Valentine/Chords: Difference between revisions
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Below are listed the [[ | Below are listed the [[dyadic chord]]s of 11-limit [[Valentine|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11. | ||
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine. | If only [[126/125]] needs to be tempered out, the chord is labeled starling, if [[121/120]], biyatismic, if [[176/175]], valinorsmic, if [[385/384]], keenanismic, and if [[441/440]], werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine. | ||
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[ | Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha. | ||
In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves. | In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves. | ||
=Triads= | == Triads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-4 | |||
| 1-11/10-6/5 | |||
| otonal | |||
|- | |- | ||
| 2 | |||
| 0-2-5 | |||
| 1-11/10-5/4 | |||
| valinorsmic | |||
|- | |- | ||
| 3 | |||
| 0-3-5 | |||
| 1-8/7-5/4 | |||
| valinorsmic | |||
|- | |- | ||
| 4 | |||
| 0-2-7 | |||
| 1-11/10-11/8 | |||
| utonal | |||
|- | |- | ||
| 5 | |||
| 0-3-7 | |||
| 1-8/7-11/8 | |||
| keenanismic | |||
|- | |- | ||
| 6 | |||
| 0-4-7 | |||
| 1-6/5-11/8 | |||
| keenanismic | |||
|- | |- | ||
| 7 | |||
| 0-5-7 | |||
| 1-5/4-11/8 | |||
| otonal | |||
|- | |- | ||
| 8 | |||
| 0-3-8 | |||
| 1-8/7-10/7 | |||
| otonal | |||
|- | |- | ||
| 9 | |||
| 0-4-8 | |||
| 1-6/5-10/7 | |||
| starling | |||
|- | |- | ||
| 10 | |||
| 0-5-8 | |||
| 1-5/4-10/7 | |||
| utonal | |||
|- | |- | ||
| 11 | |||
| 0-2-9 | |||
| 1-12/11-3/2 | |||
| utonal | |||
|- | |- | ||
| 12 | |||
| 0-4-9 | |||
| 1-6/5-3/2 | |||
| utonal | |||
|- | |- | ||
| 13 | |||
| 0-5-9 | |||
| 1-5/4-3/2 | |||
| otonal | |||
|- | |- | ||
| 14 | |||
| 0-7-9 | |||
| 1-11/8-3/2 | |||
| otonal | |||
|- | |- | ||
| 15 | |||
| 0-2-10 | |||
| 1-11/10-11/7 | |||
| utonal | |||
|- | |- | ||
| 16 | |||
| 0-3-10 | |||
| 1-8/7-11/7 | |||
| otonal | |||
|- | |- | ||
| 17 | |||
| 0-5-10 | |||
| 1-5/4-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 18 | |||
| 0-7-10 | |||
| 1-11/8-11/7 | |||
| utonal | |||
|- | |- | ||
| 19 | |||
| 0-8-10 | |||
| 1-10/7-11/7 | |||
| otonal | |||
|- | |- | ||
| 20 | |||
| 0-2-11 | |||
| 1-12/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 21 | |||
| 0-3-11 | |||
| 1-8/7-18/11 | |||
| werckismic | |||
|- | |- | ||
| 22 | |||
| 0-4-11 | |||
| 1-6/5-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 23 | |||
| 0-7-11 | |||
| 1-11/8-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 24 | |||
| 0-8-11 | |||
| 1-10/7-18/11 | |||
| werckismic | |||
|- | |- | ||
| 25 | |||
| 0-9-11 | |||
| 1-3/2-18/11 | |||
| utonal | |||
|- | |- | ||
| 26 | |||
| 0-2-12 | |||
| 1-12/11-12/7 | |||
| utonal | |||
|- | |- | ||
| 27 | |||
| 0-3-12 | |||
| 1-8/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 28 | |||
| 0-4-12 | |||
| 1-6/5-12/7 | |||
| utonal | |||
|- | |- | ||
| 29 | |||
| 0-5-12 | |||
