Chords of valentine
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Below are listed the dyadic chords of 11-limit 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.
(Note that this preference for 20/11 over 11/6 is only true for the "transversal" column -- and there aren't any there. As the person who created the list of inversions, I (Jake) would rather know about an 11/6 than a 20/11, so the "as generated" and inversion columns show 11/6. That sometimes required tempering out 121/120 where the original list didn't indicate the need. All that being said, the transversals are untouched from the original entry.)
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.
Relationship to Carlos Alpha
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.
Chord ordering
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: Triad #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 in valentine[15] (because 15-9=6) .
Example 2: Triad #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 in valentine[15] (because 15-13=2).
Each of the triads generated has three inversions, i.e., can be written starting on any one of the three tones in the triad. Traditional music theory uses a traditional chord, e.g., the major triad, as the basis for the other two inversions. In this list, that place is taken by the chord that gets generated after a certain number of generator steps is taken to reach the tones needed for the chord. 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, triad #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. The same type of thinking goes into the list of tetrads, pentads, and hexads.
Note that, unlike in traditional music theory, there is nothing canonical, key-centric, harmonically relevant, or otherwise musically important about these orderings and inversions. It's just how the math works out.
Triads
| Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion |
|---|---|---|---|---|---|---|
| 1 | 0-2-4 | 1-11/10-6/5 | otonal | 1/1-11/10-6/5 | 1/1-11/10-11/6 | 1/1-5/3-11/6 |
| 2 | 0-2-5 | 1-11/10-5/4 | valinorsmic | 1/1-11/10-5/4 | 1/1-8/7-11/6 | 1/1-8/5-7/4 |
| 3 | 0-3-5 | 1-8/7-5/4 | valinorsmic | 1/1-8/7-5/4 | 1/1-11/10-7/4 | 1/1-8/5-11/6 |
| 4 | 0-2-7 | 1-11/10-11/8 | utonal | 1/1-11/10-11/8 | 1/1-5/4-11/6 | 1/1-16/11-8/5 |
| 5 | 0-3-7 | 1-8/7-11/8 | keenanismic | 1/1-8/7-11/8 | 1/1-6/5-7/4 | 1/1-16/11-5/3 |
| 6 | 0-4-7 | 1-6/5-11/8 | keenanismic | 1/1-6/5-11/8 | 1/1-8/7-5/3 | 1/1-16/11-7/4 |
| 7 | 0-5-7 | 1-5/4-11/8 | otonal | 1/1-5/4-11/8 | 1/1-11/10-8/5 | 1/1-16/11-11/6 |
| 8 | 0-3-8 | 1-8/7-10/7 | otonal | 1/1-8/7-10/7 | 1/1-5/4-7/4 | 1/1-7/5-8/5 |
| 9 | 0-4-8 | 1-6/5-10/7 | starling | 1/1-6/5-10/7 | 1/1-6/5-5/3 | 1/1-7/5-5/3 |
| 10 | 0-5-8 | 1-5/4-10/7 | utonal | 1/1-5/4-10/7 | 1/1-8/7-8/5 | 1/1-7/5-7/4 |
| 11 | 0-2-9 | 1-11/10-3/2 | utonal | 1/1-11/10-3/2 | 1/1-11/8-11/6 | 1/1-4/3-16/11 |
| 12 | 0-4-9 | 1-6/5-3/2 | utonal | 1/1-6/5-3/2 | 1/1-5/4-5/3 | 1/1-4/3-8/5 |
| 13 | 0-5-9 | 1-5/4-3/2 | otonal | 1/1-5/4-3/2 | 1/1-6/5-8/5 | 1/1-4/3-5/3 |
| 14 | 0-7-9 | 1-11/8-3/2 | otonal | 1/1-11/8-3/2 | 1/1-11/10-16/11 | 1/1-4/3-11/6 |
| 15 | 0-2-10 | 1-11/10-11/7 | utonal | 1/1-11/10-11/7 | 1/1-10/7-11/6 | 1/1-14/11-7/5 |
| 16 | 0-3-10 | 1-8/7-11/7 | otonal | 1/1-8/7-11/7 | 1/1-11/8-7/4 | 1/1-14/11-16/11 |
| 17 | 0-5-10 | 1-5/4-11/7 | valinorsmic | 1/1-5/4-11/7 | 1/1-5/4-8/5 | 1/1-14/11-8/5 |
| 18 | 0-7-10 | 1-11/8-11/7 | utonal | 1/1-11/8-11/7 | 1/1-8/7-16/11 | 1/1-14/11-7/4 |
| 19 | 0-8-10 | 1-10/7-11/7 | otonal | 1/1-10/7-11/7 | 1/1-11/10-7/5 | 1/1-14/11-11/6 |
| 20 | 0-2-11 | 1-11/10-18/11 | otonal | 1/1-11/10-18/11 | 1/1-3/2-11/6 | 1/1-11/9-4/3 |
| 21 | 0-3-11 | 1-8/7-18/11 | werckismic | 1/1-8/7-18/11 | 1/1-10/7-7/4 | 1/1-11/9-7/5 |
| 22 | 0-4-11 | 1-6/5-18/11 | biyatismic | 1/1-6/5-18/11 | 1/1-11/8-5/3 | 1/1-11/9-16/11 |
| 23 | 0-7-11 | 1-11/8-18/11 | biyatismic | 1/1-11/8-18/11 | 1/1-6/5-16/11 | 1/1-11/9-5/3 |
| 24 | 0-8-11 | 1-10/7-18/11 | werckismic | 1/1-10/7-18/11 | 1/1-8/7-7/5 | 1/1-11/9-7/4 |
| 25 | 0-9-11 | 1-3/2-18/11 | utonal | 1/1-3/2-18/11 | 1/1-11/10-4/3 | 1/1-11/9-11/6 |
| 26 | 0-2-12 | 1-11/10-12/7 | utonal | 1/1-11/10-12/7 | 1/1-11/7-11/6 | 1/1-7/6-14/11 |
| 27 | 0-3-12 | 1-8/7-12/7 | otonal | 1/1-8/7-12/7 | 1/1-3/2-7/4 | 1/1-7/6-4/3 |
