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| == Theory == | | == Theory == |
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| '''47-EDO''' divides the octave into 47 equal parts of 25.5 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N_subgroups|2*47 subgroup]] of the [[23-limit|23-limit]], on which it tempers out the same commas as [[94edo|94edo]]. It provides a good tuning for [[Chromatic_pairs#Baldy|baldy]] and [[Chromatic_pairs#Silver|silver]] temperaments and relatives. | | '''47-EDO''' divides the octave into 47 equal parts of 25.5 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N_subgroups|2*47 subgroup]] of the [[23-limit|23-limit]], on which it tempers out the same commas as [[94edo|94edo]]. It provides a good tuning for [[Chromatic_pairs#Baldy|baldy]] and [[Chromatic_pairs#Silver|silver]] temperaments and relatives. |
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| D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. | | D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. |
| {{Odd harmonics in edo|edo=47}} | | {{Odd harmonics in edo|edo=47}} |
| | |
| == Intervals == | | == Intervals == |
| | | {| class="wikitable center-all right-2" |
| {| class="wikitable" | |
| |- | | |- |
| ! | Degree | | ! Degree |
| ! | Size (Cents) | | ! Size ({{cent}}) |
| ! colspan="2" | relative notation | | ! colspan="2" | Relative notation |
| ! | absolute notation | | ! Absolute notation |
| |- | | |- |
| | style="text-align:center;" | 0
| | | 0 |
| | style="text-align:right;" | 0.0000
| | | 0.0000 |
| | style="text-align:center;" | perfect unison
| | | perfect unison |
| | style="text-align:center;" | P1
| | | P1 |
| | style="text-align:center;" | D
| | | D |
| |- | | |- |
| | style="text-align:center;" | 1
| | | 1 |
| | style="text-align:right;" | 25.5319
| | | 25.5319 |
| | style="text-align:center;" | aug 1sn
| | | aug 1sn |
| | style="text-align:center;" | A1
| | | A1 |
| | style="text-align:center;" | D#
| | | D# |
| |- | | |- |
| | style="text-align:center;" | 2
| | | 2 |
| | style="text-align:right;" | 51.0638
| | | 51.0638 |
| | style="text-align:center;" | double-aug 1sn
| | | double-aug 1sn |
| | style="text-align:center;" | AA1
| | | AA1 |
| | style="text-align:center;" | Dx
| | | Dx |
| |- | | |- |
| | style="text-align:center;" | 3
| | | 3 |
| | style="text-align:right;" | 76.5957
| | | 76.5957 |
| | style="text-align:center;" | triple-aug 1sn, triple-dim 2nd
| | | triple-aug 1sn, triple-dim 2nd |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>1, d<span style="font-size: 90%; vertical-align: super;">3</span>2
| | | A<sup>3</sup>1, d<sup>3</sup>2 |
| | style="text-align:center;" | D#<span style="font-size: 90%; vertical-align: super;">3</span>, Eb<span style="font-size: 90%; vertical-align: super;">4</span>
| | | D#<sup>3</sup>, Eb<sup>4</sup> |
| |- | | |- |
| | style="text-align:center;" | 4
| | | 4 |
| | style="text-align:right;" | 102.1277
| | | 102.1277 |
| | style="text-align:center;" | double-dim 2nd
| | | double-dim 2nd |
| | style="text-align:center;" | dd2
| | | dd2 |
| | style="text-align:center;" | Eb<span style="font-size: 90%; vertical-align: super;">3</span>
| | | Eb<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 5
| | | 5 |
| | style="text-align:right;" | 127.6596
| | | 127.6596 |
| | style="text-align:center;" | dim 2nd
| | | dim 2nd |
| | style="text-align:center;" | d2
| | | d2 |
| | style="text-align:center;" | Ebb
