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=47 tone Equal Temperament=
{{Infobox ET}}
{{ED intro}}


'''47-EDO''' divides the octave into 47 equal parts of 25.5319 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.
== Theory ==
47edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths, as both fall between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. The fifth closest to [[3/2]] is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft diatonic scale generated from its flat fifth is so soft, with {{nowrap|L:s {{=}} 7:6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. The hard diatonic scale generated from its sharp fifth is extremely hard, with {{nowrap|L:s {{=}} 9:1}}. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.


47edo is the 15th [[prime_numbers|prime]] edo, following [[43edo|43edo]] and preceding [[53edo|53edo]].
47edo is one of the most difficult diatonic edos to notate in [[native fifth notation|native fifths]], because no other diatonic edo's fifth is as extreme.  


47edo is a [[Ups_and_Downs_Notation#Other EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as flat (see 42edo for the opposite extreme).
=== Odd harmonics ===
{{Harmonics in equal|47}}


A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale:
47edo 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]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament.


D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.
 
D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#<span style="font-size: 90%; vertical-align: super;">3</span> - F#<span style="font-size: 90%; vertical-align: super;">5</span> - A#<span style="font-size: 90%; vertical-align: super;">3</span> - C# or as Eb<span style="font-size: 90%; vertical-align: super;">4</span> - Gbb - Ab<span style="font-size: 90%; vertical-align: super;">4</span> - Db<span style="font-size: 90%; vertical-align: super;">6</span>. This is an aug-three double-dim-seven chord, written D#<span style="font-size: 90%; vertical-align: super;">3</span>(A3)dd7 or Eb<span style="font-size: 90%; vertical-align: super;">4</span>(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#<span style="font-size: 90%; vertical-align: super;">3</span>(#3)b<span style="font-size: 90%; vertical-align: super;">3</span>7 or Eb<span style="font-size: 90%; vertical-align: super;">4</span>(#3)b<span style="vertical-align: super;">3</span>7.
 
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
 
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
 
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.


==Intervals of 47edo==
=== Subsets and supersets ===
47edo is the 15th [[prime edo]], following [[43edo]] and preceding [[53edo]], so it does not contain any nontrivial subset edos, though it contains [[47ed4]]. [[94edo]], which doubles it, corrects its approximations of harmonics 3 and 11 to near-just qualities.