| 28 | 0-4-12 | 1-6/5-12/7 | utonal | 1/1-6/5-12/7 | 1/1-10/7-5/3 | 1/1-7/6-7/5 |
| 29 | 0-5-12 | 1-5/4-12/7 | keenanismic | 1/1-5/4-12/7 | 1/1-11/8-8/5 | 1/1-7/6-16/11 |
| 30 | 0-7-12 | 1-11/8-12/7 | keenanismic | 1/1-11/8-12/7 | 1/1-5/4-16/11 | 1/1-7/6-8/5 |
| 31 | 0-8-12 | 1-10/7-12/7 | otonal | 1/1-10/7-12/7 | 1/1-6/5-7/5 | 1/1-7/6-5/3 |
| 32 | 0-9-12 | 1-3/2-12/7 | utonal | 1/1-3/2-12/7 | 1/1-8/7-4/3 | 1/1-7/6-7/4 |
| 33 | 0-10-12 | 1-11/7-12/7 | otonal | 1/1-11/7-12/7 | 1/1-11/10-14/11 | 1/1-7/6-11/6 |
| 34 | 0-2-13 | 1-11/10-9/5 | otonal | 1/1-11/10-9/5 | 1/1-18/11-11/6 | 1/1-10/9-11/9 |
| 35 | 0-3-13 | 1-8/7-9/5 | werckismic | 1/1-8/7-9/5 | 1/1-11/7-7/4 | 1/1-10/9-14/11 |
| 36 | 0-4-13 | 1-6/5-9/5 | otonal | 1/1-6/5-9/5 | 1/1-3/2-5/3 | 1/1-10/9-4/3 |
| 37 | 0-5-13 | 1-5/4-9/5 | starling | 1/1-5/4-9/5 | 1/1-10/7-8/5 | 1/1-10/9-7/5 |
| 38 | 0-8-13 | 1-10/7-9/5 | starling | 1/1-10/7-9/5 | 1/1-5/4-7/5 | 1/1-10/9-8/5 |
| 39 | 0-9-13 | 1-3/2-9/5 | utonal | 1/1-3/2-9/5 | 1/1-6/5-4/3 | 1/1-10/9-5/3 |
| 40 | 0-10-13 | 1-11/7-9/5 | werckismic | 1/1-11/7-9/5 | 1/1-8/7-14/11 | 1/1-10/9-7/4 |
| 41 | 0-11-13 | 1-18/11-9/5 | utonal | 1/1-18/11-9/5 | 1/1-11/10-11/9 | 1/1-10/9-11/6 |
| 42 | 0-5-18 | 1-5/4-9/8 | otonal | 1/1-9/8-5/4 | 1/1-10/9-16/9 | 1/1-8/5-9/5 |
| 43 | 0-7-18 | 1-11/8-9/8 | otonal | 1/1-9/8-11/8 | 1/1-11/9-16/9 | 1/1-16/11-18/11 |
| 44 | 0-8-18 | 1-10/7-9/8 | werckismic | 1/1-9/8-10/7 | 1/1-14/11-16/9 | 1/1-7/5-11/7 |
| 45 | 0-9-18 | 1-3/2-9/8 | ambitonal | 1/1-9/8-3/2 | 1/1-4/3-16/9 | 1/1-4/3-3/2 |
| 46 | 0-10-18 | 1-11/7-9/8 | werckismic | 1/1-9/8-11/7 | 1/1-7/5-16/9 | 1/1-14/11-10/7 |
| 47 | 0-11-18 | 1-18/11-9/8 | utonal | 1/1-9/8-18/11 | 1/1-16/11-16/9 | 1/1-11/9-11/8 |
| 48 | 0-13-18 | 1-9/5-9/8 | utonal | 1/1-9/8-9/5 | 1/1-8/5-16/9 | 1/1-10/9-5/4 |
| 49 | 0-3-21 | 1-8/7-9/7 | otonal | 1/1-8/7-9/7 | 1/1-9/8-7/4 | 1/1-14/9-16/9 |
| 50 | 0-8-21 | 1-10/7-9/7 | otonal | 1/1-9/7-10/7 | 1/1-10/9-14/9 | 1/1-7/5-9/5 |
| 51 | 0-9-21 | 1-3/2-9/7 | utonal | 1/1-9/7-3/2 | 1/1-7/6-14/9 | 1/1-4/3-12/7 |
| 52 | 0-10-21 | 1-11/7-9/7 | otonal | 1/1-9/7-11/7 | 1/1-11/9-14/9 | 1/1-14/11-18/11 |
| 53 | 0-11-21 | 1-18/11-9/7 | utonal | 1/1-9/7-18/11 | 1/1-14/11-14/9 | 1/1-11/9-11/7 |
| 54 | 0-12-21 | 1-12/7-9/7 | otonal | 1/1-9/7-12/7 | 1/1-4/3-14/9 | 1/1-7/6-3/2 |
| 55 | 0-13-21 | 1-9/5-9/7 | utonal | 1/1-9/7-9/5 | 1/1-7/5-14/9 | 1/1-10/9-10/7 |
| 56 | 0-18-21 | 1-9/8-9/7 | utonal | 1/1-9/8-9/7 | 1/1-8/7-16/9 | 1/1-14/9-7/4 |
Tetrads
| Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | 3rd inversion |
|---|---|---|---|---|---|---|---|
| 1 | 0-2-4-7 | 1-11/10-6/5-11/8 | zeus | 1/1-11/10-6/5-11/8 | 1/1-11/10-5/4-11/6 | 1/1-8/7-5/3-11/6 | 1/1-16/11-8/5-7/4 |
| 2 | 0-2-5-7 | 1-11/10-5/4-11/8 | valinorsmic | 1/1-11/10-5/4-11/8 | 1/1-8/7-5/4-11/6 | 1/1-11/10-8/5-7/4 | 1/1-16/11-8/5-11/6 |
| 3 | 0-3-5-7 | 1-8/7-5/4-11/8 | zeus | 1/1-8/7-5/4-11/8 | 1/1-11/10-6/5-7/4 | 1/1-11/10-8/5-11/6 | 1/1-16/11-5/3-11/6 |
| 4 | 0-3-5-8 | 1-8/7-5/4-10/7 | valinorsmic | 1/1-8/7-5/4-10/7 | 1/1-11/10-5/4-7/4 | 1/1-8/7-8/5-11/6 | 1/1-7/5-8/5-7/4 |
| 5 | 0-2-4-9 | 1-11/10-6/5-3/2 | utonal | 1/1-11/10-6/5-3/2 | 1/1-11/10-11/8-11/6 | 1/1-5/4-5/3-11/6 | 1/1-4/3-16/11-8/5 |
| 6 | 0-2-5-9 | 1-11/10-5/4-3/2 | zeus | 1/1-11/10-5/4-3/2 | 1/1-8/7-11/8-11/6 | 1/1-6/5-8/5-7/4 | 1/1-4/3-16/11-5/3 |
| 7 | 0-2-7-9 | 1-11/10-11/8-3/2 | biyatismic | 1/1-11/10-11/8-3/2 | 1/1-5/4-11/8-11/6 | 1/1-11/10-16/11-8/5 | 1/1-4/3-16/11-11/6 |
| 8 | 0-4-7-9 | 1-6/5-11/8-3/2 | zeus | 1/1-6/5-11/8-3/2 | 1/1-8/7-5/4-5/3 | 1/1-11/10-16/11-7/4 | 1/1-4/3-8/5-11/6 |
| 9 | 0-5-7-9 | 1-5/4-11/8-3/2 | otonal | 1/1-5/4-11/8-3/2 | 1/1-11/10-6/5-8/5 | 1/1-11/10-16/11-11/6 | 1/1-4/3-5/3-11/6 |
| 10 | 0-2-5-10 | 1-11/10-5/4-11/7 | valinorsmic | 1/1-11/10-5/4-11/7 | 1/1-8/7-10/7-11/6 | 1/1-5/4-8/5-7/4 | 1/1-14/11-7/5-8/5 |
| 11 | 0-3-5-10 | 1-8/7-5/4-11/7 | valinorsmic | 1/1-8/7-5/4-11/7 | 1/1-11/10-11/8-7/4 | 1/1-5/4-8/5-11/6 | 1/1-14/11-16/11-8/5 |
| 12 | 0-2-7-10 | 1-11/10-11/8-11/7 | utonal | 1/1-11/10-11/8-11/7 | 1/1-5/4-10/7-11/6 | 1/1-8/7-16/11-8/5 | 1/1-14/11-7/5-7/4 |
| 13 | 0-3-7-10 | 1-8/7-11/8-11/7 | keenanismic | 1/1-8/7-11/8-11/7 | 1/1-6/5-11/8-7/4 | 1/1-8/7-16/11-5/3 | 1/1-14/11-16/11-7/4 |
| 14 | 0-5-7-10 | 1-5/4-11/8-11/7 | valinorsmic | 1/1-5/4-11/8-11/7 | 1/1-11/10-5/4-8/5 | 1/1-8/7-16/11-11/6 | 1/1-14/11-8/5-7/4 |
