Luna and hemithirds/Chords: Difference between revisions
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Below are listed the [[ | Below are listed the [[dyadic chord]]s of [[11-limit]] [[hemithirds]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic. | ||
Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS. | Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS. | ||
=Triads= | == Triads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-5 | |||
| 1-5/4-7/4 | |||
| otonal | |||
|- | |- | ||
| 2 | |||
| 0-3-5 | |||
| 1-7/5-7/4 | |||
| utonal | |||
|- | |- | ||
| 3 | |||
| 0-2-7 | |||
| 1-5/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 4 | |||
| 0-5-7 | |||
| 1-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 5 | |||
| 0-3-8 | |||
| 1-7/5-11/9 | |||
| werckismic | |||
|- | |- | ||
| 6 | |||
| 0-5-8 | |||
| 1-7/4-11/9 | |||
| werckismic | |||
|- | |- | ||
| 7 | |||
| 0-7-15 | |||
| 1-12/11-4/3 | |||
| utonal | |||
|- | |- | ||
| 8 | |||
| 0-8-15 | |||
| 1-11/9-4/3 | |||
| otonal | |||
|- | |- | ||
| 9 | |||
| 0-2-17 | |||
| 1-5/4-5/3 | |||
| utonal | |||
|- | |- | ||
| 10 | |||
| 0-15-17 | |||
| 1-4/3-5/3 | |||
| otonal | |||
|- | |- | ||
| 11 | |||
| 0-3-20 | |||
| 1-7/5-7/6 | |||
| utonal | |||
|- | |- | ||
| 12 | |||
| 0-5-20 | |||
| 1-7/4-7/6 | |||
| utonal | |||
|- | |- | ||
| 13 | |||
| 0-15-20 | |||
| 1-4/3-7/6 | |||
| otonal | |||
|- | |- | ||
| 14 | |||
| 0-17-20 | |||
| 1-5/3-7/6 | |||
| otonal | |||
|- | |- | ||
| 15 | |||
| 0-2-22 | |||
| 1-5/4-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 16 | |||
| 0-5-22 | |||
| 1-7/4-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 17 | |||
| 0-7-22 | |||
| 1-12/11-16/11 | |||
| otonal | |||
|- | |- | ||
| 18 | |||
| 0-15-22 | |||
| 1-4/3-16/11 | |||
| utonal | |||
|- | |- | ||
| 19 | |||
| 0-17-22 | |||
| 1-5/3-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 20 | |||
| 0-20-22 | |||
| 1-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 21 | |||
| 0-2-24 | |||
| 1-5/4-20/11 | |||
| utonal | |||
|- | |- | ||
| 22 | |||
| 0-7-24 | |||
| 1-12/11-20/11 | |||
| otonal | |||
|- | |- | ||
| 23 | |||
| 0-17-24 | |||
| 1-5/3-20/11 | |||
| utonal | |||
|- | |- | ||
| 24 | |||
| 0-22-24 | |||
| 1-16/11-20/11 | |||
| otonal | |||
|- | |- | ||
| 25 | |||
| 0-3-27 | |||
| 1-7/5-14/11 | |||
| utonal | |||
|- | |- | ||
| 26 | |||
| 0-5-27 | |||
| 1-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 27 | |||
| 0-7-27 | |||
| 1-12/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 28 | |||
| 0-20-27 | |||
| 1-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 29 | |||
| 0-22-27 | |||
| 1-16/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 30 | |||
| 0-24-27 | |||
| 1-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 31 | |||
| 0-3-30 | |||
| 1-7/5-16/9 | |||
| werckismic | |||
|- | |- | ||
| 32 | |||
| 0-8-30 | |||
| 1-11/9-16/9 | |||
| otonal | |||
|- | |- | ||
| 33 | |||
| 0-15-30 | |||
| 1-4/3-16/9 | |||
| ambitonal | |||
|- | |- | ||
| 34 | |||
| 0-22-30 | |||
| 1-16/11-16/9 | |||
| utonal | |||
|- | |- | ||
| 35 | |||
| 0-27-30 | |||
| 1-14/11-16/9 | |||
| werckismic | |||
|- | |- | ||
| 36 | |||
| 0-2-32 | |||
