User:Ganaram inukshuk/Notes: Difference between revisions

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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.

For a given mos xL ys at a ~~given~~ mode u|~~d, 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~~.

For a given mos xL ys, note names are based on a mode u|p; the choice of mode is up to the user. Starting at N0, or 0-mosstep, successive pitch classes are named N1, N2, and so on. 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.

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|+Example for 5L 2s (LLsLLLs, mode 5|Example with standard notation (5L 2s, mode 5|1)

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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.

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 dividing both by xL+ys produces 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.

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, C# and Db are not equivalent but B# and Cb are equivalent.

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|+Examples with standard diatonic notation

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 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.
-For a given mos xL ys at a given mode u|d, 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.
+For a given mos xL ys, note names are based on a mode u|p; the choice of mode is up to the user. Starting at N0, or 0-mosstep, successive pitch classes are named N1, N2, and so on. 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.
 {| class="wikitable"
 |+Example for 5L 2s (LLsLLLs, mode 5|Example with standard notation (5L 2s, mode 5|1)
@@ Line 1,539: / Line 1,539: @@
 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.
+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 dividing both by xL+ys produces 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.
+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, C# and Db are not equivalent but B# and Cb are equivalent.
 {| class="wikitable"
 |+Examples with standard diatonic notation