{| class="wikitable"
== Intervals ==
{| class="wikitable center-all right-2"
|-
|-
! | Degree
! [[Degree|#]]
! | Size (Cents)
! [[Cent]]s
!7mus
! colspan="2" | Relative notation
! colspan="2" | relative notation
! Absolute notation
! | absolute notation
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 0.0000
| 0.0
|0
| perfect unison
| style="text-align:center;" | perfect unison
| P1
| style="text-align:center;" | P1
| D
| style="text-align:center;" | D
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:right;" | 25.5319
| 25.5
|32.68085 (20.AE4C<sub>16</sub>)
| aug 1sn
| style="text-align:center;" | aug 1sn
| A1
| style="text-align:center;" | A1
| D#
| style="text-align:center;" | D#
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:right;" | 51.0638
| 51.1
|65.3617 (41.5C988<sub>16</sub>)
| double-aug 1sn
| style="text-align:center;" | double-aug 1sn
| AA1
| style="text-align:center;" | AA1
| Dx
| style="text-align:center;" | Dx
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:right;" | 76.5957
| 76.6
|98.04255 (62.0AE5<sub>16</sub>)
| triple-aug 1sn, triple-dim 2nd
| style="text-align:center;" | triple-aug 1sn, triple-dim 2nd
| A<sup>3</sup>1, d<sup>3</sup>2
| 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
| D#<sup>3</sup>, Eb<sup>4</sup>
| 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>
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:right;" | 102.1277
| 102.1
|130.7234 (82.B931<sub>16</sub>)
| double-dim 2nd
| style="text-align:center;" | double-dim 2nd
| dd2
| style="text-align:center;" | dd2
| Eb<sup>3</sup>
| style="text-align:center;" | Eb<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:right;" | 127.6596
| 127.7
|163.4043 (A3.677D<sub>16</sub>)
| dim 2nd
| style="text-align:center;" | dim 2nd
| d2
| style="text-align:center;" | d2
| Ebb
| style="text-align:center;" | Ebb
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:right;" | 153.1915
| 153.2
|196.0851 (C4.15CA<sub>16</sub>)
| minor 2nd
| style="text-align:center;" | minor 2nd
| m2
| style="text-align:center;" | m2
| Eb
| style="text-align:center;" | Eb
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:right;" | 178.7234
| 178.7
|228.766 (E4.C416<sub>16</sub>)
| major 2nd
| style="text-align:center;" | major 2nd
| M2
| style="text-align:center;" | M2
| E
| style="text-align:center;" | E
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:right;" | 204.2553
| 204.3
|261.4468 (105.7262<sub>16</sub>)
| aug 2nd
| style="text-align:center;" | aug 2nd
| A2
| style="text-align:center;" | A2
| E#
| style="text-align:center;" | E#
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:right;" | 229.7872
| 229.8
|294.1277 (126.20AE<sub>16</sub>)
| double-aug 2nd
| style="text-align:center;" | double-aug 2nd
| AA2
| style="text-align:center;" | AA2
| Ex
| style="text-align:center;" | Ex
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:right;" | 255.31915
| 255.3
|326.8085 (146.CEFB<sub>16</sub>)
| triple-aug 2nd, triple-dim 3rd
| style="text-align:center;" | triple-aug 2nd, triple-dim 3rd
| A<sup>3</sup>2, d<sup>3</sup>3
| 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
| E#<sup>3</sup>, Fb<sup>3</sup>
| 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>
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:right;" | 280.8511
| 280.9
|359.4894 (167.7D47<sub>16</sub>)
| double-dim 3rd
| style="text-align:center;" | double-dim 3rd
| dd3
| style="text-align:center;" | dd3
| Fbb
| style="text-align:center;" | Fbb
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:right;" | 306.383
| 306.4
|392.1702 (188.2B93<sub>16</sub>)
| dim 3rd
| style="text-align:center;" | dim 3rd
| d3
| style="text-align:center;" | d3
| Fb
| style="text-align:center;" | Fb
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:right;" | 331.9149
| 331.9
|424.8511 (1A8.D9DF<sub>16</sub>)
| minor 3rd
| style="text-align:center;" | minor 3rd
| m3
| style="text-align:center;" | m3
| F
| style="text-align:center;" | F
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:right;" | 357.4468
| 357.4
|457.5319 (1C9.882C<sub>16</sub>)
| major 3rd
| style="text-align:center;" | major 3rd
| M3
| style="text-align:center;" | M3
| F#
| style="text-align:center;" | F#
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:right;" | 382.9787
| 383.0
|490.2128 (1EA.3678<sub>16</sub>)
| aug 3rd
| style="text-align:center;" | aug 3rd
| A3
| style="text-align:center;" | A3
| Fx
| style="text-align:center;" | Fx
