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 include 5, 12, 19, 26, etc.

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 include 10, 17, 24, 31, etc.

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 include 8, 15, 22, 29, etc.

This is where you really want to use ups and downs.

Step offset	7	6	5	4	3	2	1	0
Sharp symbol
Flat symbol

Sharp-4

Sharp-4 EDOs have a sharp that raises 4 steps. EDOs of this category include 13, 20, 27, 34, etc.

A full combination of semisharps, semiflats, ups and downs looks very neat.

Step offset	9	8	7	6	5	4	3	2	1	0
Sharp symbol
Flat symbol

Sharp-5

Sharp-5 EDOs have a sharp that raises 5 steps. EDOs of this category include 18, 25, 32, 39, etc.

Starting with sharp-5, which includes the famous 53edo, you'll have to use double ups and downs.

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

Sharp-6

Sharp-6 EDOs have a sharp that raises 6 steps. EDOs of this category include 30, 37, 44, 51, etc.

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

Sharp-7

Sharp-7 EDOs have a sharp that raises 7 steps. EDOs of this category include 42, 49, 56, 63, etc.

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

Sharp-8

Sharp-8 EDOs have a sharp that raises 8 steps. EDOs of this category include 54, 61, 68, etc.

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

Provided with more stacks of arrows, EDOs of higher sharpness value can be notated in the same method as above.

The rest will be discussed below.

Flat-1

Flat-1 EDOs have a sharp that lowers 1 step. EDOs of this category include 9, 16, and 23. To have a sharp that actually lowers the tone can be counter-intuitive, yet reasonable for the system. Regardless, you could just flip it around.

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.

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

Zero

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 7, 14, 21, 28, and 35.

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

Limitations

Some notes cannot be reached in EDOs of sharpness value higher than 9 due to MuseScore not providing the stacks of arrows required. EDOs below 72 known to be impractical for this reason: 59, 66, and 71. Therefore, such EDOs are capped from its full strength.

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