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Jdfreivald (talk | contribs) Altered the explanation of the listing, broke out the Carlos Alpha stuff under its own heading, other minor tweaks. |
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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. | 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. | ||
(Note that this preference for 20/11 over 11/6 is only true for the "transversal" column. 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. | 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 [[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. | 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. | 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. | 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: | 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: | 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 | 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 == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
Revision as of 14:12, 16 February 2022
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. 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 | 1/1-8/7-20/11 | 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 | 1/1-8/5-20/11 |
| 4 | 0-2-7 | 1-11/10-11/8 | utonal | 1/1-11/10-11/8 | 1/1-5/4-20/11 | 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 | 1-12/11-3/2 | utonal | 1/1-12/11-3/2 | 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 | 1/1-41/31-11/6 |
| 15 | 0-2-10 | 1-11/10-11/7 | utonal | 1/1-11/10-11/7 | 1/1-10/7-11/6 | 1/1-68/53-7/5 |
| 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 | 1-12/11-18/11 | otonal | 1/1-12/11-18/11 | 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 | 1/1-97/80-11/6 |
| 26 | 0-2-12 | 1-12/11-12/7 | utonal | 1/1-12/11-12/7 | 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 | 1/1-12/11-14/11 | 1/1-7/6-146/79 |
| 34 | 0-2-13 | 1-11/10-9/5 | otonal | 1/1-11/10-9/5 | 1/1-18/11-20/11 | 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 | 1-12/11-6/5-3/2 | utonal | 1/1-12/11-6/5-3/2 | 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 | 1-12/11-3/2-18/11 | ambitonal | 1/1-12/11-3/2-18/11 | 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 | 1-12/11-6/5-12/7 | utonal | 1/1-12/11-6/5-12/7 | 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 | 1-12/11-3/2-12/7 | utonal | 1/1-12/11-3/2-12/7 | 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 |
|---|---|---|---|
| 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
| 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 |