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43edo: Difference between revisions

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Line 38: Line 38:
| 0
| 0
| 0.0
| 0.0
| 1/1
| [[1/1]]
| P1
| P1
| perfect unison
| perfect unison
Line 45: Line 45:
| 1
| 1
| 27.9
| 27.9
| ''36/35'', 50/49, 64/63, 65/64, 66/65
| ''[[36/35]]'', [[50/49]], [[64/63]], [[65/64]], [[66/65]]
| ^1, d2
| ^1, d2
| up unison, dim 2nd
| up unison, dim 2nd
Line 52: Line 52:
| 2
| 2
| 55.8
| 55.8
| 26/25, 27/26, 33/32, 40/39, ''49/48''
| [[26/25]], [[27/26]], [[33/32]], [[40/39]], ''[[49/48]]''
| vA1, ^d2
| vA1, ^d2
| downaug unison, updim 2nd
| downaug unison, updim 2nd
Line 59: Line 59:
| 3
| 3
| 83.7
| 83.7
| ''18/17'', 21/20, 22/21, 25/24, ''28/27''
| ''[[18/17]]'', [[21/20]], [[22/21]], [[25/24]], ''[[28/27]]''
| A1, vm2
| A1, vm2
| aug 1sn, downminor 2nd
| aug 1sn, downminor 2nd
Line 66: Line 66:
| 4
| 4
| 111.6
| 111.6
| 15/14, 16/15, 17/16
| [[15/14]], [[16/15]], [[17/16]]
| m2
| m2
| minor 2nd
| minor 2nd
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| 5
| 5
| 139.5
| 139.5
| 12/11, 13/12, 14/13
| [[12/11]], [[13/12]], [[14/13]]
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
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| 6
| 6
| 167.4
| 167.4
| 11/10
| [[11/10]]
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 87: Line 87:
| 7
| 7
| 195.3
| 195.3
| 9/8, 10/9
| [[9/8]], [[10/9]]
| M2
| M2
| major 2nd
| major 2nd
Line 94: Line 94:
| 8
| 8
| 223.3
| 223.3
| 8/7
| [[8/7]]
| ^M2, d3
| ^M2, d3
| upmajor 2nd, dim 3rd
| upmajor 2nd, dim 3rd
Line 101: Line 101:
| 9
| 9
| 251.2
| 251.2
| 15/13
| [[15/13]]
| vA2, ^d3
| vA2, ^d3
| downaug 2nd, updim 3rd
| downaug 2nd, updim 3rd
Line 108: Line 108:
| 10
| 10
| 279.1
| 279.1
| 7/6, 13/11
| [[7/6]], [[13/11]], [[20/17]]
| A2, vm3
| A2, vm3
| aug 2nd, downminor 3rd
| aug 2nd, downminor 3rd
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| 11
| 11
| 307.0
| 307.0
| 6/5
| [[6/5]]
| m3
| m3
| minor 3rd
| minor 3rd
Line 122: Line 122:
| 12
| 12
| 334.9
| 334.9
| 17/14, ''27/22'', 39/32, 40/33
| [[17/14]], ''[[27/22]]'', [[39/32]], [[40/33]]
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 129: Line 129:
| 13
| 13
| 362.8
| 362.8
| ''11/9'', 16/13, 21/17, 26/21
| ''[[11/9]]'', [[16/13]], [[21/17]], [[26/21]]
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 136: Line 136:
| 14
| 14
| 390.7
| 390.7
| 5/4
| [[5/4]]
| M3
| M3
| major 3rd
| major 3rd
Line 143: Line 143:
| 15
| 15
| 418.6
| 418.6
| ''9/7'', 14/11
| ''[[9/7]]'', [[14/11]]
| ^M3, d4
| ^M3, d4
| upmajor 3rd, dim 4th
| upmajor 3rd, dim 4th
Line 150: Line 150:
| 16
| 16
| 446.5
| 446.5
| 13/10, 22/17
| [[13/10]], [[22/17]]
| vA3, ^d4
| vA3, ^d4
| downaug 3rd, updim 4th
| downaug 3rd, updim 4th
Line 157: Line 157:
| 17
| 17
| 474.4
| 474.4
| 21/16
| [[21/16]]
| v4
| v4
| down 4th
| down 4th
Line 164: Line 164:
| 18
| 18
| 502.3
| 502.3
| 4/3
| [[4/3]]
| P4
| P4
| perfect 4th
| perfect 4th
Line 171: Line 171:
| 19
| 19
| 530.2
| 530.2
| 15/11
| [[15/11]]
| ^4
| ^4
| up 4th
| up 4th
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| 20
| 20
| 558.1
| 558.1
| 11/8, 18/13
| [[11/8]], [[18/13]]
| vA4
| vA4
| downaug 4th
| downaug 4th
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| 21
| 21
| 586.0
| 586.0
| 7/5, 24/17, 45/32
| [[7/5]], [[24/17]], [[45/32]]
| A4, vd5
| A4, vd5
| aug 4th, downdim 5th
| aug 4th, downdim 5th
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| 22
| 22
| 614.0
| 614.0
| 10/7, 17/12, 64/45
| [[10/7]], [[17/12]], [[64/45]]
| ^A4, d5
| ^A4, d5
| upaug 4th, dim 5th
| upaug 4th, dim 5th
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| 23
| 23
| 641.9
| 641.9
| 13/9, 16/11
| [[13/9]], [[16/11]]
| ^d5
| ^d5
| updim 5th
| updim 5th
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| 24
| 24
| 669.8
| 669.8
| 22/15
| [[22/15]]
| v5
| v5
| down 5th
