Enumeration, of rhythmic cells


>>> import math

Mikhïal Malt analyzes Brian Ferneyhough’s Unsichtbare Farben (1999) in The OM Composer’s Book 2. Malt explains that Ferneyhough used OpenMusic to create an “exhaustive catalogue of rhythmic cells” such that two conditions are met. First, rhythmic cells are subdivided into two pulses, with proportions from 1:1 to 1:11. Second, the second pulse of each cell is subdivided into 1, 2, 3, 4, 5, 6 parts. Malt adds that Ferneyhough later enumerates the retrograde of these cells.

The following functions recreate Malt’s results in Abjad:

>>> def make_tuplet(outer, inner, retrograde=False):
...     numerator = 1 + outer
...     exponent = int(math.log(numerator, 2))
...     denominator = 2**exponent
...     outer_string = f"{numerator}:{denominator}"
...     lone_note_denominator = denominator * 4
...     lone_note_duration = (1, lone_note_denominator)
...     lone_note = abjad.Note("c'", lone_note_duration)
...     duration = (outer, lone_note_denominator)
...     ratio = inner * [1]
...     maker = abjad.makers.tuplet_from_duration_and_ratio
...     inner_tuplet = maker(duration, ratio)
...     inner_tuplet.multiplier = inner_tuplet.multiplier.with_denominator(inner)
...     inner_tuplet.hide = inner_tuplet.trivial()
...     if retrograde:
...         contents = [inner_tuplet, lone_note]
...         label = f'"({outer} | {inner}) : 1"'
...     else:
...         label = f'"1 : ({outer} | {inner})"'
...         contents = [lone_note, inner_tuplet]
...     outer_tuplet = abjad.Tuplet(outer_string, contents)
...     markup = abjad.Markup(rf"\markup {label}")
...     note = abjad.select.note(outer_tuplet, 0)
...     abjad.attach(markup, note, direction=abjad.UP)
...     outer_tuplet.hide = outer_tuplet.trivial()
...     abjad.tweak(inner_tuplet, r"\tweak staff-padding 0")
...     abjad.tweak(outer_tuplet, r"\tweak staff-padding 2")
...     return outer_tuplet
... 
>>> def make_row(outer, column_count, retrograde=False):
...     tuplets = []
...     for inner in range(1, column_count + 1):
...         tuplet = make_tuplet(outer, inner, retrograde=retrograde)
...         tuplets.append(tuplet)
...     return tuplets
... 
>>> def make_score(row_count, column_count, retrograde=False):
...     score = abjad.Score(name="Score")
...     for row_number in range(1, row_count + 1):
...         tuplets = make_row(row_number, column_count, retrograde=retrograde)
...         voice = abjad.Voice(tuplets, name=f"Row_{row_number}_Voice")
...         staff = abjad.Staff([voice], name=f"Row_{row_number}_Staff")
...         score.append(staff)
...     return score
... 
>>> preamble = r"""#(set-global-staff-size 12)
... 
... \layout {
...     \context {
...         \Staff
...         \override VerticalAxisGroup.staff-staff-spacing.minimum-distance = 20
...     }
...     \context {
...         \Score
...         \override BarLine.stencil = ##f
...         \override Clef.stencil = ##f
...         \override StaffSymbol.stencil = ##f
...         \override SystemStartBar.stencil = ##f
...         \override TextScript.color = #blue
...         \override TextScript.staff-padding = #6
...         \override TimeSignature.stencil = ##f
...         \override TupletNumber.text = #tuplet-number::calc-fraction-text
...         proportionalNotationDuration = #(ly:make-moment 1 40)
...         tupletFullLength = ##t
...     }
... }
... """

Here are 11 rows and 6 columns:

>>> score = make_score(11, 6)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)

Here’s the rhythmic retrograde of the same:

>>> score = make_score(11, 6, retrograde=True)
>>> lilypond_file = abjad.LilyPondFile([preamble, score])
>>> abjad.show(lilypond_file)

[Bača (1.1, 3.2)]