Design, by dyads¶
The function below pairs pitches at corresponding positions in a segment partitioned into halves. A sequence of two-note chords results. A first optional parameter flips the pitches in chords specified by index. A second optional parameter transposes chords, specified again by index. Two examples follow. The first operates on the regular structure of an ascending chromatic scale. The second successively tranforms a segment with greater intervallic variety. The implementation given here generalizes a process due to Luigi Nono:
>>> def partition(string, flip=None, transpositions=None):
... strings = string.split()
... assert len(strings) % 2 == 0, repr(string)
... segment = [abjad.NamedPitch(_) for _ in strings]
... flip = flip or []
... transpositions = dict(transpositions or [])
... center = int(len(segment) / 2)
... left = segment[:center]
... right = segment[center:]
... pairs = zip(left, right)
... chords = []
... for i, pair in enumerate(pairs):
... chord = abjad.Chord(pair, (1, 4))
... if i in flip:
... pitches = chord.written_pitches
... lower, higher = pitches
... while lower < higher:
... lower = lower + "+P8"
... chord.written_pitches = [lower, higher]
... interval = transpositions.get(i, "P1")
... pitches = tuple(_.transpose(interval) for _ in chord.written_pitches)
... chord.written_pitches = pitches
... chords.append(chord)
... return chords
...
LilyPond settings to format examples:
>>> preamble = r"""#(set-global-staff-size 16)
...
... \layout {
... \context {
... \Score
... \override BarLine.stencil = ##f
... \override BarNumber.stencil = ##f
... \override Beam.stencil = ##f
... \override Flag.stencil = ##f
... \override Rest.stencil = ##f
... \override SpacingSpanner.strict-note-spacing = ##t
... \override SpanBar.stencil = ##f
... \override Stem.stencil = ##f
... \override TimeSignature.transparent = ##t
... proportionalNotationDuration = #(ly:make-moment 1 16)
... }
... }
... """
Examples¶
Example 1a. Ascending chromatic scale:
>>> string = "cs'' d'' ef'' e'' f'' fs'' g'' gs'' a'' bf'' b'' c'''"
>>> notes = [abjad.Note(_, (1, 4)) for _ in string.split()]
>>> score = abjad.illustrators.make_piano_score(notes)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 1b. Starting segment; partitioned:
>>> string = "cs'' d'' ef'' e'' f'' fs'' g'' gs'' a'' bf'' b'' c'''"
>>> chords = partition(string)
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 1c. Starting segment; partitioned; chords at indexes 1, 2, 4, 5 flipped:
>>> string = "cs'' d'' ef'' e'' f'' fs'' g'' gs'' a'' bf'' b'' c'''"
>>> chords = partition(string, flip=[1, 2, 4, 5])
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 1d. Starting segment; partitioned; chords 1, 2, 4, 5 flipped; chords at indexes 2, 3, 4, 5 selectively transposed:
>>> string = "cs'' d'' ef'' e'' f'' fs'' g'' gs'' a'' bf'' b'' c'''"
>>> transpositions = [(2, "+12"), (3, "+12"), (4, "-12"), (5, "-24")]
>>> chords = partition(string, flip=[1, 2, 4, 5], transpositions=transpositions)
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
This example reproduces violin double stops in Luigi Nono’s Fragment — Stille, an Diotima (1980).
Example 2a. Starting segment written by hand:
>>> string = "d, b af c'' a' fs'' g'' gs'' as'' b'' d'' f' g' ef' e df c bf,"
>>> notes = [abjad.Note(_, (1, 4)) for _ in string.split()]
>>> score = abjad.illustrators.make_piano_score(notes)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 2b. Starting segment; partitioned:
>>> string = "d, b af c'' a' fs'' g'' gs'' as'' b'' d'' f' g' ef' e df c bf,"
>>> chords = partition(string)
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 2c. Starting segment; partitioned; chords at indexes 0, 1, 2, 4 flipped:
>>> string = "d, b af c'' a' fs'' g'' gs'' as'' b'' d'' f' g' ef' e df c bf,"
>>> chords = partition(string, flip=[0, 1, 2, 4])
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
Example 2d. Starting segment; partitioned; chords 0, 1, 2, 4 flipped; chords at indexes 0, 1 selectively transposed:
>>> string = "d, b af c'' a' fs'' g'' gs'' as'' b'' d'' f' g' ef' e df c bf,"
>>> transpositions = [(0, "-36"), (1, "-24")]
>>> chords = partition(string, flip=[0, 1, 2, 4], transpositions=transpositions)
>>> score = abjad.illustrators.make_piano_score(chords)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)
