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Valentine/Chords: Difference between revisions

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== Triads ==
== Triads ==
The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.
Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9) in valentine[15].
Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13) in valentine[15].
Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad. The first chord is based on the number of generator steps for each tone. This ordering makes it easy to see how often it will occur in a given MOS, as noted in the examples above, but it may seem surprising if you're new to it: For example, chord #8 is 1/1-8/7-10/7, but it might seem more "natural" to use 1/1-5/4-7/4, which is listed as the second inversion. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.


{| class="wikitable"
{| class="wikitable"
Line 15: Line 22:
! Transversal
! Transversal
! Type
! Type
! As generated
! 1st inversion
! 2nd inversion
|-
|-
|-
| 1
| 1
Line 20: Line 31:
| 1-11/10-6/5
| 1-11/10-6/5
| otonal
| otonal
| 1/1-11/10-6/5
| 1/1-11/10-11/6
| 1/1-5/3-11/6
|-
|-
| 2
| 2
Line 25: Line 39:
| 1-11/10-5/4
| 1-11/10-5/4
| valinorsmic
| valinorsmic
| 1/1-11/10-5/4
| 1/1-8/7-20/11
| 1/1-8/5-7/4
|-
|-
| 3
| 3
Line 30: Line 47:
| 1-8/7-5/4
| 1-8/7-5/4
| valinorsmic
| valinorsmic
| 1/1-8/7-5/4
| 1/1-11/10-7/4
| 1/1-8/5-20/11
|-
|-
| 4
| 4
Line 35: Line 55:
| 1-11/10-11/8
| 1-11/10-11/8
| utonal
| utonal
| 1/1-11/10-11/8
| 1/1-5/4-20/11
| 1/1-16/11-8/5
|-
|-
| 5
| 5
Line 40: Line 63:
| 1-8/7-11/8
| 1-8/7-11/8
| keenanismic
| keenanismic
| 1/1-8/7-11/8
| 1/1-6/5-7/4
| 1/1-16/11-5/3
|-
|-
| 6
| 6
Line 45: Line 71:
| 1-6/5-11/8
| 1-6/5-11/8
| keenanismic
| keenanismic
| 1/1-6/5-11/8
| 1/1-8/7-5/3
| 1/1-16/11-7/4
|-
|-
| 7
| 7
Line 50: Line 79:
| 1-5/4-11/8
| 1-5/4-11/8
| otonal
| otonal
| 1/1-5/4-11/8
| 1/1-11/10-8/5
| 1/1-16/11-11/6
|-
|-
| 8
| 8
Line 55: Line 87:
| 1-8/7-10/7
| 1-8/7-10/7
| otonal
| otonal
| 1/1-8/7-10/7
| 1/1-5/4-7/4
| 1/1-7/5-8/5
|-
|-
| 9
| 9
Line 60: Line 95:
| 1-6/5-10/7
| 1-6/5-10/7
| starling
| starling
| 1/1-6/5-10/7
| 1/1-6/5-5/3
| 1/1-7/5-5/3
|-
|-
| 10
| 10
Line 65: Line 103:
| 1-5/4-10/7
| 1-5/4-10/7
| utonal
| utonal
| 1/1-5/4-10/7
| 1/1-8/7-8/5
| 1/1-7/5-7/4
|-
|-
| 11
| 11
Line 70: Line 111:
| 1-12/11-3/2
| 1-12/11-3/2
| utonal
| utonal
| 1/1-12/11-3/2
| 1/1-11/8-11/6
| 1/1-4/3-16/11
|-
|-
| 12
| 12
Line 75: Line 119:
| 1-6/5-3/2
| 1-6/5-3/2
| utonal
| utonal
| 1/1-6/5-3/2
| 1/1-5/4-5/3
| 1/1-4/3-8/5
|-
|-
| 13
| 13
Line 80: Line 127:
| 1-5/4-3/2
| 1-5/4-3/2
| otonal
| otonal
| 1/1-5/4-3/2
| 1/1-6/5-8/5
| 1/1-4/3-5/3
|-
|-
| 14
| 14
Line 85: Line 135:
| 1-11/8-3/2
| 1-11/8-3/2
| otonal
| otonal
| 1/1-11/8-3/2
| 1/1-11/10-16/11
