Catakleismic/11-limit chords: Difference between revisions
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Below are listed the [[ | Below are listed the [[dyadic chord]]s of 11-limit [[Catakleismic|catakleismic temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are labeled [[Swetismic chords|swetismic]], by [[385/384]] [[Keenanismic chords|keenanismic]], and by [[225/224]] [[Marvel chords|marvel]]. Chords requiring any two of 540/539, 385/384 or 225/224 are labeled [[Undecimal marvel chords|unimarvel]]. | ||
Catakleismic has MOS of size 7, 11, 15, 19, 34, 53 and 72. It is a complex temperament and not much attention has been paid to it, but one notable feature it has is that 11-limit marvel (unimarvel) shrinks the kleisma to a very small interval in an optimal tuning, so very little tuning damage is incurred by catakleismic over that of marvel. Hence, catakleismic can be thought of as one way of organizing the chords of marvel, which are also listed below. | Catakleismic has MOS of size 7, 11, 15, 19, 34, 53 and 72. It is a complex temperament and not much attention has been paid to it, but one notable feature it has is that 11-limit marvel (unimarvel) shrinks the kleisma to a very small interval in an optimal tuning, so very little tuning damage is incurred by catakleismic over that of marvel. Hence, catakleismic can be thought of as one way of organizing the chords of marvel, which are also listed below. | ||
=Triads= | == Triads == | ||
{| class="wikitable" | {| class="wikitable center-1" | ||
|- | |- | ||
! # | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-1-6 | |||
| 1-6/5-3/2 | |||
| utonal | |||
|- | |- | ||
| 2 | |||
| 0-5-6 | |||
| 1-5/4-3/2 | |||
| otonal | |||
|- | |- | ||
| 3 | |||
| 0-1-7 | |||
| 1-6/5-9/5 | |||
| otonal | |||
|- | |- | ||
| 4 | |||
| 0-6-7 | |||
| 1-3/2-9/5 | |||
| utonal | |||
|- | |- | ||
| 5 | |||
| 0-5-10 | |||
| 1-5/4-14/9 | |||
| marvel | |||
|- | |- | ||
| 6 | |||
| 0-5-12 | |||
| 1-5/4-9/8 | |||
| otonal | |||
|- | |- | ||
| 7 | |||
| 0-6-12 | |||
| 1-3/2-9/8 | |||
| ambitonal | |||
|- | |- | ||
| 8 | |||
| 0-7-12 | |||
| 1-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 9 | |||
| 0-6-16 | |||
| 1-3/2-7/6 | |||
| otonal | |||
|- | |- | ||
| 10 | |||
| 0-10-16 | |||
| 1-14/9-7/6 | |||
| utonal | |||
|- | |- | ||
| 11 | |||
| 0-1-17 | |||
| 1-6/5-7/5 | |||
| otonal | |||
|- | |- | ||
| 12 | |||
| 0-5-17 | |||
| 1-5/4-7/5 | |||
| marvel | |||
|- | |- | ||
| 13 | |||
| 0-7-17 | |||
| 1-9/5-7/5 | |||
| otonal | |||
|- | |- | ||
| 14 | |||
| 0-10-17 | |||
| 1-14/9-7/5 | |||
| utonal | |||
|- | |- | ||
| 15 | |||
| 0-12-17 | |||
| 1-9/8-7/5 | |||
| marvel | |||
|- | |- | ||
| 16 | |||
| 0-16-17 | |||
| 1-7/6-7/5 | |||
| utonal | |||
|- | |- | ||
| 17 | |||
| 0-5-21 | |||
| 1-5/4-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 18 | |||
| 0-16-21 | |||
| 1-7/6-16/11 | |||
| keenanismic | |||
|- | |- | ||
| 19 | |||
| 0-1-22 | |||
| 1-6/5-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 20 | |||
| 0-5-22 | |||
| 1-5/4-7/4 | |||
| otonal | |||
|- | |- | ||
| 21 | |||
| 0-6-22 | |||
| 1-3/2-7/4 | |||
| otonal | |||
|- | |- | ||
| 22 | |||
| 0-10-22 | |||
| 1-14/9-7/4 | |||
| utonal | |||
|- | |- | ||
| 23 | |||
| 0-12-22 | |||
| 1-9/8-7/4 | |||
| otonal | |||
|- | |- | ||
| 24 | |||
| 0-16-22 | |||
| 1-7/6-7/4 | |||
| utonal | |||
|- | |- | ||
| 25 | |||
| 0-17-22 | |||
| 1-7/5-7/4 | |||
| utonal | |||
|- | |- | ||
| 26 | |||
| 0-21-22 | |||
| 1-16/11-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 27 | |||
| 0-5-26 | |||
| 1-5/4-20/11 | |||
