Xenharmonic Wiki

26edt: Difference between revisions

← Older editNewer edit →
VisualWikitext
No edit summary
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
fix table formatting, column alignment, unify precision
Line 3: Line 3:
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).
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==
== Intervals ==


{| class="wikitable"
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | Steps
! Steps
! | Cents
! Cents
!hekts
! hekts
! | BP nonatonic degree
! BP nonatonic degree
! | Diatonic degree
! Diatonic degree
! | Corresponding JI intervals
! Corresponding JI intervals
! | Comments
! Comments
! | Generator for...
! Generator for...
|-
|-
| | 1
| 1
| | 73.15
| 73.2
|50
| 50
| | Sa1/sd2
| Sa1/sd2
| | A1/dd2
| A1/dd2
| | 25/24
| 25/24
| |  
|  
| |  
|  
|-
|-
| | 2
| 2
| | 146.3
| 146.3
|100
| 100
| | A1/m2
| A1/m2
| | AA1/sm2
| AA1/sm2
| | 27/25~49/45
| 27/25~49/45
| |  
|  
| |  
|  
|-
|-
| | 3
| 3
| | 219.5
| 219.5
|150
| 150
| | N2
| N2
| | m2
| m2
| | 9/8~312/275
| 9/8~312/275
| |  
|  
| |  
|  
|-
|-
| | 4
| 4
| | 292.6
| 292.6
|200
| 200
| | M2/d3
| M2/d3
| | M2
| M2
| | 25/21~13/11
| 25/21~13/11
| |  
|  
| |  
|  
|-
|-
| | 5
| 5
| | 365.8
| 365.8
|250
| 250
| | Sa2/sd3
| Sa2/sd3
| | SM2/dd3
| SM2/dd3
| | 5/4~243/196
| 5/4~243/196
| | False 11/9
| False 11/9
| |  
|  
|-
|-
| | 6
| 6
| | 438.9
| 438.9
|300
| 300
| | A2/P3/d4
| A2/P3/d4
| | AA2/sm3
| AA2/sm3
| | 9/7
| 9/7
| |  
|  
| |  
|  
|-
|-
| | 7
| 7
| | 512.1
| 512.1
|350
| 350
| | Sa3/sd4
| Sa3/sd4
| | m3
| m3
| | 27/20
| 27/20
| | False 21/16
| False 21/16
| |  
|  
|-
|-
| | 8
| 8
| | 585.2
| 585.2
|400
| 400
| | A3/m4/d5
| A3/m4/d5
| | M3
| M3
| | 7/5
| 7/5
| |  
|  
| |  
|  
|-
|-
| | 9
| 9
| | 658.4
| 658.4
|450
| 450
| | N4/sd5
| N4/sd5
| | SM3/dd4
| SM3/dd4
| | 16/11
| 16/11
| | False 13/9
| False 13/9
| |  
|  
|-
|-
| | 10
| 10
| | 731.5
| 731.5
|500
| 500
| | M4/m5
| M4/m5
| | AA3/d4
| AA3/d4
| | 75/49
| 75/49
| | False 3/2
| False 3/2
| |  
|  
|-
|-
| | 11
| 11
| | 804.7
| 804.7
|550
| 550
| | Sa4/N5
| Sa4/N5
| | P4
| P4
| | 8/5
| 8/5
| | False 11/7
| False 11/7
| |  
|  
|-
|-
| | 12
| 12
| | 877.8
| 877.8
|600
| 600
| | A4/M5/d6
| A4/M5/d6
| | A4
| A4
| | 5/3
| 5/3
| | False 27/16
| False 27/16
| |  
|  
|-
|-
| | 13
| 13
| | 951
| 951.0
|650
| 650
| | Sa5/sd6
| Sa5/sd6
| | AA4/dd5
| AA4/dd5
| | 125/72
| 125/72
| |  
|  
| |  
|  
|-
|-
| | 14
| 14
| | 1024.1
| 1024.1
|700
| 700
| | A5/m6/d7
| A5/m6/d7
| | d5
| d5
| | 9/5
| 9/5
| | False 16/9
| False 16/9
| |  
|  
|-
|-
| | 15
| 15
| | 1097.3
| 1097.3
|750
| 750
| | N6/sd7
| N6/sd7
| | P5
| P5
| | 15/8
| 15/8
| | False 21/11
| False 21/11
| |  
|  
|-
|-
| | 16
| 16
| | 1170.4
| 1170.4
|800
| 800
| | M6/m7
| M6/m7
| | A5/dd6
| A5/dd6
| | 49/25
| 49/25
| | False 2/1
| False 2/1
| |  
|  
|-
|-
| | 17
| 17
| | 1243.6
| 1243.6
|850
| 850
| | Sa6/N7
| Sa6/N7
| | AA5/sm6
| AA5/sm6
| | 33/16
| 33/16
| | False 27/13
| False 27/13
| |  
|  
|-
|-
| | 18
| 18
| | 1316.7
| 1316.7
|900
| 900
| | A6/M7/d8
| A6/M7/d8
| | m6
| m6
| | 15/7
| 15/7
| |  
|  
| |  
|  
|-
|-
| | 19
| 19
| | 1389.9
| 1389.9
|950
| 950
| | Sa7/sd8
| Sa7/sd8
| | M6
| M6
| | 20/9
| 20/9
| | False 16/7
| False 16/7
| |  
|  
|-
|-
| | 20
| 20
| | 1463
| 1463.0
|1000
| 1000
| | A7/P8/d9
| A7/P8/d9
| | SM6/dd7
| SM6/dd7
| | 7/3
| 7/3
| |  
|  
| |  
|  
|-
|-
| | 21
| 21
| | 1536.2
| 1536.2
|1050
| 1050
| | Sa8/sd9
| Sa8/sd9
| | AA6/sm7
| AA6/sm7
| | 12/5~196/81
| 12/5~196/81
| | False 27/11
| False 27/11
| |  
|  
|-
|-
| | 22
| 22
| | 1609.3
| 1609.3
|1100
| 1100
| | A8/m9
| A8/m9
| | m7
| m7
| | 63/25~33/13
| 63/25~33/13
| |  
|  
| |  
|  
|-
|-
| | 23
| 23
| | 1682.5
| 1682.5
|1150
| 1150
| | N9
| N9
| | M7
| M7
| | 8/3~275/104
| 8/3~275/104
| |  
|  
| |  
|  
|-
|-
| | 24
| 24
| | 1755.65
| 1755.7
|1200
| 1200
| | M9/d10
| M9/d10
| | SM7/dd8
| SM7/dd8
| | 25/9~135/49
| 25/9~135/49
| |  
|  
| |  
|  
|-
|-
| | 25
| 25
| | 1828.8
| 1828.8
|1250
| 1250
| | Sa9/sd10
| Sa9/sd10
| | A7/d8
| A7/d8
| | 72/25
| 72/25
| |  
|  
| |  
|  
|-
|-
| | 26
| 26
| | 1902
| 1902.0
|1300
| 1300
| | A9/P10
| A9/P10
| | P8
| P8
| | 3/1
| 3/1
| | Tritave
| 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:
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:


{| class="wikitable"
{| class="wikitable right-all"
|-
|-
! | 26edt
! 26edt
! | 26edo
! 26edo
! | Discrepancy
! Discrepancy
|-
|-
| | 365.761
| 365.761
| | 369.231
| 369.231
| | -3.47
| -3.470
|-
|-
| | 512.065
| 512.065
| | 507.692
| 507.692
| | +4.373
| +4.373
|-
|-
| | 877.825
| 877.825
| | 876.923
| 876.923
| | +0.902
| +0.902
|-
|-
| | 1243.586
| 1243.586
| | 1246.154
| 1246.154
| | -2.168
| -2.168
|-
|-
| | 1389.89
| 1389.890
| | 1384.615
| 1384.615
| | +5.275
| +5.275
|-
|-
| | 1755.651
| 1755.651
| | 1753.846
| 1753.846
| | +1.805
| +1.805
|-
|-
| | 2121.411
| 2121.411
| | 2123.077
| 2123.077
| | -1.666
| -1.666
|-
|-
| | 2633.476
| 2633.476
| | 2630.769
| 2630.769
| | +2.647
| +2.647
|}
|}
etc.
etc.


==Music==
== Music ==
 
*''The Eel And Loach To Attack In Lasciviousness Are Insane'': [https://www.youtube.com/watch?v=AhWJ2yJsODs video] | [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20The%20Eel%20And%20Loach%20To%20Attack%20In%20Lasciviousness%20Are%20Insane.mp3 MP3] by Omega9
*''The Eel And Loach To Attack In Lasciviousness Are Insane'': [https://www.youtube.com/watch?v=AhWJ2yJsODs video] | [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20The%20Eel%20And%20Loach%20To%20Attack%20In%20Lasciviousness%20Are%20Insane.mp3 MP3] by Omega9


Retrieved from "https://en.xen.wiki/w/26edt"