Hemififths/Chords
Below are listed the dyadic chords of 11-limit hemififths temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 896/891 pentacircle, by 243/242 rastmic, and by 1344/1331 hemimin. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove. Those requiring both 441/440 and 896/891 are labeled pele. Those requiring any two of 243/242, 896/891 or 1344/1331 are labeled parahemif. If the full hemififths is required because of the tempering out of three independent hemififths commas, the chord is labeled "hemififths".
A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.
Chords are named with ups and downs, using pergen #4 (P8, P5/2) in the notation guide for rank-2 pergens. One up is 7 generators. The tilde ~ means mid, half-way between major and minor. ~4 = ^4 = vA4 and ~5 = v5 = ^d5. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add 7". To facilitate chord naming, lifts and drops are also used. Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c, where c = the amount in cents the tempered fifth exceeds 700¢. /1 = ~81/80 = ~64/63 and ^1 = ~33/32. To convert to 41edo, ^1 = 2\41 and /1 = 1\41.
| Genspan | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ... | 20 | 21 | ... | 23 | ... | 25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cents (41edo) | 0 | 351 | 702 | 1054 | 205 | 556 | 907 | 59 | 410 | 761 | 1112 | 263 | 615 | 966 | 1024 | 176 | 878 | 380 | |||
| Ratio | 1/1 | 11/9
16/13 |
3/2 | 11/6
24/13 |
9/8 | 11/8
18/13 |
27/16
22/13 |
28/27
33/32 |
14/11 | 14/9 | 40/21
21/11 |
7/6 | 10/7 | 7/4 | 20/11 | 10/9 | 5/3 | 5/4 | |||
| Interval | P1 | ~3 | P5 | ~7 | M2 | ~4
\b5 |
M6 | ^1
\m2 |
M3 | ^5
\m6 |
M7 | ^M2
\m3 |
A4
\~5 |
^M6
\m7 |
A6
\~7 |
^A1
\M2 |
^A5
\M6 |
^A2
\M3 |
TODO: Complete the tables
Triads
| # | Chord | Transversal | Type | Name | Inversion |
|---|---|---|---|---|---|
| 1 | 0-1-2 | 1-11/9-3/2 | rastmic | ~ | |
| 2 | 0-1-3 | 1-11/9-11/6 | utonal | ~7no5 | |
| 3 | 0-2-3 | 1-3/2-11/6 | otonal | ~7no3 | |
| 4 | 0-1-4 | 1-11/9-9/8 | rastmic | ~,9no5 | |
| 5 | 0-2-4 | 1-3/2-9/8 | ambitonal | 2 or 4 | 1-4/3-9/8 |
| 6 | 0-3-4 | 1-11/6-9/8 | rastmic | ~9no35 | |
| 7 | 0-1-5 | 1-11/9-11/8 | utonal | ~(\b5) | |
