Sharpness: Difference between revisions

m Update link to MuseScore plugin
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added an explanation of the importance to notation, extended the concept to penta-sharpness, clarified the link to the original paper
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A sharp-0 edo is also known as a "perfect edo".
A sharp-0 edo is also known as a "perfect edo".
The sharpness of an edo has implications for the heptatonic fifth-generated notation of that edo. For example, all sharp-1 edos (5, 12, 19, 26...) can be notated conventionally with just 7 letters and #/b. Another example: the half-sharp and half-flat accidentals are applicable to an edo only if its sharpness is an even number.


== Table ==
== Table ==
Below is a table showing the characteristics of each edo up to 72 in the context of traditional fifth-generator heptatonic ups and downs notation. Each row represents the steps of a chromatic semitone. Each column represents the steps of a diatonic semitone (limma, [[256/243]]), located between E–F and B–C.
Below is a table showing the characteristics of each edo up to 72 in the context of traditional fifth-generator heptatonic ups and downs notation. Each row represents the steps of a chromatic semitone. Each column represents the steps of a diatonic semitone (limma, [[256/243]]), located between E–F and B–C. If one's notation were pentatonic instead of heptatonic, the concept of sharpness would be applied to the limna not the apotome to get penta-sharpness. In the table below, the sharp-0 edos and the pentasharp-0 edos are bolded.


{| class="wikitable center-all"
{| class="wikitable center-all"
|+Sharpness value \ steps of a diatonic semitone
|+Sharpness value \ penta-sharpness value
!|
!|
!|-2
!|-2
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|
|
|
|
|7
|'''7'''
|14
|'''14'''
|21
|'''21'''
|28
|'''28'''
|35
|'''35'''
|42b
|'''42b'''
|
|
|
|
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|
|
|
|
|5
|'''5'''
|12
|12
|19
|19
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|
|
|3
|3
|10
|'''10'''
|17
|17
|24
|24
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|1
|1
|8
|8
|15
|'''15'''
|22
|22
|29
|29
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|6
|6
|13
|13
|20
|'''20'''
|27
|27
|34
|34
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|11b
|11b
|18
|18
|25
|'''25'''
|32
|32
|39
|39
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|
|
|23b
|23b
|30
|'''30'''
|37
|37
|44
|44
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|
|
|
|
|35b
|'''35b'''
|42
|42
|49
|49
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== External links ==
== External links ==
* [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Kite's theory using the nomenclature of sharpness]: (perhaps introducing?)
* [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Notation Guide to EDOs 5-72]: (paper by [[Kite Giedraitis]] introducing the concept)
* [https://github.com/euwbah/musescore-microtonal-edo-plugin n-EDO Retuner plugin for Musescore 3.4+]: uses sharpness to categorize EDOs for retuning  
* [https://github.com/euwbah/musescore-microtonal-edo-plugin n-EDO Retuner plugin for Musescore 3.4+]: uses sharpness to categorize EDOs for retuning  
* [https://sagittal.org/Periodic%20table%20of%20small%20EDOs%20large.png Sagittal notation's Periodic Table of EDOs]: arranges EDOs by their sharpness
* [https://sagittal.org/Periodic%20table%20of%20small%20EDOs%20large.png Sagittal notation's Periodic Table of EDOs]: arranges EDOs by their sharpness and penta-sharpness


[[Category:EDO theory pages]]
[[Category:EDO theory pages]]