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Nominal-accidental chain: Difference between revisions

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'''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 temperament]]s, the number of steps this interval is mapped to is called the [[sharpness]].
'''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 temperament]]s, 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.
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.


{{Wikipedia| Enharmonic equivalence }}
[[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.


'''Equivalence''' may arise from this approach. This is when you have multiple names for the same pitch. The equivalence that occurs in 12edo is '''enharmonic equivalence'''. C-sharp is enharmonically equivalent to D-flat, but only in 12edo, 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.  
== 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:
{| class="wikitable center-all"
|+ style="font-size: 105%" | Edo alterations
|-
! colspan="2" rowspan="2" | Accidentals
! colspan="2" | Inflections
|-
! colspan="2" | Arrows
|-
| Sharp
| Flat
| Up
| Down
|-
| ♯
| ♭
| ^
| v
|}
 
{| class="wikitable center-all"
|+ style="font-size: 105%" | [[Pergen]] alterations
|-
! colspan="2" rowspan="2" | Accidentals
! colspan="4" | Inflections
|-
! colspan="2" | Arrows
! colspan="2" | Slashes
|-
| Sharp
| Flat
| Up
| Down
| Lift
| Drop
|-
| ♯
| ♭
| ^
| v
| /
| \
|}
 
{| class="wikitable center-all"
|+ style="font-size: 105%" | Just intonation alterations
|-
! rowspan="2" |
! colspan="2" rowspan="2" | Accidentals
! colspan="6" | Inflections
|-
! colspan="2" | Prime 5
! colspan="2" | Prime 7
! colspan="2" | Prime 11
|-
! rowspan="2" | 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
| ♯
| ♭
| \!
| <nowiki>/|</nowiki>
| !)
| <nowiki>|)</nowiki>
| <nowiki>/|\</nowiki>
| \!/
|}
 
Each JI inflection inflects by a certain [[formal comma|comma]].
 
These usages of the terms accidental, inflection and alteration were coined by [[Kite Giedraitis]].


== Specific notation schemes ==
== Specific notation schemes ==
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* [[Circle-of-fifths notation]] (and neutral circle-of-fifths notation)
* [[Circle-of-fifths notation]] (and neutral circle-of-fifths notation)
** [[Ups and downs notation]]
** [[Ups and downs notation]]
** [[Syntonic-rastmic subchroma notation]]
** [[Syntonic&ndash;rastmic subchroma notation]]
** [[Sagittal notation]]
** [[Sagittal notation]]


; Nondiatonic
; Nondiatonic
* [[4L 5s (3/1-equivalent)#Notation|Bohlen-Pierce notation]] (based on the [[lambda]] scale)
* [[4L 5s (3/1-equivalent)#Notation|Bohlen&ndash;Pierce "Lambda" notation]]
* [[Armodue]] number notation (based on the [[superdiatonic]] scale)
* [[Armodue]] number notation (based on the [[superdiatonic]] scale)
* [[Fox-Raven notation]] (based on the [[oneirotonic]] scale)
* [[Fox&ndash;Raven notation]] (based on the [[oneirotonic]] scale)
* [[Arcturus hendecatonic notation]] (based on the [[Arcturus]][11] scale)
* [[Arcturus hendecatonic notation]] (based on the [[Arcturus]][11] scale)
* [[Diamond-mos notation]]
* [[Diamond-mos notation]]


; Unsorted
; Unsorted
* [[Erv Wilson]]'s greek letters <!-- what's this? -->
* [[Erv Wilson]]'s Greek letters <!-- what's this? -->
* [[Aaron Hunt]]'s system
* [[Aaron Hunt]]'s system


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{{Todo| update |inline=1|comment=Find materials for these topics.}}
{{Todo| update |inline=1|comment=Find materials for these topics.}}


* The term "albitonic"
* The term "albitonic" (see [[Chromatic pairs]])
* [[Mark Gould]]'s connection of accidentals to [[bi-level MOS]]
* [[Mark Gould]]'s connection of accidentals to [[bi-level MOS]]
== See also ==
* [[Enharmonic]] (disambiguation page)


[[Category:Notation]]
[[Category:Notation]]
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