| | | Ebb |
| |- | | |- |
| | style="text-align:center;" | 6
| | | 6 |
| | style="text-align:right;" | 153.1915
| | | 153.1915 |
| | style="text-align:center;" | minor 2nd
| | | minor 2nd |
| | style="text-align:center;" | m2
| | | m2 |
| | style="text-align:center;" | Eb
| | | Eb |
| |- | | |- |
| | style="text-align:center;" | 7
| | | 7 |
| | style="text-align:right;" | 178.7234
| | | 178.7234 |
| | style="text-align:center;" | major 2nd
| | | major 2nd |
| | style="text-align:center;" | M2
| | | M2 |
| | style="text-align:center;" | E
| | | E |
| |- | | |- |
| | style="text-align:center;" | 8
| | | 8 |
| | style="text-align:right;" | 204.2553
| | | 204.2553 |
| | style="text-align:center;" | aug 2nd
| | | aug 2nd |
| | style="text-align:center;" | A2
| | | A2 |
| | style="text-align:center;" | E#
| | | E# |
| |- | | |- |
| | style="text-align:center;" | 9
| | | 9 |
| | style="text-align:right;" | 229.7872
| | | 229.7872 |
| | style="text-align:center;" | double-aug 2nd
| | | double-aug 2nd |
| | style="text-align:center;" | AA2
| | | AA2 |
| | style="text-align:center;" | Ex
| | | Ex |
| |- | | |- |
| | style="text-align:center;" | 10
| | | 10 |
| | style="text-align:right;" | 255.31915
| | | 255.31915 |
| | style="text-align:center;" | triple-aug 2nd, triple-dim 3rd
| | | triple-aug 2nd, triple-dim 3rd |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>2, d<span style="font-size: 90%; vertical-align: super;">3</span>3
| | | A<sup>3</sup>2, d<sup>3</sup>3 |
| | style="text-align:center;" | E#<span style="font-size: 90%; vertical-align: super;">3</span>, Fb<span style="font-size: 90%; vertical-align: super;">3</span>
| | | E#<sup>3</sup>, Fb<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 11
| | | 11 |
| | style="text-align:right;" | 280.8511
| | | 280.8511 |
| | style="text-align:center;" | double-dim 3rd
| | | double-dim 3rd |
| | style="text-align:center;" | dd3
| | | dd3 |
| | style="text-align:center;" | Fbb
| | | Fbb |
| |- | | |- |
| | style="text-align:center;" | 12
| | | 12 |
| | style="text-align:right;" | 306.383
| | | 306.383 |
| | style="text-align:center;" | dim 3rd
| | | dim 3rd |
| | style="text-align:center;" | d3
| | | d3 |
| | style="text-align:center;" | Fb
| | | Fb |
| |- | | |- |
| | style="text-align:center;" | 13
| | | 13 |
| | style="text-align:right;" | 331.9149
| | | 331.9149 |
| | style="text-align:center;" | minor 3rd
| | | minor 3rd |
| | style="text-align:center;" | m3
| | | m3 |
| | style="text-align:center;" | F
| | | F |
| |- | | |- |
| | style="text-align:center;" | 14
| | | 14 |
| | style="text-align:right;" | 357.4468
| | | 357.4468 |
| | style="text-align:center;" | major 3rd
| | | major 3rd |
| | style="text-align:center;" | M3
| | | M3 |
| | style="text-align:center;" | F#
| | | F# |
| |- | | |- |
| | style="text-align:center;" | 15
| | | 15 |
| | style="text-align:right;" | 382.9787
| | | 382.9787 |
| | style="text-align:center;" | aug 3rd
| | | aug 3rd |
| | style="text-align:center;" | A3
| | | A3 |
| | style="text-align:center;" | Fx
| | | Fx |
| |- | | |- |
| | style="text-align:center;" | 16
| | | 16 |
| | style="text-align:right;" | 408.5106
| | | 408.5106 |
| | style="text-align:center;" | double-aug 3rd
| | | double-aug 3rd |
| | style="text-align:center;" | AA3
| | | AA3 |
| | style="text-align:center;" | F#<span style="font-size: 90%; vertical-align: super;">3</span>
