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=== Nk note name notation ===
=== Nk note name notation ===
Rather than using alphabetical names, notes of the form Nk are used. These are used to indicate position on a staff, where N0 is middle C. These names serve as an alternative to using different notations for different scales, but may be interpreted as blanks for one to fill in with different, more specific notation. Chromas are denoted using the letter c, and are expressed as a multiple of c being added (or subtracted) from a note Nk. Half-accidentals are denoted as fractions (such as c/2) or decimals (such as 0.5c). Dieses, if present, are expressed similarly using the letter d. Chromas and dieses don't change position on a staff, but modify the pitch at that position.
Rather than using alphabetical names, notes of the form Nk are used. These are used to indicate position on a staff, where N0 is middle C, unless specified otherwise. These names serve as an alternative to using different notations for different scales, but may be interpreted as blanks for one to fill in with different, more specific notation. If k is unbounded, then this notation denotes position on a staff. However, k may be bounded within the range [0, n), where n is the note count, to indicate pitch classes.


If k is unbounded, then this notation denotes position on a staff. However, k may be bounded within the range [0, n), where n is the note count, to indicate pitch classes.
For a given mos xL ys, pitch classes defined by some number of mossteps from the root are assigned note names starting at N0, which is 0 mossteps from the root. If two pitches, reached by going up or down some quantity of mossteps, have the same remainder when divided by xL+ys (which is the same as octave-reducing), then they are in the same pitch class. In this regard, a pitch Nk corresponds to and is the shorthand for the scale degree reached by going up an octave-reduced interval denoted as a quantity of mossteps iL+js that is smaller than xL+ys.
{| class="wikitable"
|+Example for 5L 2s (LLsLLLs, mode 5|1)
!Mossteps from root
!Substring
!Mosstep sum
!Standard note name
!Nk note name
|-
|0
|''none''
|0
|C
|N0
|-
|1
|L
|L
|D
|N1
|-
|2
|LL
|2L
|E
|N2
|-
|3
|LLs
|2L+s
|F
|N3
|-
|4
|LLsL
|3L+s
|G
|N4
|-
|5
|LLsLL
|4L+s
|A
|N5
|-
|6
|LLsLLL
|5L+s
|B
|N6
|-
|7
|LLsLLLs
|5L+2s
|C
|N7 (same as N0)
|}
Chromas are denoted using the letter c, and are expressed as a multiple of c being added (or subtracted) from a note Nk. Half-accidentals are denoted as fractions (such as c/2) or decimals (such as 0.5c). Dieses, if present, are expressed similarly using the letter d. If this notation denotes position on a staff, then chromas and dieses don't change position on a staff, but modify the pitch at that position. If this notation is treated as placeholders for more specific notation, then adding or subtracting c represents the use of sharp or flat (or equivalent) accidentals.
 
Since chromas and dieses can be expressed in terms of L and s – where a chroma is L - s and a diesis is the absolute value of L - 2s – modifying a note by a chroma or diesis can equivalently expressed as going up (or down) some interval iL+js. If, for a given step ratio L:s, two pitch classes Np and Nq are modified by different amounts of chromas uc and vc to produce pitch classes Np+uc and Nq+vc, if both are expressed in terms of L's and s's and, when divided by xL+ys, produce the same remainder, then the two pitches are enharmonic equivalents.
 
As an example, the table below denotes diatonic (5L 2s) pitch classes as sums of L's and s's, and shows how different step ratios produce different enharmonic equivalences; namely, in 12edo, C# and Db are equivalent, but in 19edo, B# and Cb are equivalent.
{| class="wikitable"
{| class="wikitable"
|+Examples with standard diatonic notation
|+Examples with standard diatonic notation
!Note name
!Note name
!Nk notation
!Nk note name with chroma
!Mosstep sum
!Like terms combined
!If L:s = 2:1
!If L:s = 3:2
|-
|-
|C (middle C)
|C
|N0
|N0
|-
|0
|Ct (C half-sharp)
|0
|N0+0.5c
|0
|0
|-
|-
|C#
|C#
|N0+c
|N0+c
|-
|L-s
|C#t (C sesquisharp)
|L-s
|N0+1.5c
|1
|-
|1
|Cx
|N0+2c
|-
|Dbb
|N1-2c
|-
|-
|Db
|Db
|N1-c
|N1-c
|L-(L-s)
|s
|1
|2
|-
|-
|D
|D
|N1
|N1
|L
|L
|2
|3
|-
|-
|B
|B
|N7
|N6
|5L+s
|5L+s
|11
|17
|-
|B#
|N6+c
|5L+s+(L-s)
|6L
|12
|18
|-
|Cb
|N7-c
|5L+2s-(L-s)
|4L+3s
|11
|18
|-
|-
|C (one octave up from middle C)
|C (one octave up)
|N8 (or N0 if it's a pitch class)
|N7 (same as N0, as a pitch class)
|5L+2s (reduced to 0 due to modular arithmetic)
|5L+2s (reduced to 0)
|12 (reduced to 0)
|19 (reduced to 0)
|}
|}


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