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# Simplemusic and Pitch Class Sets

## Simplemusic

`simplemusic.``mod12`(n)

    >>> simplemusic.mod12(13)
    1

`simplemusic.``interval`(x, y)

  Return the numeric interval between two notes.

`simplemusic.``transposition`(notes, index)

  Transpose a set of notes by a numerical index.

`simplemusic.``transposition_startswith`(notes, start)

  Transpose a set of notes so it begins with start note.

`simplemusic.``is_related_by_transposition`(notes1, notes2)

  Check if two groups of notes are related by transposition.

  We use brute force here; the best way is to check for the normal or prime forms.

`simplemusic.``inversion`(notes, index=0)

  > Invert a set of notes though an inversion index.

  > The inversion index is not very musical. the function `inversion_startswith()` is probably more useful.

  `simplemusic.``inversion_startswith`(notes, start)

    Invert a set of notes so it begins with start note.

    >>> simplemusic.inversion_startswith([0, 4, 7], 2)
    [2, 10, 7]

`simplemusic.``rotate_set`(notes)

  Return all rotations of a collection of notes.

## Pitch Class Set

`simplemusic.``name_to_diatonic`(note_string)

  Return a number from 0 to 6 for the note name without the accidental.

`simplemusic.``dotted_duration`(duration, dots)

  Sn = a(1 - r^n)/1 - r where a is the first term, r is the common ration (1/2 in our case) and n is the number of terms.