| 1-5/4-10/9 | |||
| utonal | |||
|- | |- | ||
| 37 | |||
| 0-5-32 | |||
| 1-7/4-10/9 | |||
| werckismic | |||
|- | |- | ||
| 38 | |||
| 0-8-32 | |||
| 1-11/9-10/9 | |||
| otonal | |||
|- | |- | ||
| 39 | |||
| 0-15-32 | |||
| 1-4/3-10/9 | |||
| otonal | |||
|- | |- | ||
| 40 | |||
| 0-17-32 | |||
| 1-5/3-10/9 | |||
| utonal | |||
|- | |- | ||
| 41 | |||
| 0-24-32 | |||
| 1-20/11-10/9 | |||
| utonal | |||
|- | |- | ||
| 42 | |||
| 0-27-32 | |||
| 1-14/11-10/9 | |||
| werckismic | |||
|- | |- | ||
| 43 | |||
| 0-30-32 | |||
| 1-16/9-10/9 | |||
| otonal | |||
|- | |- | ||
| 44 | |||
| 0-3-35 | |||
| 1-7/5-14/9 | |||
| utonal | |||
|- | |- | ||
| 45 | |||
| 0-5-35 | |||
| 1-7/4-14/9 | |||
| utonal | |||
|- | |- | ||
| 46 | |||
| 0-8-35 | |||
| 1-11/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 47 | |||
| 0-15-35 | |||
| 1-4/3-14/9 | |||
| otonal | |||
|- | |- | ||
| 48 | |||
| 0-20-35 | |||
| 1-7/6-14/9 | |||
| utonal | |||
|- | |- | ||
| 49 | |||
| 0-27-35 | |||
| 1-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 50 | |||
| 0-30-35 | |||
| 1-16/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 51 | |||
| 0-32-35 | |||
| 1-10/9-14/9 | |||
| otonal | |||
|} | |} | ||
=Tetrads= | == Tetrads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-5-7 | |||
| 1-5/4-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 2 | |||
| 0-3-5-8 | |||
| 1-7/5-7/4-11/9 | |||
| werckismic | |||
|- | |- | ||
| 3 | |||
| 0-3-5-20 | |||
| 1-7/5-7/4-7/6 | |||
| utonal | |||
|- | |- | ||
| 4 | |||
| 0-15-17-20 | |||
| 1-4/3-5/3-7/6 | |||
| otonal | |||
|- | |- | ||
| 5 | |||
| 0-2-5-22 | |||
| 1-5/4-7/4-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 6 | |||
| 0-2-7-22 | |||
| 1-5/4-12/11-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 7 | |||
| 0-5-7-22 | |||
| 1-7/4-12/11-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 8 | |||
| 0-7-15-22 | |||
| 1-12/11-4/3-16/11 | |||
| ambitonal | |||
|- | |- | ||
| 9 | |||
| 0-2-17-22 | |||
| 1-5/4-5/3-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 10 | |||
| 0-15-17-22 | |||
| 1-4/3-5/3-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 11 | |||
| 0-5-20-22 | |||
| 1-7/4-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 12 | |||
| 0-15-20-22 | |||
| 1-4/3-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 13 | |||
| 0-17-20-22 | |||
| 1-5/3-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 14 | |||
| 0-2-7-24 | |||
| 1-5/4-12/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 15 | |||
| 0-2-17-24 | |||
| 1-5/4-5/3-20/11 | |||
| utonal | |||
|- | |- | ||
| 16 | |||
| 0-2-22-24 | |||
| 1-5/4-16/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 17 | |||
| 0-7-22-24 | |||
| 1-12/11-16/11-20/11 | |||
| otonal | |||
|- | |- | ||
| 18 | |||
| 0-17-22-24 | |||
| 1-5/3-16/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 19 | |||
| 0-3-5-27 | |||
| 1-7/5-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 20 | |||
| 0-5-7-27 | |||
| 1-7/4-12/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 21 | |||
| 0-3-20-27 | |||
| 1-7/5-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 22 | |||
| 0-5-20-27 | |||