| 8 | 0-2-5 | 1-3/2-11/8 | otonal | ~7sus4no5 | 1-4/3-11/6 |
| 9 | 0-3-5 | 1-11/6-11/8 | utonal | ~2 | 1-12/11-3/2 |
| 10 | 0-4-5 | 1-9/8-11/8 | otonal | ~,7no5 | 1-11/9-16/9 |
| 11 | 0-3-8 | 1-11/6-14/11 | hemimin | ,~7no5 | |
| 12 | 0-4-8 | 1-9/8-14/11 | pentacircle | ,9no5 | |
| 13 | 0-5-8 | 1-11/8-14/11 | hemimin | (\b5) | |
| 14 | 0-1-9 | 1-11/9-14/9 | otonal | ~(^5) | |
| 15 | 0-4-9 | 1-9/8-14/9 | pentacircle | 7~4no5 | 1-11/8-16/9 |
| 16 | 0-5-9 | 1-11/8-14/9 | pentacircle | 2(~5) or
/,7no5 |
1-9/8-13/9
1-9/7-16/9 |
| 17 | 0-8-9 | 1-14/11-14/9 | utonal | (^5) | |
| 18 | 0-2-11 | 1-3/2-7/6 | otonal | \m | |
| 19 | 0-3-11 | 1-11/6-7/6 | otonal | \m~7no5 | |
| 20 | 0-8-11 | 1-14/11-7/6 | utonal | ~2/6 | 1-12/11-12/7 |
| 21 | 0-9-11 | 1-14/9-7/6 | utonal | / | 1-9/7-3/2 |
| 22 | 0-1-12 | 1-11/9-10/7 | swetismic | ~(\~5) | |
| 23 | 0-3-12 | 1-11/6-10/7 | swetismic | /(b5) | 1-9/7-7/5 |
| 24 | 0-4-12 | 1-9/8-10/7 | werckismic | 2(\~5) | |
| 25 | 0-8-12 | 1-14/11-10/7 | werckismic | (\~5) | |
| 26 | 0-9-12 | 1-14/9-10/7 | swetismic | ~2(b5) | 1-12/11-7/5 |
| 27 | 0-11-12 | 1-7/6-10/7 | swetismic | \m(\~5) | |
| 28 | 0-1-13 | 1-11/9-7/4 | werckismic | ~,\7no5 | |
| 29 | 0-2-13 | 1-3/2-7/4 | otonal | \7no3 | |
| 30 | 0-4-13 | 1-9/8-7/4 | otonal | \9no35 | |
| 31 | 0-5-13 | 1-11/8-7/4 | otonal | (~5) | 1-14/11-16/11 |
| 32 | 0-8-13 | 1-14/11-7/4 | utonal | ,\7 | |
| 33 | 0-9-13 | 1-14/9-7/4 | utonal | /,2no5 | 1-9/8-9/7 |
| 34 | 0-11-13 | 1-7/6-7/4 | utonal | \m7no5 | |
| 35 | 0-12-13 | 1-10/7-7/4 | werckismic | ~(b5) | 1-11/9-7/5 |
| 36 | 0-8-20 | 1-14/11-20/11 | otonal | ,\~7no5 | |
| 37 | 0-9-20 | 1-14/9-20/11 | swetismic | ||
| 38 | 0-11-20 | 1-7/6-20/11 | swetismic | \m\~7no5 | |
| 39 | 0-12-20 | 1-10/7-20/11 | utonal | (b5) | |
| 40 | 0-1-21 | 1-11/9-10/9 | otonal | ~,\9no5 | |
| 41 | 0-8-21 | 1-14/11-10/9 | werckismic | ,\9no5 | |
| 42 | 0-9-21 | 1-14/9-10/9 | otonal | /(\~5) | 1-9/7-10/7 |
| 43 | 0-12-21 | 1-10/7-10/9 | utonal | \2(\~5) | |
| 44 | 0-13-21 | 1-7/4-10/9 | werckismic | \2\m7no5 | |
| 45 | 0-20-21 | 1-20/11-10/9 | utonal | ||
| 46 | 0-2-23 | 1-3/2-5/3 | otonal | \m7no5 | 1-6/5-9/5 |
| 47 | 0-3-23 | 1-11/6-5/3 | otonal | ||
