Alternative symbols for ups and downs notation: Difference between revisions
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The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]). | The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]). | ||
The Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to [[ | The Stein-Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to [[edo]]s of even sharpness value only. | ||
The Gould arrow quartertone symbols are up and down arrows attached to sharps, flats or naturals. They modify the note by one step. The syntonic comma in Helmholtz-Ellis just intonation accidentals looks very similar, and ''can be used interchangeably''. | The Gould arrow quartertone symbols are up and down arrows attached to sharps, flats or naturals. They modify the note by one step. The syntonic comma in Helmholtz-Ellis just intonation accidentals looks very similar, and ''can be used interchangeably''. | ||
== Usage guide for each sharpness value == | == Usage guide for each sharpness value == | ||
{{See also|Sharpness}} | {{See also| Sharpness }} | ||
A usage guide for | |||
A usage guide for edos of sharpness value below 8 will be provided here. | |||
=== Sharp-1 === | === Sharp-1 === | ||
Sharp-1 | Sharp-1 edos have a sharp that raises 1 step. Edos of this category are {{EDOs| 5, 12, 19, 26, and 33 }}. | ||
Traditional notation can be used since an up is exactly equivalent to a sharp. | Traditional notation can be used since an up is exactly equivalent to a sharp. | ||
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=== Sharp-2 === | === Sharp-2 === | ||
Sharp-2 | Sharp-2 edos have a sharp that raises 2 steps. Edos of this category are {{EDOs| 10, 17, 24, 31, 38, 45, and 52 }}. | ||
As are commonly seen in 24edo and 31edo, semisharps and semiflats could be used for a substitution of the tilde. | As are commonly seen in 24edo and 31edo, semisharps and semiflats could be used for a substitution of the tilde. | ||
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=== Sharp-3 === | === Sharp-3 === | ||
Sharp-3 | Sharp-3 edos have a sharp that raises 3 steps. Edos of this category are {{EDOs| 8, 15, 22, 29, 36, 43, 50, 57, and 64 }}. | ||
This is where you ''really'' want to use ups and downs. | This is where you ''really'' want to use ups and downs. | ||
{ | {{Sharpness-sharp3}} | ||
=== Sharp-4 === | === Sharp-4 === | ||
Sharp-4 | Sharp-4 edos have a sharp that raises 4 steps. EDOs of this category are {{EDOs| 13, 20, 27, 34, 41, 48, 55, 62, 69, and 76 }}. | ||
A full combination of semisharps, semiflats, ups and downs looks very neat. | A full combination of semisharps, semiflats, ups and downs looks very neat. | ||
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=== Sharp-5 === | === Sharp-5 === | ||
Sharp-5 | Sharp-5 edos have a sharp that raises 5 steps. EDOs of this category are {{EDOs| 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, and 88 }}. | ||
{{Sharpness-sharp5}} | {{Sharpness-sharp5}} | ||
=== Sharp-6 === | === Sharp-6 === | ||
Sharp-6 | Sharp-6 edos have a sharp that raises 6 steps. EDOs of this category are {{EDOs| 30, 37, 44, 51, 58, 65, 72, 79, 86, 93, and 100 }}. | ||
{{Sharpness-sharp6}} | {{Sharpness-sharp6}} | ||
=== Sharp-7 === | === Sharp-7 === | ||
Sharp-7 | Sharp-7 edos have a sharp that raises 7 steps. EDOs of this category are {{EDOs| 42, 49, 56, 63, 70, 77, 84, 91, 98, and 105 }}. | ||
{{Sharpness-sharp7}} | {{Sharpness-sharp7}} | ||
=== Sharp-8 === | === Sharp-8 === | ||
Sharp-8 | Sharp-8 edos have a sharp that raises 8 steps. EDOs of this category are {{EDOs| 54, 61, 68, 75, 82, 89, 96, 103, 110, and 117 }}. | ||
{{Sharpness-sharp8}} | {{Sharpness-sharp8}} | ||
=== Higher sharpness values === | === Higher sharpness values === | ||
Provided with more stacks of arrows, or the ability to attach arrows to demi- and sesqui-sharps and flats, | Provided with more stacks of arrows, or the ability to attach arrows to demi- and sesqui-sharps and flats, edos of higher sharpness value can be notated in the same method as above. For example, sharp-10 edos ({{EDOs| 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, and 141 }}) can be notated as follows: | ||
{{Sharpness-sharp10-qt1}} | {{Sharpness-sharp10-qt1}} | ||
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=== Flat-1 === | === Flat-1 === | ||
Flat-1 | Flat-1 edos have a sharp that ''lowers'' 1 step. Edos of this category are {{EDOs| 9, 16, 23, and 30 }}. To have a sharp that actually lowers the pitch is logical for these edos, yet counter-intuitive. Since none of these edos' fifths will generate a normal [[diatonic scale]], it makes the most sense to notate each of them as a [[subset notation|subset of a larger edo]]. | ||
{{Sharpness-flat1}} | {{Sharpness-flat1}} | ||
=== Flat-2 === | === Flat-2 === | ||
Flat-2 | Flat-2 edos (virtually [[11edo]] only) have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets. | ||
{{Sharpness-flat2}} | {{Sharpness-flat2}} | ||
=== Zero === | === Zero === | ||
Perfect | Perfect edos (sharp-0 edos) are even more special in that the traditional accidentals cannot raise or lower the pitch, so the notes can only be modified by arrows. Edos of this category include {{EDOs| 7, 14, 21, 28, and 35 }}. | ||
{{Sharpness-0}} | {{Sharpness-0}} | ||
== Limitations == | == Limitations == | ||
Some | Some edos have odd-numbered sharpness values 9 and above, and are difficult to notate due to the lack of support for the stacks of arrows required. Edos below 72 known to be impractical for this reason are {{EDOs| 59 and 66 }}. Therefore, such edos are capped from their full strength. | ||
Conclusively, this set of symbols still covers most | Conclusively, this set of symbols still covers most edos up to 72. | ||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category:Ups and Downs Notation]] | [[Category:Ups and Downs Notation]] | ||