| 15 | 0-3-8-10 | 1-8/7-10/7-11/7 | otonal | 1/1-8/7-10/7-11/7 | 1/1-5/4-11/8-7/4 | 1/1-11/10-7/5-8/5 | 1/1-14/11-16/11-11/6 |
| 16 | 0-5-8-10 | 1-5/4-10/7-11/7 | valinorsmic | 1/1-5/4-10/7-11/7 | 1/1-8/7-5/4-8/5 | 1/1-11/10-7/5-7/4 | 1/1-14/11-8/5-11/6 |
| 17 | 0-2-4-11 | 1-11/10-6/5-18/11 | biyatismic | 1/1-11/10-6/5-18/11 | 1/1-11/10-3/2-11/6 | 1/1-11/8-5/3-11/6 | 1/1-11/9-4/3-16/11 |
| 18 | 0-2-7-11 | 1-11/10-11/8-18/11 | biyatismic | 1/1-11/10-11/8-18/11 | 1/1-5/4-3/2-11/6 | 1/1-6/5-16/11-8/5 | 1/1-11/9-4/3-5/3 |
| 19 | 0-3-7-11 | 1-8/7-11/8-18/11 | valentine | 1/1-8/7-11/8-18/11 | 1/1-6/5-10/7-7/4 | 1/1-6/5-16/11-5/3 | 1/1-11/9-7/5-5/3 |
| 20 | 0-4-7-11 | 1-6/5-11/8-18/11 | zeus | 1/1-6/5-11/8-18/11 | 1/1-8/7-11/8-5/3 | 1/1-6/5-16/11-7/4 | 1/1-11/9-16/11-5/3 |
| 21 | 0-3-8-11 | 1-8/7-10/7-18/11 | werckismic | 1/1-8/7-10/7-18/11 | 1/1-5/4-10/7-7/4 | 1/1-8/7-7/5-8/5 | 1/1-11/9-7/5-7/4 |
| 22 | 0-4-8-11 | 1-6/5-10/7-18/11 | valentine | 1/1-6/5-10/7-18/11 | 1/1-6/5-11/8-5/3 | 1/1-8/7-7/5-5/3 | 1/1-11/9-16/11-7/4 |
| 23 | 0-2-9-11 | 1-11/10-3/2-18/11 | ambitonal | 1/1-11/10-3/2-18/11 | 1/1-11/8-3/2-11/6 | 1/1-11/10-4/3-16/11 | 1/1-11/9-4/3-11/6 |
| 24 | 0-4-9-11 | 1-6/5-3/2-18/11 | biyatismic | 1/1-6/5-3/2-18/11 | 1/1-5/4-11/8-5/3 | 1/1-11/10-4/3-8/5 | 1/1-11/9-16/11-11/6 |
| 25 | 0-7-9-11 | 1-11/8-3/2-18/11 | biyatismic | 1/1-11/8-3/2-18/11 | 1/1-11/10-6/5-16/11 | 1/1-11/10-4/3-11/6 | 1/1-11/9-5/3-11/6 |
| 26 | 0-2-4-12 | 1-11/10-6/5-12/7 | utonal | 1/1-11/10-6/5-12/7 | 1/1-11/10-11/7-11/6 | 1/1-10/7-5/3-11/6 | 1/1-7/6-14/11-7/5 |
| 27 | 0-2-5-12 | 1-11/10-5/4-12/7 | zeus | 1/1-11/10-5/4-12/7 | 1/1-8/7-11/7-11/6 | 1/1-11/8-8/5-7/4 | 1/1-7/6-14/11-16/11 |
| 28 | 0-3-5-12 | 1-8/7-5/4-12/7 | zeus | 1/1-8/7-5/4-12/7 | 1/1-11/10-3/2-7/4 | 1/1-11/8-8/5-11/6 | 1/1-7/6-4/3-16/11 |
| 29 | 0-2-7-12 | 1-11/10-11/8-12/7 | zeus | 1/1-11/10-11/8-12/7 | 1/1-5/4-11/7-11/6 | 1/1-5/4-16/11-8/5 | 1/1-7/6-14/11-8/5 |
| 30 | 0-3-7-12 | 1-8/7-11/8-12/7 | keenanismic | 1/1-8/7-11/8-12/7 | 1/1-6/5-3/2-7/4 | 1/1-5/4-16/11-5/3 | 1/1-7/6-4/3-8/5 |
| 31 | 0-4-7-12 | 1-6/5-11/8-12/7 | keenanismic | 1/1-6/5-11/8-12/7 | 1/1-8/7-10/7-5/3 | 1/1-5/4-16/11-7/4 | 1/1-7/6-7/5-8/5 |
| 32 | 0-5-7-12 | 1-5/4-11/8-12/7 | keenanismic | 1/1-5/4-11/8-12/7 | 1/1-11/10-11/8-8/5 | 1/1-5/4-16/11-11/6 | 1/1-7/6-16/11-8/5 |
| 33 | 0-3-8-12 | 1-8/7-10/7-12/7 | otonal | 1/1-8/7-10/7-12/7 | 1/1-5/4-3/2-7/4 | 1/1-6/5-7/5-8/5 | 1/1-7/6-4/3-5/3 |
| 34 | 0-4-8-12 | 1-6/5-10/7-12/7 | starling | 1/1-6/5-10/7-12/7 | 1/1-6/5-10/7-5/3 | 1/1-6/5-7/5-5/3 | 1/1-7/6-7/5-5/3 |
| 35 | 0-5-8-12 | 1-5/4-10/7-12/7 | keenanismic | 1/1-5/4-10/7-12/7 | 1/1-8/7-11/8-8/5 | 1/1-6/5-7/5-7/4 | 1/1-7/6-16/11-5/3 |
| 36 | 0-2-9-12 | 1-11/10-3/2-12/7 | utonal | 1/1-11/10-3/2-12/7 | 1/1-11/8-11/7-11/6 | 1/1-8/7-4/3-16/11 | 1/1-7/6-14/11-7/4 |
| 37 | 0-4-9-12 | 1-6/5-3/2-12/7 | utonal | 1/1-6/5-3/2-12/7 | 1/1-5/4-10/7-5/3 | 1/1-8/7-4/3-8/5 | 1/1-7/6-7/5-7/4 |
| 38 | 0-5-9-12 | 1-5/4-3/2-12/7 | keenanismic | 1/1-5/4-3/2-12/7 | 1/1-6/5-11/8-8/5 | 1/1-8/7-4/3-5/3 | 1/1-7/6-16/11-7/4 |
| 39 | 0-7-9-12 | 1-11/8-3/2-12/7 | zeus | 1/1-11/8-3/2-12/7 | 1/1-11/10-5/4-16/11 | 1/1-8/7-4/3-11/6 | 1/1-7/6-8/5-7/4 |
| 40 | 0-2-10-12 | 1-11/10-11/7-12/7 | biyatismic | 1/1-11/10-11/7-12/7 | 1/1-10/7-11/7-11/6 | 1/1-11/10-14/11-7/5 | 1/1-7/6-14/11-11/6 |
| 41 | 0-3-10-12 | 1-8/7-11/7-12/7 | otonal | 1/1-8/7-11/7-12/7 | 1/1-11/8-3/2-7/4 | 1/1-11/10-14/11-16/11 | 1/1-7/6-4/3-11/6 |
| 42 | 0-5-10-12 | 1-5/4-11/7-12/7 | zeus | 1/1-5/4-11/7-12/7 | 1/1-5/4-11/8-8/5 | 1/1-11/10-14/11-8/5 | 1/1-7/6-16/11-11/6 |
| 43 | 0-7-10-12 | 1-11/8-11/7-12/7 | zeus | 1/1-11/8-11/7-12/7 | 1/1-8/7-5/4-16/11 | 1/1-11/10-14/11-7/4 | 1/1-7/6-8/5-11/6 |
| 44 | 0-8-10-12 | 1-10/7-11/7-12/7 | otonal | 1/1-10/7-11/7-12/7 | 1/1-11/10-6/5-7/5 | 1/1-11/10-14/11-11/6 | 1/1-7/6-5/3-11/6 |
| 45 | 0-2-4-13 | 1-11/10-6/5-9/5 | otonal | 1/1-11/10-6/5-9/5 | 1/1-11/10-18/11-11/6 | 1/1-3/2-5/3-11/6 | 1/1-10/9-11/9-4/3 |
| 46 | 0-2-5-13 | 1-11/10-5/4-9/5 | thrush | 1/1-11/10-5/4-9/5 | 1/1-8/7-18/11-11/6 | 1/1-10/7-8/5-7/4 | 1/1-10/9-11/9-7/5 |
| 47 | 0-3-5-13 | 1-8/7-5/4-9/5 | thrush | 1/1-8/7-5/4-9/5 | 1/1-11/10-11/7-7/4 | 1/1-10/7-8/5-11/6 | 1/1-10/9-14/11-7/5 |
| 48 | 0-3-8-13 | 1-8/7-10/7-9/5 | thrush | 1/1-8/7-10/7-9/5 | 1/1-5/4-11/7-7/4 | 1/1-5/4-7/5-8/5 | 1/1-10/9-14/11-8/5 |