| 48 | 0-11-23 | 1-7/6-5/3 | otonal | \m6no5 | |
| 49 | 0-12-23 | 1-10/7-5/3 | utonal | /dim | 1-7/6-7/5 |
| 50 | 0-20-23 | 1-20/11-5/3 | utonal | ||
| 51 | 0-21-23 | 1-10/9-5/3 | utonal | /7no3 | 1-3/2-9/5 |
| 52 | 0-2-25 | 1-3/2-5/4 | otonal | \ | |
| 53 | 0-4-25 | 1-9/8-5/4 | otonal | \,9no5 | |
| 54 | 0-5-25 | 1-11/8-5/4 | otonal | \(\b5) | |
| 55 | 0-12-25 | 1-10/7-5/4 | utonal | \(\~5) | |
| 56 | 0-13-25 | 1-7/4-5/4 | otonal | \7no5 | |
| 57 | 0-20-25 | 1-20/11-5/4 | utonal | \,\~7no5 | |
| 58 | 0-21-25 | 1-10/9-5/4 | utonal | /9no35 | 1-9/5-9/4 |
| 59 | 0-23-25 | 1-5/3-5/4 | utonal | /m | 1-6/5-3/2 |
Tetrads
| # | Chord | Transversal | Type | Name | Inversion |
|---|---|---|---|---|---|
| 1 | 0-1-2-3 | 1-11/9-3/2-11/6 | rastmic | ~7 | |
| 2 | 0-1-2-4 | 1-11/9-3/2-9/8 | rastmic | ~,9 | |
| 3 | 0-1-3-4 | 1-11/9-11/6-9/8 | rastmic | ~9no5 | |
| 4 | 0-2-3-4 | 1-3/2-11/6-9/8 | rastmic | ~9no3 | |
| 5 | 0-1-2-5 | 1-11/9-3/2-11/8 | rastmic | ~,~11 | |
| 6 | 0-1-3-5 | 1-11/9-11/6-11/8 | utonal | 2~6 or
4~9 |
1-9/8-3/2-13/8
1-4/3-3/2-24/11 |
| 7 | 0-2-3-5 | 1-3/2-11/6-11/8 | ambitonal | ~4~7 | |
| 8 | 0-1-4-5 | 1-11/9-9/8-11/8 | rastmic | ||
| 9 | 0-2-4-5 | 1-3/2-9/8-11/8 | otonal | 4~7 | 1-4/3-3/2-11/6 |
| 10 | 0-3-4-5 | 1-11/6-9/8-11/8 | rastmic | ~11no35 | |
| 11 | 0-3-4-8 | 1-11/6-9/8-14/11 | parahemif | 9(~7)no5 | |
| 12 | 0-3-5-8 | 1-11/6-11/8-14/11 | hemimin | ~2~11 | 1-12/11-11/8-3/2 |
| 13 | 0-4-5-8 | 1-9/8-11/8-14/11 | parahemif | ~,~9 | 1-11/9-3/2-13/12 |
| 14 | 0-1-4-9 | 1-11/9-9/8-14/9 | parahemif | ~,9(^5) | |
| 15 | 0-1-5-9 | 1-11/9-11/8-14/9 | pentacircle | ,~6,9no5 | 1-14/11-18/11-9/4 |
| 16 | 0-4-5-9 | 1-9/8-11/8-14/9 | pentacircle | ~,7(\b5) | 1-11/9-11/8-16/9 |
| 17 | 0-4-8-9 | 1-9/8-14/11-14/9 | pentacircle | ||
| 18 | 0-5-8-9 | 1-11/8-14/11-14/9 | parahemif | ||
| 19 | 0-2-3-11 | 1-3/2-11/6-7/6 | otonal | \m~7 | |
| 20 | 0-3-8-11 | 1-11/6-14/11-7/6 | hemimin | ||
| 21 | 0-8-9-11 | 1-14/11-14/9-7/6 | utonal | /,~6 | 1-9/7-3/2-18/11 |
| 22 | 0-1-3-12 | 1-11/9-11/6-10/7 | swetismic | \m~6 | 1-7/6-3/2-13/8 |
| 23 | 0-1-4-12 | 1-11/9-9/8-10/7 | jove | ||
| 24 | 0-3-4-12 | 1-11/6-9/8-10/7 | jove | ||