| 1/1-41/31-11/6
|-
|-
| 15
| 15
Line 90: Line 143:
| 1-11/10-11/7
| 1-11/10-11/7
| utonal
| utonal
| 1/1-11/10-11/7
| 1/1-10/7-11/6
| 1/1-68/53-7/5
|-
|-
| 16
| 16
Line 95: Line 151:
| 1-8/7-11/7
| 1-8/7-11/7
| otonal
| otonal
| 1/1-8/7-11/7
| 1/1-11/8-7/4
| 1/1-14/11-16/11
|-
|-
| 17
| 17
Line 100: Line 159:
| 1-5/4-11/7
| 1-5/4-11/7
| valinorsmic
| valinorsmic
| 1/1-5/4-11/7
| 1/1-5/4-8/5
| 1/1-14/11-8/5
|-
|-
| 18
| 18
Line 105: Line 167:
| 1-11/8-11/7
| 1-11/8-11/7
| utonal
| utonal
| 1/1-11/8-11/7
| 1/1-8/7-16/11
| 1/1-14/11-7/4
|-
|-
| 19
| 19
Line 110: Line 175:
| 1-10/7-11/7
| 1-10/7-11/7
| otonal
| otonal
| 1/1-10/7-11/7
| 1/1-11/10-7/5
| 1/1-14/11-11/6
|-
|-
| 20
| 20
Line 115: Line 183:
| 1-12/11-18/11
| 1-12/11-18/11
| otonal
| otonal
| 1/1-12/11-18/11
| 1/1-3/2-11/6
| 1/1-11/9-4/3
|-
|-
| 21
| 21
Line 120: Line 191:
| 1-8/7-18/11
| 1-8/7-18/11
| werckismic
| werckismic
| 1/1-8/7-18/11
| 1/1-10/7-7/4
| 1/1-11/9-7/5
|-
|-
| 22
| 22
Line 125: Line 199:
| 1-6/5-18/11
| 1-6/5-18/11
| biyatismic
| biyatismic
| 1/1-6/5-18/11
| 1/1-11/8-5/3
| 1/1-11/9-16/11
|-
|-
| 23
| 23
Line 130: Line 207:
| 1-11/8-18/11
| 1-11/8-18/11
| biyatismic
| biyatismic
| 1/1-11/8-18/11
| 1/1-6/5-16/11
| 1/1-11/9-5/3
|-
|-
| 24
| 24
Line 135: Line 215:
| 1-10/7-18/11
| 1-10/7-18/11
| werckismic
| werckismic
| 1/1-10/7-18/11
| 1/1-8/7-7/5
| 1/1-11/9-7/4
|-
|-
| 25
| 25
Line 140: Line 223:
| 1-3/2-18/11
| 1-3/2-18/11
| utonal
| utonal
| 1/1-3/2-18/11
| 1/1-11/10-4/3
| 1/1-97/80-11/6
|-
|-
| 26
| 26
Line 145: Line 231:
| 1-12/11-12/7
| 1-12/11-12/7
| utonal
| utonal
| 1/1-12/11-12/7
| 1/1-11/7-11/6
| 1/1-7/6-14/11
|-
|-
| 27
| 27
Line 150: Line 239:
| 1-8/7-12/7
| 1-8/7-12/7
| otonal
| otonal
| 1/1-8/7-12/7
| 1/1-3/2-7/4
| 1/1-7/6-4/3
|-
|-
| 28
| 28
Line 155: Line 247:
| 1-6/5-12/7
| 1-6/5-12/7
| utonal
| utonal
| 1/1-6/5-12/7
| 1/1-10/7-5/3
| 1/1-7/6-7/5
|-
|-
| 29
| 29
Line 160: Line 255:
| 1-5/4-12/7
| 1-5/4-12/7
| keenanismic
| keenanismic
| 1/1-5/4-12/7
| 1/1-11/8-8/5
| 1/1-7/6-16/11
|-
|-
| 30
| 30
Line 165: Line 263:
| 1-11/8-12/7
| 1-11/8-12/7
| keenanismic
| keenanismic
| 1/1-11/8-12/7
| 1/1-5/4-16/11
| 1/1-7/6-8/5
|-
|-
| 31
| 31
Line 170: Line 271:
| 1-10/7-12/7
| 1-10/7-12/7
| otonal
| otonal
| 1/1-10/7-12/7
| 1/1-6/5-7/5
| 1/1-7/6-5/3
|-
|-
| 32
| 32
Line 175: Line 279:
| 1-3/2-12/7
| 1-3/2-12/7
| utonal
| utonal
| 1/1-3/2-12/7
| 1/1-8/7-4/3
| 1/1-7/6-7/4
|-
|-
| 33
| 33
Line 180: Line 287:
| 1-11/7-12/7
| 1-11/7-12/7
| otonal
| otonal
| 1/1-11/7-12/7
| 1/1-12/11-14/11
| 1/1-7/6-146/79
|-
|-
| 34
| 34
Line 185: Line 295:
| 1-11/10-9/5
| 1-11/10-9/5
| otonal
| otonal
| 1/1-11/10-9/5
| 1/1-18/11-20/11
| 1/1-10/9-11/9
|-
|-
| 35
| 35
Line 190: Line 303:
| 1-8/7-9/5
| 1-8/7-9/5
| werckismic
| werckismic
| 1/1-8/7-9/5
