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Pinetone: Difference between revisions

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m →Intervals and triads: table formatting
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!Triads in cents
!Triads in cents
|-
|-
|D
! rowspan="2" |D
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
major
|minor
|minor
minor
|minor
|minor
major-minor
|10:12:15
|10:12:15
18:22:27
|318.667, 704.101
|318.667, 704.101
351.784, 704.101
|-
|-
|D♯
|(4, 3)
|major
|minor
|major-minor
|18:22:27
|351.784, 704.101
|-
! rowspan="2" |D♯
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
dim 4
|minor
|minor
min 4
|minor
|minor
dim min 4
| 10:12:15
| 10:12:15
10:13:15
|318.667, 704.101
|318.667, 704.101
461.443, 704.101
|-
|-
|E
|(4, 3)
|dim 4
|min 4
|dim min 4
|10:13:15
|461.443, 704.101
|-
! rowspan="2" |E
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
major
|minor
|minor
major
| minor
| minor
major
|10:12:15
|10:12:15
4:5:6
|318.667, 704.101
|318.667, 704.101
385.433, 704.101
|-
|-
|F
|(4, 3)
|major
|major
|major
|4:5:6
|385.433, 704.101
|-
! rowspan="2" |F
|(3, 4)
|(3, 4)
(4, 3)
|aug 2
|aug 2
major
|maj 2
|maj 2
major
|aug maj 2
|aug maj 2
major
| (14:16:21 or 6:7:9)
| (14:16:21 or 6:7:9)
4:5:6
|242.658, 704.101
|242.658, 704.101
385.433, 704.101
|-
|-
| F♯
|(4, 3)
|major
|major
|major
|4:5:6
|385.433, 704.101
|-
! rowspan="2" | F♯
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
major
|major
|major
major
|minor-major
|minor-major
major
|22:27:33
|22:27:33
4:5:6
| 352.317, 704.101
| 352.317, 704.101
385.433, 704.101
|-
|-
|G
|(4, 3)
|major
|major
|major
|4:5:6
|385.433, 704.101
|-
! rowspan="2" |G
|(3, 4)
|(3, 4)
(4, 3)
|aug 2
|aug 2
major
|maj 2
|maj 2
major
|aug maj 2
|aug maj 2
major
|(14:16:21 or 6:7:9)
|(14:16:21 or 6:7:9)
4:5:6
| 242.658, 704.101
| 242.658, 704.101
385.433, 704.101
|-
|-
|G♯
|(4, 3)
|major
|major
|major
|4:5:6
|385.433, 704.101
|-
! rowspan="2" |G♯
| (3, 4)
| (3, 4)
(4, 3)
|minor
|minor
dim 4
|diminished
|diminished
diminished min 4
| minor diminished
| minor diminished
dim min 4 diminished
|15:18:22
|15:18:22
30:39:44
|318.667, 670.451
|318.667, 670.451
461.443, 670.451
|-
|-
|A
|(4, 3)
|dim 4
|diminished min 4
|dim min 4 diminished
|30:39:44
|461.443, 670.451
|-
! rowspan="2" |A
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
major
| diminished
| diminished
diminished
|minor diminished
|minor diminished
major diminished
|15:18:22
|15:18:22
27:33:40
|318.667, 670.451
|318.667, 670.451
351.784, 670.451
|-
|-
|A♯
|(4, 3)
|major
|diminished
|major diminished
|27:33:40
|351.784, 670.451
|-
! rowspan="2" |A♯
|(3, 4)
|(3, 4)
(4, 3)
|minor dim 6
|minor dim 6
dim 4 dim 6
|minor (sub) min 6
|minor (sub) min 6
min 4 sub minor 6
| minor (sub) dim min 6
| minor (sub) dim min 6
dim min 4 (sub) dim min 6
|25:30:39
|25:30:39
50:65:78
| 318.667, 780.120
| 318.667, 780.120
461.443, 780.120
|-
|-
| B
|(4, 3)
|dim 4 dim 6
|min 4 sub minor 6
|dim min 4 (sub) dim min 6
|50:65:78
|461.443, 780.120
|-
! rowspan="2" | B
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
major
|diminished
|diminished
diminished
|minor diminished
|minor diminished
major diminished
|15:18:22
|15:18:22
27:33:40
|318.667, 670.451
|318.667, 670.451
351.784, 670.451
|-
|-
|C
|(4, 3)
|major
|diminished
|major diminished
|27:33:40
|351.784, 670.451
|-
! rowspan="2" |C
|(3, 4)
|(3, 4)
(4, 3)
|aug 2
|aug 2
major
|diminished min 2
|diminished min 2
diminished
|aug min 2 diminished
|aug min 2 diminished
major diminished
|243:275:360
|243:275:360
27:33:40
|209.008, 670.451
|209.008, 670.451
351.784, 670.451
|-
|-
|C♯
|(4, 3)
|major
|diminished
|major diminished
|27:33:40
|351.784, 670.451
|-
! rowspan="2" |C♯
|(3, 4)
|(3, 4)
(4, 3)
|minor
|minor
dim 4
|minor
|minor
min 4
|minor
|minor
dim min 4
| 10:12:15
| 10:12:15
10:13:15
|318.667, 704.101
|318.667, 704.101
 
|-
461.443, 704.101
|(4, 3)
|dim 4
|min 4
|dim min 4
|10:13:15
|461.443, 704.101
|}
|}
Note the major minor third approximating 11/9 and the minor major third approximating 27/22 are very similar in size in this tuning (351.784 and 352.317 respectively). If we equate these intervals, we additionally temper out 243/242, leading to an extension of Tetracot (Wollemia or Monkey if we also equate 13/10 with 9/7 or 21/16 respectively).  
Note the major minor third approximating 11/9 and the minor major third approximating 27/22 are very similar in size in this tuning (351.784 and 352.317 respectively). If we equate these intervals, we additionally temper out 243/242, leading to an extension of Tetracot (Wollemia or Monkey if we also equate 13/10 with 9/7 or 21/16 respectively).  
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