| 49 | 0-4-8-13 | 1-6/5-10/7-9/5 | starling | 1/1-6/5-10/7-9/5 | 1/1-6/5-3/2-5/3 | 1/1-5/4-7/5-5/3 | 1/1-10/9-4/3-8/5 |
| 50 | 0-5-8-13 | 1-5/4-10/7-9/5 | starling | 1/1-5/4-10/7-9/5 | 1/1-8/7-10/7-8/5 | 1/1-5/4-7/5-7/4 | 1/1-10/9-7/5-8/5 |
| 51 | 0-2-9-13 | 1-11/10-3/2-9/5 | biyatismic | 1/1-11/10-3/2-9/5 | 1/1-11/8-18/11-11/6 | 1/1-6/5-4/3-16/11 | 1/1-10/9-11/9-5/3 |
| 52 | 0-4-9-13 | 1-6/5-3/2-9/5 | ambitonal | 1/1-6/5-3/2-9/5 | 1/1-5/4-3/2-5/3 | 1/1-6/5-4/3-8/5 | 1/1-10/9-4/3-5/3 |
| 53 | 0-5-9-13 | 1-5/4-3/2-9/5 | starling | 1/1-5/4-3/2-9/5 | 1/1-6/5-10/7-8/5 | 1/1-6/5-4/3-5/3 | 1/1-10/9-7/5-5/3 |
| 54 | 0-2-10-13 | 1-11/10-11/7-9/5 | werckismic | 1/1-11/10-11/7-9/5 | 1/1-10/7-18/11-11/6 | 1/1-8/7-14/11-7/5 | 1/1-10/9-11/9-7/4 |
| 55 | 0-3-10-13 | 1-8/7-11/7-9/5 | werckismic | 1/1-8/7-11/7-9/5 | 1/1-11/8-11/7-7/4 | 1/1-8/7-14/11-16/11 | 1/1-10/9-14/11-7/4 |
| 56 | 0-5-10-13 | 1-5/4-11/7-9/5 | thrush | 1/1-5/4-11/7-9/5 | 1/1-5/4-10/7-8/5 | 1/1-8/7-14/11-8/5 | 1/1-10/9-7/5-7/4 |
| 57 | 0-8-10-13 | 1-10/7-11/7-9/5 | thrush | 1/1-10/7-11/7-9/5 | 1/1-11/10-5/4-7/5 | 1/1-8/7-14/11-11/6 | 1/1-10/9-8/5-7/4 |
| 58 | 0-2-11-13 | 1-11/10-18/11-9/5 | biyatismic | 1/1-11/10-18/11-9/5 | 1/1-3/2-18/11-11/6 | 1/1-11/10-11/9-4/3 | 1/1-10/9-11/9-11/6 |
| 59 | 0-3-11-13 | 1-8/7-18/11-9/5 | werckismic | 1/1-8/7-18/11-9/5 | 1/1-10/7-11/7-7/4 | 1/1-11/10-11/9-7/5 | 1/1-10/9-14/11-11/6 |
| 60 | 0-4-11-13 | 1-6/5-18/11-9/5 | biyatismic | 1/1-6/5-18/11-9/5 | 1/1-11/8-3/2-5/3 | 1/1-11/10-11/9-16/11 | 1/1-10/9-4/3-11/6 |
| 61 | 0-8-11-13 | 1-10/7-18/11-9/5 | thrush | 1/1-10/7-18/11-9/5 | 1/1-8/7-5/4-7/5 | 1/1-11/10-11/9-7/4 | 1/1-10/9-8/5-11/6 |
| 62 | 0-9-11-13 | 1-3/2-18/11-9/5 | utonal | 1/1-3/2-18/11-9/5 | 1/1-11/10-6/5-4/3 | 1/1-11/10-11/9-11/6 | 1/1-10/9-5/3-11/6 |
| 63 | 0-5-7-18 | 1-5/4-11/8-9/8 | otonal | 1/1-9/8-5/4-11/8 | 1/1-10/9-11/9-16/9 | 1/1-11/10-8/5-9/5 | 1/1-16/11-18/11-11/6 |
| 64 | 0-5-8-18 | 1-5/4-10/7-9/8 | werckismic | 1/1-9/8-5/4-10/7 | 1/1-10/9-14/11-16/9 | 1/1-8/7-8/5-9/5 | 1/1-7/5-11/7-7/4 |
| 65 | 0-5-9-18 | 1-5/4-3/2-9/8 | otonal | 1/1-9/8-5/4-3/2 | 1/1-10/9-4/3-16/9 | 1/1-6/5-8/5-9/5 | 1/1-4/3-3/2-5/3 |
| 66 | 0-7-9-18 | 1-11/8-3/2-9/8 | otonal | 1/1-9/8-11/8-3/2 | 1/1-11/9-4/3-16/9 | 1/1-11/10-16/11-18/11 | 1/1-4/3-3/2-11/6 |
| 67 | 0-5-10-18 | 1-5/4-11/7-9/8 | thrush | 1/1-9/8-5/4-11/7 | 1/1-10/9-7/5-16/9 | 1/1-5/4-8/5-9/5 | 1/1-14/11-10/7-8/5 |
| 68 | 0-7-10-18 | 1-11/8-11/7-9/8 | werckismic | 1/1-9/8-11/8-11/7 | 1/1-11/9-7/5-16/9 | 1/1-8/7-16/11-18/11 | 1/1-14/11-10/7-7/4 |
| 69 | 0-8-10-18 | 1-10/7-11/7-9/8 | werckismic | 1/1-9/8-10/7-11/7 | 1/1-14/11-7/5-16/9 | 1/1-11/10-7/5-11/7 | 1/1-14/11-10/7-11/6 |
| 70 | 0-7-11-18 | 1-11/8-18/11-9/8 | biyatismic | 1/1-9/8-11/8-18/11 | 1/1-11/9-16/11-16/9 | 1/1-6/5-16/11-18/11 | 1/1-11/9-11/8-5/3 |
| 71 | 0-8-11-18 | 1-10/7-18/11-9/8 | werckismic | 1/1-9/8-10/7-18/11 | 1/1-14/11-16/11-16/9 | 1/1-8/7-7/5-11/7 | 1/1-11/9-11/8-7/4 |
| 72 | 0-9-11-18 | 1-3/2-18/11-9/8 | utonal | 1/1-9/8-3/2-18/11 | 1/1-4/3-16/11-16/9 | 1/1-11/10-4/3-3/2 | 1/1-11/9-11/8-11/6 |
| 73 | 0-5-13-18 | 1-5/4-9/5-9/8 | starling | 1/1-9/8-5/4-9/5 | 1/1-10/9-8/5-16/9 | 1/1-10/7-8/5-9/5 | 1/1-10/9-5/4-25/18 |
| 74 | 0-8-13-18 | 1-10/7-9/5-9/8 | thrush | 1/1-9/8-10/7-9/5 | 1/1-14/11-8/5-16/9 | 1/1-5/4-7/5-11/7 | 1/1-10/9-5/4-8/5 |
| 75 | 0-9-13-18 | 1-3/2-9/5-9/8 | utonal | 1/1-9/8-3/2-9/5 | 1/1-4/3-8/5-16/9 | 1/1-6/5-4/3-3/2 | 1/1-10/9-5/4-5/3 |
| 76 | 0-10-13-18 | 1-11/7-9/5-9/8 | werckismic | 1/1-9/8-11/7-9/5 | 1/1-7/5-8/5-16/9 | 1/1-8/7-14/11-10/7 | 1/1-10/9-5/4-7/4 |
| 77 | 0-11-13-18 | 1-18/11-9/5-9/8 | utonal | 1/1-9/8-18/11-9/5 | 1/1-16/11-8/5-16/9 | 1/1-11/10-11/9-11/8 | 1/1-10/9-5/4-11/6 |
| 78 | 0-3-8-21 | 1-8/7-10/7-9/7 | otonal | 1/1-8/7-9/7-10/7 | 1/1-9/8-5/4-7/4 | 1/1-10/9-14/9-16/9 | 1/1-7/5-8/5-9/5 |
| 79 | 0-3-10-21 | 1-8/7-11/7-9/7 | otonal | 1/1-8/7-9/7-11/7 | 1/1-9/8-11/8-7/4 | 1/1-11/9-14/9-16/9 | 1/1-14/11-16/11-18/11 |
| 80 | 0-8-10-21 | 1-10/7-11/7-9/7 | otonal | 1/1-9/7-10/7-11/7 | 1/1-10/9-11/9-14/9 | 1/1-11/10-7/5-9/5 | 1/1-14/11-18/11-11/6 |
| 81 | 0-3-11-21 | 1-8/7-18/11-9/7 | werckismic | 1/1-8/7-9/7-18/11 | 1/1-9/8-10/7-7/4 | 1/1-14/11-14/9-16/9 | 1/1-11/9-7/5-11/7 |
| 82 | 0-8-11-21 | 1-10/7-18/11-9/7 | werckismic | 1/1-9/7-10/7-18/11 | 1/1-10/9-14/11-14/9 | 1/1-8/7-7/5-9/5 | 1/1-11/9-11/7-7/4 |
