | [[27/25]]
|-
|-
| | 4
| | 4
| | 176.926
| | 176.926
| |
|-
|-
| | 5
| | 5
| | 221.158
| | 221.158
| | [[25/22]]
|-
|-
| | 6
| | 6
| | 265.389
| | 265.389
| | ([[7/6]])
|-
|-
| | 7
| | 7
| | 309.621
| | 309.621
| |
|-
|-
| | 8
| | 8
| | 353.852
| | 353.852
| | [[27/22]]
|-
|-
| | 9
| | 9
| | 398.084
| | 398.084
| |
|-
|-
| | 10
| | 10
| | 442.315
| | 442.315
| |
|-
|-
| | 11
| | 11
| | 486.547
| | 486.547
| | (45/34)
|-
|-
| | 12
| | 12
| | 530.778
| | 530.778
| | (34/25)
|-
|-
| | 13
| | 13
| | 575.010
| | 575.010
| | (39/28)
|-
|-
| | 14
| | 14
| | 619.241
| | 619.241
| | ([[10/7]])
|-
|-
| | 15
| | 15
| | 663.473
| | 663.473
| | [[22/15]]
|-
|-
| | 16
| | 16
| | 707.704
| | 707.704
| |
|-
|-
| | 17
| | 17
| | 751.936
| | 751.936
| |
|-
|-
| | 18
| | 18
| | 796.167
| | 796.167
| | [[19/12]]
|-
|-
| | 19
| | 19
| | 840.399
| | 840.399
| | [[13/8]]
|-
|-
| | 20
| | 20
| | 884.630
| | 884.630
| | [[5/3]]
|-
|-
| | 21
| | 21
| | 928.862
| | 928.862
| |
|-
|-
| | 22
| | 22
| | 973.093
| | 973.093
| |
|-
|-
| | 23
| | 23
| | 1017.325
| | 1017.325
| | [[9/5]]
|-
|-
| | 24
| | 24
| | 1061.556
| | 1061.556
| | [[24/13]]
|-
|-
| | 25
| | 25
| | 1105.788
| | 1105.788
| | [[36/19]]
|-
|-
| | 26
| | 26
| | 1150.019
| | 1150.019
| | 68/35
|-
|-
| | 27
| | 27
| | 1194.251
| | 1194.251
| |
|-
|-
| | 28
| | 28
| | 1238.482
| | 1238.482
| | [[45/44|45/22]]
|-
|-
| | 29
| | 29
| | 1282.713
| | 1282.713
| | ([[21/20|21/10]])
|-
|-
| | 30
| | 30
| | 1326.946
| | 1326.946
| | ([[14/13|28/13]])
|-
|-
| | 31
| | 31
| | 1371.177
| | 1371.177
| |
|-
|-
| | 32
| | 32
| | 1415.408
| | 1415.408
| | ([[17/15|34/15]])
|-
|-
| | 33
| | 33
| | 1459.640
| | 1459.640
| |
|-
|-
| | 34
| | 34
| | 1503.871
| | 1503.871
| |
|-
|-
| | 35
| | 35
| | 1548.193
| | 1548.193
| | [[11/9|22/9]]
|-
|-
| | 36
| | 36
| | 1592.334
| | 1592.334
| |
|-
|-
| | 37
| | 37
| | 1636.566
| | 1636.566
| | ([[9/7|18/7]])
|-
|-
| | 38
| | 38
| | 1680.797
| | 1680.797
| | [[33/25|66/25]]
|-
|-
| | 39
| | 39
| | 1725.029
| | 1725.029
| |
|-
|-
| | 40
| | 40
| | 1769.261
| | 1769.261
| | [[25/9]]
|-
|-
| | 41
| | 41
| | 1813.492
| | 1813.492
| | 57/20
|-
|-
| | 42
| | 42
| | 1857.724
| | 1857.724
| | [[19/13|38/13]]
|-
|-
| | 43
| | 43
| | 1901.955
| | 1901.955
| | '''exact [[3/1]]'''
|}
|}


[[Category:edt]]
[[Category:Edt]]
[[Category:tritave]]
[[Category:Edonoi]]

Revision as of 00:30, 2 March 2019

Division of the third harmonic into 43 equal parts (43EDT) is related to 27 EDO, but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the 10-integer-limit.

43 EDT

This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO is a "sharp tending" system, and flattening its octaves has been suggested before as an improvement (I think by no less than Ivor Darreg, but I'll have to check that).

However, in addition to its rich octave-based harmony, the 43EDT is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that 13EDT is not. The 4L+5s MOS has L=7 s=3.

degrees cents value corresponding
JI intervals
1 44.232 40/39, 39/38
2 88.463 20/19
3 132.695 27/25
4 176.926
5 221.158 25/22
6 265.389 (7/6)
7 309.621
8 353.852 27/22
9 398.084
10 442.315
11 486.547 (45/34)
12 530.778 (34/25)
13 575.010 (39/28)
14 619.241 (10/7)
15 663.473 22/15
16 707.704
17 751.936
18 796.167 19/12
19 840.399 13/8
20 884.630 5/3
21 928.862
22 973.093
23 1017.325 9/5
24 1061.556 24/13
25 1105.788 36/19
26 1150.019 68/35
27 1194.251
28 1238.482 45/22
29 1282.713 (21/10)
30 1326.946 (28/13)
31 1371.177
32 1415.408 (34/15)
33 1459.640
34 1503.871
35 1548.193 22/9
36 1592.334
37 1636.566 (18/7)
38 1680.797 66/25
39 1725.029
40 1769.261 25/9
41 1813.492 57/20
42 1857.724 38/13
43 1901.955 exact 3/1
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