| 1-5/4-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 30 | |||
| 0-7-12 | |||
| 1-11/8-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 31 | |||
| 0-8-12 | |||
| 1-10/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 32 | |||
| 0-9-12 | |||
| 1-3/2-12/7 | |||
| utonal | |||
|- | |- | ||
| 33 | |||
| 0-10-12 | |||
| 1-11/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 34 | |||
| 0-2-13 | |||
| 1-11/10-9/5 | |||
| otonal | |||
|- | |- | ||
| 35 | |||
| 0-3-13 | |||
| 1-8/7-9/5 | |||
| werckismic | |||
|- | |- | ||
| 36 | |||
| 0-4-13 | |||
| 1-6/5-9/5 | |||
| otonal | |||
|- | |- | ||
| 37 | |||
| 0-5-13 | |||
| 1-5/4-9/5 | |||
| starling | |||
|- | |- | ||
| 38 | |||
| 0-8-13 | |||
| 1-10/7-9/5 | |||
| starling | |||
|- | |- | ||
| 39 | |||
| 0-9-13 | |||
| 1-3/2-9/5 | |||
| utonal | |||
|- | |- | ||
| 40 | |||
| 0-10-13 | |||
| 1-11/7-9/5 | |||
| werckismic | |||
|- | |- | ||
| 41 | |||
| 0-11-13 | |||
| 1-18/11-9/5 | |||
| utonal | |||
|- | |- | ||
| 42 | |||
| 0-5-18 | |||
| 1-5/4-9/8 | |||
| otonal | |||
|- | |- | ||
| 43 | |||
| 0-7-18 | |||
| 1-11/8-9/8 | |||
| otonal | |||
|- | |- | ||
| 44 | |||
| 0-8-18 | |||
| 1-10/7-9/8 | |||
| werckismic | |||
|- | |- | ||
| 45 | |||
| 0-9-18 | |||
| 1-3/2-9/8 | |||
| ambitonal | |||
|- | |- | ||
| 46 | |||
| 0-10-18 | |||
| 1-11/7-9/8 | |||
| werckismic | |||
|- | |- | ||
| 47 | |||
| 0-11-18 | |||
| 1-18/11-9/8 | |||
| utonal | |||
|- | |- | ||
| 48 | |||
| 0-13-18 | |||
| 1-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 49 | |||
| 0-3-21 | |||
| 1-8/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 50 | |||
| 0-8-21 | |||
| 1-10/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 51 | |||
| 0-9-21 | |||
| 1-3/2-9/7 | |||
| utonal | |||
|- | |- | ||
| 52 | |||
| 0-10-21 | |||
| 1-11/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 53 | |||
| 0-11-21 | |||
| 1-18/11-9/7 | |||
| utonal | |||
|- | |- | ||
| 54 | |||
| 0-12-21 | |||
| 1-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 55 | |||
| 0-13-21 | |||
| 1-9/5-9/7 | |||
| utonal | |||
|- | |- | ||
| 56 | |||
| 0-18-21 | |||
| 1-9/8-9/7 | |||
| utonal | |||
|} | |} | ||
=Tetrads= | == Tetrads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-4-7 | |||
| 1-11/10-6/5-11/8 | |||
| zeus | |||
|- | |- | ||
| 2 | |||
| 0-2-5-7 | |||
| 1-11/10-5/4-11/8 | |||
| valinorsmic | |||
|- | |- | ||
| 3 | |||
| 0-3-5-7 | |||
| 1-8/7-5/4-11/8 | |||
| zeus | |||
|- | |- | ||
| 4 | |||
| 0-3-5-8 | |||
| 1-8/7-5/4-10/7 | |||
| valinorsmic | |||
|- | |- | ||
| 5 | |||
| 0-2-4-9 | |||
| 1-12/11-6/5-3/2 | |||
| utonal | |||
|- | |- | ||
| 6 | |||
| 0-2-5-9 | |||
| 1-11/10-5/4-3/2 | |||
| zeus | |||
|- | |- | ||
| 7 | |||
| 0-2-7-9 | |||
| 1-11/10-11/8-3/2 | |||
| biyatismic | |||
|- | |- | ||
| 8 | |||
| 0-4-7-9 | |||
| 1-6/5-11/8-3/2 | |||
| zeus | |||
|- | |- | ||
| 9 | |||
| 0-5-7-9 | |||
| 1-5/4-11/8-3/2 | |||
| otonal | |||
|- | |- | ||
| 10 | |||
| 0-2-5-10 | |||
| 1-11/10-5/4-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 11 | |||