| 1-7/4-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 23 | |||
| 0-5-22-27 | |||
| 1-7/4-16/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 24 | |||
| 0-7-22-27 | |||
| 1-12/11-16/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 25 | |||
| 0-20-22-27 | |||
| 1-7/6-16/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 26 | |||
| 0-7-24-27 | |||
| 1-12/11-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 27 | |||
| 0-22-24-27 | |||
| 1-16/11-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 28 | |||
| 0-3-8-30 | |||
| 1-7/5-11/9-16/9 | |||
| werckismic | |||
|- | |- | ||
| 29 | |||
| 0-8-15-30 | |||
| 1-11/9-4/3-16/9 | |||
| otonal | |||
|- | |- | ||
| 30 | |||
| 0-15-22-30 | |||
| 1-4/3-16/11-16/9 | |||
| utonal | |||
|- | |- | ||
| 31 | |||
| 0-3-27-30 | |||
| 1-7/5-14/11-16/9 | |||
| werckismic | |||
|- | |- | ||
| 32 | |||
| 0-22-27-30 | |||
| 1-16/11-14/11-16/9 | |||
| werckismic | |||
|- | |- | ||
| 33 | |||
| 0-2-5-32 | |||
| 1-5/4-7/4-10/9 | |||
| werckismic | |||
|- | |- | ||
| 34 | |||
| 0-5-8-32 | |||
| 1-7/4-11/9-10/9 | |||
| werckismic | |||
|- | |- | ||
| 35 | |||
| 0-8-15-32 | |||
| 1-11/9-4/3-10/9 | |||
| otonal | |||
|- | |- | ||
| 36 | |||
| 0-2-17-32 | |||
| 1-5/4-5/3-10/9 | |||
| utonal | |||
|- | |- | ||
| 37 | |||
| 0-15-17-32 | |||
| 1-4/3-5/3-10/9 | |||
| ambitonal | |||
|- | |- | ||
| 38 | |||
| 0-2-24-32 | |||
| 1-5/4-20/11-10/9 | |||
| utonal | |||
|- | |- | ||
| 39 | |||
| 0-17-24-32 | |||
| 1-5/3-20/11-10/9 | |||
| utonal | |||
|- | |- | ||
| 40 | |||
| 0-5-27-32 | |||
| 1-7/4-14/11-10/9 | |||
| werckismic | |||
|- | |- | ||
| 41 | |||
| 0-24-27-32 | |||
| 1-20/11-14/11-10/9 | |||
| werckismic | |||
|- | |- | ||
| 42 | |||
| 0-8-30-32 | |||
| 1-11/9-16/9-10/9 | |||
| otonal | |||
|- | |- | ||
| 43 | |||
| 0-15-30-32 | |||
| 1-4/3-16/9-10/9 | |||
| otonal | |||
|- | |- | ||
| 44 | |||
| 0-27-30-32 | |||
| 1-14/11-16/9-10/9 | |||
| werckismic | |||
|- | |- | ||
| 45 | |||
| 0-3-5-35 | |||
| 1-7/5-7/4-14/9 | |||
| utonal | |||
|- | |- | ||
| 46 | |||
| 0-3-8-35 | |||
| 1-7/5-11/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 47 | |||
| 0-5-8-35 | |||
| 1-7/4-11/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 48 | |||
| 0-8-15-35 | |||
| 1-11/9-4/3-14/9 | |||
| otonal | |||
|- | |- | ||
| 49 | |||
| 0-3-20-35 | |||
| 1-7/5-7/6-14/9 | |||
| utonal | |||
|- | |- | ||
| 50 | |||
| 0-5-20-35 | |||
| 1-7/4-7/6-14/9 | |||
| utonal | |||
|- | |- | ||
| 51 | |||
| 0-15-20-35 | |||
| 1-4/3-7/6-14/9 | |||
| ambitonal | |||
|- | |- | ||
| 52 | |||
| 0-3-27-35 | |||
| 1-7/5-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 53 | |||
| 0-5-27-35 | |||
| 1-7/4-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 54 | |||
| 0-20-27-35 | |||
| 1-7/6-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 55 | |||
| 0-3-30-35 | |||
| 1-7/5-16/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 56 | |||
| 0-8-30-35 | |||
| 1-11/9-16/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 57 | |||
| 0-15-30-35 | |||
| 1-4/3-16/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 58 | |||
| 0-27-30-35 | |||
| 1-14/11-16/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 59 | |||
| 0-5-32-35 | |||