| down 5th
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| 25
| 25
| 697.7
| 697.7
| 3/2
| [[3/2]]
| P5
| P5
| perfect 5th
| perfect 5th
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| 26
| 26
| 725.6
| 725.6
| 32/21
| [[32/21]]
| ^5
| ^5
| up 5th
| up 5th
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| 27
| 27
| 753.5
| 753.5
| 17/11, 20/13
| [[17/11]], [[20/13]]
| vA5, ^d6
| vA5, ^d6
| downaug 5th, updim 6th
| downaug 5th, updim 6th
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| 28
| 28
| 781.4
| 781.4
| 11/7, ''14/9''
| [[11/7]], ''[[14/9]]''
| A5, vm6
| A5, vm6
| aug 5th, downminor 6th
| aug 5th, downminor 6th
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| 29
| 29
| 809.3
| 809.3
| 8/5
| [[8/5]]
| m6
| m6
| minor 6th
| minor 6th
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| 30
| 30
| 837.2
| 837.2
| 13/8, ''18/11'', 21/13, 34/21
| [[13/8]], ''[[18/11]]'', [[21/13]], [[34/21]]
| ^m6
| ^m6
| upminor 6th
| upminor 6th
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| 31
| 31
| 865.1
| 865.1
| 28/17, 33/20, ''44/27'', 64/39
| [[28/17]], [[33/20]], ''[[44/27]]'', [[64/39]]
| vM6
| vM6
| downmajor 6th
| downmajor 6th
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| 32
| 32
| 893.0
| 893.0
| 5/3
| [[5/3]]
| M6
| M6
| major 6th
| major 6th
Line 269: Line 269:
| 33
| 33
| 920.9
| 920.9
| 12/7, 22/13
| [[12/7]], [[22/13]], [[17/10]]
| ^M6, d7
| ^M6, d7
| upmajor 6th, dim 7th
| upmajor 6th, dim 7th
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| 34
| 34
| 948.8
| 948.8
| 26/15
| [[26/15]]
| vA6, ^d7
| vA6, ^d7
| downaug 6th, updim 7th
| downaug 6th, updim 7th
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| 35
| 35
| 976.7
| 976.7
| 7/4
| [[7/4]]
| A6, vm7
| A6, vm7
| aug 6th, downminor 7th
| aug 6th, downminor 7th
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| 36
| 36
| 1004.7
| 1004.7
| 9/5, 16/9
| [[9/5]], [[16/9]]
| m7
| m7
| minor 7th
| minor 7th
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| 37
| 37
| 1032.6
| 1032.6
| 20/11
| [[20/11]]
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 304: Line 304:
| 38
| 38
| 1060.5
| 1060.5
| 11/6, 13/7, 24/13
| [[11/6]], [[13/7]], [[24/13]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
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| 39
| 39
| 1088.4
| 1088.4
| 15/8, 28/15, 32/17
| [[15/8]], [[28/15]], [[32/17]]
| M7
| M7
| major 7th
| major 7th
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| 40
| 40
| 1116.3
| 1116.3
| ''17/9'', 21/11, ''27/14'', 40/21, 48/25
| ''[[17/9]]'', [[21/11]], ''[[27/14]]'', [[40/21]], [[48/25]]
| ^M7, d8
| ^M7, d8
| upmajor 7th, dim 8ve
| upmajor 7th, dim 8ve
Line 325: Line 325:
| 41
| 41
| 1144.2
| 1144.2
| 25/13, 39/20, 52/27, 64/33, ''96/49''
| [[25/13]], [[39/20]], [[52/27]], [[64/33]], ''[[96/49]]''
| vA7, ^d8
| vA7, ^d8
| downaug 7th, updim 8ve
| downaug 7th, updim 8ve
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| 42
| 42
| 1172.1
| 1172.1
| ''35/18'', 49/25, 63/32, 65/33, 128/65
| ''[[35/18]]'', [[49/25]], [[63/32]], [[65/33]], [[128/65]]
| A7, v8
| A7, v8
| aug 7th, down 8ve
| aug 7th, down 8ve
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| 43
| 43
| 1200.0
| 1200.0
| 2/1
| [[2/1]]
| P8
| P8
| perfect 8ve
| perfect 8ve
Line 352: Line 352:
Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A♯ and B♭ are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.
Because 43edo is a meantone system, this makes it easier to adapt traditional Western notation to it than to some other tunings. A♯ and B♭ are distinct and the distance between them is one meride. The whole tone is divided into seven merides so this means we can use "third-sharps", "two-thirds-sharps", "third-flats", and "two-thirds-flats" to reach the remaining notes between A and B; notes elsewhere on the scale can be notated similarly.


