Ferneyhough: Unsichtbare Farben¶

Note

Explore the `abjad/demos/ferneyhough/` directory for the complete code to this example, or import it into your Python session directly with ```from abjad.demos import ferneyhough```.

Mikhïal Malt analyzes the rhythmic materials of Ferneyhough’s Unsichtbare Farben in The OM Composer’s Book 2.

Malt explains that Ferneyhough used OpenMusic to create an “exhaustive catalogue of rhythmic cells” such that:

1. They are subdivided into two pulses, with proportions from `1/1` to `1/11`.
2. The second pulse is subdivided successively by `1`, `2`, `3`, `4`, `5` and `6`.

Let’s recreate Malt’s results in Abjad.

The proportions¶

First we define proportions:

```>>> proportions = [(1, n) for n in range(1, 11 + 1)]
```
```>>> proportions
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]
```

The transforms¶

Next we’ll show how to divide a quarter note into various ratios, and then divide the final logical tie of the resulting tuplet into yet another ratio:

```def make_nested_tuplet(
tuplet_duration,
outer_tuplet_proportions,
inner_tuplet_subdivision_count,
):
r'''Makes nested tuplet.
'''

outer_tuplet = scoretools.Tuplet.from_duration_and_ratio(
tuplet_duration, outer_tuplet_proportions)
inner_tuplet_proportions = inner_tuplet_subdivision_count * [1]
selector = select().by_leaf(flatten=True)
last_leaf = selector(outer_tuplet)[-1]
right_logical_tie = inspect_(last_leaf).get_logical_tie()
right_logical_tie.to_tuplet(inner_tuplet_proportions)
return outer_tuplet
```
```>>> tuplet = make_nested_tuplet(Duration(1, 4), (1, 1), 5)
>>> staff = scoretools.Staff([tuplet], context_name='RhythmicStaff')
>>> show(staff)
```
```>>> tuplet = make_nested_tuplet(Duration(1, 4), (2, 1), 5)
>>> staff = scoretools.Staff([tuplet], context_name='RhythmicStaff')
>>> show(staff)
```
```>>> tuplet = make_nested_tuplet(Duration(1, 4), (3, 1), 5)
>>> staff = scoretools.Staff([tuplet], context_name='RhythmicStaff')
>>> show(staff)
```

A logical tie is a selection of notes or chords connected by ties. It lets us talk about a notated rhythm of `5/16`, for example, which can not be expressed with only a single leaf.

Note how we can divide a tuplet whose outer proportions are `3/5`, where the second logical tie requires two notes to express the `5/16` duration:

```>>> normal_tuplet = Tuplet.from_duration_and_ratio(Duration(1, 4), (3, 5))
>>> staff = scoretools.Staff([normal_tuplet], context_name='RhythmicStaff')
>>> show(staff)
```
```>>> subdivided_tuplet = make_nested_tuplet(Duration(1, 4), (3, 5), 3)
>>> staff = scoretools.Staff([subdivided_tuplet], context_name='RhythmicStaff')
>>> show(staff)
```

The rhythms¶

Now that we know how to make the basic building block, let’s make a lot of tuplets all at once.

We’ll set the duration of each tuplet equal to a quarter note:

```>>> duration = Fraction(1, 4)
```

And then we make one row of rhythms, with the last logical tie increasingly subdivided:

```def make_row_of_nested_tuplets(
tuplet_duration,
outer_tuplet_proportions,
column_count,
):
r'''Makes row of nested tuplets.
'''

assert 0 < column_count
row_of_nested_tuplets = []
for n in range(column_count):
inner_tuplet_subdivision_count = n + 1
nested_tuplet = make_nested_tuplet(
tuplet_duration,
outer_tuplet_proportions,
inner_tuplet_subdivision_count,
)
row_of_nested_tuplets.append(nested_tuplet)
return row_of_nested_tuplets
```
```>>> tuplets = make_row_of_nested_tuplets(duration, (2, 1), 6)
>>> staff = scoretools.Staff(tuplets, context_name='RhythmicStaff')
>>> show(staff)
```

If we can make one single row of rhythms, we can make many rows of rhythms. Let’s try:

```def make_rows_of_nested_tuplets(tuplet_duration, row_count, column_count):
r'''Makes rows of nested tuplets.
'''

assert 0 < row_count
rows_of_nested_tuplets = []
for n in range(row_count):
outer_tuplet_proportions = (1, n + 1)
row_of_nested_tuplets = make_row_of_nested_tuplets(
tuplet_duration, outer_tuplet_proportions, column_count)
rows_of_nested_tuplets.append(row_of_nested_tuplets)
return rows_of_nested_tuplets
```
```>>> score = Score()
>>> for tuplet_row in make_rows_of_nested_tuplets(duration, 4, 6):
...     score.append(scoretools.Staff(tuplet_row, context_name='RhythmicStaff'))
...
>>> show(score)
```

That’s getting close to what we want, but the typography isn’t as good as it could be.

The score¶

First we’ll package up the logic for making the un-styled score into a single function:

```def make_score(tuplet_duration, row_count, column_count):
r'''Makes score.
'''

score = scoretools.Score()
rows_of_nested_tuplets = \
tuplet_duration, row_count, column_count)
for row_of_nested_tuplets in rows_of_nested_tuplets:
staff = scoretools.Staff(row_of_nested_tuplets)
staff.context_name = 'RhythmicStaff'
time_signature = indicatortools.TimeSignature((1, 4))
attach(time_signature, staff)
score.append(staff)
return score
```
```>>> score = make_score(Duration(1, 4), 4, 6)
>>> show(score)
```

Then we’ll apply some formatting overrides to improve its overall appearance:

```def configure_score(score):
r'''Configured score.
'''

moment = schemetools.SchemeMoment(1, 56)
set_(score).proportional_notation_duration = moment
set_(score).tuplet_full_length = True
override(score).bar_line.stencil = False
override(score).bar_number.transparent = True
override(score).spacing_spanner.uniform_stretching = True
override(score).spacing_spanner.strict_note_spacing = True
override(score).time_signature.stencil = False
scheme = schemetools.Scheme('tuplet-number::calc-fraction-text')
override(score).tuplet_number.text = scheme
```
```>>> configure_score(score)
>>> show(score)
```

The proportional spacing makes the score much easier to read, but now the notation is much too big. We’ll clean that up next.

The LilyPond file¶

Let’s adjust the overall size of our output, and put everything together:

```def make_lilypond_file(tuplet_duration, row_count, column_count):
r'''Makes LilyPond file.
'''

tuplet_duration,
row_count,
column_count,
)
lilypond_file = lilypondfiletools.LilyPondFile.new(score)
return lilypond_file
```
```def configure_lilypond_file(lilypond_file):
r'''Configures LilyPond file.
'''

lilypond_file._default_paper_size = '11x17', 'portrait'
lilypond_file._global_staff_size = 12
lilypond_file.layout_block.indent = 0
lilypond_file.layout_block.ragged_right = True
lilypond_file.paper_block.ragged_bottom = True
spacing_vector = schemetools.make_spacing_vector(0, 0, 8, 0)
lilypond_file.paper_block.system_system_spacing = spacing_vector
```
```>>> lilypond_file = make_lilypond_file(Duration(1, 4), 11, 6)
>>> show(lilypond_file)
```