| | | F#<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 17
| | | 17 |
| | style="text-align:right;" | 434.04255
| | | 434.04255 |
| | style="text-align:center;" | triple-aug 3rd, triple-dim 4th
| | | triple-aug 3rd, triple-dim 4th |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>3, d<span style="font-size: 90%; vertical-align: super;">3</span>4
| | | A<sup>3</sup>3, d<sup>3</sup>4 |
| | style="text-align:center;" | F#<span style="font-size: 90%; vertical-align: super;">4</span>, Gb<span style="font-size: 90%; vertical-align: super;">3</span>
| | | F#<sup>4</sup>, Gb<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 18
| | | 18 |
| | style="text-align:right;" | 459.5745
| | | 459.5745 |
| | style="text-align:center;" | double-dim 4th
| | | double-dim 4th |
| | style="text-align:center;" | dd4
| | | dd4 |
| | style="text-align:center;" | Gbb
| | | Gbb |
| |- | | |- |
| | style="text-align:center;" | 19
| | | 19 |
| | style="text-align:right;" | 485.1064
| | | 485.1064 |
| | style="text-align:center;" | dim 4th
| | | dim 4th |
| | style="text-align:center;" | d4
| | | d4 |
| | style="text-align:center;" | Gb
| | | Gb |
| |- | | |- |
| | style="text-align:center;" | 20
| | | 20 |
| | style="text-align:right;" | 510.6383
| | | 510.6383 |
| | style="text-align:center;" | perfect 4th
| | | perfect 4th |
| | style="text-align:center;" | P4
| | | P4 |
| | style="text-align:center;" | G
| | | G |
| |- | | |- |
| | style="text-align:center;" | 21
| | | 21 |
| | style="text-align:right;" | 536.1702
| | | 536.1702 |
| | style="text-align:center;" | aug 4th
| | | aug 4th |
| | style="text-align:center;" | A4
| | | A4 |
| | style="text-align:center;" | G#
| | | G# |
| |- | | |- |
| | style="text-align:center;" | 22
| | | 22 |
| | style="text-align:right;" | 561.7021
| | | 561.7021 |
| | style="text-align:center;" | double-aug 4th
| | | double-aug 4th |
| | style="text-align:center;" | AA4
| | | AA4 |
| | style="text-align:center;" | Gx
| | | Gx |
| |- | | |- |
| | style="text-align:center;" | 23
| | | 23 |
| | style="text-align:right;" | 587.2340
| | | 587.2340 |
| | style="text-align:center;" | triple-aug 4th
| | | triple-aug 4th |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4
| | | A<sup>3</sup>4 |
| | style="text-align:center;" | G#<span style="font-size: 90%; vertical-align: super;">3</span>
| | | G#<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 24
| | | 24 |
| | style="text-align:right;" | 612.7660
| | | 612.7660 |
| | style="text-align:center;" | triple-dim 5th
| | | triple-dim 5th |
| | style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5
| | | d<sup>3</sup>5 |
| | style="text-align:center;" | Ab<span style="font-size: 90%; vertical-align: super;">3</span>
| | | Ab<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 25
| | | 25 |
| | style="text-align:right;" | 638.2979
| | | 638.2979 |
| | style="text-align:center;" | double-dim 5th
| | | double-dim 5th |
| | style="text-align:center;" | dd5
| | | dd5 |
| | style="text-align:center;" | Abb
| | | Abb |
| |- | | |- |
| | style="text-align:center;" | 26
| | | 26 |
| | style="text-align:right;" | 663.8298
| | | 663.8298 |
| | style="text-align:center;" | dim 5th
| | | dim 5th |
| | style="text-align:center;" | d5
| | | d5 |
| | style="text-align:center;" | Ab
| | | Ab |
| |- | | |- |
| | style="text-align:center;" | 27
| | | 27 |
| | style="text-align:right;" | 689.3617
| | | 689.3617 |
| | style="text-align:center;" | perfect 5th
