45edo: Difference between revisions

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Yourmusic Productions (talk | contribs)
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Still filling in table.
Yourmusic Productions (talk | contribs)
autopatrolled, emailconfirmed
2,020 edits
Still adding intervals.
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|<nowiki>-9.219</nowiki>
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|800
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|<nowiki>-13.686</nowiki>
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|880
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|<nowiki>-4.359</nowiki>
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|<nowiki>-8.826</nowiki>
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|<nowiki>-9.423</nowiki>
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|<nowiki>-4.262</nowiki>
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|<nowiki>-0.095</nowiki>
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|<nowiki>-0.060</nowiki>
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Revision as of 07:26, 9 July 2020

45edo divides the octave into 45 equal parts of 26.667 cents. It has two major thirds, each almost equally far from Just, but as the flat one is slightly closer, it qualifies as a meantone temperament, forming a good approximation to 2/5 comma meantone. It is the optimal patent val for flattone temperament, the 7-limit 525/512 planar avicennmic temperament, the 11-limit calliope temperament tempering out 45/44 and 81/80, and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up ennealimmal, if you want. Since 45 is a multiple of 5 and 9, it can be used to model Indonesian music in both Slendro (~ 5edo) and Pelog (~ modes of 9edo) tunings.

Step # ET Just Difference
(ET minus Just) 		Ups and Downs Notation
Cents Interval Cents
0 0¢ 1:1 0 0 unison 1 D
1 26.666 65:64 26.841 -0.174 D^
2 53.333 33:32 53.273 0.060 D#
3 80.0 22:21 80.537 -0.537 D#^
4 106.666 17:16 104.955 1.7112 Ebv
5 133.333 27:25 133.238 0.095 Eb
6 160 11:10 165.004 -5.004 Ev
7 186.666 10:9 182.404 4.262 E
8 213.333 9:8 203.910 9.423 E^
9 240 8:7 231.174 8.826 E#
10 266.666 7:6 266.871 -0.205 Fb
11 293.333 32:27 294.135 -0.802 Fv
12 320 6:5 315.641 4.359 F
13 346.666 11:9 347.408 -0.741 F^
14 373.333 5:4- 386.314 -12.980 F#
15 400 5:4+ 386.314 13.686 F#^
16 426.666 9:7 435.084 -8.418 Gbv
17 453.333 13:10 454.294 -0.961 Gb
18 480 21:16 470.781 9.219 Gv
19 506.666 4:3 498.045 8.622 G
20 533.333 49:36 533.742 -0.409 G^
21 560 18:13 -3.382 G#
22 586.666 7:5 582.512 4.155 G#^
23 613.333 10:7 617.488 -4.155 Abv
24 640 13:9 3.382 Ab
25 666.666 72:49 66.258 0.409 Av
26 693.333 3:2 701.955 -8.622 A
27 720 32:21 -9.219 A^
28 746.666 20:13 0.961 A#
29 773.333 14:9 8.418 A#^
30 800 8:5- -13.686 Bbv
31 826.666 8:5+ 12.980 Bb
32 853.333 18:11 0.741 Bv
33 880 5:3 -4.359 B
34 906.666 27:16 0.802 B^
35 933.333 12:7 0.205 B#
36 960 7:4 -8.826 Cb
37 986.666 16:9 -9.423 Cv
38 1013.333 9:5 -4.262 C
39 1040 20:11 5.004 C^
40 1066.666 50:27 -0.095 C#
41 1093.333 32:17 -1.7112 C#^
42 1120 21:11 0.537 Dbv
43 1146.666 64:33 -0.060 Db
44 1173.333 128:65 0.174 Dv
45 1200 2:1 1200 0 Octave D
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