Cadences

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%load_ext autoreload
%autoreload 2
import os
from collections import Counter, defaultdict

import dimcat as dc
import ms3
import pandas as pd
import plotly.express as px
from dimcat import plotting
from dimcat.steps import filters, groupers, slicers

import utils

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RESULTS_PATH = os.path.abspath(os.path.join(utils.OUTPUT_FOLDER, "cadences"))
os.makedirs(RESULTS_PATH, exist_ok=True)


def make_output_path(
    filename: str,
    extension=None,
    path=RESULTS_PATH,
) -> str:
    return utils.make_output_path(filename=filename, extension=extension, path=path)


def save_figure_as(
    fig, filename, formats=("png", "pdf"), directory=RESULTS_PATH, **kwargs
):
    if formats is not None:
        for fmt in formats:
            plotting.write_image(fig, filename, directory, format=fmt, **kwargs)
    else:
        plotting.write_image(fig, filename, directory, **kwargs)

Loading data

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D = utils.get_dataset("beethoven_piano_sonatas", corpus_release="v2.5")
package = D.inputs.get_package()
package_info = package._package.custom
git_tag = package_info.get("git_tag")
utils.print_heading("Data and software versions")
print("Ludwig van Beethoven – Piano Sonatas version v2.5")
print(f"Datapackage '{package.package_name}' @ {git_tag}")
print(f"dimcat version {dc.__version__}\n")
D

Data and software versions
--------------------------

Ludwig van Beethoven – Piano Sonatas version v2.5
Datapackage 'beethoven_piano_sonatas' @ v2.5
dimcat version 3.4.0

Dataset
=======
{'inputs': {'basepath': None,
            'packages': {'beethoven_piano_sonatas': ["'beethoven_piano_sonatas.measures' "
                                                     '(MuseScoreFacetName.MuseScoreMeasures)',
                                                     "'beethoven_piano_sonatas.notes' "
                                                     '(MuseScoreFacetName.MuseScoreNotes)',
                                                     "'beethoven_piano_sonatas.expanded' "
                                                     '(MuseScoreFacetName.MuseScoreHarmonies)',
                                                     "'beethoven_piano_sonatas.chords' "
                                                     '(MuseScoreFacetName.MuseScoreChords)',
                                                     "'beethoven_piano_sonatas.metadata' (FeatureName.Metadata)"]}},
 'outputs': {'basepath': None, 'packages': {}},
 'pipeline': []}

try:
    cadence_labels = D.get_feature("cadencelabels")
except Exception:
    raise ValueError("Corpus has no cadence annotations.")
cadence_labels

			mc	mn	quarterbeats	duration_qb	mc_onset	mn_onset	timesig	staff	voice	volta	...	globalkey	localkey	globalkey_is_minor	localkey_is_minor	globalkey_mode	localkey_mode	localkey_resolved	localkey_and_mode	cadence_type	cadence
corpus	piece	i
beethoven_piano_sonatas	01-1	7	9	8	30	2.00	1/4	1/4	2/2	2	1	<NA>	...	f	i	True	True	minor	minor	i	i, minor	HC	HC
		16	17	16	61	3.00	0	0	2/2	2	1	<NA>	...	f	III	True	False	minor	major	III	III, minor	HC	HC
		21	19	18	69	3.00	0	0	2/2	2	1	<NA>	...	f	III	True	False	minor	major	III	III, minor	HC	HC
		26	21	20	77	3.00	0	0	2/2	2	1	<NA>	...	f	III	True	False	minor	major	III	III, minor	HC	HC
		62	42	41	161	2.00	0	0	2/2	2	1	<NA>	...	f	III	True	False	minor	major	III	III, minor	PAC	PAC
	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
	32-2	770	169	155	647/2	2.25	0	0	9/16	2	1	<NA>	...	C	I	False	False	major	major	I	I, major	HC	HC
		784	173	159	1337/4	4.25	7/16	7/16	9/16	2	1	<NA>	...	C	I	False	False	major	major	I	I, major	HC	HC
		820	185	171	361	0.75	3/8	3/8	9/16	2	1	<NA>	...	C	I	False	False	major	major	I	I, major	HC	HC
		866	189	175	737/2	1.50	0	0	9/16	2	1	<NA>	...	C	I	False	False	major	major	I	I, major	PAC	PAC
		868	190	176	372	3.25	5/16	5/16	9/16	2	1	<NA>	...	C	I	False	False	major	major	I	I, major	PAC	PAC

