View source for Diatonic notation

'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music, which notates systems that are [[octave]]-periodic and generated by a (just or tempered) [[3/2|perfect fifth]]. Many tuning systems may be notated this way. EDOs can be notated using unmodified diatonic notation if they contain a single chain of fifths that generates a diatonic scale. For example, 23edo cannot be notated with standard diatonic notation because it does not have a diatonic scale, and 24edo cannot be notated with standard diatonic notation because it has two distinct chains of fifths.

Diatonic notation uses the 7 [[Notation#Nominals|nominals]] (C, D, E, F, G, A, B) to form the C [[Scale quality|major scale]], and the [[Notation#Accidentals|accidentals]] (#, b) to raise and lower by a [[chromatic semitone]] respectively. Note that a chromatic semitone is the difference between a [[diatonic major second]] and a [[diatonic semitone]], and is in general not equal to a diatonic semitone, so, for example, C# and Db are in general not the same note.

== Stacking intervals ==
The result of stacking two diatonic intervals can be determined by consulting this [[isomorphic]] table. Each step down is a major second, and each step to the right is a chromatic semitone. Add the two intervals as vectors from P1, and the result is the proper notation for the interval formed by stacking them.
{| class="wikitable"
|+Monocot isomorphic table
! colspan="1" rowspan="2" |Degree
! colspan="7" rowspan="1" |Quality
|-
!-3
!-2
!-1
!0
!1
!2
!3
|-
!1sn
|4d1
|3d1
|dd1
|d1
|'''<u>P1</u>'''
|A1
|AA1
|-
!2nd
|3d2
|dd2
|d2
|'''m2'''
|'''M2'''
|A2
|AA2
|-
!3rd
|3d3
|dd3
|d3
|'''m3'''
|'''M3'''
|A3
|AA3
|-
!4th
|3d4
|dd4
|d4
|'''P4'''
|A4
|AA4
|3A4
|-
!5th
|3d5
|dd5
|d5
|'''P5'''
|A5
|AA5
|3A5
|-
!6th
|dd6
|d6
|'''m6'''
|'''M6'''
|A6
|AA6
|3A6
|-
!7th
|dd7
|d7
|'''m7'''
|'''M7'''
|A7
|AA7
|3A7
|-
!8ve
|dd8
|d8
|'''<u>P8</u>'''
|A8
|AA8
|3A8
|4A8
|}

== Extensions ==

=== Neutral diatonic notation ===
Neutral diatonic notation introduces two new accidentals: semisharp (+ or t) and semiflat (d) to raise and lower by half of a chromatic semitone respectively. This allows the notation of  neutral intervals, specifically [[dicot]] intervals. #t is called "sesquisharp" and db is called "sesquiflat".

=== Ups and downs notation ===
Ups and downs notation allows edos to be easily notated by providing the up (^) and down (v) accidentals to raise and lower by a single edostep. For example, in 29edo, the 372c interval is often used as a [[classical major third]], and can be notated C-vE (a "downmajor third") instead of notating it as a diminished fourth (C-Fb), which would otherwise be necessary. Note that ups and downs always go before notes and interval names. Neutral intervals are notated with the symbol ~ (e.g. neutral 3rd, neutral 4th = ~3, ~4). 

The up and down arrows may also be used to notate steps smaller than a chromatic semitone in rank-2 systems. For example, the generator of [[porcupine]], a submajor second of about 160c, may be notated C-vD.

=== Melodic antidiatonic notation ===
Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
{{Cat|Notation}}