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:right;" | 408.5106
| 408.5
|522.8936 (20A.E4C4<sub>16</sub>)
| double-aug 3rd
| style="text-align:center;" | double-aug 3rd
| AA3
| style="text-align:center;" | AA3
| F#<sup>3</sup>
| style="text-align:center;" | F#<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:right;" | 434.04255
| 434.0
|555.5745 (22B.931<sub>16</sub>)
| triple-aug 3rd, triple-dim 4th
| style="text-align:center;" | triple-aug 3rd, triple-dim 4th
| A<sup>3</sup>3, d<sup>3</sup>4
| 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
| F#<sup>4</sup>, Gb<sup>3</sup>
| 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>
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:right;" | 459.5745
| 459.6
|588.2553 (24C.415D<sub>16</sub>)
| double-dim 4th
| style="text-align:center;" | double-dim 4th
| dd4
| style="text-align:center;" | dd4
| Gbb
| style="text-align:center;" | Gbb
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:right;" | 485.1064
| 485.1
|620.9362 (26C.EFA9<sub>16</sub>)
| dim 4th
| style="text-align:center;" | dim 4th
| d4
| style="text-align:center;" | d4
| Gb
| style="text-align:center;" | Gb
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:right;" | 510.6383
| 510.6
|653.617 (28D.9DF5<sub>16</sub>)
| perfect 4th
| style="text-align:center;" | perfect 4th
| P4
| style="text-align:center;" | P4
| G
| style="text-align:center;" | G
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:right;" | 536.1702
| 536.2
|686.2979 (2AE.4C41<sub>16</sub>)
| aug 4th
| style="text-align:center;" | aug 4th
| A4
| style="text-align:center;" | A4
| G#
| style="text-align:center;" | G#
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:right;" | 561.7021
| 561.7
|718.9787 (2CE.FA8E<sub>16</sub>)
| double-aug 4th
| style="text-align:center;" | double-aug 4th
| AA4
| style="text-align:center;" | AA4
| Gx
| style="text-align:center;" | Gx
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:right;" | 587.2340
| 587.2
|751.6595 (2EF.A8DA<sub>16</sub>)
| triple-aug 4th
| style="text-align:center;" | triple-aug 4th
| A<sup>3</sup>4
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4
| G#<sup>3</sup>
| style="text-align:center;" | G#<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:right;" | 612.7660
| 612.8
|784.3404 (310.5726<sub>16</sub>)
| triple-dim 5th
| style="text-align:center;" | triple-dim 5th
| d<sup>3</sup>5
| style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5
| Ab<sup>3</sup>
| style="text-align:center;" | Ab<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:right;" | 638.2979
| 638.3
|817.0213 (331.0572<sub>16</sub>)
| double-dim 5th
| style="text-align:center;" | double-dim 5th
| dd5
| style="text-align:center;" | dd5
| Abb
| style="text-align:center;" | Abb
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:right;" | 663.8298
| 663.8
|849.7021 (351.B3BF<sub>16</sub>)
| dim 5th
| style="text-align:center;" | dim 5th
| d5
| style="text-align:center;" | d5
| Ab
| style="text-align:center;" | Ab
|-
|-
| style="text-align:center;" | 27
| 27
| style="text-align:right;" | 689.3617
| 689.4
|882.383 (372.620B<sub>16</sub>)
| perfect 5th
| style="text-align:center;" | perfect 5th
| P5
| style="text-align:center;" | P5
| A
| style="text-align:center;" | A
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:right;" | 714.8936
| 714.9
|915.0638 (393.1057<sub>16</sub>)
| aug 5th
| style="text-align:center;" | aug 5th
| A5
| style="text-align:center;" | A5
| A#
| style="text-align:center;" | A#
|-
|-
| style="text-align:center;" | 29
| 29
| style="text-align:right;" | 740.4255
| 740.4
|947.7447 (3B3.BEA3<sub>16</sub>)
| double-aug 5th
| style="text-align:center;" | double-aug 5th
| AA5
| style="text-align:center;" | AA5
| Ax
| style="text-align:center;" | Ax
|-
|-
| style="text-align:center;" | 30
| 30
| style="text-align:right;" | 765.95745
| 766.0
|980.4255 (3D4.6CF<sub>16</sub>)
| triple-aug 5th, triple-dim 6th
| style="text-align:center;" | triple-aug 5th, triple-dim 6th
| 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>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6
| A#<sup>3</sup>, Bb<sup>4</sup>
| 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>
|-
|-
| style="text-align:center;" | 31
| 31
| style="text-align:right;" | 791.4894
| 791.5
|1013.1064 (3F5.1B3C<sub>16</sub>)
| double-dim 6th
| style="text-align:center;" | double-dim 6th
| dd6
| style="text-align:center;" | dd6
| Bb<sup>3</sup>
| style="text-align:center;" | Bb<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 32