| | | perfect 5th |
| | style="text-align:center;" | P5
| | | P5 |
| | style="text-align:center;" | A
| | | A |
| |- | | |- |
| | style="text-align:center;" | 28
| | | 28 |
| | style="text-align:right;" | 714.8936
| | | 714.8936 |
| | style="text-align:center;" | aug 5th
| | | aug 5th |
| | style="text-align:center;" | A5
| | | A5 |
| | style="text-align:center;" | A#
| | | A# |
| |- | | |- |
| | style="text-align:center;" | 29
| | | 29 |
| | style="text-align:right;" | 740.4255
| | | 740.4255 |
| | style="text-align:center;" | double-aug 5th
| | | double-aug 5th |
| | style="text-align:center;" | AA5
| | | AA5 |
| | style="text-align:center;" | Ax
| | | Ax |
| |- | | |- |
| | style="text-align:center;" | 30
| | | 30 |
| | style="text-align:right;" | 765.95745
| | | 765.95745 |
| | style="text-align:center;" | triple-aug 5th, triple-dim 6th
| | | triple-aug 5th, triple-dim 6th |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6
| | | A<sup>3</sup>5, d<sup>3</sup>6 |
| | style="text-align:center;" | A#<span style="font-size: 90%; vertical-align: super;">3</span>, Bb<span style="font-size: 90%; vertical-align: super;">4</span>
| | | A#<sup>3</sup>, Bb<sup>4</sup> |
| |- | | |- |
| | style="text-align:center;" | 31
| | | 31 |
| | style="text-align:right;" | 791.4894
| | | 791.4894 |
| | style="text-align:center;" | double-dim 6th
| | | double-dim 6th |
| | style="text-align:center;" | dd6
| | | dd6 |
| | style="text-align:center;" | Bb<span style="font-size: 90%; vertical-align: super;">3</span>
| | | Bb<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 32
| | | 32 |
| | style="text-align:right;" | 817.0213
| | | 817.0213 |
| | style="text-align:center;" | dim 6th
| | | dim 6th |
| | style="text-align:center;" | d6
| | | d6 |
| | style="text-align:center;" | Bbb
| | | Bbb |
| |- | | |- |
| | style="text-align:center;" | 33
| | | 33 |
| | style="text-align:right;" | 842.5532
| | | 842.5532 |
| | style="text-align:center;" | minor 6th
| | | minor 6th |
| | style="text-align:center;" | m6
| | | m6 |
| | style="text-align:center;" | Bb
| | | Bb |
| |- | | |- |
| | style="text-align:center;" | 34
| | | 34 |
| | style="text-align:right;" | 868.0851
| | | 868.0851 |
| | style="text-align:center;" | major 6th
| | | major 6th |
| | style="text-align:center;" | M6
| | | M6 |
| | style="text-align:center;" | B
| | | B |
| |- | | |- |
| | style="text-align:center;" | 35
| | | 35 |
| | style="text-align:right;" | 893.617
| | | 893.617 |
| | style="text-align:center;" | aug 6th
| | | aug 6th |
| | style="text-align:center;" | A6
| | | A6 |
| | style="text-align:center;" | B#
| | | B# |
| |- | | |- |
| | style="text-align:center;" | 36
| | | 36 |
| | style="text-align:right;" | 919.1489
| | | 919.1489 |
| | style="text-align:center;" | double-aug 6th
| | | double-aug 6th |
| | style="text-align:center;" | AA6
| | | AA6 |
| | style="text-align:center;" | Bx
| | | Bx |
| |- | | |- |
| | style="text-align:center;" | 37
| | | 37 |
| | style="text-align:right;" | 944.68085
| | | 944.68085 |
| | style="text-align:center;" | triple-aug 6th, triple-dim 7th
| | | triple-aug 6th, triple-dim 7th |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>6, d<span style="font-size: 90%; vertical-align: super;">3</span>7
| | | A<sup>3</sup>6, d<sup>3</sup>7 |
| | style="text-align:center;" | B#<span style="font-size: 90%; vertical-align: super;">3</span>, Cb<span style="font-size: 90%; vertical-align: super;">3</span>
