26edt: Difference between revisions

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Line 9: Line 9:
! | Steps
! | Steps
! | Cents
! | Cents
!hekts
! | BP nonatonic degree
! | BP nonatonic degree
! | Diatonic degree
! | Diatonic degree
Line 17: Line 18:
| | 1
| | 1
| | 73.15
| | 73.15
|50
| | Sa1/sd2
| | Sa1/sd2
| | A1/dd2
| | A1/dd2
Line 25: Line 27:
| | 2
| | 2
| | 146.3
| | 146.3
|100
| | A1/m2
| | A1/m2
| | AA1/sm2
| | AA1/sm2
Line 33: Line 36:
| | 3
| | 3
| | 219.5
| | 219.5
|150
| | N2
| | N2
| | m2
| | m2
Line 41: Line 45:
| | 4
| | 4
| | 292.6
| | 292.6
|200
| | M2/d3
| | M2/d3
| | M2
| | M2
Line 49: Line 54:
| | 5
| | 5
| | 365.8
| | 365.8
|250
| | Sa2/sd3
| | Sa2/sd3
| | SM2/dd3
| | SM2/dd3
Line 57: Line 63:
| | 6
| | 6
| | 438.9
| | 438.9
|300
| | A2/P3/d4
| | A2/P3/d4
| | AA2/sm3
| | AA2/sm3
Line 65: Line 72:
| | 7
| | 7
| | 512.1
| | 512.1
|350
| | Sa3/sd4
| | Sa3/sd4
| | m3
| | m3
Line 73: Line 81:
| | 8
| | 8
| | 585.2
| | 585.2
|400
| | A3/m4/d5
| | A3/m4/d5
| | M3
| | M3
Line 81: Line 90:
| | 9
| | 9
| | 658.4
| | 658.4
|450
| | N4/sd5
| | N4/sd5
| | SM3/dd4
| | SM3/dd4
Line 89: Line 99:
| | 10
| | 10
| | 731.5
| | 731.5
|500
| | M4/m5
| | M4/m5
| | AA3/d4
| | AA3/d4
Line 97: Line 108:
| | 11
| | 11
| | 804.7
| | 804.7
|550
| | Sa4/N5
| | Sa4/N5
| | P4
| | P4
Line 105: Line 117:
| | 12
| | 12
| | 877.8
| | 877.8
|600
| | A4/M5/d6
| | A4/M5/d6
| | A4
| | A4
Line 112: Line 125:
|-
|-
| | 13
| | 13
| | 951.0
| | 951
|650
| | Sa5/sd6
| | Sa5/sd6
| | AA4/dd5
| | AA4/dd5
Line 121: Line 135:
| | 14
| | 14
| | 1024.1
| | 1024.1
|700
| | A5/m6/d7
| | A5/m6/d7
| | d5
| | d5
Line 129: Line 144:
| | 15
| | 15
| | 1097.3
| | 1097.3
|750
| | N6/sd7
| | N6/sd7
| | P5
| | P5
Line 137: Line 153:
| | 16
| | 16
| | 1170.4
| | 1170.4
|800
| | M6/m7
| | M6/m7
| | A5/dd6
| | A5/dd6
Line 145: Line 162:
| | 17
| | 17
| | 1243.6
| | 1243.6
|850
| | Sa6/N7
| | Sa6/N7
| | AA5/sm6
| | AA5/sm6
Line 153: Line 171:
| | 18
| | 18
| | 1316.7
| | 1316.7
|900
| | A6/M7/d8
| | A6/M7/d8
| | m6
| | m6
Line 161: Line 180:
| | 19
| | 19
| | 1389.9
| | 1389.9
|950
| | Sa7/sd8
| | Sa7/sd8
| | M6
| | M6
Line 168: Line 188:
|-
|-
| | 20
| | 20
| | 1463.0
| | 1463
|1000
| | A7/P8/d9
| | A7/P8/d9
| | SM6/dd7
| | SM6/dd7
Line 177: Line 198:
| | 21
| | 21
| | 1536.2
| | 1536.2
|1050
| | Sa8/sd9
| | Sa8/sd9
| | AA6/sm7
| | AA6/sm7
Line 185: Line 207:
| | 22
| | 22
| | 1609.3
| | 1609.3
|1100
| | A8/m9
| | A8/m9
| | m7
| | m7
Line 193: Line 216:
| | 23
| | 23
| | 1682.5
| | 1682.5
|1150
| | N9
| | N9
| | M7
| | M7
Line 201: Line 225:
| | 24
| | 24
| | 1755.65
| | 1755.65
|1200
| | M9/d10
| | M9/d10
| | SM7/dd8
| | SM7/dd8
Line 209: Line 234:
| | 25
| | 25
| | 1828.8
| | 1828.8
|1250
| | Sa9/sd10
| | Sa9/sd10
| | A7/d8
| | A7/d8
Line 216: Line 242:
|-
|-
| | 26
| | 26
| | 1902.0
| | 1902
|1300
| | A9/P10
| | A9/P10
| | P8
| | P8