| utonal | |||
|- | |- | ||
| 28 | |||
| 0-10-26 | |||
| 1-14/9-20/11 | |||
| swetismic | |||
|- | |- | ||
| 29 | |||
| 0-16-26 | |||
| 1-7/6-20/11 | |||
| swetismic | |||
|- | |- | ||
| 30 | |||
| 0-21-26 | |||
| 1-16/11-20/11 | |||
| otonal | |||
|- | |- | ||
| 31 | |||
| 0-1-27 | |||
| 1-6/5-12/11 | |||
| utonal | |||
|- | |- | ||
| 32 | |||
| 0-5-27 | |||
| 1-5/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 33 | |||
| 0-6-27 | |||
| 1-3/2-12/11 | |||
| utonal | |||
|- | |- | ||
| 34 | |||
| 0-10-27 | |||
| 1-14/9-12/11 | |||
| swetismic | |||
|- | |- | ||
| 35 | |||
| 0-17-27 | |||
| 1-7/5-12/11 | |||
| swetismic | |||
|- | |- | ||
| 36 | |||
| 0-21-27 | |||
| 1-16/11-12/11 | |||
| otonal | |||
|- | |- | ||
| 37 | |||
| 0-22-27 | |||
| 1-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 38 | |||
| 0-26-27 | |||
| 1-20/11-12/11 | |||
| otonal | |||
|- | |- | ||
| 39 | |||
| 0-6-33 | |||
| 1-3/2-18/11 | |||
| utonal | |||
|- | |- | ||
| 40 | |||
| 0-7-33 | |||
| 1-9/5-18/11 | |||
| utonal | |||
|- | |- | ||
| 41 | |||
| 0-12-33 | |||
| 1-9/8-18/11 | |||
| utonal | |||
|- | |- | ||
| 42 | |||
| 0-16-33 | |||
| 1-7/6-18/11 | |||
| swetismic | |||
|- | |- | ||
| 43 | |||
| 0-17-33 | |||
| 1-7/5-18/11 | |||
| swetismic | |||
|- | |- | ||
| 44 | |||
| 0-21-33 | |||
| 1-16/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 45 | |||
| 0-26-33 | |||
| 1-20/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 46 | |||
| 0-27-33 | |||
| 1-12/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 47 | |||
| 0-10-43 | |||
| 1-14/9-14/11 | |||
| utonal | |||
|- | |- | ||
| 48 | |||
| 0-16-43 | |||
| 1-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 49 | |||
| 0-17-43 | |||
| 1-7/5-14/11 | |||
| utonal | |||
|- | |- | ||
| 50 | |||
| 0-21-43 | |||
| 1-16/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 51 | |||
| 0-22-43 | |||
| 1-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 52 | |||
| 0-26-43 | |||
| 1-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 53 | |||
| 0-27-43 | |||
| 1-12/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 54 | |||
| 0-33-43 | |||
| 1-18/11-14/11 | |||
| otonal | |||
|} | |} | ||
=Tetrads= | == Tetrads == | ||
{| class="wikitable" | {| class="wikitable center-1" | ||
|- | |- | ||
! # | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-1-6-7 | |||
| 1-6/5-3/2-9/5 | |||
| ambitonal | |||
|- | |- | ||
| 2 | |||
| 0-5-6-12 | |||
| 1-5/4-3/2-9/8 | |||
| otonal | |||
|- | |- | ||
| 3 | |||
| 0-6-7-12 | |||
| 1-3/2-9/5-9/8 | |||
| utonal | |||
|- | |- | ||
| 4 | |||
| 0-1-7-17 | |||
| 1-6/5-9/5-7/5 | |||
| otonal | |||
|- | |- | ||
| 5 | |||
| 0-5-10-17 | |||
| 1-5/4-14/9-7/5 | |||
| marvel | |||
|- | |- | ||
| 6 | |||
| 0-5-12-17 | |||
| 1-5/4-9/8-7/5 | |||
| marvel | |||
|- | |- | ||
| 7 | |||
| 0-7-12-17 | |||
| 1-9/5-9/8-7/5 | |||
| marvel | |||
|- | |- | ||
| 8 | |||
| 0-10-16-17 | |||
| 1-14/9-7/6-7/5 | |||
| utonal | |||
|- | |- | ||
| 9 | |||
| 0-1-6-22 | |||
| 1-6/5-3/2-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 10 | |||
| 0-5-6-22 | |||
| 1-5/4-3/2-7/4 | |||
| otonal | |||
|- | |- | ||
| 11 | |||
| 0-5-10-22 | |||
| 1-5/4-14/9-7/4 | |||
| marvel | |||
|- | |- | ||
| 12 | |||
| 0-5-12-22 | |||
| 1-5/4-9/8-7/4 | |||
| otonal | |||
|- | |- | ||
| 13 | |||
| 0-6-12-22 | |||
| 1-3/2-9/8-7/4 | |||
| otonal | |||
|- | |- | ||
| 14 | |||
| 0-6-16-22 | |||
| 1-3/2-7/6-7/4 | |||
| ambitonal | |||
|- | |- | ||
| 15 | |||
| 0-10-16-22 | |||
| 1-14/9-7/6-7/4 | |||
| utonal | |||
|- | |- | ||
| 16 | |||
| 0-1-17-22 | |||
