Alternative symbols for ups and downs notation

Main article: 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) with and up and down arrows via Gould arrow quarter tone symbols or 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 accidentals are up and down arrows attached to sharps, flats, or naturals, and modify the note by one step. They appear very similar to Helmholtz–Ellis accidentals, and are fully interchangeable with them.

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:

Step offset	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

Attaching arrows to semi- and sesquisharps and flats is also another option instead of using double arrows:

Step offset	0	1	2	3	4	5	6	7	8	9	10	11	12	13
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.

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.

Sharp-10 (example)

Sharp-10 edos have a sharp that raises 10 steps. Edos of this category are 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, and 141.

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

Step offset	13	14	15	16	17	18	19	20	21	22
Sharp symbol
Flat symbol

Sharp-14 (example)

Sharp-14 edos have a sharp that raises 14 steps.

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

Step Offset	18	19	20	21	22	23	24	25	26	27	28	29	30	31
Sharp Symbol
Flat Symbol

Flat-1

For edos such as 9, 16, 23, and 30, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually lowers by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.

Step offset	−2	−1	0	+1	+2
Symbol

However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).

Flat-2

Flat-2 edos (virtually 11edo only), if you pretend their native antidiatonic scales are diatonic, 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.