1333 rows × 22 columns

cadence_labels.plot_grouped(
    title="Distribution of cadence types over the DLC",
    output=make_output_path("all_cadences_pie"),
    width=1000,
    height=1000,
)

Metadata

cadence_filter = filters.HasCadenceAnnotationsFilter()
filtered_D = cadence_filter.process(D)

hascadence_metadata = filtered_D.get_metadata()
chronological_corpus_names = hascadence_metadata.get_corpus_names()

cadence_counts = cadence_labels.apply_step("Counter")
cadence_counts.plot_grouped("corpus")

mean_composition_years = (
    hascadence_metadata.groupby(level=0).composed_end.mean().astype(int).sort_values()
)
chronological_corpus_names = hascadence_metadata.get_corpus_names()
bar_data = pd.concat(
    [
        mean_composition_years.rename("year"),
        hascadence_metadata.groupby(level="corpus").size().rename("pieces"),
    ],
    axis=1,
).reset_index()
fig = px.bar(
    bar_data,
    x="year",
    y="pieces",
    color="corpus",
    title="Pieces contained in the dataset",
)
fig.update_traces(width=5)

Overall

• PAC: Perfect Authentic Cadence

• IAC: Imperfect Authentic Cadence

• HC: Half Cadence

• DC: Deceptive Cadence

• EC: Evaded Cadence

• PC: Plagal Cadence

print(f"{len(cadence_labels)} cadence labels.")
utils.value_count_df(cadence_labels.cadence)

1333 cadence labels.

	counts	%
cadence
PAC	603	45.24
HC	406	30.46
IAC	275	20.63
EC	31	2.33
DC	15	1.13
PC	3	0.23

Per dataset

all_labels = D.get_feature("harmonylabels")
cadence_count_per_dataset = all_labels.groupby("corpus").cadence.value_counts()
cadence_fraction_per_dataset = (
    cadence_count_per_dataset / cadence_count_per_dataset.groupby(level=0).sum()
)
cadence_fraction_per_dataset = cadence_fraction_per_dataset.rename(
    "fraction"
).reset_index()
cadence_fraction_per_dataset["corpus_name"] = cadence_fraction_per_dataset.corpus.map(
    utils.get_corpus_display_name
)
fig = px.bar(
    cadence_fraction_per_dataset,
    x="corpus_name",
    y="fraction",
    title="Distribution of cadence types per corpus",
    color="cadence",
    color_discrete_map=plotting.CADENCE_COLORS,
    labels=dict(corpus_name="", fraction="Fraction of all cadences"),
    category_orders=dict(corpus_name=chronological_corpus_names),
)
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "all_cadences_corpuswise_stacked_bars", height=1000)
fig.show()

fig = px.pie(
    cadence_count_per_dataset.rename("count").reset_index(),
    names="cadence",
    color="cadence",
    values="count",
    facet_col="corpus",
    facet_col_wrap=4,
    height=2000,
    color_discrete_map=plotting.CADENCE_COLORS,
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "all_cadences_corpuswise_pies")
fig.show()

cadence_count_per_mode = (
    all_labels.groupby("localkey_is_minor").cadence.value_counts().reset_index()
)
cadence_count_per_mode["mode"] = cadence_count_per_mode.localkey_is_minor.map(
    {False: "major", True: "minor"}
)
fig = px.pie(
    cadence_count_per_mode,
    names="cadence",
    color="cadence",
    values="count",
    facet_col="mode",
    height=2000,
    color_discrete_map=plotting.CADENCE_COLORS,
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "all_cadences_modewise_pies")
fig.show()

corelli = dc.Dataset()
CORELLI_PATH = os.path.abspath(os.path.join("..", "corelli"))
corelli.load(directory=CORELLI_PATH, parse_tsv=False)
annotated_view = corelli.data.get_view("annotated")
annotated_view.include("facets", "expanded")
annotated_view.pieces_with_incomplete_facets = False
corelli.data.set_view(annotated_view)
corelli.data.parse_tsv(choose="auto")
corelli.get_indices()
corelli_labels = corelli.get_facet("expanded")
corelli_cadence_count_per_mode = (
    corelli_labels.groupby("localkey_is_minor").cadence.value_counts().reset_index()
)
corelli_cadence_count_per_mode["mode"] = (
    corelli_cadence_count_per_mode.localkey_is_minor.map(
        {False: "major", True: "minor"}
    )
)
fig = px.pie(
    corelli_cadence_count_per_mode,
    names="cadence",
    color="cadence",
    values="count",
    facet_col="mode",
    height=2000,
    color_discrete_map=plotting.CADENCE_COLORS,
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "all_corelli_cadences_modewise_pies")
fig.show()