| | | B#<sup>3</sup>, Cb<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 38
| | | 38 |
| | style="text-align:right;" | 970.2128
| | | 970.2128 |
| | style="text-align:center;" | double-dim 7th
| | | double-dim 7th |
| | style="text-align:center;" | dd7
| | | dd7 |
| | style="text-align:center;" | Cbb
| | | Cbb |
| |- | | |- |
| | style="text-align:center;" | 39
| | | 39 |
| | style="text-align:right;" | 995.7447
| | | 995.7447 |
| | style="text-align:center;" | dim 7th
| | | dim 7th |
| | style="text-align:center;" | d7
| | | d7 |
| | style="text-align:center;" | Cb
| | | Cb |
| |- | | |- |
| | style="text-align:center;" | 40
| | | 40 |
| | style="text-align:right;" | 1021.2766
| | | 1021.2766 |
| | style="text-align:center;" | minor 7th
| | | minor 7th |
| | style="text-align:center;" | m7
| | | m7 |
| | style="text-align:center;" | C
| | | C |
| |- | | |- |
| | style="text-align:center;" | 41
| | | 41 |
| | style="text-align:right;" | 1046.8085
| | | 1046.8085 |
| | style="text-align:center;" | major 7th
| | | major 7th |
| | style="text-align:center;" | M7
| | | M7 |
| | style="text-align:center;" | C#
| | | C# |
| |- | | |- |
| | style="text-align:center;" | 42
| | | 42 |
| | style="text-align:right;" | 1072.3404
| | | 1072.3404 |
| | style="text-align:center;" | aug 7th
| | | aug 7th |
| | style="text-align:center;" | A7
| | | A7 |
| | style="text-align:center;" | Cx
| | | Cx |
| |- | | |- |
| | style="text-align:center;" | 43
| | | 43 |
| | style="text-align:right;" | 1097.8723
| | | 1097.8723 |
| | style="text-align:center;" | double-aug 7th
| | | double-aug 7th |
| | style="text-align:center;" | AA7
| | | AA7 |
| | style="text-align:center;" | C#<span style="font-size: 90%; vertical-align: super;">3</span>
| | | C#<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 44
| | | 44 |
| | style="text-align:right;" | 1123.4043
| | | 1123.4043 |
| | style="text-align:center;" | triple-aug 7th, triple-dim 8ve
| | | triple-aug 7th, triple-dim 8ve |
| | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>7, d<span style="font-size: 90%; vertical-align: super;">3</span>8
| | | A<sup>3</sup>7, d<sup>3</sup>8 |
| | style="text-align:center;" | C#<span style="font-size: 90%; vertical-align: super;">4</span>, Db<span style="font-size: 90%; vertical-align: super;">3</span>
| | | C#<sup>4</sup>, Db<sup>3</sup> |
| |- | | |- |
| | style="text-align:center;" | 45
| | | 45 |
| | style="text-align:right;" | 1148.9362
| | | 1148.9362 |
| | style="text-align:center;" | double-dim 8ve
| | | double-dim 8ve |
| | style="text-align:center;" | dd8
| | | dd8 |
| | style="text-align:center;" | Dbb
| | | Dbb |
| |- | | |- |
| | style="text-align:center;" | 46
| | | 46 |
| | style="text-align:right;" | 1174.4681
| | | 1174.4681 |
| | style="text-align:center;" | dim 8ve
| | | dim 8ve |
| | style="text-align:center;" | d8
| | | d8 |
| | style="text-align:center;" | Db
| | | Db |
| |- | | |- |
| | style="text-align:center;" | 47
| | | 47 |
| | style="text-align:right;" | 1200
| | | 1200 |
| | style="text-align:center;" | perfect 8ve
| | | perfect 8ve |
| | style="text-align:center;" | P8
| | | P8 |
| | style="text-align:center;" | D
| | | D |
| |} | | |} |
|
| |
|
| [[Category:Equal divisions of the octave]] | | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> |
| [[Category:Prime EDO]] | | [[Category:Prime EDO]] |
| [[Category:Subgroup]] | | [[Category:Subgroup]] |