| 83 | 0-9-11-21 | 1-3/2-18/11-9/7 | utonal | 1/1-9/7-3/2-18/11 | 1/1-7/6-14/11-14/9 | 1/1-11/10-4/3-12/7 | 1/1-11/9-11/7-11/6 |
| 84 | 0-3-12-21 | 1-8/7-12/7-9/7 | otonal | 1/1-8/7-9/7-12/7 | 1/1-9/8-3/2-7/4 | 1/1-4/3-14/9-16/9 | 1/1-7/6-4/3-3/2 |
| 85 | 0-8-12-21 | 1-10/7-12/7-9/7 | otonal | 1/1-9/7-10/7-12/7 | 1/1-10/9-4/3-14/9 | 1/1-6/5-7/5-9/5 | 1/1-7/6-3/2-5/3 |
| 86 | 0-9-12-21 | 1-3/2-12/7-9/7 | ambitonal | 1/1-9/7-3/2-12/7 | 1/1-7/6-4/3-14/9 | 1/1-8/7-4/3-12/7 | 1/1-7/6-3/2-7/4 |
| 87 | 0-10-12-21 | 1-11/7-12/7-9/7 | otonal | 1/1-9/7-11/7-12/7 | 1/1-11/9-4/3-14/9 | 1/1-11/10-14/11-18/11 | 1/1-7/6-3/2-11/6 |
| 88 | 0-3-13-21 | 1-8/7-9/5-9/7 | werckismic | 1/1-8/7-9/7-9/5 | 1/1-9/8-11/7-7/4 | 1/1-7/5-14/9-16/9 | 1/1-10/9-14/11-10/7 |
| 89 | 0-8-13-21 | 1-10/7-9/5-9/7 | starling | 1/1-9/7-10/7-9/5 | 1/1-10/9-7/5-14/9 | 1/1-5/4-7/5-9/5 | 1/1-10/9-10/7-8/5 |
| 90 | 0-9-13-21 | 1-3/2-9/5-9/7 | utonal | 1/1-9/7-3/2-9/5 | 1/1-7/6-7/5-14/9 | 1/1-6/5-4/3-12/7 | 1/1-10/9-10/7-5/3 |
| 91 | 0-10-13-21 | 1-11/7-9/5-9/7 | werckismic | 1/1-9/7-11/7-9/5 | 1/1-11/9-7/5-14/9 | 1/1-8/7-14/11-18/11 | 1/1-10/9-10/7-7/4 |
| 92 | 0-11-13-21 | 1-18/11-9/5-9/7 | utonal | 1/1-9/7-18/11-9/5 | 1/1-14/11-7/5-14/9 | 1/1-11/10-11/9-11/7 | 1/1-10/9-10/7-11/6 |
| 93 | 0-8-18-21 | 1-10/7-9/8-9/7 | werckismic | 1/1-9/8-9/7-10/7 | 1/1-8/7-14/11-16/9 | 1/1-10/9-14/9-7/4 | 1/1-7/5-11/7-9/5 |
| 94 | 0-9-18-21 | 1-3/2-9/8-9/7 | utonal | 1/1-9/8-9/7-3/2 | 1/1-8/7-4/3-16/9 | 1/1-7/6-14/9-7/4 | 1/1-4/3-3/2-12/7 |
| 95 | 0-10-18-21 | 1-11/7-9/8-9/7 | werckismic | 1/1-9/8-9/7-11/7 | 1/1-8/7-7/5-16/9 | 1/1-11/9-14/9-7/4 | 1/1-14/11-10/7-18/11 |
| 96 | 0-11-18-21 | 1-18/11-9/8-9/7 | utonal | 1/1-9/8-9/7-18/11 | 1/1-8/7-16/11-16/9 | 1/1-14/11-14/9-7/4 | 1/1-11/9-11/8-11/7 |
| 97 | 0-13-18-21 | 1-9/5-9/8-9/7 | utonal | 1/1-9/8-9/7-9/5 | 1/1-8/7-8/5-16/9 | 1/1-7/5-14/9-7/4 | 1/1-10/9-5/4-10/7 |
Pentads
| Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | 3rd inversion | 4th inversion |
|---|---|---|---|---|---|---|---|---|
| 1 | 0-2-4-7-9 | 1-11/10-6/5-11/8-3/2 | zeus | 1/1-11/10-6/5-11/8-3/2 | 1/1-11/10-5/4-11/8-11/6 | 1/1-8/7-5/4-5/3-11/6 | 1/1-11/10-16/11-8/5-7/4 | 1/1-4/3-16/11-8/5-11/6 |
| 2 | 0-2-5-7-9 | 1-11/10-5/4-11/8-3/2 | zeus | 1/1-11/10-5/4-11/8-3/2 | 1/1-8/7-5/4-11/8-11/6 | 1/1-11/10-6/5-8/5-7/4 | 1/1-11/10-16/11-8/5-11/6 | 1/1-4/3-16/11-5/3-11/6 |
| 3 | 0-2-5-7-10 | 1-11/10-5/4-11/8-11/7 | valinorsmic | 1/1-11/10-5/4-11/8-11/7 | 1/1-8/7-5/4-10/7-11/6 | 1/1-11/10-5/4-8/5-7/4 | 1/1-8/7-16/11-8/5-11/6 | 1/1-14/11-7/5-8/5-7/4 |
| 4 | 0-3-5-7-10 | 1-8/7-5/4-11/8-11/7 | zeus | 1/1-8/7-5/4-11/8-11/7 | 1/1-11/10-6/5-11/8-7/4 | 1/1-11/10-5/4-8/5-11/6 | 1/1-8/7-16/11-5/3-11/6 | 1/1-14/11-16/11-8/5-7/4 |
| 5 | 0-3-5-8-10 | 1-8/7-5/4-10/7-11/7 | valinorsmic | 1/1-8/7-5/4-10/7-11/7 | 1/1-11/10-5/4-11/8-7/4 | 1/1-8/7-5/4-8/5-11/6 | 1/1-11/10-7/5-8/5-7/4 | 1/1-14/11-16/11-8/5-11/6 |
| 6 | 0-2-4-7-11 | 1-11/10-6/5-11/8-18/11 | zeus | 1/1-11/10-6/5-11/8-18/11 | 1/1-11/10-5/4-3/2-11/6 | 1/1-8/7-11/8-5/3-11/6 | 1/1-6/5-16/11-8/5-7/4 | 1/1-11/9-4/3-16/11-5/3 |
| 7 | 0-2-4-9-11 | 1-11/10-6/5-3/2-18/11 | biyatismic | 1/1-11/10-6/5-3/2-18/11 | 1/1-11/10-11/8-3/2-11/6 | 1/1-5/4-11/8-5/3-11/6 | 1/1-11/10-4/3-16/11-8/5 | 1/1-11/9-4/3-16/11-11/6 |
| 8 | 0-2-7-9-11 | 1-11/10-11/8-3/2-18/11 | biyatismic | 1/1-11/10-11/8-3/2-18/11 | 1/1-5/4-11/8-3/2-11/6 | 1/1-11/10-6/5-16/11-8/5 | 1/1-11/10-4/3-16/11-11/6 | 1/1-11/9-4/3-5/3-11/6 |
| 9 | 0-4-7-9-11 | 1-6/5-11/8-3/2-18/11 | zeus | 1/1-6/5-11/8-3/2-18/11 | 1/1-8/7-5/4-11/8-5/3 | 1/1-11/10-6/5-16/11-7/4 | 1/1-11/10-4/3-8/5-11/6 | 1/1-11/9-16/11-5/3-11/6 |
| 10 | 0-2-4-7-12 | 1-11/10-6/5-11/8-12/7 | zeus | 1/1-11/10-6/5-11/8-12/7 | 1/1-11/10-5/4-11/7-11/6 | 1/1-8/7-10/7-5/3-11/6 | 1/1-5/4-16/11-8/5-7/4 | 1/1-7/6-14/11-7/5-8/5 |
| 11 | 0-2-5-7-12 | 1-11/10-5/4-11/8-12/7 | zeus | 1/1-11/10-5/4-11/8-12/7 | 1/1-8/7-5/4-11/7-11/6 | 1/1-11/10-11/8-8/5-7/4 | 1/1-5/4-16/11-8/5-11/6 | 1/1-7/6-14/11-16/11-8/5 |
| 12 | 0-3-5-7-12 | 1-8/7-5/4-11/8-12/7 | zeus | 1/1-8/7-5/4-11/8-12/7 | 1/1-11/10-6/5-3/2-7/4 | 1/1-11/10-11/8-8/5-11/6 | 1/1-5/4-16/11-5/3-11/6 | 1/1-7/6-4/3-16/11-8/5 |
| 13 | 0-3-5-8-12 | 1-8/7-5/4-10/7-12/7 | zeus | 1/1-8/7-5/4-10/7-12/7 | 1/1-11/10-5/4-3/2-7/4 | 1/1-8/7-11/8-8/5-11/6 | 1/1-6/5-7/5-8/5-7/4 | 1/1-7/6-4/3-16/11-5/3 |