| 1-6/5-7/5-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 17 | |||
| 0-5-17-22 | |||
| 1-5/4-7/5-7/4 | |||
| marvel | |||
|- | |- | ||
| 18 | |||
| 0-10-17-22 | |||
| 1-14/9-7/5-7/4 | |||
| utonal | |||
|- | |- | ||
| 19 | |||
| 0-12-17-22 | |||
| 1-9/8-7/5-7/4 | |||
| marvel | |||
|- | |- | ||
| 20 | |||
| 0-16-17-22 | |||
| 1-7/6-7/5-7/4 | |||
| utonal | |||
|- | |- | ||
| 21 | |||
| 0-5-21-22 | |||
| 1-5/4-16/11-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 22 | |||
| 0-16-21-22 | |||
| 1-7/6-16/11-7/4 | |||
| keenanismic | |||
|- | |- | ||
| 23 | |||
| 0-5-10-26 | |||
| 1-5/4-14/9-20/11 | |||
| unimarv | |||
|- | |- | ||
| 24 | |||
| 0-10-16-26 | |||
| 1-14/9-7/6-20/11 | |||
| swetismic | |||
|- | |- | ||
| 25 | |||
| 0-5-21-26 | |||
| 1-5/4-16/11-20/11 | |||
| keenanismic | |||
|- | |- | ||
| 26 | |||
| 0-16-21-26 | |||
| 1-7/6-16/11-20/11 | |||
| unimarv | |||
|- | |- | ||
| 27 | |||
| 0-1-6-27 | |||
| 1-6/5-3/2-12/11 | |||
| utonal | |||
|- | |- | ||
| 28 | |||
| 0-5-6-27 | |||
| 1-5/4-3/2-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 29 | |||
| 0-5-10-27 | |||
| 1-5/4-14/9-12/11 | |||
| unimarv | |||
|- | |- | ||
| 30 | |||
| 0-1-17-27 | |||
| 1-6/5-7/5-12/11 | |||
| swetismic | |||
|- | |- | ||
| 31 | |||
| 0-5-17-27 | |||
| 1-5/4-7/5-12/11 | |||
| unimarv | |||
|- | |- | ||
| 32 | |||
| 0-10-17-27 | |||
| 1-14/9-7/5-12/11 | |||
| swetismic | |||
|- | |- | ||
| 33 | |||
| 0-5-21-27 | |||
| 1-5/4-16/11-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 34 | |||
| 0-1-22-27 | |||
| 1-6/5-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 35 | |||
| 0-5-22-27 | |||
| 1-5/4-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 36 | |||
| 0-6-22-27 | |||
| 1-3/2-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 37 | |||
| 0-10-22-27 | |||
| 1-14/9-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 38 | |||
| 0-17-22-27 | |||
| 1-7/5-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 39 | |||
| 0-21-22-27 | |||
| 1-16/11-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 40 | |||
| 0-5-26-27 | |||
| 1-5/4-20/11-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 41 | |||
| 0-10-26-27 | |||
| 1-14/9-20/11-12/11 | |||
| swetismic | |||
|- | |- | ||
| 42 | |||
| 0-21-26-27 | |||
| 1-16/11-20/11-12/11 | |||
| otonal | |||
|- | |- | ||
| 43 | |||
| 0-6-7-33 | |||
| 1-3/2-9/5-18/11 | |||
| utonal | |||
|- | |- | ||
| 44 | |||
| 0-6-12-33 | |||
| 1-3/2-9/8-18/11 | |||
| utonal | |||
|- | |- | ||
| 45 | |||
| 0-7-12-33 | |||
| 1-9/5-9/8-18/11 | |||
| utonal | |||
|- | |- | ||
| 46 | |||
| 0-6-16-33 | |||
| 1-3/2-7/6-18/11 | |||
| swetismic | |||
|- | |- | ||
| 47 | |||
| 0-7-17-33 | |||
| 1-9/5-7/5-18/11 | |||
| swetismic | |||
|- | |- | ||
| 48 | |||
| 0-12-17-33 | |||
| 1-9/8-7/5-18/11 | |||
| unimarv | |||
|- | |- | ||
| 49 | |||
| 0-16-17-33 | |||
| 1-7/6-7/5-18/11 | |||
| swetismic | |||
|- | |- | ||
| 50 | |||
| 0-16-21-33 | |||
| 1-7/6-16/11-18/11 | |||
| unimarv | |||
|- | |- | ||
| 51 | |||
| 0-16-26-33 | |||
| 1-7/6-20/11-18/11 | |||
| swetismic | |||
|- | |- | ||
| 52 | |||
| 0-21-26-33 | |||
| 1-16/11-20/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 53 | |||
| 0-6-27-33 | |||
| 1-3/2-12/11-18/11 | |||
| ambitonal | |||
|- | |- | ||
| 54 | |||
| 0-17-27-33 | |||
| 1-7/5-12/11-18/11 | |||
| swetismic | |||
|- | |- | ||
| 55 | |||
| 0-21-27-33 | |||
| 1-16/11-12/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 56 | |||
| 0-26-27-33 | |||
| 1-20/11-12/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 57 | |||
| 0-10-16-43 | |||
| 1-14/9-7/6-14/11 | |||