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[14], line 3
      1 corelli = dc.Dataset()
      2 CORELLI_PATH = os.path.abspath(os.path.join("..", "corelli"))
----> 3 corelli.load(directory=CORELLI_PATH, parse_tsv=False)
      4 annotated_view = corelli.data.get_view("annotated")
      5 annotated_view.include("facets", "expanded")

TypeError: Dataset.load() got an unexpected keyword argument 'directory'

combined_cadences = pd.concat(
    [cadence_count_per_mode, corelli_cadence_count_per_mode],
    keys=["couperin", "corelli"],
    names=["corpus", None],
).reset_index(level=0)
fig = px.pie(
    combined_cadences,
    names="cadence",
    color="cadence",
    values="count",
    facet_col="mode",
    facet_row="corpus",
    height=2000,
    color_discrete_map=plotting.CADENCE_COLORS,
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
updated_layout = dict(utils.STD_LAYOUT, font=dict(size=40))
fig.update_layout(**updated_layout)
save_figure_as(fig, "couperin_corelli_cadences_modewise_pies")
fig.show()

Per phrase

Number of cadences per phrase

grouped_by_corpus = groupers.CorpusGrouper().process(D)
segmented = slicers.PhraseSlicer().process_data(grouped_by_corpus)
phrases = segmented.get_slice_info()
phrase_segments = segmented.get_facet("expanded")
phrase_gpb = phrase_segments.groupby(level=[0, 1, 2])
local_keys_per_phrase = phrase_gpb.localkey.unique().map(tuple)
n_local_keys_per_phrase = local_keys_per_phrase.map(len)
phrases_with_keys = pd.concat(
    [
        n_local_keys_per_phrase.rename("n_local_keys"),
        local_keys_per_phrase.rename("local_keys"),
        phrases,
    ],
    axis=1,
)
phrases_with_cadences = pd.concat(
    [
        phrase_gpb.cadence.nunique().rename("n_cadences"),
        phrase_gpb.cadence.unique()
        .rename("cadences")
        .map(lambda arr: tuple(e for e in arr if not pd.isnull(e))),
        phrases_with_keys,
    ],
    axis=1,
)
utils.value_count_df(phrases_with_cadences.n_cadences, counts_column="#phrases")

n_cad = (
    phrases_with_cadences.groupby(level="corpus")
    .n_cadences.value_counts()
    .rename("counts")
    .reset_index()
    .sort_values("n_cadences")
)
n_cad.n_cadences = n_cad.n_cadences.astype(str)
fig = px.bar(
    n_cad,
    x="corpus",
    y="counts",
    color="n_cadences",
    height=800,
    barmode="group",
    labels=dict(n_cadences="#cadences in a phrase"),
    category_orders=dict(dataset=chronological_corpus_names),
)
save_figure_as(fig, "n_cadences_per_phrase_corpuswise_absolute_grouped_bars")
fig.show()

Combinations of cadence types for phrases with more than one cadence

utils.value_count_df(
    phrases_with_cadences[phrases_with_cadences.n_cadences > 1].cadences
)

Positioning of cadences within phrases

df_rows = []
y_position = 0
for ix in (
    phrases_with_cadences[phrases_with_cadences.n_cadences > 0]
    .sort_values("duration_qb")
    .index
):
    df = phrase_segments.loc[ix]
    description = str(ix)
    if df.cadence.notna().any():
        interval = ix[2]
        df_rows.append((y_position, interval.length, "end of phrase", description))
        start_pos = interval.left
        cadences = df.loc[df.cadence.notna(), ["quarterbeats", "cadence"]]
        cadences.quarterbeats -= start_pos
        for cadence_x, cadence_type in cadences.itertuples(index=False, name=None):
            df_rows.append((y_position, cadence_x, cadence_type, description))
        y_position += 1
    # else:
    #    df_rows.append((y_position, pd.NA, pd.NA, description))

data = pd.DataFrame(df_rows, columns=["phrase_ix", "x", "marker", "description"])

fig = px.scatter(
    data[data.x.notna()],
    x="x",
    y="phrase_ix",
    color="marker",
    hover_name="description",
    height=3000,
    labels=dict(marker="legend"),
    color_discrete_map=plotting.CADENCE_COLORS,
)
fig.update_traces(marker_size=5)
fig.update_yaxes(autorange="reversed")
save_figure_as(fig, "cadence_positions_within_all_phrases")
fig.show()

