# Chords of ennealimnic

(Redirected from Chords of ennealimmic)

Below are listed the dyadic chords of 11-limit ennealimnic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, 441/440 werckismic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.

The normal mapping for ennealimnic is enn = [<9 1 1 12 -2|, <0 2 3 2 5|]. From this we may derive a val v = enn[1] + 100 enn[2] = <9 201 301 212 498| which we may use to sort and normalize the chords of ennealimmic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v, and the nnextw column gives a transversal which tempers to the chord by ennealimmic tempering. Finally, the Graham complexity is listed in the last column.

Ennealimmic has MOS of size 18, 27, 45 and 72. It may be seen that the 18 note MOS has some triads and tetrads, and 27 considerably more.

## Contents

 Number Chord Transversal Type Complexity 1 0-7-96 1-12/7-11/9 swetismic 9 2 0-2-98 1-7/6-10/7 swetismic 9 3 0-7-98 1-12/7-10/7 otonal 9 4 0-96-98 1-11/9-10/7 swetismic 9 5 0-2-100 1-7/6-5/3 otonal 9 6 0-98-100 1-10/7-5/3 utonal 9 7 0-7-188 1-12/7-11/10 swetismic 18 8 0-96-188 1-11/9-11/10 utonal 18 9 0-101-188 1-9/5-11/10 otonal 18 10 0-2-190 1-7/6-9/7 swetismic 18 11 0-7-190 1-12/7-9/7 otonal 18 12 0-98-190 1-10/7-9/7 otonal 18 13 0-101-190 1-9/5-9/7 utonal 18 14 0-188-190 1-11/10-9/7 swetismic 18 15 0-2-192 1-7/6-3/2 otonal 18 16 0-7-192 1-12/7-3/2 utonal 18 17 0-96-192 1-11/9-3/2 rastmic 18 18 0-100-192 1-5/3-3/2 otonal 18 19 0-101-192 1-9/5-3/2 utonal 18 20 0-190-192 1-9/7-3/2 utonal 18 21 0-2-194 1-7/6-7/4 utonal 18 22 0-96-194 1-11/9-7/4 werckismic 18 23 0-98-194 1-10/7-7/4 werckismic 18 24 0-192-194 1-3/2-7/4 otonal 18 25 0-98-283 1-10/7-5/4 utonal 27 26 0-100-283 1-5/3-5/4 utonal 27 27 0-192-283 1-3/2-5/4 otonal 27 28 0-194-283 1-7/4-5/4 otonal 27 29 0-7-286 1-12/7-11/7 otonal 27 30 0-96-286 1-11/9-11/7 utonal 27 31 0-98-286 1-10/7-11/7 otonal 27 32 0-101-286 1-9/5-11/7 werckismic 27 33 0-188-286 1-11/10-11/7 utonal 27 34 0-190-286 1-9/7-11/7 otonal 27 35 0-194-286 1-7/4-11/7 werckismic 27 36 0-2-288 1-7/6-11/6 otonal 27 37 0-96-288 1-11/9-11/6 utonal 27 38 0-98-288 1-10/7-11/6 swetismic 27 39 0-100-288 1-5/3-11/6 otonal 27 40 0-188-288 1-11/10-11/6 utonal 27 41 0-190-288 1-9/7-11/6 swetismic 27 42 0-192-288 1-3/2-11/6 otonal 27 43 0-286-288 1-11/7-11/6 utonal 27 44 0-96-375 1-11/9-9/8 rastmic 36 45 0-98-375 1-10/7-9/8 werckismic 36 46 0-101-375 1-9/5-9/8 utonal 36 47 0-190-375 1-9/7-9/8 utonal 36 48 0-192-375 1-3/2-9/8 ambitonal 36 49 0-194-375 1-7/4-9/8 otonal 36 50 0-283-375 1-5/4-9/8 otonal 36 51 0-286-375 1-11/7-9/8 werckismic 36 52 0-288-375 1-11/6-9/8 rastmic 36 53 0-96-471 1-11/9-11/8 utonal 45 54 0-188-471 1-11/10-11/8 utonal 45 55 0-192-471 1-3/2-11/8 otonal 45 56 0-194-471 1-7/4-11/8 otonal 45 57 0-283-471 1-5/4-11/8 otonal 45 58 0-286-471 1-11/7-11/8 utonal 45 59 0-288-471 1-11/6-11/8 utonal 45 60 0-375-471 1-9/8-11/8 otonal 45