| 0-3-5-10 | |||
| 1-8/7-5/4-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 12 | |||
| 0-2-7-10 | |||
| 1-11/10-11/8-11/7 | |||
| utonal | |||
|- | |- | ||
| 13 | |||
| 0-3-7-10 | |||
| 1-8/7-11/8-11/7 | |||
| keenanismic | |||
|- | |- | ||
| 14 | |||
| 0-5-7-10 | |||
| 1-5/4-11/8-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 15 | |||
| 0-3-8-10 | |||
| 1-8/7-10/7-11/7 | |||
| otonal | |||
|- | |- | ||
| 16 | |||
| 0-5-8-10 | |||
| 1-5/4-10/7-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 17 | |||
| 0-2-4-11 | |||
| 1-11/10-6/5-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 18 | |||
| 0-2-7-11 | |||
| 1-11/10-11/8-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 19 | |||
| 0-3-7-11 | |||
| 1-8/7-11/8-18/11 | |||
| valentine | |||
|- | |- | ||
| 20 | |||
| 0-4-7-11 | |||
| 1-6/5-11/8-18/11 | |||
| zeus | |||
|- | |- | ||
| 21 | |||
| 0-3-8-11 | |||
| 1-8/7-10/7-18/11 | |||
| werckismic | |||
|- | |- | ||
| 22 | |||
| 0-4-8-11 | |||
| 1-6/5-10/7-18/11 | |||
| valentine | |||
|- | |- | ||
| 23 | |||
| 0-2-9-11 | |||
| 1-12/11-3/2-18/11 | |||
| ambitonal | |||
|- | |- | ||
| 24 | |||
| 0-4-9-11 | |||
| 1-6/5-3/2-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 25 | |||
| 0-7-9-11 | |||
| 1-11/8-3/2-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 26 | |||
| 0-2-4-12 | |||
| 1-12/11-6/5-12/7 | |||
| utonal | |||
|- | |- | ||
| 27 | |||
| 0-2-5-12 | |||
| 1-11/10-5/4-12/7 | |||
| zeus | |||
|- | |- | ||
| 28 | |||
| 0-3-5-12 | |||
| 1-8/7-5/4-12/7 | |||
| zeus | |||
|- | |- | ||
| 29 | |||
| 0-2-7-12 | |||
| 1-11/10-11/8-12/7 | |||
| zeus | |||
|- | |- | ||
| 30 | |||
| 0-3-7-12 | |||
| 1-8/7-11/8-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 31 | |||
| 0-4-7-12 | |||
| 1-6/5-11/8-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 32 | |||
| 0-5-7-12 | |||
| 1-5/4-11/8-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 33 | |||
| 0-3-8-12 | |||
| 1-8/7-10/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 34 | |||
| 0-4-8-12 | |||
| 1-6/5-10/7-12/7 | |||
| starling | |||
|- | |- | ||
| 35 | |||
| 0-5-8-12 | |||
| 1-5/4-10/7-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 36 | |||
| 0-2-9-12 | |||
| 1-12/11-3/2-12/7 | |||
| utonal | |||
|- | |- | ||
| 37 | |||
| 0-4-9-12 | |||
| 1-6/5-3/2-12/7 | |||
| utonal | |||
|- | |- | ||
| 38 | |||
| 0-5-9-12 | |||
| 1-5/4-3/2-12/7 | |||
| keenanismic | |||
|- | |- | ||
| 39 | |||
| 0-7-9-12 | |||
| 1-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 40 | |||
| 0-2-10-12 | |||
| 1-11/10-11/7-12/7 | |||
| biyatismic | |||
|- | |- | ||
| 41 | |||
| 0-3-10-12 | |||
| 1-8/7-11/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 42 | |||
| 0-5-10-12 | |||
| 1-5/4-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 43 | |||
| 0-7-10-12 | |||
| 1-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 44 | |||
| 0-8-10-12 | |||
| 1-10/7-11/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 45 | |||
| 0-2-4-13 | |||
| 1-11/10-6/5-9/5 | |||
| otonal | |||