| 25 | 0-3-8-12 | 1-11/6-14/11-10/7 | hemififths | ||
| 26 | 0-4-8-12 | 1-9/8-14/11-10/7 | pele | 9no5 | 1-9/8-14/11-16/9 |
| 27 | 0-1-9-12 | 1-11/9-14/9-10/7 | swetismic | ||
| 28 | 0-4-9-12 | 1-9/8-14/9-10/7 | hemififths | ||
| 29 | 0-8-9-12 | 1-14/11-14/9-10/7 | jove | ||
| 30 | 0-3-11-12 | 1-11/6-7/6-10/7 | swetismic | ||
| 31 | 0-8-11-12 | 1-14/11-7/6-10/7 | jove | ||
| 32 | 0-9-11-12 | 1-14/9-7/6-10/7 | swetismic | ||
| 33 | 0-1-2-13 | 1-11/9-3/2-7/4 | jove | ~,\7 | |
| 34 | 0-1-4-13 | 1-11/9-9/8-7/4 | jove | ||
| 35 | 0-2-4-13 | 1-3/2-9/8-7/4 | otonal | \9no3 | |
| 36 | 0-1-5-13 | 1-11/9-11/8-7/4 | werckismic | ||
| 37 | 0-2-5-13 | 1-3/2-11/8-7/4 | otonal | ~4,\7 | |
| 38 | 0-4-5-13 | 1-9/8-11/8-7/4 | otonal | ~4\7,9 or ~,7(^5) | 1-11/9-14/9-16/9 |
| 39 | 0-4-8-13 | 1-9/8-14/11-7/4 | pentacircle | ||
| 40 | 0-5-8-13 | 1-11/8-14/11-7/4 | hemimin | ||
| 41 | 0-1-9-13 | 1-11/9-14/9-7/4 | werckismic | ||
| 42 | 0-4-9-13 | 1-9/8-14/9-7/4 | pentacircle | ||
| 43 | 0-5-9-13 | 1-11/8-14/9-7/4 | pentacircle | ||
| 44 | 0-8-9-13 | 1-14/11-14/9-7/4 | utonal | ||
| 45 | 0-2-11-13 | 1-3/2-7/6-7/4 | ambitonal | \m7 | |
| 46 | 0-8-11-13 | 1-14/11-7/6-7/4 | utonal | ||
| 47 | 0-9-11-13 | 1-14/9-7/6-7/4 | utonal | /,9 | 1-9/7-3/2-9/4 |
| 48 | 0-1-12-13 | 1-11/9-10/7-7/4 | jove | ||
| 49 | 0-4-12-13 | 1-9/8-10/7-7/4 | werckismic | ||
| 50 | 0-8-12-13 | 1-14/11-10/7-7/4 | werckismic | ||
| 51 | 0-9-12-13 | 1-14/9-10/7-7/4 | jove | ||
| 52 | 0-11-12-13 | 1-7/6-10/7-7/4 | jove | ~,/6 | 1-11/9-3/2-12/7 |
| 53 | 0-8-9-20 | 1-14/11-14/9-20/11 | swetismic | ||
| 54 | 0-8-11-20 | 1-14/11-7/6-20/11 | swetismic | ||
| 55 | 0-9-11-20 | 1-14/9-7/6-20/11 | swetismic | ||
| 56 | 0-8-12-20 | 1-14/11-10/7-20/11 | werckismic | ||
| 57 | 0-9-12-20 | 1-14/9-10/7-20/11 | swetismic | ||
| 58 | 0-11-12-20 | 1-7/6-10/7-20/11 | swetismic | ||
| 59 | 0-1-9-21 | 1-11/9-14/9-10/9 | otonal | ||
| 60 | 0-8-9-21 | 1-14/11-14/9-10/9 | werckismic | ||
| 61 | 0-1-12-21 | 1-11/9-10/7-10/9 | swetismic | ||
| 62 | 0-8-12-21 | 1-14/11-10/7-10/9 | werckismic | ||
| 63 | 0-9-12-21 | 1-14/9-10/7-10/9 | swetismic | ||
| 64 | 0-1-13-21 | 1-11/9-7/4-10/9 | werckismic | ||
| 65 | 0-8-13-21 | 1-14/11-7/4-10/9 | werckismic | ||