Cadence ultima

phrase_segments = segmented.get_facet("expanded")
cadence_selector = phrase_segments.cadence.notna()
missing_chord_selector = phrase_segments.chord.isna()
cadence_with_missing_chord_selector = cadence_selector & missing_chord_selector
missing = phrase_segments[cadence_with_missing_chord_selector]
expanded = ms3.expand_dcml.expand_labels(
    phrase_segments[cadence_with_missing_chord_selector],
    propagate=False,
    chord_tones=True,
    skip_checks=True,
)
phrase_segments.loc[cadence_with_missing_chord_selector] = expanded
print(
    f"Ultima harmony missing for {(phrase_segments.cadence.notna() & phrase_segments.bass_note.isna()).sum()} cadence "
    f"labels."
)

Ultimae as Roman numeral

def highlight(row, color="#ffffb3"):
    if row.counts < 10:
        return [None, None, None, None]
    else:
        return ["background-color: {color};"] * 4


cadence_counts = all_labels.cadence.value_counts()
ultima_root = (
    phrase_segments.groupby(["localkey_is_minor", "cadence"])
    .numeral.value_counts()
    .rename("counts")
    .to_frame()
    .reset_index()
)
ultima_root.localkey_is_minor = ultima_root.localkey_is_minor.map(
    {False: "in major", True: "in minor"}
)
# ultima_root.style.apply(highlight, axis=1)

fig = px.pie(
    ultima_root,
    names="numeral",
    values="counts",
    facet_row="cadence",
    facet_col="localkey_is_minor",
    height=1500,
    category_orders={"cadence": cadence_counts.index},
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_traces(textposition="inside", textinfo="percent+label")
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "ultima_root_distributions_over_cadence_types_maj_min_pies")
fig.show()

# phrase_segments.groupby(level=[0,1,2], group_keys=False).apply(lambda df: df if ((df.cadence == 'PAC') &
# (df.numeral == 'V')).any() else None)

Ultimae bass note as scale degree

ultima_bass = (
    phrase_segments.groupby(["localkey_is_minor", "cadence"])
    .bass_note.value_counts()
    .rename("counts")
    .reset_index()
)
ultima_bass.bass_note = ms3.transform(
    ultima_bass, ms3.fifths2sd, dict(fifths="bass_note", minor="localkey_is_minor")
)
ultima_bass.localkey_is_minor = ultima_bass.localkey_is_minor.map(
    {False: "in major", True: "in minor"}
)
# ultima_bass.style.apply(highlight, axis=1)

fig = px.pie(
    ultima_bass,
    names="bass_note",
    values="counts",
    facet_row="cadence",
    facet_col="localkey_is_minor",
    height=1500,
    category_orders={"cadence": cadence_counts.index},
)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_traces(textposition="inside", textinfo="percent+label")
fig.update_layout(**utils.STD_LAYOUT)
save_figure_as(fig, "ultima_degree_distributions_over_cadence_types_maj_min_pies")
fig.show()

Chord progressions

PACs with ultima I/i

def remove_immediate_duplicates(lst):
    return tuple(a for a, b in zip(lst, (None,) + lst) if a != b)


def get_progressions(
    selected="PAC",
    last_row={},
    feature="chord",
    dataset=None,
    as_series=True,
    remove_duplicates=False,
):
    """Uses the nonlocal variable phrase_segments."""
    last_row = {k: v if isinstance(v, tuple) else (v,) for k, v in last_row.items()}
    progressions = []