|- | |- | ||
| 46 | |||
| 0-2-5-13 | |||
| 1-11/10-5/4-9/5 | |||
| thrush | |||
|- | |- | ||
| 47 | |||
| 0-3-5-13 | |||
| 1-8/7-5/4-9/5 | |||
| thrush | |||
|- | |- | ||
| 48 | |||
| 0-3-8-13 | |||
| 1-8/7-10/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 49 | |||
| 0-4-8-13 | |||
| 1-6/5-10/7-9/5 | |||
| starling | |||
|- | |- | ||
| 50 | |||
| 0-5-8-13 | |||
| 1-5/4-10/7-9/5 | |||
| starling | |||
|- | |- | ||
| 51 | |||
| 0-2-9-13 | |||
| 1-11/10-3/2-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 52 | |||
| 0-4-9-13 | |||
| 1-6/5-3/2-9/5 | |||
| ambitonal | |||
|- | |- | ||
| 53 | |||
| 0-5-9-13 | |||
| 1-5/4-3/2-9/5 | |||
| starling | |||
|- | |- | ||
| 54 | |||
| 0-2-10-13 | |||
| 1-11/10-11/7-9/5 | |||
| werckismic | |||
|- | |- | ||
| 55 | |||
| 0-3-10-13 | |||
| 1-8/7-11/7-9/5 | |||
| werckismic | |||
|- | |- | ||
| 56 | |||
| 0-5-10-13 | |||
| 1-5/4-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 57 | |||
| 0-8-10-13 | |||
| 1-10/7-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 58 | |||
| 0-2-11-13 | |||
| 1-11/10-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 59 | |||
| 0-3-11-13 | |||
| 1-8/7-18/11-9/5 | |||
| werckismic | |||
|- | |- | ||
| 60 | |||
| 0-4-11-13 | |||
| 1-6/5-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 61 | |||
| 0-8-11-13 | |||
| 1-10/7-18/11-9/5 | |||
| thrush | |||
|- | |- | ||
| 62 | |||
| 0-9-11-13 | |||
| 1-3/2-18/11-9/5 | |||
| utonal | |||
|- | |- | ||
| 63 | |||
| 0-5-7-18 | |||
| 1-5/4-11/8-9/8 | |||
| otonal | |||
|- | |- | ||
| 64 | |||
| 0-5-8-18 | |||
| 1-5/4-10/7-9/8 | |||
| werckismic | |||
|- | |- | ||
| 65 | |||
| 0-5-9-18 | |||
| 1-5/4-3/2-9/8 | |||
| otonal | |||
|- | |- | ||
| 66 | |||
| 0-7-9-18 | |||
| 1-11/8-3/2-9/8 | |||
| otonal | |||
|- | |- | ||
| 67 | |||
| 0-5-10-18 | |||
| 1-5/4-11/7-9/8 | |||
| thrush | |||
|- | |- | ||
| 68 | |||
| 0-7-10-18 | |||
| 1-11/8-11/7-9/8 | |||
| werckismic | |||
|- | |- | ||
| 69 | |||
| 0-8-10-18 | |||
| 1-10/7-11/7-9/8 | |||
| werckismic | |||
|- | |- | ||
| 70 | |||
| 0-7-11-18 | |||
| 1-11/8-18/11-9/8 | |||
| biyatismic | |||
|- | |- | ||
| 71 | |||
| 0-8-11-18 | |||
| 1-10/7-18/11-9/8 | |||
| werckismic | |||
|- | |- | ||
| 72 | |||
| 0-9-11-18 | |||
| 1-3/2-18/11-9/8 | |||
| utonal | |||
|- | |- | ||
| 73 | |||
| 0-5-13-18 | |||
| 1-5/4-9/5-9/8 | |||
| starling | |||
|- | |- | ||
| 74 | |||
| 0-8-13-18 | |||
| 1-10/7-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 75 | |||
| 0-9-13-18 | |||
| 1-3/2-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 76 | |||
| 0-10-13-18 | |||
| 1-11/7-9/5-9/8 | |||
| werckismic | |||
|- | |- | ||
| 77 | |||
| 0-11-13-18 | |||
| 1-18/11-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 78 | |||
| 0-3-8-21 | |||
| 1-8/7-10/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 79 | |||
| 0-3-10-21 | |||
| 1-8/7-11/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 80 | |||
| 0-8-10-21 | |||
| 1-10/7-11/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 81 | |||
| 0-3-11-21 | |||
