Alternative symbols for ups and downs notation

From Xenharmonic Wiki
Jump to: navigation, search

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 n-Edo Retuner Plugin. (Feel free to address others.)

Detail

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 ETs 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.

Below is a table showing the characteristics of each ET below 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.

Sharpness value \ steps of a diatonic semitone
-2 -1 0 1 2 3 4 5 6 7 8
-3 6b
-2 4 11 18b
-1 2 9 16 23 30b
0 7 14 21 28 35 42b
1 5 12 19 26 33 40 47 54b
2 3 10 17 24 31 38 45 52 59b
3 1 8 15 22 29 36 43 50 57 64 71b
4 6 13 20 27 34 41 48 55 62 69
5 11b 18 25 32 39 46 53 60 67
6 23b 30 37 44 51 58 65 72
7 35b 42 49 56 63 70
8 47b 54 61 68
9 52b 59 66
10 64b 71

Usage guide for each sharpness value

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

Sharp 1

Sharp-1 ETs have a sharp that raises 1 step. ETs 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 Accidental doublesharp.png Accidental sharp.png Accidental natural.png Accidental flat.png Accidental doubleflat.png

Sharp 2

Sharp-2 ETs have a sharp that raises 2 steps. ETs of this category include 10, 17, 24, 31, etc.

As are commonly seen in 24-edo and 31-edo, semisharps and semiflats could be used for a substitution of the tilde.

Step offset +4 +3 +2 +1 0 -1 -2 -3 -4
Symbol Accidental doublesharp.png Accidental sesquisharp.png Accidental sharp.png Accidental semisharp.png Accidental natural.png Accidental semiflat.png Accidental flat.png Accidental sesquiflat.png Accidental doubleflat.png

Sharp-3

Sharp-3 ETs have a sharp that raises 3 steps. ETs of this category include 22, 29, 36, 43, etc.

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

Step offset 7 6 5 4 3 2 1 0
Sharp symbol Accidental doublesharp up.png Accidental doublesharp.png Accidental doublesharp down.png Accidental sharp up.png Accidental sharp.png Accidental sharp down.png Accidental natural up.png Accidental natural.png
Flat symbol Accidental doubleflat down.png Accidental doubleflat.png Accidental doubleflat up.png Accidental flat down.png Accidental flat.png Accidental flat up.png Accidental natural down.png

Sharp-4

Sharp-4 ETs have a sharp that raises 4 steps. ETs of this category include 27, 34, 41, 48, 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 Accidental doublesharp up.png Accidental doublesharp.png Accidental doublesharp down.png Accidental sesquisharp.png Accidental sharp up.png Accidental sharp.png Accidental sharp down.png Accidental semisharp.png Accidental natural up.png Accidental natural.png
Flat symbol Accidental doubleflat down.png Accidental doubleflat.png Accidental doubleflat up.png Accidental sesquiflat.png Accidental flat down.png Accidental flat.png Accidental flat up.png Accidental semiflat.png Accidental natural down.png

Sharp-5

Starting with sharp-5, which includes the famous 53-ET, 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 Accidental doublesharp up2.png Accidental doublesharp up1.png Accidental doublesharp.png Accidental doublesharp down1.png Accidental doublesharp down2.png Accidental sharp up2.png Accidental sharp up1.png Accidental sharp.png Accidental sharp down1.png Accidental sharp down2.png Accidental natural up2.png Accidental natural up1.png Accidental natural.png
Flat symbol Accidental doubleflat down2.png Accidental doubleflat down1.png Accidental doubleflat.png Accidental doubleflat up1.png Accidental doubleflat up2.png Accidental flat down2.png Accidental flat down1.png Accidental flat.png Accidental flat up1.png Accidental flat up2.png Accidental natural down2.png Accidental natural down1.png