| 32
| style="text-align:right;" | 817.0213
| 817.0
|1045.7872 (415.C988<sub>16</sub>)
| dim 6th
| style="text-align:center;" | dim 6th
| d6
| style="text-align:center;" | d6
| Bbb
| style="text-align:center;" | Bbb
|-
|-
| style="text-align:center;" | 33
| 33
| style="text-align:right;" | 842.5532
| 842.6
|1078.4681 (436.77D4<sub>16</sub>)
| minor 6th
| style="text-align:center;" | minor 6th
| m6
| style="text-align:center;" | m6
| Bb
| style="text-align:center;" | Bb
|-
|-
| style="text-align:center;" | 34
| 34
| style="text-align:right;" | 868.0851
| 868.1
|1111.1489 (457.2621<sub>16</sub>)
| major 6th
| style="text-align:center;" | major 6th
| M6
| style="text-align:center;" | M6
| B
| style="text-align:center;" | B
|-
|-
| style="text-align:center;" | 35
| 35
| style="text-align:right;" | 893.617
| 893.6
|1143.8298 (477.D46D<sub>16</sub>)
| aug 6th
| style="text-align:center;" | aug 6th
| A6
| style="text-align:center;" | A6
| B#
| style="text-align:center;" | B#
|-
|-
| style="text-align:center;" | 36
| 36
| style="text-align:right;" | 919.1489
| 919.1
|1176.5106 (498.82B9<sub>16</sub>)
| double-aug 6th
| style="text-align:center;" | double-aug 6th
| AA6
| style="text-align:center;" | AA6
| Bx
| style="text-align:center;" | Bx
|-
|-
| style="text-align:center;" | 37
| 37
| style="text-align:right;" | 944.68085
| 944.7
|1209.1915 (4B9.3105<sub>16</sub>)
| triple-aug 6th, triple-dim 7th
| style="text-align:center;" | triple-aug 6th, triple-dim 7th
| A<sup>3</sup>6, d<sup>3</sup>7
| 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
| B#<sup>3</sup>, Cb<sup>3</sup>
| 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>
|-
|-
| style="text-align:center;" | 38
| 38
| style="text-align:right;" | 970.2128
| 970.2
|1241.8723 (4D9.DF52<sub>16</sub>)
| double-dim 7th
| style="text-align:center;" | double-dim 7th
| dd7
| style="text-align:center;" | dd7
| Cbb
| style="text-align:center;" | Cbb
|-
|-
| style="text-align:center;" | 39
| 39
| style="text-align:right;" | 995.7447
| 995.7
|1274.5532 (4FA.8D9E<sub>16</sub>)
| dim 7th
| style="text-align:center;" | dim 7th
| d7
| style="text-align:center;" | d7
| Cb
| style="text-align:center;" | Cb
|-
|-
| style="text-align:center;" | 40
| 40
| style="text-align:right;" | 1021.2766
| 1021.3
|1307.234 (51B.3BEA<sub>16</sub>)
| minor 7th
| style="text-align:center;" | minor 7th
| m7
| style="text-align:center;" | m7
| C
| style="text-align:center;" | C
|-
|-
| style="text-align:center;" | 41
| 41
| style="text-align:right;" | 1046.8085
| 1046.8
|1339.9149 (53B.EA36<sub>16</sub>)
| major 7th
| style="text-align:center;" | major 7th
| M7
| style="text-align:center;" | M7
| C#
| style="text-align:center;" | C#
|-
|-
| style="text-align:center;" | 42
| 42
| style="text-align:right;" | 1072.3404
| 1072.3
|1372.5957 (55C.9883<sub>16</sub>)
| aug 7th
| style="text-align:center;" | aug 7th
| A7
| style="text-align:center;" | A7
| Cx
| style="text-align:center;" | Cx
|-
|-
| style="text-align:center;" | 43
| 43
| style="text-align:right;" | 1097.8723
| 1097.9
|1405.2766 (57D.46CF<sub>16</sub>)
| double-aug 7th
| style="text-align:center;" | double-aug 7th
| AA7
| style="text-align:center;" | AA7
| C#<sup>3</sup>
| style="text-align:center;" | C#<span style="font-size: 90%; vertical-align: super;">3</span>
|-
|-
| style="text-align:center;" | 44
| 44
| style="text-align:right;" | 1123.4043
| 1123.4
|1437.95745 (59D.F51B<sub>16</sub>)
| triple-aug 7th, triple-dim 8ve
| style="text-align:center;" | triple-aug 7th, triple-dim 8ve
| A<sup>3</sup>7, d<sup>3</sup>8
| 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
| C#<sup>4</sup>, Db<sup>3</sup>
| 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>
|-
|-
| style="text-align:center;" | 45
| 45
| style="text-align:right;" | 1148.9362
| 1148.9
|1470.6383 (5BE.A3678<sub>16</sub>)
| double-dim 8ve
| style="text-align:center;" | double-dim 8ve
| dd8
| style="text-align:center;" | dd8
| Dbb
| style="text-align:center;" | Dbb
|-
|-
| style="text-align:center;" | 46
| 46
| style="text-align:right;" | 1174.4681
| 1174.5
|1503.31915 (5DF.51B4<sub>16</sub>)
| dim 8ve
| style="text-align:center;" | dim 8ve
| d8
| style="text-align:center;" | d8
| Db
| style="text-align:center;" | Db
|-
|-
| style="text-align:center;" | 47
| 47
| style="text-align:right;" | 1200
| 1200.0
|1536 (600<sub>16</sub>)
| perfect 8ve
| style="text-align:center;" | perfect 8ve
| P8
| style="text-align:center;" | P8
| D
| style="text-align:center;" | D
|}
|}