| 1-8/7-18/11-9/7 | |||
| werckismic | |||
|- | |- | ||
| 82 | |||
| 0-8-11-21 | |||
| 1-10/7-18/11-9/7 | |||
| werckismic | |||
|- | |- | ||
| 83 | |||
| 0-9-11-21 | |||
| 1-3/2-18/11-9/7 | |||
| utonal | |||
|- | |- | ||
| 84 | |||
| 0-3-12-21 | |||
| 1-8/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 85 | |||
| 0-8-12-21 | |||
| 1-10/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 86 | |||
| 0-9-12-21 | |||
| 1-3/2-12/7-9/7 | |||
| ambitonal | |||
|- | |- | ||
| 87 | |||
| 0-10-12-21 | |||
| 1-11/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 88 | |||
| 0-3-13-21 | |||
| 1-8/7-9/5-9/7 | |||
| werckismic | |||
|- | |- | ||
| 89 | |||
| 0-8-13-21 | |||
| 1-10/7-9/5-9/7 | |||
| starling | |||
|- | |- | ||
| 90 | |||
| 0-9-13-21 | |||
| 1-3/2-9/5-9/7 | |||
| utonal | |||
|- | |- | ||
| 91 | |||
| 0-10-13-21 | |||
| 1-11/7-9/5-9/7 | |||
| werckismic | |||
|- | |- | ||
| 92 | |||
| 0-11-13-21 | |||
| 1-18/11-9/5-9/7 | |||
| utonal | |||
|- | |- | ||
| 93 | |||
| 0-8-18-21 | |||
| 1-10/7-9/8-9/7 | |||
| werckismic | |||
|- | |- | ||
| 94 | |||
| 0-9-18-21 | |||
| 1-3/2-9/8-9/7 | |||
| utonal | |||
|- | |- | ||
| 95 | |||
| 0-10-18-21 | |||
| 1-11/7-9/8-9/7 | |||
| werckismic | |||
|- | |- | ||
| 96 | |||
| 0-11-18-21 | |||
| 1-18/11-9/8-9/7 | |||
| utonal | |||
|- | |- | ||
| 97 | |||
| 0-13-18-21 | |||
| 1-9/5-9/8-9/7 | |||
| utonal | |||
|} | |} | ||
=Pentads= | == Pentads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-4-7-9 | |||
| 1-11/10-6/5-11/8-3/2 | |||
| zeus | |||
|- | |- | ||
| 2 | |||
| 0-2-5-7-9 | |||
| 1-11/10-5/4-11/8-3/2 | |||
| zeus | |||
|- | |- | ||
| 3 | |||
| 0-2-5-7-10 | |||
| 1-11/10-5/4-11/8-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 4 | |||
| 0-3-5-7-10 | |||
| 1-8/7-5/4-11/8-11/7 | |||
| zeus | |||
|- | |- | ||
| 5 | |||
| 0-3-5-8-10 | |||
| 1-8/7-5/4-10/7-11/7 | |||
| valinorsmic | |||
|- | |- | ||
| 6 | |||
| 0-2-4-7-11 | |||
| 1-11/10-6/5-11/8-18/11 | |||
| zeus | |||
|- | |- | ||
| 7 | |||
| 0-2-4-9-11 | |||
| 1-11/10-6/5-3/2-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 8 | |||
| 0-2-7-9-11 | |||
| 1-11/10-11/8-3/2-18/11 | |||
| biyatismic | |||
|- | |- | ||
| 9 | |||
| 0-4-7-9-11 | |||
| 1-6/5-11/8-3/2-18/11 | |||
| zeus | |||
|- | |- | ||
| 10 | |||
| 0-2-4-7-12 | |||
| 1-11/10-6/5-11/8-12/7 | |||
| zeus | |||
|- | |- | ||
| 11 | |||
| 0-2-5-7-12 | |||
| 1-11/10-5/4-11/8-12/7 | |||
| zeus | |||
|- | |- | ||
| 12 | |||
| 0-3-5-7-12 | |||
| 1-8/7-5/4-11/8-12/7 | |||
| zeus | |||
|- | |- | ||
| 13 | |||
| 0-3-5-8-12 | |||
| 1-8/7-5/4-10/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 14 | |||
| 0-2-4-9-12 | |||
| 1-12/11-6/5-3/2-12/7 | |||
| utonal | |||
|- | |- | ||
| 15 | |||
| 0-2-5-9-12 | |||
| 1-11/10-5/4-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 16 | |||
| 0-2-7-9-12 | |||
| 1-11/10-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 17 | |||
| 0-4-7-9-12 | |||
| 1-6/5-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 18 | |||
| 0-5-7-9-12 | |||