| 14 | 0-2-4-9-12 | 1-11/10-6/5-3/2-12/7 | utonal | 1/1-11/10-6/5-3/2-12/7 | 1/1-11/10-11/8-11/7-11/6 | 1/1-5/4-10/7-5/3-11/6 | 1/1-8/7-4/3-16/11-8/5 | 1/1-7/6-14/11-7/5-7/4 |
| 15 | 0-2-5-9-12 | 1-11/10-5/4-3/2-12/7 | zeus | 1/1-11/10-5/4-3/2-12/7 | 1/1-8/7-11/8-11/7-11/6 | 1/1-6/5-11/8-8/5-7/4 | 1/1-8/7-4/3-16/11-5/3 | 1/1-7/6-14/11-16/11-7/4 |
| 16 | 0-2-7-9-12 | 1-11/10-11/8-3/2-12/7 | zeus | 1/1-11/10-11/8-3/2-12/7 | 1/1-5/4-11/8-11/7-11/6 | 1/1-11/10-5/4-16/11-8/5 | 1/1-8/7-4/3-16/11-11/6 | 1/1-7/6-14/11-8/5-7/4 |
| 17 | 0-4-7-9-12 | 1-6/5-11/8-3/2-12/7 | zeus | 1/1-6/5-11/8-3/2-12/7 | 1/1-8/7-5/4-10/7-5/3 | 1/1-11/10-5/4-16/11-7/4 | 1/1-8/7-4/3-8/5-11/6 | 1/1-7/6-7/5-8/5-7/4 |
| 18 | 0-5-7-9-12 | 1-5/4-11/8-3/2-12/7 | zeus | 1/1-5/4-11/8-3/2-12/7 | 1/1-11/10-6/5-11/8-8/5 | 1/1-11/10-5/4-16/11-11/6 | 1/1-8/7-4/3-5/3-11/6 | 1/1-7/6-16/11-8/5-7/4 |
| 19 | 0-2-5-10-12 | 1-11/10-5/4-11/7-12/7 | zeus | 1/1-11/10-5/4-11/7-12/7 | 1/1-8/7-10/7-11/7-11/6 | 1/1-5/4-11/8-8/5-7/4 | 1/1-11/10-14/11-7/5-8/5 | 1/1-7/6-14/11-16/11-11/6 |
| 20 | 0-3-5-10-12 | 1-8/7-5/4-11/7-12/7 | zeus | 1/1-8/7-5/4-11/7-12/7 | 1/1-11/10-11/8-3/2-7/4 | 1/1-5/4-11/8-8/5-11/6 | 1/1-11/10-14/11-16/11-8/5 | 1/1-7/6-4/3-16/11-11/6 |
| 21 | 0-2-7-10-12 | 1-11/10-11/8-11/7-12/7 | zeus | 1/1-11/10-11/8-11/7-12/7 | 1/1-5/4-10/7-11/7-11/6 | 1/1-8/7-5/4-16/11-8/5 | 1/1-11/10-14/11-7/5-7/4 | 1/1-7/6-14/11-8/5-11/6 |
| 22 | 0-3-7-10-12 | 1-8/7-11/8-11/7-12/7 | zeus | 1/1-8/7-11/8-11/7-12/7 | 1/1-6/5-11/8-3/2-7/4 | 1/1-8/7-5/4-16/11-5/3 | 1/1-11/10-14/11-16/11-7/4 | 1/1-7/6-4/3-8/5-11/6 |
| 23 | 0-5-7-10-12 | 1-5/4-11/8-11/7-12/7 | zeus | 1/1-5/4-11/8-11/7-12/7 | 1/1-11/10-5/4-11/8-8/5 | 1/1-8/7-5/4-16/11-11/6 | 1/1-11/10-14/11-8/5-7/4 | 1/1-7/6-16/11-8/5-11/6 |
| 24 | 0-3-8-10-12 | 1-8/7-10/7-11/7-12/7 | otonal | 1/1-8/7-10/7-11/7-12/7 | 1/1-5/4-11/8-3/2-7/4 | 1/1-11/10-6/5-7/5-8/5 | 1/1-11/10-14/11-16/11-11/6 | 1/1-7/6-4/3-5/3-11/6 |
| 25 | 0-5-8-10-12 | 1-5/4-10/7-11/7-12/7 | zeus | 1/1-5/4-10/7-11/7-12/7 | 1/1-8/7-5/4-11/8-8/5 | 1/1-11/10-6/5-7/5-7/4 | 1/1-11/10-14/11-8/5-11/6 | 1/1-7/6-16/11-5/3-11/6 |
| 26 | 0-3-5-8-13 | 1-8/7-5/4-10/7-9/5 | thrush | 1/1-8/7-5/4-10/7-9/5 | 1/1-11/10-5/4-11/7-7/4 | 1/1-8/7-10/7-8/5-11/6 | 1/1-5/4-7/5-8/5-7/4 | 1/1-10/9-14/11-7/5-8/5 |
| 27 | 0-2-4-9-13 | 1-11/10-6/5-3/2-9/5 | biyatismic | 1/1-11/10-6/5-3/2-9/5 | 1/1-11/10-11/8-18/11-11/6 | 1/1-5/4-3/2-5/3-11/6 | 1/1-6/5-4/3-16/11-8/5 | 1/1-10/9-11/9-4/3-5/3 |
| 28 | 0-2-5-9-13 | 1-11/10-5/4-3/2-9/5 | valentine | 1/1-11/10-5/4-3/2-9/5 | 1/1-8/7-11/8-18/11-11/6 | 1/1-6/5-10/7-8/5-7/4 | 1/1-6/5-4/3-16/11-5/3 | 1/1-10/9-11/9-7/5-5/3 |
| 29 | 0-2-5-10-13 | 1-11/10-5/4-11/7-9/5 | thrush | 1/1-11/10-5/4-11/7-9/5 | 1/1-8/7-10/7-18/11-11/6 | 1/1-5/4-10/7-8/5-7/4 | 1/1-8/7-14/11-7/5-8/5 | 1/1-10/9-11/9-7/5-7/4 |
| 30 | 0-3-5-10-13 | 1-8/7-5/4-11/7-9/5 | thrush | 1/1-8/7-5/4-11/7-9/5 | 1/1-11/10-11/8-11/7-7/4 | 1/1-5/4-10/7-8/5-11/6 | 1/1-8/7-14/11-16/11-8/5 | 1/1-10/9-14/11-7/5-7/4 |
| 31 | 0-3-8-10-13 | 1-8/7-10/7-11/7-9/5 | thrush | 1/1-8/7-10/7-11/7-9/5 | 1/1-5/4-11/8-11/7-7/4 | 1/1-11/10-5/4-7/5-8/5 | 1/1-8/7-14/11-16/11-11/6 | 1/1-10/9-14/11-8/5-7/4 |
| 32 | 0-5-8-10-13 | 1-5/4-10/7-11/7-9/5 | thrush | 1/1-5/4-10/7-11/7-9/5 | 1/1-8/7-5/4-10/7-8/5 | 1/1-11/10-5/4-7/5-7/4 | 1/1-8/7-14/11-8/5-11/6 | 1/1-10/9-7/5-8/5-7/4 |
| 33 | 0-2-4-11-13 | 1-11/10-6/5-18/11-9/5 | biyatismic | 1/1-11/10-6/5-18/11-9/5 | 1/1-11/10-3/2-18/11-11/6 | 1/1-11/8-3/2-5/3-11/6 | 1/1-11/10-11/9-4/3-16/11 | 1/1-10/9-11/9-4/3-11/6 |
| 34 | 0-3-8-11-13 | 1-8/7-10/7-18/11-9/5 | thrush | 1/1-8/7-10/7-18/11-9/5 | 1/1-5/4-10/7-11/7-7/4 | 1/1-8/7-5/4-7/5-8/5 | 1/1-11/10-11/9-7/5-7/4 | 1/1-10/9-14/11-8/5-11/6 |
| 35 | 0-4-8-11-13 | 1-6/5-10/7-18/11-9/5 | valentine | 1/1-6/5-10/7-18/11-9/5 | 1/1-6/5-11/8-3/2-5/3 | 1/1-8/7-5/4-7/5-5/3 | 1/1-11/10-11/9-16/11-7/4 | 1/1-10/9-4/3-8/5-11/6 |
| 36 | 0-2-9-11-13 | 1-11/10-3/2-18/11-9/5 | biyatismic | 1/1-11/10-3/2-18/11-9/5 | 1/1-11/8-3/2-18/11-11/6 | 1/1-11/10-6/5-4/3-16/11 | 1/1-11/10-11/9-4/3-11/6 | 1/1-10/9-11/9-5/3-11/6 |
| 37 | 0-4-9-11-13 | 1-6/5-3/2-18/11-9/5 | biyatismic | 1/1-6/5-3/2-18/11-9/5 | 1/1-5/4-11/8-3/2-5/3 | 1/1-11/10-6/5-4/3-8/5 | 1/1-11/10-11/9-16/11-11/6 | 1/1-10/9-4/3-5/3-11/6 |