| utonal | |||
|- | |- | ||
| 58 | |||
| 0-10-17-43 | |||
| 1-14/9-7/5-14/11 | |||
| utonal | |||
|- | |- | ||
| 59 | |||
| 0-16-17-43 | |||
| 1-7/6-7/5-14/11 | |||
| utonal | |||
|- | |- | ||
| 60 | |||
| 0-16-21-43 | |||
| 1-7/6-16/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 61 | |||
| 0-10-22-43 | |||
| 1-14/9-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 62 | |||
| 0-16-22-43 | |||
| 1-7/6-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 63 | |||
| 0-17-22-43 | |||
| 1-7/5-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 64 | |||
| 0-21-22-43 | |||
| 1-16/11-7/4-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 65 | |||
| 0-10-26-43 | |||
| 1-14/9-20/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 66 | |||
| 0-16-26-43 | |||
| 1-7/6-20/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 67 | |||
| 0-21-26-43 | |||
| 1-16/11-20/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 68 | |||
| 0-10-27-43 | |||
| 1-14/9-12/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 69 | |||
| 0-17-27-43 | |||
| 1-7/5-12/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 70 | |||
| 0-21-27-43 | |||
| 1-16/11-12/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 71 | |||
| 0-22-27-43 | |||
| 1-7/4-12/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 72 | |||
| 0-26-27-43 | |||
| 1-20/11-12/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 73 | |||
| 0-16-33-43 | |||
| 1-7/6-18/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 74 | |||
| 0-17-33-43 | |||
| 1-7/5-18/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 75 | |||
| 0-21-33-43 | |||
| 1-16/11-18/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 76 | |||
| 0-26-33-43 | |||
| 1-20/11-18/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 77 | |||
| 0-27-33-43 | |||
| 1-12/11-18/11-14/11 | |||
| otonal | |||
|} | |} | ||
=Pentads= | == Pentads == | ||
{| class="wikitable" | {| class="wikitable center-1" | ||
|- | |- | ||
! # | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-5-6-12-22 | |||
| 1-5/4-3/2-9/8-7/4 | |||
| otonal | |||
|- | |- | ||
| 2 | |||
| 0-5-10-17-22 | |||
| 1-5/4-14/9-7/5-7/4 | |||
| marvel | |||
|- | |- | ||
| 3 | |||
| 0-5-12-17-22 | |||
| 1-5/4-9/8-7/5-7/4 | |||
| marvel | |||
|- | |- | ||
| 4 | |||
| 0-10-16-17-22 | |||
| 1-14/9-7/6-7/5-7/4 | |||
| utonal | |||
|- | |- | ||
| 5 | |||
| 0-5-10-17-27 | |||
| 1-5/4-14/9-7/5-12/11 | |||
| unimarv | |||
|- | |- | ||
| 6 | |||
| 0-1-6-22-27 | |||
| 1-6/5-3/2-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 7 | |||
| 0-5-6-22-27 | |||
| 1-5/4-3/2-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 8 | |||
| 0-5-10-22-27 | |||
| 1-5/4-14/9-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 9 | |||
| 0-1-17-22-27 | |||
| 1-6/5-7/5-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 10 | |||
| 0-5-17-22-27 | |||
| 1-5/4-7/5-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 11 | |||
| 0-10-17-22-27 | |||
| 1-14/9-7/5-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 12 | |||
| 0-5-21-22-27 | |||
| 1-5/4-16/11-7/4-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 13 | |||
| 0-5-10-26-27 | |||
| 1-5/4-14/9-20/11-12/11 | |||
| unimarv | |||
|- | |- | ||
| 14 | |||
| 0-5-21-26-27 | |||
| 1-5/4-16/11-20/11-12/11 | |||
| keenanismic | |||
|- | |- | ||
| 15 | |||
| 0-6-7-12-33 | |||
| 1-3/2-9/5-9/8-18/11 | |||
| utonal | |||
|- | |- | ||
| 16 | |||
| 0-7-12-17-33 | |||
| 1-9/5-9/8-7/5-18/11 | |||
| unimarv | |||
|- | |- | ||
| 17 | |||
| 0-16-21-26-33 | |||
| 1-7/6-16/11-20/11-18/11 | |||
| unimarv | |||