| 1/1-11/7-7/4
| 1/1-10/9-14/11
|-
|-
| 36
| 36
Line 195: Line 311:
| 1-6/5-9/5
| 1-6/5-9/5
| otonal
| otonal
| 1/1-6/5-9/5
| 1/1-3/2-5/3
| 1/1-10/9-4/3
|-
|-
| 37
| 37
Line 200: Line 319:
| 1-5/4-9/5
| 1-5/4-9/5
| starling
| starling
| 1/1-5/4-9/5
| 1/1-10/7-8/5
| 1/1-10/9-7/5
|-
|-
| 38
| 38
Line 205: Line 327:
| 1-10/7-9/5
| 1-10/7-9/5
| starling
| starling
| 1/1-10/7-9/5
| 1/1-5/4-7/5
| 1/1-10/9-8/5
|-
|-
| 39
| 39
Line 210: Line 335:
| 1-3/2-9/5
| 1-3/2-9/5
| utonal
| utonal
| 1/1-3/2-9/5
| 1/1-6/5-4/3
| 1/1-10/9-5/3
|-
|-
| 40
| 40
Line 215: Line 343:
| 1-11/7-9/5
| 1-11/7-9/5
| werckismic
| werckismic
| 1/1-11/7-9/5
| 1/1-8/7-14/11
| 1/1-10/9-7/4
|-
|-
| 41
| 41
Line 220: Line 351:
| 1-18/11-9/5
| 1-18/11-9/5
| utonal
| utonal
| 1/1-18/11-9/5
| 1/1-11/10-11/9
| 1/1-10/9-11/6
|-
|-
| 42
| 42
Line 225: Line 359:
| 1-5/4-9/8
| 1-5/4-9/8
| otonal
| otonal
| 1/1-9/8-5/4
| 1/1-10/9-16/9
| 1/1-8/5-9/5
|-
|-
| 43
| 43
Line 230: Line 367:
| 1-11/8-9/8
| 1-11/8-9/8
| otonal
| otonal
| 1/1-9/8-11/8
| 1/1-11/9-16/9
| 1/1-16/11-18/11
|-
|-
| 44
| 44
Line 235: Line 375:
| 1-10/7-9/8
| 1-10/7-9/8
| werckismic
| werckismic
| 1/1-9/8-10/7
| 1/1-14/11-16/9
| 1/1-7/5-11/7
|-
|-
| 45
| 45
Line 240: Line 383:
| 1-3/2-9/8
| 1-3/2-9/8
| ambitonal
| ambitonal
| 1/1-9/8-3/2
| 1/1-4/3-16/9
| 1/1-4/3-3/2
|-
|-
| 46
| 46
Line 245: Line 391:
| 1-11/7-9/8
| 1-11/7-9/8
| werckismic
| werckismic
| 1/1-9/8-11/7
| 1/1-7/5-16/9
| 1/1-14/11-10/7
|-
|-
| 47
| 47
Line 250: Line 399:
| 1-18/11-9/8
| 1-18/11-9/8
| utonal
| utonal
| 1/1-9/8-18/11
| 1/1-16/11-16/9
| 1/1-11/9-11/8
|-
|-
| 48
| 48
Line 255: Line 407:
| 1-9/5-9/8
| 1-9/5-9/8
| utonal
| utonal
| 1/1-9/8-9/5
| 1/1-8/5-16/9
| 1/1-10/9-5/4
|-
|-
| 49
| 49
Line 260: Line 415:
| 1-8/7-9/7
| 1-8/7-9/7
| otonal
| otonal
| 1/1-8/7-9/7
| 1/1-9/8-7/4
| 1/1-14/9-16/9
|-
|-
| 50
| 50
Line 265: Line 423:
| 1-10/7-9/7
| 1-10/7-9/7
| otonal
| otonal
| 1/1-9/7-10/7
| 1/1-10/9-14/9
| 1/1-7/5-9/5
|-
|-
| 51
| 51
Line 270: Line 431:
| 1-3/2-9/7
| 1-3/2-9/7
| utonal
| utonal
| 1/1-9/7-3/2
| 1/1-7/6-14/9
| 1/1-4/3-12/7
|-
|-
| 52
| 52
Line 275: Line 439:
| 1-11/7-9/7
| 1-11/7-9/7
| otonal
| otonal
| 1/1-9/7-11/7
| 1/1-11/9-14/9
| 1/1-14/11-18/11
|-
|-
| 53
| 53
Line 280: Line 447:
| 1-18/11-9/7
| 1-18/11-9/7
| utonal
| utonal
| 1/1-9/7-18/11
| 1/1-14/11-14/9
| 1/1-11/9-11/7
|-
|-
| 54
| 54
Line 285: Line 455:
| 1-12/7-9/7
| 1-12/7-9/7
| otonal
| otonal
| 1/1-9/7-12/7
| 1/1-4/3-14/9
| 1/1-7/6-3/2
|-
|-
| 55
| 55
Line 290: Line 463:
| 1-9/5-9/7
| 1-9/5-9/7
| utonal
| utonal
| 1/1-9/7-9/5
| 1/1-7/5-14/9
| 1/1-10/9-10/7
|-
|-
| 56
| 56
Line 295: Line 471:
| 1-9/8-9/7
| 1-9/8-9/7
| utonal
| utonal
| 1/1-9/8-9/7
| 1/1-8/7-16/9
| 1/1-14/9-7/4
|}
|}


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