| 38 | 0-5-7-9-18 | 1-5/4-11/8-3/2-9/8 | otonal | 1/1-9/8-5/4-11/8-3/2 | 1/1-10/9-11/9-4/3-16/9 | 1/1-11/10-6/5-8/5-9/5 | 1/1-11/10-16/11-18/11-11/6 | 1/1-4/3-3/2-5/3-11/6 |
| 39 | 0-5-7-10-18 | 1-5/4-11/8-11/7-9/8 | thrush | 1/1-9/8-5/4-11/8-11/7 | 1/1-10/9-11/9-7/5-16/9 | 1/1-11/10-5/4-8/5-9/5 | 1/1-8/7-16/11-18/11-11/6 | 1/1-14/11-10/7-8/5-7/4 |
| 40 | 0-5-8-10-18 | 1-5/4-10/7-11/7-9/8 | thrush | 1/1-9/8-5/4-10/7-11/7 | 1/1-10/9-14/11-7/5-16/9 | 1/1-8/7-5/4-8/5-9/5 | 1/1-11/10-7/5-11/7-7/4 | 1/1-14/11-10/7-8/5-11/6 |
| 41 | 0-7-9-11-18 | 1-11/8-3/2-18/11-9/8 | biyatismic | 1/1-9/8-11/8-3/2-18/11 | 1/1-11/9-4/3-16/11-16/9 | 1/1-11/10-6/5-16/11-18/11 | 1/1-11/10-4/3-3/2-11/6 | 1/1-11/9-11/8-5/3-11/6 |
| 42 | 0-5-8-13-18 | 1-5/4-10/7-9/5-9/8 | thrush | 1/1-9/8-5/4-10/7-9/5 | 1/1-10/9-14/11-8/5-16/9 | 1/1-8/7-10/7-8/5-9/5 | 1/1-5/4-7/5-11/7-7/4 | 1/1-10/9-5/4-7/5-8/5 |
| 43 | 0-5-9-13-18 | 1-5/4-3/2-9/5-9/8 | starling | 1/1-9/8-5/4-3/2-9/5 | 1/1-10/9-4/3-8/5-16/9 | 1/1-6/5-10/7-8/5-9/5 | 1/1-6/5-4/3-3/2-5/3 | 1/1-10/9-5/4-7/5-5/3 |
| 44 | 0-5-10-13-18 | 1-5/4-11/7-9/5-9/8 | thrush | 1/1-9/8-5/4-11/7-9/5 | 1/1-10/9-7/5-8/5-16/9 | 1/1-5/4-10/7-8/5-9/5 | 1/1-8/7-14/11-10/7-8/5 | 1/1-10/9-5/4-7/5-7/4 |
| 45 | 0-8-10-13-18 | 1-10/7-11/7-9/5-9/8 | thrush | 1/1-9/8-10/7-11/7-9/5 | 1/1-14/11-7/5-8/5-16/9 | 1/1-11/10-5/4-7/5-11/7 | 1/1-8/7-14/11-10/7-11/6 | 1/1-10/9-5/4-8/5-7/4 |
| 46 | 0-8-11-13-18 | 1-10/7-18/11-9/5-9/8 | thrush | 1/1-9/8-10/7-18/11-9/5 | 1/1-14/11-16/11-8/5-16/9 | 1/1-8/7-5/4-7/5-11/7 | 1/1-11/10-11/9-11/8-7/4 | 1/1-10/9-5/4-8/5-11/6 |
| 47 | 0-9-11-13-18 | 1-3/2-18/11-9/5-9/8 | utonal | 1/1-9/8-3/2-18/11-9/5 | 1/1-4/3-16/11-8/5-16/9 | 1/1-11/10-6/5-4/3-3/2 | 1/1-11/10-11/9-11/8-11/6 | 1/1-10/9-5/4-5/3-11/6 |
| 48 | 0-3-8-10-21 | 1-8/7-10/7-11/7-9/7 | otonal | 1/1-8/7-9/7-10/7-11/7 | 1/1-9/8-5/4-11/8-7/4 | 1/1-10/9-11/9-14/9-16/9 | 1/1-11/10-7/5-8/5-9/5 | 1/1-14/11-16/11-18/11-11/6 |
| 49 | 0-3-8-11-21 | 1-8/7-10/7-18/11-9/7 | werckismic | 1/1-8/7-9/7-10/7-18/11 | 1/1-9/8-5/4-10/7-7/4 | 1/1-10/9-14/11-14/9-16/9 | 1/1-8/7-7/5-8/5-9/5 | 1/1-11/9-7/5-11/7-7/4 |
| 50 | 0-3-8-12-21 | 1-8/7-10/7-12/7-9/7 | otonal | 1/1-8/7-9/7-10/7-12/7 | 1/1-9/8-5/4-3/2-7/4 | 1/1-10/9-4/3-14/9-16/9 | 1/1-6/5-7/5-8/5-9/5 | 1/1-7/6-4/3-3/2-5/3 |
| 51 | 0-3-10-12-21 | 1-8/7-11/7-12/7-9/7 | otonal | 1/1-8/7-9/7-11/7-12/7 | 1/1-9/8-11/8-3/2-7/4 | 1/1-11/9-4/3-14/9-16/9 | 1/1-11/10-14/11-16/11-18/11 | 1/1-7/6-4/3-3/2-11/6 |
| 52 | 0-8-10-12-21 | 1-10/7-11/7-12/7-9/7 | otonal | 1/1-9/7-10/7-11/7-12/7 | 1/1-10/9-11/9-4/3-14/9 | 1/1-11/10-6/5-7/5-9/5 | 1/1-11/10-14/11-18/11-11/6 | 1/1-7/6-3/2-5/3-11/6 |
| 53 | 0-3-8-13-21 | 1-8/7-10/7-9/5-9/7 | thrush | 1/1-8/7-9/7-10/7-9/5 | 1/1-9/8-5/4-11/7-7/4 | 1/1-10/9-7/5-14/9-16/9 | 1/1-5/4-7/5-8/5-9/5 | 1/1-10/9-14/11-10/7-8/5 |
| 54 | 0-3-10-13-21 | 1-8/7-11/7-9/5-9/7 | werckismic | 1/1-8/7-9/7-11/7-9/5 | 1/1-9/8-11/8-11/7-7/4 | 1/1-11/9-7/5-14/9-16/9 | 1/1-8/7-14/11-16/11-18/11 | 1/1-10/9-14/11-10/7-7/4 |
| 55 | 0-8-10-13-21 | 1-10/7-11/7-9/5-9/7 | thrush | 1/1-9/7-10/7-11/7-9/5 | 1/1-10/9-11/9-7/5-14/9 | 1/1-11/10-5/4-7/5-9/5 | 1/1-8/7-14/11-18/11-11/6 | 1/1-10/9-10/7-8/5-7/4 |
| 56 | 0-3-11-13-21 | 1-8/7-18/11-9/5-9/7 | werckismic | 1/1-8/7-9/7-18/11-9/5 | 1/1-9/8-10/7-11/7-7/4 | 1/1-14/11-7/5-14/9-16/9 | 1/1-11/10-11/9-7/5-11/7 | 1/1-10/9-14/11-10/7-11/6 |
| 57 | 0-8-11-13-21 | 1-10/7-18/11-9/5-9/7 | thrush | 1/1-9/7-10/7-18/11-9/5 | 1/1-10/9-14/11-7/5-14/9 | 1/1-8/7-5/4-7/5-9/5 | 1/1-11/10-11/9-11/7-7/4 | 1/1-10/9-10/7-8/5-11/6 |
| 58 | 0-9-11-13-21 | 1-3/2-18/11-9/5-9/7 | utonal | 1/1-9/7-3/2-18/11-9/5 | 1/1-7/6-14/11-7/5-14/9 | 1/1-11/10-6/5-4/3-12/7 | 1/1-11/10-11/9-11/7-11/6 | 1/1-10/9-10/7-5/3-11/6 |
| 59 | 0-8-10-18-21 | 1-10/7-11/7-9/8-9/7 | werckismic | 1/1-9/8-9/7-10/7-11/7 | 1/1-8/7-14/11-7/5-16/9 | 1/1-10/9-11/9-14/9-7/4 | 1/1-11/10-7/5-11/7-9/5 | 1/1-14/11-10/7-18/11-11/6 |
| 60 | 0-8-11-18-21 | 1-10/7-18/11-9/8-9/7 | werckismic | 1/1-9/8-9/7-10/7-18/11 | 1/1-8/7-14/11-16/11-16/9 | 1/1-10/9-14/11-14/9-7/4 | 1/1-8/7-7/5-11/7-9/5 | 1/1-11/9-11/8-11/7-7/4 |
| 61 | 0-9-11-18-21 | 1-3/2-18/11-9/8-9/7 | utonal | 1/1-9/8-9/7-3/2-18/11 | 1/1-8/7-4/3-16/11-16/9 | 1/1-7/6-14/11-14/9-7/4 | 1/1-11/10-4/3-3/2-12/7 | 1/1-11/9-11/8-11/7-11/6 |