| 66 | 0-9-13-21 | 1-14/9-7/4-10/9 | werckismic | ||
| 67 | 0-12-13-21 | 1-10/7-7/4-10/9 | werckismic | ||
| 68 | 0-8-20-21 | 1-14/11-20/11-10/9 | werckismic | ||
| 69 | 0-9-20-21 | 1-14/9-20/11-10/9 | swetismic | ||
| 70 | 0-12-20-21 | 1-10/7-20/11-10/9 | utonal | ||
| 71 | 0-2-3-23 | 1-3/2-11/6-5/3 | otonal | ||
| 72 | 0-2-11-23 | 1-3/2-7/6-5/3 | otonal | \m6 | |
| 73 | 0-3-11-23 | 1-11/6-7/6-5/3 | otonal | \m6~7no5 | |
| 74 | 0-3-12-23 | 1-11/6-10/7-5/3 | swetismic | ||
| 75 | 0-11-12-23 | 1-7/6-10/7-5/3 | swetismic | \m6(\~5) | |
| 76 | 0-11-20-23 | 1-7/6-20/11-5/3 | swetismic | ||
| 77 | 0-12-20-23 | 1-10/7-20/11-5/3 | utonal | ||
| 78 | 0-12-21-23 | 1-10/7-10/9-5/3 | utonal | /7 | 1-9/7-3/2-9/5 |
| 79 | 0-20-21-23 | 1-20/11-10/9-5/3 | utonal | /7~13no3 | 1-3/2-18/11-9/5 |
| 80 | 0-2-4-25 | 1-3/2-9/8-5/4 | otonal | \,9 | |
| 81 | 0-2-5-25 | 1-3/2-11/8-5/4 | otonal | \,~11 | |
| 82 | 0-4-5-25 | 1-9/8-11/8-5/4 | otonal | \,9(\b5) | |
| 83 | 0-4-12-25 | 1-9/8-10/7-5/4 | werckismic | ,9(\~5) | |
| 84 | 0-2-13-25 | 1-3/2-7/4-5/4 | otonal | \7 | |
| 85 | 0-4-13-25 | 1-9/8-7/4-5/4 | otonal | \9no5 | |
| 86 | 0-5-13-25 | 1-11/8-7/4-5/4 | otonal | \7~11no5 | |
| 87 | 0-12-13-25 | 1-10/7-7/4-5/4 | werckismic | \7(\~5) | |
| 88 | 0-12-20-25 | 1-10/7-20/11-5/4 | utonal | ,\7(b5) | 1-14/11-7/5-7/4 |
| 89 | 0-12-21-25 | 1-10/7-10/9-5/4 | utonal | /9no5 | 1-9/7-9/5-9/4 |
| 90 | 0-13-21-25 | 1-7/4-10/9-5/4 | werckismic | \7\9no5 | |
| 91 | 0-20-21-25 | 1-20/11-10/9-5/4 | utonal | 2~6^7no5 | 1-18/11-9/5-9/4 |
| 92 | 0-2-23-25 | 1-3/2-5/3-5/4 | ambitonal | \6 or /m7 | 1-6/5-3/2-9/5 |
| 93 | 0-12-23-25 | 1-10/7-5/3-5/4 | utonal | /m6
\m7(b5) |
1-6/5-3/2-12/7
1-7/6-7/5-7/4 |
| 94 | 0-20-23-25 | 1-20/11-5/3-5/4 | utonal | /m,~9 | 1-6/5-3/2-12/11 |
| 95 | 0-21-23-25 | 1-10/9-5/3-5/4 | utonal | /9no3 | 1-3/2-9/5-9/4 |
Pentads
| # | Chord | Transversal | Type | Name | Inversion |
|---|---|---|---|---|---|
| 1 | 0-1-2-3-4 | 1-11/9-3/2-11/6-9/8 | rastmic | ~9 | |
| 2 | 0-1-2-3-5 | 1-11/9-3/2-11/6-11/8 | rastmic | ~11no9 | |
| 3 | 0-1-2-4-5 | 1-11/9-3/2-9/8-11/8 | rastmic | ~11no7 | |
| 4 | 0-1-3-4-5 | 1-11/9-11/6-9/8-11/8 | rastmic | ~11no5 | |
