Nominal-accidental chain

"Sharp" and "flat" redirect here. For the temperaments that used to go by those names, see Sharpie and Flattie.

This is a neologism for the common pattern in notating microtonal pitch systems. These are analogous extensions of basic Western musical notation.

Nominals are pitch elements that have specific names. In Western musical notation, these names are the seven letters A, B, C, D, E, F, and G (historically, H has also been used). In a pentatonic notation, there would be only five names.

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Accidental (music)

Accidentals are additional pitches that arise as modifications of the nominals. Unmodified pitches are natural notes. In diatonic circle-of-fifths notation, the additional pitches are denoted by adding sharps or flats to the natural notes. The sharp accidental denotes a pitch raise by a chromatic semitone, equivalent to a raise by 7 fifths minus 4 octaves. Conversely, the flat accidental denotes a pitch drop by the same amount. In equal temperaments, the number of steps this interval is mapped to is called the sharpness.

These pitches form a chain, with each one separated from the next by a specific interval. This interval can be said to generate the notation, or the notation can be said to be based on this interval. In diatonic circle-of-fifths notation, this interval has been a just or near-just 3/2. Other intervals are possible, and even desirable for certain edos like 13, 18, and 23.

Enharmonic equivalence may arise from this approach, which is when the same pitch can have multiple names. People are often taught that C♯ is enharmonically equivalent to D♭ but this is only true in 12edo and its multiples (24edo, 36edo, etc). The same term is sometimes used to refer to equivalence in general, but each edo technically has its own equivalence. 7edo has the type of equivalence that could be called chromatic equivalence, for example, since in 7edo the fact that stacking seven fifths takes one back to the root note means that sharps and flats are redundant.

Inflections and alterations

Microtonal accidentals are sometimes referred to as inflections. Using this term allows the term accidental to refer exclusively to sharps, flats and naturals. Accidentals and inflections may then be referred to collectively as alterations. This terminology facilitates discussions of microtonal scores, especially in rank-1 and rank-2 systems.

Examples:

Edo alterations

Accidentals		Inflections
		Arrows
Sharp	Flat	Up	Down
♯	♭	^	v

Pergen alterations

Accidentals		Inflections
		Arrows		Slashes
Sharp	Flat	Up	Down	Lift	Drop
♯	♭	^	v	/	\

Just intonation alterations

	Accidentals		Inflections
			Prime 5		Prime 7		Prime 11
Color notation	Sharp	Flat	Yo	Gu	Zo	Ru	iLo	Lu
	♯	♭	y	g	z	r	1o	1u
FJS notation	♯	♭	5	/5	7	/7	11	/11
Prime-factor Sagittal	♯	♭	\!	/|	!)	|)	/|\	\!/

Each JI inflection inflects by a certain comma.

These usages of the terms accidental, inflection and alteration were coined by Kite Giedraitis.

Specific notation schemes

Diatonic

• Circle-of-fifths notation (and neutral circle-of-fifths notation)
  • Ups and downs notation
  • Syntonic–rastmic subchroma notation
  • Sagittal notation

Nondiatonic

• Bohlen–Pierce "Lambda" notation
• Armodue number notation (based on the superdiatonic scale)
• Fox–Raven notation (based on the oneirotonic scale)
• Arcturus hendecatonic notation (based on the Arcturus[11] scale)
• Diamond-mos notation

Unsorted

• Erv Wilson's Greek letters
• Aaron Hunt's system

Related topics

Todo: update Find materials for these topics.

• The term "albitonic" (see Chromatic pairs)
• Mark Gould's connection of accidentals to bi-level MOS