    for (corp, fname, *_), df in phrase_segments[
        phrase_segments[feature].notna()
    ].groupby(level=[0, 1, 2]):
        if dataset is not None and dataset not in corp:
            continue
        if (df.cadence == selected).fillna(False).any():
            # remove chords after the last cadence label
            df = df[df.cadence.bfill().notna()]
            # group segments leading up to a cadence label
            cadence_groups = df.cadence.notna().shift().fillna(False).cumsum()
            for i, cadence in df.groupby(cadence_groups):
                last_r = cadence.iloc[-1]
                typ = last_r.cadence
                if typ != selected:
                    continue
                if any(last_r[feat] not in values for feat, values in last_row.items()):
                    continue
                if remove_duplicates:
                    progressions.append(
                        remove_immediate_duplicates(cadence[feature].to_list())
                    )
                else:
                    progressions.append(tuple(cadence[feature]))
    if as_series:
        return pd.Series(progressions, dtype="object")
    return progressions

chord_progressions = get_progressions("PAC", dict(numeral=("I", "i")), "chord")
print(f"Progressions for {len(chord_progressions)} cadences:")
utils.value_count_df(chord_progressions, "chord progressions")

numeral_progressions = get_progressions("PAC", dict(numeral=("I", "i")), "numeral")
utils.value_count_df(numeral_progressions, "numeral progressions")

numeral_prog_no_dups = numeral_progressions.map(remove_immediate_duplicates)
utils.value_count_df(numeral_prog_no_dups)

PACs ending on scale degree 1

Scale degrees expressed w.r.t. major scale, regardless of actual key.

bass_progressions = get_progressions("PAC", dict(bass_note=0), "bass_note")
bass_prog = bass_progressions.map(ms3.fifths2sd)
print(f"Progressions for {len(bass_progressions)} cadences:")
utils.value_count_df(bass_prog, "bass progressions")

bass_prog_no_dups = bass_prog.map(remove_immediate_duplicates)
utils.value_count_df(bass_prog_no_dups)

def progressions2graph_data(progressions, cut_at_stage=None):
    stage_nodes = defaultdict(dict)
    edge_weights = Counter()
    node_counter = 0
    for progression in progressions:
        previous_node = None
        for stage, current in enumerate(reversed(progression)):
            if cut_at_stage and stage > cut_at_stage:
                break
            if current in stage_nodes[stage]:
                current_node = stage_nodes[stage][current]
            else:
                stage_nodes[stage][current] = node_counter
                current_node = node_counter
                node_counter += 1
            if previous_node is not None:
                edge_weights.update([(current_node, previous_node)])
            previous_node = current_node
    return stage_nodes, edge_weights


def plot_progressions(progressions, cut_at_stage=None, **kwargs):
    stage_nodes, edge_weights = progressions2graph_data(
        progressions, cut_at_stage=cut_at_stage
    )
    return utils.graph_data2sankey(stage_nodes, edge_weights, **kwargs)

Chordal roots for the 3 last stages

fig = plot_progressions(
    numeral_prog_no_dups,
    cut_at_stage=3,
    font=dict(size=30),
)
save_figure_as(fig, "last_3_roots_before_pacs_ending_on_1_sankey", height=800)
fig.show()

Complete chords for the last four stages in major

pac_major = get_progressions("PAC", dict(numeral="I", localkey_is_minor=False), "chord")
fig = plot_progressions(pac_major, cut_at_stage=4)
save_figure_as(fig, "last_4_stages_before_pacs_in_major_sankey")
fig.show()

Bass degrees for the last 6 stages.

fig = plot_progressions(bass_prog_no_dups, cut_at_stage=7)
save_figure_as(fig, "last_7_degrees_before_pacs_ending_on_1_sankey")
fig.show()

Bass degrees without accidentals

def remove_sd_accidentals(t):
    return tuple(map(lambda sd: sd[-1], t))


bass_prog_no_acc_no_dup = bass_prog.map(remove_sd_accidentals).map(
    remove_immediate_duplicates
)
fig = plot_progressions(bass_prog_no_acc_no_dup, cut_at_stage=7)
save_figure_as(fig, "last_7_degrees_before_pacs_ending_on_1_without_accdentals_sankey")
fig.show()

HCs ending on V

half = get_progressions("HC", dict(numeral="V"), "bass_note").map(ms3.fifths2sd)
print(f"Progressions for {len(half)} cadences:")
fig = plot_progressions(half.map(remove_immediate_duplicates), cut_at_stage=5)
save_figure_as(fig, "last_7_degrees_before_hcs_ending_on_V_sankey")
fig.show()