| 5 | 0-2-3-4-5 | 1-3/2-11/6-9/8-11/8 | rastmic | ~11no3 | |
| 6 | 0-3-4-5-8 | 1-11/6-9/8-11/8-14/11 | parahemif | ||
| 7 | 0-1-4-5-9 | 1-11/9-9/8-11/8-14/9 | parahemif | ||
| 8 | 0-4-5-8-9 | 1-9/8-11/8-14/11-14/9 | parahemif | ||
| 9 | 0-1-3-4-12 | 1-11/9-11/6-9/8-10/7 | jove | ||
| 10 | 0-3-4-8-12 | 1-11/6-9/8-14/11-10/7 | hemififths | ||
| 11 | 0-1-4-9-12 | 1-11/9-9/8-14/9-10/7 | hemififths | ||
| 12 | 0-4-8-9-12 | 1-9/8-14/11-14/9-10/7 | hemififths | ||
| 13 | 0-3-8-11-12 | 1-11/6-14/11-7/6-10/7 | hemififths | ||
| 14 | 0-8-9-11-12 | 1-14/11-14/9-7/6-10/7 | jove | ||
| 15 | 0-1-2-4-13 | 1-11/9-3/2-9/8-7/4 | jove | ~9(\m7) | |
| 16 | 0-1-2-5-13 | 1-11/9-3/2-11/8-7/4 | jove | ||
| 17 | 0-1-4-5-13 | 1-11/9-9/8-11/8-7/4 | jove | ||
| 18 | 0-2-4-5-13 | 1-3/2-9/8-11/8-7/4 | otonal | \9~11no3 | |
| 19 | 0-4-5-8-13 | 1-9/8-11/8-14/11-7/4 | parahemif | ||
| 20 | 0-1-4-9-13 | 1-11/9-9/8-14/9-7/4 | hemififths | ||
| 21 | 0-1-5-9-13 | 1-11/9-11/8-14/9-7/4 | pele | ||
| 22 | 0-4-5-9-13 | 1-9/8-11/8-14/9-7/4 | pentacircle | ||
| 23 | 0-4-8-9-13 | 1-9/8-14/11-14/9-7/4 | pentacircle | ||
| 24 | 0-5-8-9-13 | 1-11/8-14/11-14/9-7/4 | parahemif | ||
| 25 | 0-8-9-11-13 | 1-14/11-14/9-7/6-7/4 | utonal | /,~6,9 | 1-9/7-3/2-18/11-9/4 |
| 26 | 0-1-4-12-13 | 1-11/9-9/8-10/7-7/4 | jove | ||
| 27 | 0-4-8-12-13 | 1-9/8-14/11-10/7-7/4 | pele | ||
| 28 | 0-1-9-12-13 | 1-11/9-14/9-10/7-7/4 | jove | ||
| 29 | 0-4-9-12-13 | 1-9/8-14/9-10/7-7/4 | hemififths | ||
| 30 | 0-8-9-12-13 | 1-14/11-14/9-10/7-7/4 | jove | ||
| 31 | 0-8-11-12-13 | 1-14/11-7/6-10/7-7/4 | jove | ||
| 32 | 0-9-11-12-13 | 1-14/9-7/6-10/7-7/4 | jove | ||
| 33 | 0-8-9-11-20 | 1-14/11-14/9-7/6-20/11 | swetismic | ||
| 34 | 0-8-9-12-20 | 1-14/11-14/9-10/7-20/11 | jove | ||
| 35 | 0-8-11-12-20 | 1-14/11-7/6-10/7-20/11 | jove | ||
| 36 | 0-9-11-12-20 | 1-14/9-7/6-10/7-20/11 | swetismic | ||
| 37 | 0-1-9-12-21 | 1-11/9-14/9-10/7-10/9 | swetismic | ||
| 38 | 0-8-9-12-21 | 1-14/11-14/9-10/7-10/9 | jove | ||
| 39 | 0-1-9-13-21 | 1-11/9-14/9-7/4-10/9 | werckismic | ||
| 40 | 0-8-9-13-21 | 1-14/11-14/9-7/4-10/9 | werckismic | ||
| 41 | 0-1-12-13-21 | 1-11/9-10/7-7/4-10/9 | jove | ||
| 42 | 0-8-12-13-21 | 1-14/11-10/7-7/4-10/9 | werckismic | ||