=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
In [[ups and downs notation]], the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
Note that downsharp can be respelled as dup (double-up), and upflat as dud.
{{Sharpness-sharp3-szg}}
{{Ups and downs sharpness}}
 
Or one can use the [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]. They use sharps and flats with arrows, borrowed from extended [[Helmholtz-Ellis notation|Helmholtz–Ellis]] notation:
{{Sharpness-sharp3}}


The notes between A and B can then be notated as A, A{{naturalup}}, A{{sharpdown}}, A♯, B♭, B{{flatup}}, B{{naturaldown}}, B. Note that A♯ is enharmonic to B{{flatdown}}, and B♭ is enharmonic to A{{sharpup}}.
The notes between A and B can then be notated as A, A{{naturalup}}, A{{sharpdown}}, A♯, B♭, B{{flatup}}, B{{naturaldown}}, B. Note that A♯ is enharmonic to B{{flatdown}}, and B♭ is enharmonic to A{{sharpup}}.
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Double or even triple arrows may arise if the arrows are taken to have their own layer of enharmonic spellings.
Double or even triple arrows may arise if the arrows are taken to have their own layer of enharmonic spellings.
=== Kite's ups and downs notation ===
In [[Kite's ups and downs notation]], the "third-sharp" becomes an up and the "two-thirds-sharp" becomes a downsharp.
Note that downsharp can be respelled as dup (double-up), and upflat as dud.
{{Ups and downs sharpness}}


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[36edo#Sagittal notation|36-EDO]].
This notation uses the same sagittal sequence as [[36edo #Sagittal notation|36edo]].


==== Evo flavor ====
==== Evo flavor ====
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</imagemap>
</imagemap>


=== Red-Blue Notation ===
=== Red-Blue notation ===
For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. (Note that this is different than Kite's [[color notation]].) Now we have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).
For people who are not colorblind, a red-note/blue-note system (similar to that proposed for [[36edo]]) can also be used. Note that this is different from [[Kite's color notation]]. We have the following sequence of notes, each separated by one meride: {{colored note|A}}, {{colored note|red|A}}, {{colored note|blue|A♯}}, {{colored note|A♯}}, {{colored note|B♭}}, {{colored note|red|B♭}}, {{colored note|blue|B}}, {{colored note|B}}. (Note that red sharps or blue flats are enharmonically equivalent to simpler notes: {{colored note|red|A♯}} is enharmonic to B♭, and {{colored note|blue|B♭}} is actually just A♯).


The diatonic semitone is four steps, so for the region between B and C, we can use: {{colored note|B}}, {{colored note|C♭}}, {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}} (they are enharmonic equivalents), {{colored note|B♯}}, and {{colored note|C}}. All of the notes in 43edo therefore have only one name except for {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}}, and {{colored note|blue|E♯}}&nbsp;/&nbsp;{{colored note|red|F♭}}. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).
The diatonic semitone is four steps, so for the region between B and C, we can use: {{colored note|B}}, {{colored note|C♭}}, {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}} (they are enharmonic equivalents), {{colored note|B♯}}, and {{colored note|C}}. All of the notes in 43edo therefore have only one name except for {{colored note|blue|B♯}}&nbsp;/&nbsp;{{colored note|red|C♭}}, and {{colored note|blue|E♯}}&nbsp;/&nbsp;{{colored note|red|F♭}}. It might also be possible to design special symbols for those two notes (resembling a cross between the letters B and C in the former case, and E and F in the latter).
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| Spleen comma
| Spleen comma
|}
|}
<references group="note" />