[[Category:Edo]]
== Notation ==
[[Category:Prime EDO]]
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a 7edo-like scale:
[[Category:Subgroup]]
 
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
 
D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#<sup>3</sup> - F#<sup>5</sup> - A#<sup>3</sup> - C# or as Eb<sup>4</sup> - Gbb - Ab<sup>4</sup> - Db<sup>6</sup>. This is an aug-three double-dim-seven chord, written D#<sup>3</sup>(A3)dd7 or Eb<sup>4</sup>(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#<sup>3</sup>(#3)b<sup>3</sup>7 or Eb<sup>4</sup>(#3)b<sup>3</sup>7.
 
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a 5edo-like scale, with two of the notes inflected by a comma-sized edostep:
 
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
 
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.
 
=== Ups and downs notation ===
Using [[Helmholtz–Ellis]] accidentals and the sharp fifth, 47edo can be notated using [[ups and downs notation|ups and downs]]:
{{Sharpness-sharp8}}
 
With the flat fifth, notation is identical to standard notation:
{{Sharpness-sharp1}}
 
=== Sagittal notation ===
==== Best fifth notation ====
This notation uses the same sagittal sequence as [[42edo#Second-best fifth notation|42b]].
 
<imagemap>
File:47-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 519 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
default [[File:47-EDO_Sagittal.svg]]
</imagemap>
 
==== Second-best fifth notation ====
===== Evo and Revo flavors =====
<imagemap>
File:47b_Sagittal.svg
desc none
rect 80 0 280 50 [[Sagittal_notation]]
rect 280 0 440 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:47b_Sagittal.svg]]
</imagemap>
 
===== Alternative Evo flavor =====
<imagemap>
File:47b_Alternative_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 389 0 549 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 389 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:47b_Alternative_Evo_Sagittal.svg]]
</imagemap>
 
===== Evo-SZ flavor =====
<imagemap>
File:47b_Evo-SZ_Sagittal.svg
desc none
rect 80 0 335 50 [[Sagittal_notation]]
rect 335 0 495 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:47b_Evo-SZ_Sagittal.svg]]
</imagemap>
 
== Scales ==
* [[Negri in zeta-stretched 47edo]]
* Quasi-equal [[equiheptatonic]] (Dorian): 7 6 7 7 7 6 7
** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7
* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7
* Quasi-equal [[equipentatonic]]: 9 10 9 10 9
* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])
** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning)
** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)
 
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 47edo]]
 
=== Skip fretting ===
'''Skip fretting system 47 3 11''' is a [[skip-fretting]] system for [[47edo]] where strings are 11\47 and frets are 3\47. This is effectively 15.6666...-edo. All examples of this system on this page are for 5-string bass.
 
; Chords
Neutral-dominant 7th: 1 0 1 2 2
 
== Music ==
* [https://youtu.be/_TqaWw7tv_E Improvisation in 47edo (octave-compressed tuning, 7-note subset of Negri[9<nowiki>]</nowiki>)] by [[Budjarn Lambeth]], Jan 2024
 
[[Category:Listen]]
[[Category:Todo:add rank 2 temperaments table]]
Retrieved from "https://en.xen.wiki/w/47edo"