Alternative symbols for ups and downs notation

This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, ups and downs notation with a different look.

Alternative symbols may be useful for the following reasons:

1. One may prefer a more conventional look of the score;
2. The up and down symbols may not be quite accessible in computer-aided score typing.

All symbols proposed in this article are available in MuseScore 3, and is used by the Microtonal plugin for Musescore 3.4+. (Feel free to address others.)

Symbol set

The symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein-Zimmermann quartertone accidentals (semisharps and semiflats), and up and down arrows in Gould arrow quartertone symbols or part of Helmholtz-Ellis just intonation accidentals.

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 edos 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.

Usage guide for each sharpness value

See also: Sharpness

A usage guide for edos of sharpness value below 8 will be provided here.

Sharp-1

Sharp-1 edos have a sharp that raises 1 step. Edos of this category are 5, 12, 19, 26, and 33. Traditional notation can be used since an up is exactly equivalent to a sharp.

Step Offset	−2	−1	0	+1	+2
Symbol

Sharp-2

Sharp-2 edos have a sharp that raises 2 steps. Edos of this category are 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.

Step Offset	−4	−3	−2	−1	0	+1	+2	+3	+4
Symbol

Sharp-3

Sharp-3 edos have a sharp that raises 3 steps. Edos of this category are 8, 15, 22, 29, 36, 43, 50, 57, and 64. This is where you really want to use ups and downs.

Step Offset	0	1	2	3	4	5	6	7
Sharp Symbol
Flat Symbol

In some cases, some notes or intervals may be best spelled with double arrows:

Steps	0	1	2	3	4	5	6	7	8
Sharp Symbol
Flat Symbol

Sharp-4

Sharp-4 edos have a sharp that raises 4 steps. Edos of this category are 13, 20, 27, 34, 41, 48, 55, 62, 69, and 76. Many consider a full combination of semisharps, semiflats, ups and down to appear very neat.

Step Offset	0	1	2	3	4	5	6	7	8	9
Sharp Symbol
Flat Symbol

Sharp-5

Sharp-5 edos have a sharp that raises 5 steps. Edos of this category are 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, and 88.

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12
Sharp Symbol
Flat Symbol

In some cases, some notes or intervals may be best spelled with triple arrows:

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13
Sharp Symbol
Flat Symbol

Sharp-6

Sharp-6 edos have a sharp that raises 6 steps. Edos of this category are 30, 37, 44, 51, 58, 65, 72, 79, 86, 93, and 100.

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Sharp Symbol
Flat Symbol

Sharp-7

Sharp-7 edos have a sharp that raises 7 steps. Edos of this category are 42, 49, 56, 63, 70, 77, 84, 91, 98, and 105.

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
Sharp Symbol
Flat Symbol

Sharp-8

Sharp-8 edos have a sharp that raises 8 steps. Edos of this category are 54, 61, 68, 75, 82, 89, 96, 103, 110, and 117.

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
Sharp Symbol
Flat Symbol

Higher sharpness values

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 (71, 78, 85, 92, 99, 106, 113, 120, 127, 134, and 141) can be notated as follows:

Step Offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
Sharp Symbol
Flat Symbol

SMuFL curently supplies extended Stein-Zimmermann accidentals (U+E290–U+E29F), which contains demi- and sesqui-sharps and flats with a single arrow. The rest will be discussed below.

Flat-1

Flat-1 edos have a sharp that lowers 1 step. Edos of this category are 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 of a larger edo.

Step Offset	−2	−1	0	+1	+2
Symbol

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.

Step Offset	−4	−3	−2	−1	0	+1	+2	+3	+4
Symbol

Zero

On the other hand, the lower five multiples of 7 (7, 14, 21, 28, and 35) are known as "perfect" or sharp-0 edos, since, by tempering out the Pythagorean apotome of 2187/2048, the traditional sharps and flats are redundant and cannot raise or lower the pitch. Here, the notes can only be modified by arrows.

Step Offset	−3	−2	−1	0	+1	+2	+3
Symbol

Limitations

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 59 and 66. Therefore, such edos are capped from their full strength.

Conclusively, this set of symbols still covers most edos up to 72.