| 43 | 0-9-12-13-21 | 1-14/9-10/7-7/4-10/9 | jove | ||
| 44 | 0-8-9-20-21 | 1-14/11-14/9-20/11-10/9 | jove | ||
| 45 | 0-8-12-20-21 | 1-14/11-10/7-20/11-10/9 | werckismic | ||
| 46 | 0-9-12-20-21 | 1-14/9-10/7-20/11-10/9 | swetismic | ||
| 47 | 0-2-3-11-23 | 1-3/2-11/6-7/6-5/3 | otonal | \m6~7 | |
| 48 | 0-3-11-12-23 | 1-11/6-7/6-10/7-5/3 | swetismic | ||
| 49 | 0-11-12-20-23 | 1-7/6-10/7-20/11-5/3 | swetismic | ||
| 50 | 0-12-20-21-23 | 1-10/7-20/11-10/9-5/3 | utonal | /7~6 | 1-9/7-3/2-18/11-9/5 |
| 51 | 0-2-4-5-25 | 1-3/2-9/8-11/8-5/4 | otonal | \,9~11 | |
| 52 | 0-2-4-13-25 | 1-3/2-9/8-7/4-5/4 | otonal | \9 | |
| 53 | 0-2-5-13-25 | 1-3/2-11/8-7/4-5/4 | otonal | \7~11 | |
| 54 | 0-4-5-13-25 | 1-9/8-11/8-7/4-5/4 | otonal | \9~11no5 | |
| 55 | 0-4-12-13-25 | 1-9/8-10/7-7/4-5/4 | werckismic | \9(\~5) | |
| 56 | 0-12-13-21-25 | 1-10/7-7/4-10/9-5/4 | werckismic | ||
| 57 | 0-12-20-21-25 | 1-10/7-20/11-10/9-5/4 | utonal | /9~6no5 | 1-9/7-18/11-9/5-9/4 |
| 58 | 0-12-20-23-25 | 1-10/7-20/11-5/3-5/4 | utonal | /m6~9 | 1-6/5-3/2-12/7-13/6 |
| 59 | 0-12-21-23-25 | 1-10/7-10/9-5/3-5/4 | utonal | /9 | 1-9/7-3/2-9/5-9/4 |
| 60 | 0-20-21-23-25 | 1-20/11-10/9-5/3-5/4 | utonal | /9~6no3 | 1-3/2-18/11-9/5-9/4 |
Hexads
| # | Chord | Transversal | Type | Name | Inversion |
|---|---|---|---|---|---|
| 1 | 0-1-2-3-4-5 | 1-11/9-3/2-11/6-9/8-11/8 | rastmic | ~11 | |
| 2 | 0-1-2-4-5-13 | 1-11/9-3/2-9/8-11/8-7/4 | jove | ~11(\m7) | |
| 3 | 0-1-4-5-9-13 | 1-11/9-9/8-11/8-14/9-7/4 | hemififths | ||
| 4 | 0-4-5-8-9-13 | 1-9/8-11/8-14/11-14/9-7/4 | nofives | ||
| 5 | 0-1-4-9-12-13 | 1-11/9-9/8-14/9-10/7-7/4 | hemififths | ||
| 6 | 0-4-8-9-12-13 | 1-9/8-14/11-14/9-10/7-7/4 | hemififths | ||
| 7 | 0-8-9-11-12-13 | 1-14/11-14/9-7/6-10/7-7/4 | jove | ||
| 8 | 0-8-9-11-12-20 | 1-14/11-14/9-7/6-10/7-20/11 | jove | ||
| 9 | 0-1-9-12-13-21 | 1-11/9-14/9-10/7-7/4-10/9 | jove | ||
| 10 | 0-8-9-12-13-21 | 1-14/11-14/9-10/7-7/4-10/9 | jove | ||
| 11 | 0-8-9-12-20-21 | 1-14/11-14/9-10/7-20/11-10/9 | jove | ||
| 12 | 0-2-4-5-13-25 | 1-3/2-9/8-11/8-7/4-5/4 | otonal | \9~11 | |
| 13 | 0-12-20-21-23-25 | 1-10/7-20/11-10/9-5/3-5/4 | utonal | /9~6 | 1-9/7-3/2-18/11-9/5-9/4 |