Sharpness: Difference between revisions
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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 \ | |+Sharpness value \ penta-sharpness value | ||
!| | !| | ||
!|-2 | !|-2 | ||
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| | | | ||
| | | | ||
|7 | |'''7''' | ||
|14 | |'''14''' | ||
|21 | |'''21''' | ||
|28 | |'''28''' | ||
|35 | |'''35''' | ||
|42b | |'''42b''' | ||
| | | | ||
| | | | ||
| Line 80: | Line 82: | ||
| | | | ||
| | | | ||
|5 | |'''5''' | ||
|12 | |12 | ||
|19 | |19 | ||
| Line 93: | Line 95: | ||
| | | | ||
|3 | |3 | ||
|10 | |'''10''' | ||
|17 | |17 | ||
|24 | |24 | ||
| Line 106: | Line 108: | ||
|1 | |1 | ||
|8 | |8 | ||
|15 | |'''15''' | ||
|22 | |22 | ||
|29 | |29 | ||
| Line 119: | Line 121: | ||
|6 | |6 | ||
|13 | |13 | ||
|20 | |'''20''' | ||
|27 | |27 | ||
|34 | |34 | ||
| Line 132: | Line 134: | ||
|11b | |11b | ||
|18 | |18 | ||
|25 | |'''25''' | ||
|32 | |32 | ||
|39 | |39 | ||
| Line 145: | Line 147: | ||
| | | | ||
|23b | |23b | ||
|30 | |'''30''' | ||
|37 | |37 | ||
|44 | |44 | ||
| Line 158: | Line 160: | ||
| | | | ||
| | | | ||
|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 | * [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]] | ||