Notation
There are many different forms of musical notation in xenharmony. This page will serve as an introduction to some of the concepts found in xenharmonic notation, and some of the more common types. Note that this does not cover interval naming systems with no notational counterpart. Notation systems are usually designed for consistent tuning systems such as regular temperaments, or approximately consistent tuning systems.
In general, a notation system on this wiki allows for the transcription of musical information such as pitches, note durations, rhythms, etc. Most notation systems here act as extensions or modifications of standard staff notation. As this wiki focuses on xenharmony (that is, non-standard intervals), a way of naming and notating pitches (and optionally chords) is generally sufficient for a notation system. A notation system may also include an interval naming system.
Introduction
This section focuses on pitch-related aspects of staff notation.
Staff notation
Staff
A staff is a set of lines (or other reference) that symbols representing notes are placed in relation to. In most notation systems, notes are placed on or in between the lines, resulting in (2n+1) staff positions for n staff lines (without needing additional lines, called ledger lines). Different staff positions represent different pitches. In standard diatonic notation, there are five lines per staff, and therefore 11 distinct staff positions without adding ledger lines.
Clef
A clef is a symbol placed on a staff (usually at the very start) to indicate what note a particular staff line represents. The other notes can then be determined from the clef and a characteristic scale.
Characteristic scale
The characteristic scale is the "default" set of notes that serve as the basis for a system being notated. The notes of the characteristic scale are represented in text by nominals (written symbols representing notes, usually alphabetic, numerical, or drawn from some other extramusical sequence) and on the staff by distinct staff positions. For standard notation, the characteristic scale is mosdiatonic in the mode LsLLsLL on A = 440Hz. The nominals are ABCDEFG, and then A an octave up.
Note that the actual order of the alphabet may be of secondary importance to some musicians. While retaining it aids intuition for people getting into music theory through xenharmony (and thus should be the general rule for notation schemes on this wiki that are not already established or thoroughly practiced), some experienced musicians may prefer to treat the letters as arbitrary symbols (able to be shuffled out of order, reassigned based on pitch or chain position, or otherwise altered, to support their own intuition structures) in nonstandard notation schemes.
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Accidentals
Accidentals are the term for any symbol representing an alteration to a nominal. In standard notation, the # accidental raises a note by a chromatic semitone, and the b accidental lowers by a chromatic semitone. Microtonal notation systems usually add new accidentals, rather than changing the set of nominals. For example, the ^ and v accidentals (arrows) raise and lower by an edostep. Note that accidentals other than the standard # and b (and derivatives) may instead be called inflections in some sources, wherein the category as a whole are alterations. Accidentals generally continue to apply to the same staff position until the next barline is reached.
Key signatures
A key signature is a set of accidentals placed at the beginning of the sheet music that apply to the whole piece and serve as the "default" accidentals to apply to staff positions. These accidentals also apply to notes separated by octaves from their position, which is not true of other accidentals. In general, there are only about 15 key signatures in use (based on the circle of fifths) representing the various transpositions of the diatonic scale. However, key signatures are theoretically possible for any set of defined alterations from the base notes of the characteristic scale, so that (for instance) one could specify a non-MOS diatonic scale with alterations to the standard version. (Note that otherwise, accidentals work normally, so that if the key signature specifies C#, placing a b accidental before a C note will read as Cb, not C (which is what the natural accidental is used for).
Note symbols
While not directly pitch- or interval-related, an important consideration in standard notation is that note duration is represented by differences in symbol shape, rather than by physical size, which allows the precise reading of durations.
Microtonal notations
Diatonic notation
This page covers commonly accepted extensions to standard diatonic notation used in microtonality. The 7 nominals C, D, E, F, G, A, B form the C major scale, and # and b raise and lower notes by a chroma.
KISS notation
KISS notation generalizes the principles of diatonic notation to any arbitrary MOS, involving alphabetic note naming based on the MOS in question, and accidentals based on the difference between that MOS' step sizes. KISS notation refers to a family of closely-related notation schemes.
Standard KISS notation
KISS notation, in its standard form, uses numbers to name notes, but the standard # and b symbols as accidentals, and places the treble and bass clefs around the middle note as they are in diatonic notation.
Quasi-diatonic MOS notation
Quasi-diatonic MOS notation uses letters as nominals, starting from A at 440Hz as the final note of the darkest mode of the scale (much as A is the final note of the Locrian scale before it repeats at B) uses standard accidentals, and has a custom system of clefs corresponding to each nominal.
Diamond-MOS notation
Diamond-MOS notation aims to disambiguate itself from diatonic notation by using different nominals (from J onwards), different accidentals (& = #, @ = b), and a custom clef system that makes it visually apparent where J is in different octaves on the staff and what MOS is being used.
Just notation systems
Conventionally, just intonation notation systems rely on a series of accidentals that move up or down a "formal comma" for each prime from a basic Pythagorean interval.
Common formal commas include 81/80 for 5 (the difference between the classical and diatonic major thirds), 64/63 for 7 (the difference between the diatonic and septimal major thirds), 33/32 (the difference between the perfect fourth and 11th harmonic) for 11, and 513/512 (the difference between the diatonic minor third and 19th harmonic) for 19.
| FJS | HEJI | Neutral FJS | Ben Johnston | |
|---|---|---|---|---|
| Basic diatonic | Pythagorean | Zarlino | ||
| 7 | 64/63 | 36/35 | ||
| 11 | 33/32 | sqrt(243/242) | 33/32 | |
| 13 | 1053/1024 | 27/26 | sqrt(507/512) | 65/64 |
| 17 | 4131/4096 | 2187/2176 | 4131/4096 | 51/50 |
| 19 | 513/512 | 96/95 | ||
| Accidentals used | Numbers that stack multiplicatively, with otonal intervals all inflected in the same direction | A selection of symbols | Numbers that stack multiplicatively, with otonal intervals all inflected in the same direction | Numbers and inverted numbers, with otonal intervals all inflected in the same direction, except for the syntonic comma (+/-) and prime 11 (^/v), |
| Other notes | All formal commas are derived systematically. Each prime harmonic is inflected from the simplest Pythagorean interval within 54.1 cents (or 57.8 cents). | Similar to FJS, but includes "dicot" intervals for more intuitive notation of neutral intervals. Each prime harmonic is inflected from the simplest Pythagorean or neutral interval within 33.4 cents. | Uses Zarlino diatonic as nominals, 36/35 as the accidental for 7, and 96/95 as the accidental for 19. | |
Color notation
Color notation is a notation system that uses a series of syllables to notate just intervals, fully replacing the standard interval qualities. An interval's degree is determined from its mapping to 24edo.
| Syllable | Intervals | Notes |
|---|---|---|
| la | Raised by a chromatic semitone | Not used, # is used instead |
| sa | Lowered by a chromatic semitone | Not used, b is used instead |
| wa | 3-limit, no alterations | 3-limit, no alterations |
| ru | 7 under, generally supermajor | +64/63 |
| yo | 5 over, generally ptolemaic major | -81/80 |
| gu | 5 under, generally ptolemaic minor | +81/80 |
| zo | 7 over, generally subminor | -64/63 |
| lu | 11 under | -33/32, +729/704 |
| lo | 11 over | +33/32, -729/704 |
