45edo: Difference between revisions

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'''45edo''' divides the octave into 45 equal parts of 26.667 [[cent]]s. It is the [[optimal patent val]] for [[flattone]] temperament, the [[7-limit]] 525/512 planar [[Avicennmic_temperaments|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 [[wikipedia:Slendro|Slendro]] (~ 5edo) and [[wikipedia:Pelog|Pelog]] (~ modes of 9edo) tunings.
'''45edo''' divides the octave into 45 equal parts of 26.667 [[cent]]s. 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_temperaments|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 [[wikipedia:Slendro|Slendro]] (~ 5edo) and [[wikipedia:Pelog|Pelog]] (~ modes of 9edo) tunings.


[[Category:Edo]]
[[Category:Edo]]
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| 0
| 0
| 0¢
| 0¢
|  
|1:1
|  
| 0
|  
|0
| unison
| unison
| 1
| 1
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| 5
| 5
| 133.333
| 133.333
|
|27:25
|
|133.238
|
|0.095
|
|
|
|
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|160
|160
|11:10
|11:10
|
|165.004
|<nowiki>-5.004</nowiki>
|<nowiki>-5.004</nowiki>
|
|
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|320
|320
|6:5
|6:5
|
|315.641
|4.359
|4.359
|
|
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|346.666
|346.666
|11:9
|11:9
|
|347.408
|
| -0.741
|
|
|
|
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|373.333
|373.333
|5:4-
|5:4-
|
|386.314
|<nowiki>-12.980</nowiki>
|<nowiki>-12.980</nowiki>
|
|
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|400
|400
|5:4+
|5:4+
|
|386.314
|13.686
|13.686
|
|
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| 20
| 20
|533.333
|533.333
|
|49:36
|
|533.742
|
| -0.409
|
|
|
|
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|18:13
|18:13
|
|
|
|<nowiki>-3.382</nowiki>
|
|
|
|
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|586.666
|586.666
|7:5
|7:5
|
|582.512
|
|4.155
|
|
|
|
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|613.333
|613.333
|10:7
|10:7
|
|617.488
|
|<nowiki>-4.155</nowiki>
|
|
|
|
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|13:9
|13:9
|
|
|
|3.382
|
|
|
|
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| 25
| 25
|666.666
|666.666
|
|72:49
|
|66.258
|
|0.409
|
|
|
|
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|D
|D
|}
|}
[[Category:Meantone]]

Revision as of 21:39, 8 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 Gbv
17 453.333 Gb
18 480 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 A^
28 746.666 A#
29 773.333 A#^
30 800 Bbv
31 826.666 Bb
32 853.333 Bv
33 880 B
34 906.666 B^
35 933.333 B#
36 960 Cb
37 986.666 Cv
38 1013.333 C
39 1040 C^
40 1066.666 C#
41 1093.333 C#^
42 1120 Dbv
43 1146.666 Db
44 1173.333 Dv
45 1200 2:1 1200 0 Octave D
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