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
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* Fossa pentatonic scale (approximated from [[catnip]] in [[60edo]]): 5 14 6 6 12
* Fossa pentatonic scale (approximated from [[catnip]] in [[60edo]]): 5 14 6 6 12
* [[Magnetosphere scale]] (approximated from [[Hexany 1728]]): 4 10 11 11 7
* [[Magnetosphere scale]] (approximated from [[Hexany 1728]]): 4 10 11 11 7
== Instruments ==
*[[Lumatone mapping for 43edo]]
*[[Skip fretting system 43 2 9]]
=== Keyboards ===
A possible isomorphic keyboard layout for 43edo:
[[File:Fifth Comma Meantone Keyboard Layout.svg|800px|none|thumb]]


== Music ==
== Music ==
=== Modern renderings ===
=== Modern renderings ===
; {{W|Johann Sebastian Bach}}
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=v3mBkctQ4SI ''Prelude in C minor'', BWV 999] (1717–1723) – transposed into E minor, arranged for Organ and rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=v3mBkctQ4SI ''Prelude in C minor'', BWV 999] (1717–1723) – transposed into E minor, arranged for Organ and rendered by [[Claudi Meneghin]] (2024)
* [https://www.youtube.com/watch?v=u3ss3H2x_QA "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=u3ss3H2x_QA "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=E7W-t2KDeSs "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=E7W-t2KDeSs "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
Line 1,010: Line 1,020:
** [https://www.youtube.com/shorts/m408V08QAMI Sine wave version] &mdash; rendered by Claudi Meneghin (2025)
** [https://www.youtube.com/shorts/m408V08QAMI Sine wave version] &mdash; rendered by Claudi Meneghin (2025)
** [https://www.youtube.com/shorts/oZiYri-sDYo Fortepiano version] &mdash; rendered by Claudi Meneghin (2025)
** [https://www.youtube.com/shorts/oZiYri-sDYo Fortepiano version] &mdash; rendered by Claudi Meneghin (2025)
; {{W|Gabriel Fauré}}
* [https://www.youtube.com/watch?v=72YtMnmu_sw ''Pavane, Op. 50''] (1887) – arranged for harpsichord and rendered by Claudi Meneghin (2026)
; {{W|Toby Fox}}
* [https://www.youtube.com/shorts/r8gvT-CZLEI ''Shop 3''] via ''{{W|Deltarune}} Chapter 1'' (2018) – microtonal cover in 43edo by [[Bryan Deister]] (2026)


; {{W|George Frideric Handel}}
; {{W|George Frideric Handel}}
Line 1,016: Line 1,032:
; {{W|Scott Joplin}}
; {{W|Scott Joplin}}
* [https://www.youtube.com/watch?v=nV_jmn31Kiw ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=nV_jmn31Kiw ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
; {{W|Modest Mussorgsky}}
* [https://www.youtube.com/shorts/cualmBJUlrI ''«Gnomus» from «Pictures at an Exhibition»''] (1874) – arranged for harpsichord and rendered by Claudi Meneghin (2026)


; {{W|Shirō Sagisu}}
; {{W|Shirō Sagisu}}
Line 1,022: Line 1,041:
=== 21st century ===
=== 21st century ===
;; [[Claudi Meneghin]]
;; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=t83BNX1g6Jg ''DOUBLE FUGUE on «Old Mc Donald» + «Shave & a Haircut», tunedo into E43 (1/5-comma meantone)''] (2024)
* [https://www.youtube.com/watch?v=t83BNX1g6Jg ''DOUBLE FUGUE on «Old Mc Donald» + «Shave & a Haircut», tuned into E43 (1/5-comma meantone)''] (2024)


; [[Bryan Deister]]
; [[Bryan Deister]]
Line 1,051: Line 1,070:
; [[Xotla]]
; [[Xotla]]
* "Beebounce" from ''Jazzbeetle'' (2023) – [https://open.spotify.com/track/4PzANNtxXsNEsdApnYKgHK Spotify] | [https://xotla.bandcamp.com/track/beebounce-43edo Bandcamp] | [https://youtu.be/EZIg5fojFfE YouTube] – jazzy big band electronic hybrid
* "Beebounce" from ''Jazzbeetle'' (2023) – [https://open.spotify.com/track/4PzANNtxXsNEsdApnYKgHK Spotify] | [https://xotla.bandcamp.com/track/beebounce-43edo Bandcamp] | [https://youtu.be/EZIg5fojFfE YouTube] – jazzy big band electronic hybrid
== Instruments ==
*[[Lumatone mapping for 43edo]]
*[[Skip fretting system 43 2 9]]
=== Keyboards ===
A possible isomorphic keyboard layout for 43edo:
[[File:Fifth Comma Meantone Keyboard Layout.svg|800px|none|thumb]]
== Notes ==
<references group="note" />


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/43edo"