| 1-7/4-10/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 60 | |||
| 0-8-32-35 | |||
| 1-11/9-10/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 61 | |||
| 0-15-32-35 | |||
| 1-4/3-10/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 62 | |||
| 0-27-32-35 | |||
| 1-14/11-10/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 63 | |||
| 0-30-32-35 | |||
| 1-16/9-10/9-14/9 | |||
| otonal | |||
|} | |} | ||
=Pentads= | == Pentads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-2-5-7-22 | |||
| 1-5/4-7/4-12/11-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 2 | |||
| 0-15-17-20-22 | |||
| 1-4/3-5/3-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 3 | |||
| 0-2-7-22-24 | |||
| 1-5/4-12/11-16/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 4 | |||
| 0-2-17-22-24 | |||
| 1-5/4-5/3-16/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 5 | |||
| 0-3-5-20-27 | |||
| 1-7/5-7/4-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 6 | |||
| 0-5-7-22-27 | |||
| 1-7/4-12/11-16/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 7 | |||
| 0-5-20-22-27 | |||
| 1-7/4-7/6-16/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 8 | |||
| 0-7-22-24-27 | |||
| 1-12/11-16/11-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 9 | |||
| 0-2-17-24-32 | |||
| 1-5/4-5/3-20/11-10/9 | |||
| utonal | |||
|- | |- | ||
| 10 | |||
| 0-8-15-30-32 | |||
| 1-11/9-4/3-16/9-10/9 | |||
| otonal | |||
|- | |- | ||
| 11 | |||
| 0-3-5-8-35 | |||
| 1-7/5-7/4-11/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 12 | |||
| 0-3-5-20-35 | |||
| 1-7/5-7/4-7/6-14/9 | |||
| utonal | |||
|- | |- | ||
| 13 | |||
| 0-3-5-27-35 | |||
| 1-7/5-7/4-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 14 | |||
| 0-3-20-27-35 | |||
| 1-7/5-7/6-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 15 | |||
| 0-5-20-27-35 | |||
| 1-7/4-7/6-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 16 | |||
| 0-3-8-30-35 | |||
| 1-7/5-11/9-16/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 17 | |||
| 0-8-15-30-35 | |||
| 1-11/9-4/3-16/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 18 | |||
| 0-3-27-30-35 | |||
| 1-7/5-14/11-16/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 19 | |||
| 0-5-8-32-35 | |||
| 1-7/4-11/9-10/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 20 | |||
| 0-8-15-32-35 | |||
| 1-11/9-4/3-10/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 21 | |||
| 0-5-27-32-35 | |||
| 1-7/4-14/11-10/9-14/9 | |||
| werckismic | |||
|- | |- | ||
| 22 | |||
| 0-8-30-32-35 | |||
| 1-11/9-16/9-10/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 23 | |||
| 0-15-30-32-35 | |||
| 1-4/3-16/9-10/9-14/9 | |||
| otonal | |||
|- | |- | ||
| 24 | |||
| 0-27-30-32-35 | |||
| 1-14/11-16/9-10/9-14/9 | |||
| werckismic | |||
|} | |} | ||
=Hexads= | == Hexads == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Number | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-3-5-20-27-35 | |||
| 1-7/5-7/4-7/6-14/11-14/9 | |||
| utonal | |||
|- | |- | ||
| 2 | |||
| 0-8-15-30-32-35 | |||
| 1-11/9-4/3-16/9-10/9-14/9 | |||
| otonal | |||
|} | |} | ||
[[Category:Lists of chords]] | |||
[[Category:Hemithirds]] |