|- | |- | ||
| 18 | |||
| 0-21-26-27-33 | |||
| 1-16/11-20/11-12/11-18/11 | |||
| otonal | |||
|- | |- | ||
| 19 | |||
| 0-10-16-17-43 | |||
| 1-14/9-7/6-7/5-14/11 | |||
| utonal | |||
|- | |- | ||
| 20 | |||
| 0-10-16-22-43 | |||
| 1-14/9-7/6-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 21 | |||
| 0-10-17-22-43 | |||
| 1-14/9-7/5-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 22 | |||
| 0-16-17-22-43 | |||
| 1-7/6-7/5-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 23 | |||
| 0-16-21-22-43 | |||
| 1-7/6-16/11-7/4-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 24 | |||
| 0-10-16-26-43 | |||
| 1-14/9-7/6-20/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 25 | |||
| 0-16-21-26-43 | |||
| 1-7/6-16/11-20/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 26 | |||
| 0-10-17-27-43 | |||
| 1-14/9-7/5-12/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 27 | |||
| 0-10-22-27-43 | |||
| 1-14/9-7/4-12/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 28 | |||
| 0-17-22-27-43 | |||
| 1-7/5-7/4-12/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 29 | |||
| 0-21-22-27-43 | |||
| 1-16/11-7/4-12/11-14/11 | |||
| keenanismic | |||
|- | |- | ||
| 30 | |||
| 0-10-26-27-43 | |||
| 1-14/9-20/11-12/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 31 | |||
| 0-21-26-27-43 | |||
| 1-16/11-20/11-12/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 32 | |||
| 0-16-17-33-43 | |||
| 1-7/6-7/5-18/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 33 | |||
| 0-16-21-33-43 | |||
| 1-7/6-16/11-18/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 34 | |||
| 0-16-26-33-43 | |||
| 1-7/6-20/11-18/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 35 | |||
| 0-21-26-33-43 | |||
| 1-16/11-20/11-18/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 36 | |||
| 0-17-27-33-43 | |||
| 1-7/5-12/11-18/11-14/11 | |||
| swetismic | |||
|- | |- | ||
| 37 | |||
| 0-21-27-33-43 | |||
| 1-16/11-12/11-18/11-14/11 | |||
| otonal | |||
|- | |- | ||
| 38 | |||
| 0-26-27-33-43 | |||
| 1-20/11-12/11-18/11-14/11 | |||
| otonal | |||
|} | |} | ||
=Hexads= | == Hexads == | ||
{| class="wikitable" | {| class="wikitable center-1" | ||
|- | |- | ||
! # | |||
! Chord | |||
! Transversal | |||
! Type | |||
|- | |- | ||
| 1 | |||
| 0-5-10-17-22-27 | |||
| 1-5/4-14/9-7/5-7/4-12/11 | |||
| unimarv | |||
|- | |- | ||
| 2 | |||
| 0-10-16-17-22-43 | |||
| 1-14/9-7/6-7/5-7/4-14/11 | |||
| utonal | |||
|- | |- | ||
| 3 | |||
| 0-10-17-22-27-43 | |||
| 1-14/9-7/5-7/4-12/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 4 | |||
| 0-16-21-26-33-43 | |||
| 1-7/6-16/11-20/11-18/11-14/11 | |||
| unimarv | |||
|- | |- | ||
| 5 | |||
| 0-21-26-27-33-43 | |||
| 1-16/11-20/11-12/11-18/11-14/11 | |||
| otonal | |||
|} | |} | ||
[[Category:Lists of chords]] | |||
[[Category:Catakleismic]] |
Latest revision as of 21:48, 22 June 2025
Below are listed the dyadic chords of 11-limit catakleismic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, by 385/384 keenanismic, and by 225/224 marvel. Chords requiring any two of 540/539, 385/384 or 225/224 are labeled unimarvel.
Catakleismic has MOS of size 7, 11, 15, 19, 34, 53 and 72. It is a complex temperament and not much attention has been paid to it, but one notable feature it has is that 11-limit marvel (unimarvel) shrinks the kleisma to a very small interval in an optimal tuning, so very little tuning damage is incurred by catakleismic over that of marvel. Hence, catakleismic can be thought of as one way of organizing the chords of marvel, which are also listed below.