| 62 | 0-8-13-18-21 | 1-10/7-9/5-9/8-9/7 | thrush | 1/1-9/8-9/7-10/7-9/5 | 1/1-8/7-14/11-8/5-16/9 | 1/1-10/9-7/5-14/9-7/4 | 1/1-5/4-7/5-11/7-9/5 | 1/1-10/9-5/4-10/7-8/5 |
| 63 | 0-9-13-18-21 | 1-3/2-9/5-9/8-9/7 | utonal | 1/1-9/8-9/7-3/2-9/5 | 1/1-8/7-4/3-8/5-16/9 | 1/1-7/6-7/5-14/9-7/4 | 1/1-6/5-4/3-3/2-12/7 | 1/1-10/9-5/4-10/7-5/3 |
| 64 | 0-10-13-18-21 | 1-11/7-9/5-9/8-9/7 | werckismic | 1/1-9/8-9/7-11/7-9/5 | 1/1-8/7-7/5-8/5-16/9 | 1/1-11/9-7/5-14/9-7/4 | 1/1-8/7-14/11-10/7-18/11 | 1/1-10/9-5/4-10/7-7/4 |
| 65 | 0-11-13-18-21 | 1-18/11-9/5-9/8-9/7 | utonal | 1/1-9/8-9/7-18/11-9/5 | 1/1-8/7-16/11-8/5-16/9 | 1/1-14/11-7/5-14/9-7/4 | 1/1-11/10-11/9-11/8-11/7 | 1/1-10/9-5/4-10/7-11/6 |
Hexads
| Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | 3rd inversion | 4th inversion | 5th inversion |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0-2-4-7-9-11 | 1-11/10-6/5-11/8-3/2-18/11 | zeus | 1/1-11/10-6/5-11/8-3/2-18/11 | 1/1-11/10-5/4-11/8-3/2-11/9 | 1/1-8/7-5/4-11/8-5/3-11/6 | 1/1-11/10-6/5-16/11-8/5-7/4 | 1/1-11/10-4/3-16/11-8/5-11/6 | 1/1-11/9-4/3-16/11-5/3-11/6 |
| 2 | 0-2-4-7-9-12 | 1-11/10-6/5-11/8-3/2-12/7 | zeus | 1/1-11/10-6/5-11/8-3/2-12/7 | 1/1-11/10-5/4-11/8-11/7-7/6 | 1/1-8/7-5/4-10/7-5/3-11/6 | 1/1-11/10-5/4-16/11-8/5-7/4 | 1/1-8/7-4/3-16/11-8/5-11/6 | 1/1-7/6-14/11-7/5-8/5-7/4 |
| 3 | 0-2-5-7-9-12 | 1-11/10-5/4-11/8-3/2-12/7 | zeus | 1/1-11/10-5/4-11/8-3/2-12/7 | 1/1-8/7-5/4-11/8-11/7-7/6 | 1/1-11/10-6/5-11/8-8/5-7/4 | 1/1-11/10-5/4-16/11-8/5-11/6 | 1/1-8/7-4/3-16/11-5/3-11/6 | 1/1-7/6-14/11-16/11-8/5-7/4 |
| 4 | 0-2-5-7-10-12 | 1-11/10-5/4-11/8-11/7-12/7 | zeus | 1/1-11/10-5/4-11/8-11/7-12/7 | 1/1-8/7-5/4-10/7-11/7-7/6 | 1/1-11/10-5/4-11/8-8/5-7/4 | 1/1-8/7-5/4-16/11-8/5-11/6 | 1/1-11/10-14/11-7/5-8/5-7/4 | 1/1-7/6-14/11-16/11-8/5-11/6 |
| 5 | 0-3-5-7-10-12 | 1-8/7-5/4-11/8-11/7-12/7 | zeus | 1/1-8/7-5/4-11/8-11/7-12/7 | 1/1-11/10-6/5-11/8-3/2-7/6 | 1/1-11/10-5/4-11/8-8/5-11/6 | 1/1-8/7-5/4-16/11-5/3-11/6 | 1/1-11/10-14/11-16/11-8/5-7/4 | 1/1-7/6-4/3-16/11-8/5-11/6 |
| 6 | 0-3-5-8-10-12 | 1-8/7-5/4-10/7-11/7-12/7 | zeus | 1/1-8/7-5/4-10/7-11/7-12/7 | 1/1-11/10-5/4-11/8-3/2-7/6 | 1/1-8/7-5/4-11/8-8/5-11/6 | 1/1-11/10-6/5-7/5-8/5-7/4 | 1/1-11/10-14/11-16/11-8/5-11/6 | 1/1-7/6-4/3-16/11-5/3-11/6 |
| 7 | 0-3-5-8-10-13 | 1-8/7-5/4-10/7-11/7-9/5 | thrush | 1/1-8/7-5/4-10/7-11/7-9/5 | 1/1-11/10-5/4-11/8-11/7-10/9 | 1/1-8/7-5/4-10/7-8/5-11/6 | 1/1-11/10-5/4-7/5-8/5-7/4 | 1/1-8/7-14/11-16/11-8/5-11/6 | 1/1-10/9-14/11-7/5-8/5-7/4 |
| 8 | 0-2-4-9-11-13 | 1-11/10-6/5-3/2-18/11-9/5 | biyatismic | 1/1-11/10-6/5-3/2-18/11-9/5 | 1/1-11/10-11/8-3/2-18/11-10/9 | 1/1-5/4-11/8-3/2-5/3-11/6 | 1/1-11/10-6/5-4/3-16/11-8/5 | 1/1-11/10-11/9-4/3-16/11-11/6 | 1/1-10/9-11/9-4/3-5/3-11/6 |
| 9 | 0-5-8-10-13-18 | 1-5/4-10/7-11/7-9/5-9/8 | thrush | 1/1-9/8-5/4-10/7-11/7-9/5 | 1/1-10/9-14/11-7/5-8/5-10/9 | 1/1-8/7-5/4-10/7-8/5-9/5 | 1/1-11/10-5/4-7/5-11/7-7/4 | 1/1-8/7-14/11-10/7-8/5-11/6 | 1/1-10/9-5/4-7/5-8/5-7/4 |
| 10 | 0-3-8-10-12-21 | 1-8/7-10/7-11/7-12/7-9/7 | otonal | 1/1-8/7-9/7-10/7-11/7-12/7 | 1/1-9/8-5/4-11/8-3/2-7/6 | 1/1-10/9-11/9-4/3-14/9-16/9 | 1/1-11/10-6/5-7/5-8/5-9/5 | 1/1-11/10-14/11-16/11-18/11-11/6 | 1/1-7/6-4/3-3/2-5/3-11/6 |
| 11 | 0-3-8-10-13-21 | 1-8/7-10/7-11/7-9/5-9/7 | thrush | 1/1-8/7-9/7-10/7-11/7-9/5 | 1/1-9/8-5/4-11/8-11/7-10/9 | 1/1-10/9-11/9-7/5-14/9-16/9 | 1/1-11/10-5/4-7/5-8/5-9/5 | 1/1-8/7-14/11-16/11-18/11-11/6 | 1/1-10/9-14/11-10/7-8/5-7/4 |
| 12 | 0-3-8-11-13-21 | 1-8/7-10/7-18/11-9/5-9/7 | thrush | 1/1-8/7-9/7-10/7-18/11-9/5 | 1/1-9/8-5/4-10/7-11/7-10/9 | 1/1-10/9-14/11-7/5-14/9-16/9 | 1/1-8/7-5/4-7/5-8/5-9/5 | 1/1-11/10-11/9-7/5-11/7-7/4 | 1/1-10/9-14/11-10/7-8/5-11/6 |
| 13 | 0-8-10-13-18-21 | 1-10/7-11/7-9/5-9/8-9/7 | thrush | 1/1-9/8-9/7-10/7-11/7-9/5 | 1/1-8/7-14/11-7/5-8/5-10/9 | 1/1-10/9-11/9-7/5-14/9-7/4 | 1/1-11/10-5/4-7/5-11/7-9/5 | 1/1-8/7-14/11-10/7-18/11-11/6 | 1/1-10/9-5/4-10/7-8/5-7/4 |
| 14 | 0-8-11-13-18-21 | 1-10/7-18/11-9/5-9/8-9/7 | thrush | 1/1-9/8-9/7-10/7-18/11-9/5 | 1/1-8/7-14/11-16/11-8/5-10/9 | 1/1-10/9-14/11-7/5-14/9-7/4 | 1/1-8/7-5/4-7/5-11/7-9/5 | 1/1-11/10-11/9-11/8-11/7-7/4 | 1/1-10/9-5/4-10/7-8/5-11/6 |
| 15 | 0-9-11-13-18-21 | 1-3/2-18/11-9/5-9/8-9/7 | utonal | 1/1-9/8-9/7-3/2-18/11-9/5 | 1/1-8/7-4/3-16/11-8/5-10/9 | 1/1-7/6-14/11-7/5-14/9-7/4 | 1/1-11/10-6/5-4/3-3/2-12/7 | 1/1-11/10-11/9-11/8-11/7-11/6 | 1/1-10/9-5/4-10/7-5/3-11/6 |