| 1-5/4-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 19 | |||
| 0-2-5-10-12 | |||
| 1-11/10-5/4-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 20 | |||
| 0-3-5-10-12 | |||
| 1-8/7-5/4-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 21 | |||
| 0-2-7-10-12 | |||
| 1-11/10-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 22 | |||
| 0-3-7-10-12 | |||
| 1-8/7-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 23 | |||
| 0-5-7-10-12 | |||
| 1-5/4-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 24 | |||
| 0-3-8-10-12 | |||
| 1-8/7-10/7-11/7-12/7 | |||
| otonal | |||
|- | |- | ||
| 25 | |||
| 0-5-8-10-12 | |||
| 1-5/4-10/7-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 26 | |||
| 0-3-5-8-13 | |||
| 1-8/7-5/4-10/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 27 | |||
| 0-2-4-9-13 | |||
| 1-11/10-6/5-3/2-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 28 | |||
| 0-2-5-9-13 | |||
| 1-11/10-5/4-3/2-9/5 | |||
| valentine | |||
|- | |- | ||
| 29 | |||
| 0-2-5-10-13 | |||
| 1-11/10-5/4-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 30 | |||
| 0-3-5-10-13 | |||
| 1-8/7-5/4-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 31 | |||
| 0-3-8-10-13 | |||
| 1-8/7-10/7-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 32 | |||
| 0-5-8-10-13 | |||
| 1-5/4-10/7-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 33 | |||
| 0-2-4-11-13 | |||
| 1-11/10-6/5-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 34 | |||
| 0-3-8-11-13 | |||
| 1-8/7-10/7-18/11-9/5 | |||
| thrush | |||
|- | |- | ||
| 35 | |||
| 0-4-8-11-13 | |||
| 1-6/5-10/7-18/11-9/5 | |||
| valentine | |||
|- | |- | ||
| 36 | |||
| 0-2-9-11-13 | |||
| 1-11/10-3/2-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 37 | |||
| 0-4-9-11-13 | |||
| 1-6/5-3/2-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 38 | |||
| 0-5-7-9-18 | |||
| 1-5/4-11/8-3/2-9/8 | |||
| otonal | |||
|- | |- | ||
| 39 | |||
| 0-5-7-10-18 | |||
| 1-5/4-11/8-11/7-9/8 | |||
| thrush | |||
|- | |- | ||
| 40 | |||
| 0-5-8-10-18 | |||
| 1-5/4-10/7-11/7-9/8 | |||
| thrush | |||
|- | |- | ||
| 41 | |||
| 0-7-9-11-18 | |||
| 1-11/8-3/2-18/11-9/8 | |||
| biyatismic | |||
|- | |- | ||
| 42 | |||
| 0-5-8-13-18 | |||
| 1-5/4-10/7-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 43 | |||
| 0-5-9-13-18 | |||
| 1-5/4-3/2-9/5-9/8 | |||
| starling | |||
|- | |- | ||
| 44 | |||
| 0-5-10-13-18 | |||
| 1-5/4-11/7-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 45 | |||
| 0-8-10-13-18 | |||
| 1-10/7-11/7-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 46 | |||
| 0-8-11-13-18 | |||
| 1-10/7-18/11-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 47 | |||
| 0-9-11-13-18 | |||
| 1-3/2-18/11-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 48 | |||
| 0-3-8-10-21 | |||
| 1-8/7-10/7-11/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 49 | |||
| 0-3-8-11-21 | |||
| 1-8/7-10/7-18/11-9/7 | |||
| werckismic | |||
|- | |- | ||
| 50 | |||
| 0-3-8-12-21 | |||