Triads
# | Chord | Transversal | Type |
---|---|---|---|
1 | 0-1-6 | 1-6/5-3/2 | utonal |
2 | 0-5-6 | 1-5/4-3/2 | otonal |
3 | 0-1-7 | 1-6/5-9/5 | otonal |
4 | 0-6-7 | 1-3/2-9/5 | utonal |
5 | 0-5-10 | 1-5/4-14/9 | marvel |
6 | 0-5-12 | 1-5/4-9/8 | otonal |
7 | 0-6-12 | 1-3/2-9/8 | ambitonal |
8 | 0-7-12 | 1-9/5-9/8 | utonal |
9 | 0-6-16 | 1-3/2-7/6 | otonal |
10 | 0-10-16 | 1-14/9-7/6 | utonal |
11 | 0-1-17 | 1-6/5-7/5 | otonal |
12 | 0-5-17 | 1-5/4-7/5 | marvel |
13 | 0-7-17 | 1-9/5-7/5 | otonal |
14 | 0-10-17 | 1-14/9-7/5 | utonal |
15 | 0-12-17 | 1-9/8-7/5 | marvel |
16 | 0-16-17 | 1-7/6-7/5 | utonal |
17 | 0-5-21 | 1-5/4-16/11 | keenanismic |
18 | 0-16-21 | 1-7/6-16/11 | keenanismic |
19 | 0-1-22 | 1-6/5-7/4 | keenanismic |
20 | 0-5-22 | 1-5/4-7/4 | otonal |
21 | 0-6-22 | 1-3/2-7/4 | otonal |
22 | 0-10-22 | 1-14/9-7/4 | utonal |
23 | 0-12-22 | 1-9/8-7/4 | otonal |
24 | 0-16-22 | 1-7/6-7/4 | utonal |
25 | 0-17-22 | 1-7/5-7/4 | utonal |
26 | 0-21-22 | 1-16/11-7/4 | keenanismic |
27 | 0-5-26 | 1-5/4-20/11 | utonal |
28 | 0-10-26 | 1-14/9-20/11 | swetismic |
29 | 0-16-26 | 1-7/6-20/11 | swetismic |
30 | 0-21-26 | 1-16/11-20/11 | otonal |
31 | 0-1-27 | 1-6/5-12/11 | utonal |
32 | 0-5-27 | 1-5/4-12/11 | keenanismic |
33 | 0-6-27 | 1-3/2-12/11 | utonal |
34 | 0-10-27 | 1-14/9-12/11 | swetismic |
35 | 0-17-27 | 1-7/5-12/11 | swetismic |
36 | 0-21-27 | 1-16/11-12/11 | otonal |
37 | 0-22-27 | 1-7/4-12/11 | keenanismic |
38 | 0-26-27 | 1-20/11-12/11 | otonal |
39 | 0-6-33 | 1-3/2-18/11 | utonal |
40 | 0-7-33 | 1-9/5-18/11 | utonal |
41 | 0-12-33 | 1-9/8-18/11 | utonal |
42 | 0-16-33 | 1-7/6-18/11 | swetismic |
43 | 0-17-33 | 1-7/5-18/11 | swetismic |
44 | 0-21-33 | 1-16/11-18/11 | otonal |
45 | 0-26-33 | 1-20/11-18/11 | otonal |
46 | 0-27-33 | 1-12/11-18/11 | otonal |
47 | 0-10-43 | 1-14/9-14/11 | utonal |
48 | 0-16-43 | 1-7/6-14/11 | utonal |
49 | 0-17-43 | 1-7/5-14/11 | utonal |
50 | 0-21-43 | 1-16/11-14/11 | otonal |
51 | 0-22-43 | 1-7/4-14/11 | utonal |
52 | 0-26-43 | 1-20/11-14/11 | otonal |
53 | 0-27-43 | 1-12/11-14/11 | otonal |
54 | 0-33-43 | 1-18/11-14/11 | otonal |
Tetrads
# | Chord | Transversal | Type |
---|---|---|---|
1 | 0-1-6-7 | 1-6/5-3/2-9/5 | ambitonal |
2 | 0-5-6-12 | 1-5/4-3/2-9/8 | otonal |
3 | 0-6-7-12 | 1-3/2-9/5-9/8 | utonal |
4 | 0-1-7-17 | 1-6/5-9/5-7/5 | otonal |
5 | 0-5-10-17 | 1-5/4-14/9-7/5 | marvel |
6 | 0-5-12-17 | 1-5/4-9/8-7/5 | marvel |
7 | 0-7-12-17 | 1-9/5-9/8-7/5 | marvel |
8 | 0-10-16-17 | 1-14/9-7/6-7/5 | utonal |
9 | 0-1-6-22 | 1-6/5-3/2-7/4 | keenanismic |
10 | 0-5-6-22 | 1-5/4-3/2-7/4 | otonal |
11 | 0-5-10-22 | 1-5/4-14/9-7/4 | marvel |
12 | 0-5-12-22 | 1-5/4-9/8-7/4 | otonal |
13 | 0-6-12-22 | 1-3/2-9/8-7/4 | otonal |
14 | 0-6-16-22 | 1-3/2-7/6-7/4 | ambitonal |