Revision as of 18:38, 15 April 2019

26edt divides the tritave (3/1) into 26 equal parts of 73.152 cents each, corresponding to 16.404edo. It is contorted in the 7-limit, tempering out the same commas, 245/243 and 3125/3087, as 13edt. In the 11-limit it tempers out 125/121 and 3087/3025, in the 13-limit 175/169, 147/143, and 847/845, and in the 17-limit 119/117. It is the seventh zeta peak tritave division.

A reason to double 13edt to 26edt is to approximate the 8th, 13th, 17th, 20th, and 22nd harmonics particularly well. Moreover, it has an exaggerated diatonic scale with 11:16:21 supermajor triads, though only the 16:11 is particularly just due to its best 16 still being 28.04 cents sharp, or just about as bad as the 25 of 12edo (which is 27.373 cents sharp, an essentially just 100:63).

Intervals

Steps Cents hekts BP nonatonic degree Diatonic degree Corresponding JI intervals Comments Generator for...
1 73.15 50 Sa1/sd2 A1/dd2 25/24
2 146.3 100 A1/m2 AA1/sm2 27/25~49/45
3 219.5 150 N2 m2 9/8~312/275
4 292.6 200 M2/d3 M2 25/21~13/11
5 365.8 250 Sa2/sd3 SM2/dd3 5/4~243/196 False 11/9
6 438.9 300 A2/P3/d4 AA2/sm3 9/7
7 512.1 350 Sa3/sd4 m3 27/20 False 21/16
8 585.2 400 A3/m4/d5 M3 7/5
9 658.4 450 N4/sd5 SM3/dd4 16/11 False 13/9
10 731.5 500 M4/m5 AA3/d4 75/49 False 3/2
11 804.7 550 Sa4/N5 P4 8/5 False 11/7
12 877.8 600 A4/M5/d6 A4 5/3 False 27/16
13 951 650 Sa5/sd6 AA4/dd5 125/72
14 1024.1 700 A5/m6/d7 d5 9/5 False 16/9
15 1097.3 750 N6/sd7 P5 15/8 False 21/11
16 1170.4 800 M6/m7 A5/dd6 49/25 False 2/1
17 1243.6 850 Sa6/N7 AA5/sm6 33/16 False 27/13
18 1316.7 900 A6/M7/d8 m6 15/7
19 1389.9 950 Sa7/sd8 M6 20/9 False 16/7
20 1463 1000 A7/P8/d9 SM6/dd7 7/3
21 1536.2 1050 Sa8/sd9 AA6/sm7 12/5~196/81 False 27/11
22 1609.3 1100 A8/m9 m7 63/25~33/13
23 1682.5 1150 N9 M7 8/3~275/104
24 1755.65 1200 M9/d10 SM7/dd8 25/9~135/49
25 1828.8 1250 Sa9/sd10 A7/d8 72/25
26 1902 1300 A9/P10 P8 3/1 Tritave

It is a weird coincidence how 26edt intones any 26edo intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:

26edt 26edo Discrepancy
365.761 369.231 -3.47
512.065 507.692 +4.373
877.825 876.923 +0.902
1243.586 1246.154 -2.168
1389.89 1384.615 +5.275
1755.651 1753.846 +1.805
2121.411 2123.077 -1.666
2633.476 2630.769 +2.647

etc.

Music

  • The Eel And Loach To Attack In Lasciviousness Are Insane: video | MP3 by Omega9
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