| 1-8/7-10/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 51 | |||
| 0-3-10-12-21 | |||
| 1-8/7-11/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 52 | |||
| 0-8-10-12-21 | |||
| 1-10/7-11/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 53 | |||
| 0-3-8-13-21 | |||
| 1-8/7-10/7-9/5-9/7 | |||
| thrush | |||
|- | |- | ||
| 54 | |||
| 0-3-10-13-21 | |||
| 1-8/7-11/7-9/5-9/7 | |||
| werckismic | |||
|- | |- | ||
| 55 | |||
| 0-8-10-13-21 | |||
| 1-10/7-11/7-9/5-9/7 | |||
| thrush | |||
|- | |- | ||
| 56 | |||
| 0-3-11-13-21 | |||
| 1-8/7-18/11-9/5-9/7 | |||
| werckismic | |||
|- | |- | ||
| 57 | |||
| 0-8-11-13-21 | |||
| 1-10/7-18/11-9/5-9/7 | |||
| thrush | |||
|- | |- | ||
| 58 | |||
| 0-9-11-13-21 | |||
| 1-3/2-18/11-9/5-9/7 | |||
| utonal | |||
|- | |- | ||
| 59 | |||
| 0-8-10-18-21 | |||
| 1-10/7-11/7-9/8-9/7 | |||
| werckismic | |||
|- | |- | ||
| 60 | |||
| 0-8-11-18-21 | |||
| 1-10/7-18/11-9/8-9/7 | |||
| werckismic | |||
|- | |- | ||
| 61 | |||
| 0-9-11-18-21 | |||
| 1-3/2-18/11-9/8-9/7 | |||
| utonal | |||
|- | |- | ||
| 62 | |||
| 0-8-13-18-21 | |||
| 1-10/7-9/5-9/8-9/7 | |||
| thrush | |||
|- | |- | ||
| 63 | |||
| 0-9-13-18-21 | |||
| 1-3/2-9/5-9/8-9/7 | |||
| utonal | |||
|- | |- | ||
| 64 | |||
| 0-10-13-18-21 | |||
| 1-11/7-9/5-9/8-9/7 | |||
| werckismic | |||
|- | |- | ||
| 65 | |||
| 0-11-13-18-21 | |||
| 1-18/11-9/5-9/8-9/7 | |||
| utonal | |||
|} | |} | ||
=Hexads= | == Hexads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-4-7-9-11 | |||
| 1-11/10-6/5-11/8-3/2-18/11 | |||
| zeus | |||
|- | |- | ||
| 2 | |||
| 0-2-4-7-9-12 | |||
| 1-11/10-6/5-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 3 | |||
| 0-2-5-7-9-12 | |||
| 1-11/10-5/4-11/8-3/2-12/7 | |||
| zeus | |||
|- | |- | ||
| 4 | |||
| 0-2-5-7-10-12 | |||
| 1-11/10-5/4-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 5 | |||
| 0-3-5-7-10-12 | |||
| 1-8/7-5/4-11/8-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 6 | |||
| 0-3-5-8-10-12 | |||
| 1-8/7-5/4-10/7-11/7-12/7 | |||
| zeus | |||
|- | |- | ||
| 7 | |||
| 0-3-5-8-10-13 | |||
| 1-8/7-5/4-10/7-11/7-9/5 | |||
| thrush | |||
|- | |- | ||
| 8 | |||
| 0-2-4-9-11-13 | |||
| 1-11/10-6/5-3/2-18/11-9/5 | |||
| biyatismic | |||
|- | |- | ||
| 9 | |||
| 0-5-8-10-13-18 | |||
| 1-5/4-10/7-11/7-9/5-9/8 | |||
| thrush | |||
|- | |- | ||
| 10 | |||
| 0-3-8-10-12-21 | |||
| 1-8/7-10/7-11/7-12/7-9/7 | |||
| otonal | |||
|- | |- | ||
| 11 | |||
| 0-3-8-10-13-21 | |||
| 1-8/7-10/7-11/7-9/5-9/7 | |||
| thrush | |||
|- | |- | ||
| 12 | |||
| 0-3-8-11-13-21 | |||
| 1-8/7-10/7-18/11-9/5-9/7 | |||
| thrush | |||
|- | |- | ||
| 13 | |||
| 0-8-10-13-18-21 | |||
| 1-10/7-11/7-9/5-9/8-9/7 | |||
| thrush | |||
|- | |- | ||
| 14 | |||
| 0-8-11-13-18-21 | |||
| 1-10/7-18/11-9/5-9/8-9/7 | |||
| thrush | |||
|- | |- | ||
| 15 | |||
| 0-9-11-13-18-21 | |||
| 1-3/2-18/11-9/5-9/8-9/7 | |||
| utonal | |||
|} | |} | ||
[[Category:Chords]] | |||
[[Category:Valentine]] | |||
[[Category:Triad]] | |||
[[Category:Tetrad]] | |||
[[Category:Pentad]] | |||
[[Category:Hexad]] | |||