15 | 0-10-16-22 | 1-14/9-7/6-7/4 | utonal |
16 | 0-1-17-22 | 1-6/5-7/5-7/4 | keenanismic |
17 | 0-5-17-22 | 1-5/4-7/5-7/4 | marvel |
18 | 0-10-17-22 | 1-14/9-7/5-7/4 | utonal |
19 | 0-12-17-22 | 1-9/8-7/5-7/4 | marvel |
20 | 0-16-17-22 | 1-7/6-7/5-7/4 | utonal |
21 | 0-5-21-22 | 1-5/4-16/11-7/4 | keenanismic |
22 | 0-16-21-22 | 1-7/6-16/11-7/4 | keenanismic |
23 | 0-5-10-26 | 1-5/4-14/9-20/11 | unimarv |
24 | 0-10-16-26 | 1-14/9-7/6-20/11 | swetismic |
25 | 0-5-21-26 | 1-5/4-16/11-20/11 | keenanismic |
26 | 0-16-21-26 | 1-7/6-16/11-20/11 | unimarv |
27 | 0-1-6-27 | 1-6/5-3/2-12/11 | utonal |
28 | 0-5-6-27 | 1-5/4-3/2-12/11 | keenanismic |
29 | 0-5-10-27 | 1-5/4-14/9-12/11 | unimarv |
30 | 0-1-17-27 | 1-6/5-7/5-12/11 | swetismic |
31 | 0-5-17-27 | 1-5/4-7/5-12/11 | unimarv |
32 | 0-10-17-27 | 1-14/9-7/5-12/11 | swetismic |
33 | 0-5-21-27 | 1-5/4-16/11-12/11 | keenanismic |
34 | 0-1-22-27 | 1-6/5-7/4-12/11 | keenanismic |
35 | 0-5-22-27 | 1-5/4-7/4-12/11 | keenanismic |
36 | 0-6-22-27 | 1-3/2-7/4-12/11 | keenanismic |
37 | 0-10-22-27 | 1-14/9-7/4-12/11 | unimarv |
38 | 0-17-22-27 | 1-7/5-7/4-12/11 | unimarv |
39 | 0-21-22-27 | 1-16/11-7/4-12/11 | keenanismic |
40 | 0-5-26-27 | 1-5/4-20/11-12/11 | keenanismic |
41 | 0-10-26-27 | 1-14/9-20/11-12/11 | swetismic |
42 | 0-21-26-27 | 1-16/11-20/11-12/11 | otonal |
43 | 0-6-7-33 | 1-3/2-9/5-18/11 | utonal |
44 | 0-6-12-33 | 1-3/2-9/8-18/11 | utonal |
45 | 0-7-12-33 | 1-9/5-9/8-18/11 | utonal |
46 | 0-6-16-33 | 1-3/2-7/6-18/11 | swetismic |
47 | 0-7-17-33 | 1-9/5-7/5-18/11 | swetismic |
48 | 0-12-17-33 | 1-9/8-7/5-18/11 | unimarv |
49 | 0-16-17-33 | 1-7/6-7/5-18/11 | swetismic |
50 | 0-16-21-33 | 1-7/6-16/11-18/11 | unimarv |
51 | 0-16-26-33 | 1-7/6-20/11-18/11 | swetismic |
52 | 0-21-26-33 | 1-16/11-20/11-18/11 | otonal |
53 | 0-6-27-33 | 1-3/2-12/11-18/11 | ambitonal |
54 | 0-17-27-33 | 1-7/5-12/11-18/11 | swetismic |
55 | 0-21-27-33 | 1-16/11-12/11-18/11 | otonal |
56 | 0-26-27-33 | 1-20/11-12/11-18/11 | otonal |
57 | 0-10-16-43 | 1-14/9-7/6-14/11 | utonal |
58 | 0-10-17-43 | 1-14/9-7/5-14/11 | utonal |
59 | 0-16-17-43 | 1-7/6-7/5-14/11 | utonal |
60 | 0-16-21-43 | 1-7/6-16/11-14/11 | keenanismic |
61 | 0-10-22-43 | 1-14/9-7/4-14/11 | utonal |
62 | 0-16-22-43 | 1-7/6-7/4-14/11 | utonal |
63 | 0-17-22-43 | 1-7/5-7/4-14/11 | utonal |
64 | 0-21-22-43 | 1-16/11-7/4-14/11 | keenanismic |
65 | 0-10-26-43 | 1-14/9-20/11-14/11 | swetismic |
66 | 0-16-26-43 | 1-7/6-20/11-14/11 | swetismic |
67 | 0-21-26-43 | 1-16/11-20/11-14/11 | otonal |
68 | 0-10-27-43 | 1-14/9-12/11-14/11 | swetismic |
69 | 0-17-27-43 | 1-7/5-12/11-14/11 | swetismic |
70 | 0-21-27-43 | 1-16/11-12/11-14/11 | otonal |
71 | 0-22-27-43 | 1-7/4-12/11-14/11 | keenanismic |
72 | 0-26-27-43 | 1-20/11-12/11-14/11 | otonal |