Sharp-6

Step offset 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol Accidental doublesharp up2.png Accidental doublesharp up1.png Accidental doublesharp.png Accidental doublesharp down1.png Accidental doublesharp down2.png Accidental sesquisharp.png Accidental sharp up2.png Accidental sharp up1.png Accidental sharp.png Accidental sharp down1.png Accidental sharp down2.png Accidental semisharp.png Accidental natural up2.png Accidental natural up1.png Accidental natural.png
Flat symbol Accidental doubleflat down2.png Accidental doubleflat down1.png Accidental doubleflat.png Accidental doubleflat up1.png Accidental doubleflat up2.png Accidental sesquiflat.png Accidental flat down2.png Accidental flat down1.png Accidental flat.png Accidental flat up1.png Accidental flat up2.png Accidental semiflat.png Accidental natural down2.png Accidental natural down1.png

Sharp-7

Step offset 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol Accidental doublesharp up3.png Accidental doublesharp up2.png Accidental doublesharp up1.png Accidental doublesharp.png Accidental doublesharp down1.png Accidental doublesharp down2.png Accidental doublesharp down3.png Accidental sharp up3.png Accidental sharp up2.png Accidental sharp up1.png Accidental sharp.png Accidental sharp down1.png Accidental sharp down2.png Accidental sharp down3.png Accidental natural up3.png Accidental natural up2.png Accidental natural up1.png Accidental natural.png
Flat symbol Accidental doubleflat down3.png Accidental doubleflat down2.png Accidental doubleflat down1.png Accidental doubleflat.png Accidental doubleflat up1.png Accidental doubleflat up2.png Accidental doubleflat up3.png Accidental flat down3.png Accidental flat down2.png Accidental flat down1.png Accidental flat.png Accidental flat up1.png Accidental flat up2.png Accidental flat up3.png Accidental natural down3.png Accidental natural down2.png Accidental natural down1.png

Sharp-8

Step offset 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Sharp symbol Accidental doublesharp up3.png Accidental doublesharp up2.png Accidental doublesharp up1.png Accidental doublesharp.png Accidental doublesharp down1.png Accidental doublesharp down2.png Accidental doublesharp down3.png Accidental sesquisharp.png Accidental sharp up3.png Accidental sharp up2.png Accidental sharp up1.png Accidental sharp.png Accidental sharp down1.png Accidental sharp down2.png Accidental sharp down3.png Accidental semisharp.png Accidental natural up3.png Accidental natural up2.png Accidental natural up1.png Accidental natural.png
Flat symbol Accidental doubleflat down3.png Accidental doubleflat down2.png Accidental doubleflat down1.png Accidental doubleflat.png Accidental doubleflat up1.png Accidental doubleflat up2.png Accidental doubleflat up3.png Accidental sesquiflat.png Accidental flat down3.png Accidental flat down2.png Accidental flat down1.png Accidental flat.png Accidental flat up1.png Accidental flat up2.png Accidental flat up3.png Accidental semiflat.png Accidental natural down3.png Accidental natural down2.png Accidental natural down1.png

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

The rest will be discussed below.

Flat-1

Flat-1 ETs have a sharp that lowers 1 step. ETs 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 Accidental doubleflat.png Accidental flat.png Accidental natural.png Accidental sharp.png Accidental doublesharp.png

Flat-2

Flat-2 ETs (virtually 11-ET 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 Accidental doubleflat.png Accidental sesquiflat.png Accidental flat.png Accidental semiflat.png Accidental natural.png Accidental semisharp.png Accidental sharp.png Accidental sesquisharp.png Accidental doublesharp.png

Zero

The zero row is even more special in that the traditional accidentals cannot raise or lower the pitch, so the note can only be modified by arrows. ETs of this category include 7, 14, 21, 28, and 35.

Step offset +3 +2 +1 0 -1 -2 -3
Symbol Accidental natural up3.png Accidental natural up2.png Accidental natural up1.png Accidental natural.png Accidental natural down1.png Accidental natural down2.png Accidental natural down3.png

Limitations

Some notes cannot be reached in ETs of sharpness value higher than 9 due to MuseScore not providing the stacks of arrows required. ETs below 72 known to be impractical for this reason: 59, 66, 71. Some notes cannot be reached in ETs with a very flat fifth due to MuseScore not providing multiple sharps and flats. ETs below 72 known to be impractical for this reason: 21, 26, 28, 33, 35, 40, 45, 47, 52, 64. Therefore, such ETs are capped from its full strength.

Conclusively, this set of symbols still cover most ETs below 72.