For those of you with an interest in learning about microtonality, we thought it might be helpful for you to read about the nomenclature used in various microtonal mappings before viewing the presets that follow in this appendix. There are many schools of thought about how to spell the accidentals in microtonal music. We’ve used multiple approaches in the article that follows.
Certain tunings can be notated only using standard accidentals (#, b) in a single chain of fifths (12, 17, 19-ET). Some have an extended chain of fifths that goes into double or even triple accidentals (31, 41-ET), however this gets quite difficult to read and relate to pitch-class, as, for example, in tunings with fifths wider than 700c, ascending pitch order around D goes Fbbb-Ebb-D-Cx-B#x.
To help with readability and relating to pitch class, half-sharps (+) and half-flats (d) can be very helpful in any tuning which splits the sharp/flat into two equal or nearly-equal parts, e.g. 17, 24, 31, 41-ET. These are also tunings which can be generated by a chain of neutral thirds. Thus we can also create a neutral triad on D, D-F+-A.
However we still have the same problem in larger systems, which can be remedied by another symbol pair, comma-up, or simply “up” (/) and comma-down, or “down” (\), for small alterations of a “comma”, which for most listeners stay within the same pitch class, but change the intonation, so, e.g. different flavours of minor and major can be compared, e.g. filling in the third between D-A we might have \F, F, /F, \F#, F# or /F#.
| Name | Function | Rules, Examples |
# | sharp | Raises pitch by a chromatic semitone | F# always a perfect fifth above B |
b | flat | Lowers pitch by a chromatic semitone | Bb always a perfect fifth below F |
x | double-sharp | Raises pitch by two chromatic semitones | Fx always a perfect fifth above B# |
bb | double-flat | Lowers pitch by two chromatic semitones | Bbb always a perfect fifth below Fb |
+ | half-sharp | Raises pitch by half a chromatic semitone | F+ always a neutral third above D and a perfect fifth above Bd |
d | half-flat | Lowers pitch by half a chromatic semitone | Bd always a neutral third below D and a perfect fifth below F+ |
#+ | sesqui-sharp | Raises pitch by one and a half chromatic semitones | F#+ always a neutral third above D# and a perfect fifth above B+ |
db | sesqui-flat | Lowers pitch by one and a half chromatic semitones | Bdb always a neutral third below Db and a perfect fifth below Fd |
/ | (comma) up | Raises pitch by a comma (less than a chromatic semitone) | /F always a large minor third above D |
\ | (comma) down | Lowers pitch by a comma (less than a chromatic semitone) | \B always a large minor third below D |
To demonstrate different approaches to spelling pitches with different sets of accidentals, here are three ways to describe the same 25 pitches between the perfect fifth from C-G in 41-et:
Standard fifth-chain accidentals:
C B# Ebbb Db C# Bx Ebb D Cx Fbb Eb D# Gbbb Fb E Dx Gbb F E# Abbb Gb F# Ex Abb G
Half-accidentals:
C B# C+ Db C# Dd Ebb D Cx Fbb Eb D# Ed Fb E Dx Gbb F E# F+ Gb F# Gd Abb G
Half-accidentals:
C B# C+ Db C# Dd Ebb D Cx Fbb Eb D# Ed Fb E Dx Gbb F E# F+ Gb F# Gd Abb G
Comma accidentals:
C /C C+ Db /Db Dd \D D /D \Eb Eb /Eb Ed \E E /E \F F /F F+ \F# F# Gd \G G
While this can all seem complicated if you’re just starting out with microtonality, stick with it and it really will become second nature. And if you’d rather try something more colour-driven, we encourage you to check out preset 10 that ships with your Lumatone -- Dolores Catherino’s polychromatic layout -- which enables you to use “pitch colour” to understand the intervals between notes instead of thinking of it in terms of accidentals.