73 | 0-16-33-43 | 1-7/6-18/11-14/11 | swetismic |
74 | 0-17-33-43 | 1-7/5-18/11-14/11 | swetismic |
75 | 0-21-33-43 | 1-16/11-18/11-14/11 | otonal |
76 | 0-26-33-43 | 1-20/11-18/11-14/11 | otonal |
77 | 0-27-33-43 | 1-12/11-18/11-14/11 | otonal |
Pentads
# | Chord | Transversal | Type |
---|---|---|---|
1 | 0-5-6-12-22 | 1-5/4-3/2-9/8-7/4 | otonal |
2 | 0-5-10-17-22 | 1-5/4-14/9-7/5-7/4 | marvel |
3 | 0-5-12-17-22 | 1-5/4-9/8-7/5-7/4 | marvel |
4 | 0-10-16-17-22 | 1-14/9-7/6-7/5-7/4 | utonal |
5 | 0-5-10-17-27 | 1-5/4-14/9-7/5-12/11 | unimarv |
6 | 0-1-6-22-27 | 1-6/5-3/2-7/4-12/11 | keenanismic |
7 | 0-5-6-22-27 | 1-5/4-3/2-7/4-12/11 | keenanismic |
8 | 0-5-10-22-27 | 1-5/4-14/9-7/4-12/11 | unimarv |
9 | 0-1-17-22-27 | 1-6/5-7/5-7/4-12/11 | unimarv |
10 | 0-5-17-22-27 | 1-5/4-7/5-7/4-12/11 | unimarv |
11 | 0-10-17-22-27 | 1-14/9-7/5-7/4-12/11 | unimarv |
12 | 0-5-21-22-27 | 1-5/4-16/11-7/4-12/11 | keenanismic |
13 | 0-5-10-26-27 | 1-5/4-14/9-20/11-12/11 | unimarv |
14 | 0-5-21-26-27 | 1-5/4-16/11-20/11-12/11 | keenanismic |
15 | 0-6-7-12-33 | 1-3/2-9/5-9/8-18/11 | utonal |
16 | 0-7-12-17-33 | 1-9/5-9/8-7/5-18/11 | unimarv |
17 | 0-16-21-26-33 | 1-7/6-16/11-20/11-18/11 | unimarv |
18 | 0-21-26-27-33 | 1-16/11-20/11-12/11-18/11 | otonal |
19 | 0-10-16-17-43 | 1-14/9-7/6-7/5-14/11 | utonal |
20 | 0-10-16-22-43 | 1-14/9-7/6-7/4-14/11 | utonal |
21 | 0-10-17-22-43 | 1-14/9-7/5-7/4-14/11 | utonal |
22 | 0-16-17-22-43 | 1-7/6-7/5-7/4-14/11 | utonal |
23 | 0-16-21-22-43 | 1-7/6-16/11-7/4-14/11 | keenanismic |
24 | 0-10-16-26-43 | 1-14/9-7/6-20/11-14/11 | swetismic |
25 | 0-16-21-26-43 | 1-7/6-16/11-20/11-14/11 | unimarv |
26 | 0-10-17-27-43 | 1-14/9-7/5-12/11-14/11 | swetismic |
27 | 0-10-22-27-43 | 1-14/9-7/4-12/11-14/11 | unimarv |
28 | 0-17-22-27-43 | 1-7/5-7/4-12/11-14/11 | unimarv |
29 | 0-21-22-27-43 | 1-16/11-7/4-12/11-14/11 | keenanismic |
30 | 0-10-26-27-43 | 1-14/9-20/11-12/11-14/11 | swetismic |
31 | 0-21-26-27-43 | 1-16/11-20/11-12/11-14/11 | otonal |
32 | 0-16-17-33-43 | 1-7/6-7/5-18/11-14/11 | swetismic |
33 | 0-16-21-33-43 | 1-7/6-16/11-18/11-14/11 | unimarv |
34 | 0-16-26-33-43 | 1-7/6-20/11-18/11-14/11 | swetismic |
35 | 0-21-26-33-43 | 1-16/11-20/11-18/11-14/11 | otonal |
36 | 0-17-27-33-43 | 1-7/5-12/11-18/11-14/11 | swetismic |
37 | 0-21-27-33-43 | 1-16/11-12/11-18/11-14/11 | otonal |
38 | 0-26-27-33-43 | 1-20/11-12/11-18/11-14/11 | otonal |
Hexads
# | Chord | Transversal | Type |
---|---|---|---|
1 | 0-5-10-17-22-27 | 1-5/4-14/9-7/5-7/4-12/11 | unimarv |
2 | 0-10-16-17-22-43 | 1-14/9-7/6-7/5-7/4-14/11 | utonal |
3 | 0-10-17-22-27-43 | 1-14/9-7/5-7/4-12/11-14/11 | unimarv |
4 | 0-16-21-26-33-43 | 1-7/6-16/11-20/11-18/11-14/11 | unimarv |
5 | 0-21-26-27-33-43 | 1-16/11-20/11-12/11-18/11-14/11 | otonal |