feat(scripts): prototype the momentary fatness lane
scripts/fatness.py measures momentary bass fatness of rendered files with the final model from Schmedeke's dissertation (section 5.4.3, adjusted R² .773): two logistic terms on the C-weighted level and the MPEG-7 harmonic ratio below 200 Hz, over 50 ms windows, after normalising to -23 LUFS (BS.1770 integrated, gated). The thesis does not state the dB(C) of its reference, so --offset maps dBFS to dB(C) (default 100). On the seven Devath references, drops read 4-6, breakdowns near 0, and kick gaps show as 50 ms dips; SPL<200 medians of 67-69 dB(C) suggest the offset may be 2-5 dB low. Also corrects docs/ideas.md, which quoted the thesis's preliminary linear model instead of the final one.
This commit is contained in:
nvrl committed
1 parent
8ecdc03832
commit
1479854503
3 files changed
+211
-13
No files matched your search
@@ -0,0 +1,181 @@
|
||||
"""Momentary bass fatness of rendered audio, after Schmedeke's dissertation.
|
||||
|
||||
Model (L. Schmedeke, "BASS DROP! Bass in modern popular Dance Music",
|
||||
Hamburg 2021, section 5.4.3, adjusted R² .773 on dance-music excerpts):
|
||||
|
||||
l = 10 / (1 + 4.5487 · exp(0.13 · (62.9366 − SPL<200)))
|
||||
h = 10 / (1 + 1.4317 · exp(2.5575 · (0.3299 − HR<200)))
|
||||
Fat_mom = 0.14689 · l · h (0 .. 14.7)
|
||||
|
||||
SPL<200 is the C-weighted sound-pressure level below 200 Hz in dB(C), HR<200
|
||||
the MPEG-7 harmonic ratio of the same band, both over 50 ms windows, with the
|
||||
material normalised to −23 LUFS first.
|
||||
|
||||
Assumption: the thesis does not give the dB(C) its reference tone played at.
|
||||
`--offset` maps dBFS to dB(C); the default 100 dB puts −20 dBFS RMS at 80 dB(C),
|
||||
a usual studio calibration. The thesis reports most complex excerpts at 70–80
|
||||
dB(C) below 200 Hz; the summary prints where the material lands so the offset
|
||||
can be checked.
|
||||
|
||||
Requires ffmpeg, numpy and matplotlib. Describes one model's view of the low
|
||||
band; it is not a quality score.
|
||||
"""
|
||||
import os
|
||||
os.environ.setdefault('MPLCONFIGDIR', '/tmp/fatness-matplotlib')
|
||||
import argparse
|
||||
import json
|
||||
import subprocess
|
||||
from pathlib import Path
|
||||
|
||||
import numpy as np
|
||||
|
||||
RATE = 48000
|
||||
WINDOW_S = 0.05
|
||||
HR_RATE = 4000
|
||||
HR_MAX_LAG_S = 0.04
|
||||
|
||||
|
||||
def load(path):
|
||||
raw = subprocess.check_output(['ffmpeg', '-v', 'error', '-i', str(path), '-f', 'f32le',
|
||||
'-ac', '2', '-ar', str(RATE), 'pipe:1'])
|
||||
return np.frombuffer(raw, dtype='<f4').reshape(-1, 2).T.astype(np.float64)
|
||||
|
||||
|
||||
def k_weight_db(f):
|
||||
"""Magnitude of the BS.1770 K-weighting (shelf + high-pass) at `f` Hz, in dB."""
|
||||
def biquad(b, a):
|
||||
z = np.exp(-2j * np.pi * f / RATE)
|
||||
return (b[0] + b[1] * z + b[2] * z * z) / (a[0] + a[1] * z + a[2] * z * z)
|
||||
shelf = biquad([1.53512485958697, -2.69169618940638, 1.19839281085285],
|
||||
[1.0, -1.69065929318241, 0.73248077421585])
|
||||
high = biquad([1.0, -2.0, 1.0], [1.0, -1.99004745483398, 0.99007225036621])
|
||||
return 20 * np.log10(np.abs(shelf * high) + 1e-30)
|
||||
|
||||
|
||||
def c_weight_db(f):
|
||||
"""IEC 61672 C-weighting at `f` Hz, in dB."""
|
||||
f2 = np.maximum(f, 1e-3) ** 2
|
||||
r = (12194.0 ** 2 * f2) / ((f2 + 20.6 ** 2) * (f2 + 12194.0 ** 2))
|
||||
return 20 * np.log10(r) + 0.06
|
||||
|
||||
|
||||
def filtered(x, gain_db):
|
||||
"""Zero-phase filter by an FFT magnitude response; energy is what is measured."""
|
||||
n = x.shape[-1]
|
||||
size = 1 << (n - 1).bit_length() # zero padding: fast FFT sizes only
|
||||
spec = np.fft.rfft(x, n=size, axis=-1)
|
||||
f = np.fft.rfftfreq(size, 1 / RATE)
|
||||
return np.fft.irfft(spec * 10 ** (gain_db(f) / 20), n=size, axis=-1)[..., :n]
|
||||
|
||||
|
||||
def integrated_lufs(x):
|
||||
"""BS.1770-4 integrated loudness with absolute and relative gates."""
|
||||
y = filtered(x, k_weight_db)
|
||||
block, step = int(0.4 * RATE), int(0.1 * RATE)
|
||||
sq = (y * y).sum(axis=0)
|
||||
c = np.concatenate([[0.], np.cumsum(sq)])
|
||||
starts = np.arange(0, len(sq) - block + 1, step)
|
||||
power = (c[starts + block] - c[starts]) / block
|
||||
loud = -0.691 + 10 * np.log10(power + 1e-30)
|
||||
keep = power[loud > -70]
|
||||
if keep.size == 0:
|
||||
return -np.inf
|
||||
relative = -0.691 + 10 * np.log10(keep.mean()) - 10
|
||||
keep = power[(loud > -70) & (loud > relative)]
|
||||
return -0.691 + 10 * np.log10(keep.mean())
|
||||
|
||||
|
||||
def band_below(x, hz):
|
||||
return filtered(x, lambda f: np.where(f < hz, 0.0, -300.0))
|
||||
|
||||
|
||||
def harmonic_ratio(mono, rate):
|
||||
"""MPEG-7 harmonic ratio per 50 ms window: the largest normalised
|
||||
autocorrelation after the zero-lag lobe, with lags up to 40 ms."""
|
||||
n = int(WINDOW_S * rate)
|
||||
lags = int(HR_MAX_LAG_S * rate)
|
||||
out = []
|
||||
for start in range(lags, len(mono) - n + 1, n):
|
||||
s = mono[start:start + n]
|
||||
e0 = s @ s
|
||||
if e0 <= 1e-12:
|
||||
out.append(0.0)
|
||||
continue
|
||||
# Row m − 1 holds the window delayed by m samples.
|
||||
past = np.lib.stride_tricks.sliding_window_view(mono[start - lags:start - 1 + n], n)[::-1]
|
||||
gamma = (past @ s) / np.sqrt(e0 * np.einsum('ij,ij->i', past, past) + 1e-30)
|
||||
below = np.nonzero(gamma <= 0)[0]
|
||||
if below.size == 0:
|
||||
out.append(0.0)
|
||||
continue
|
||||
out.append(float(max(gamma[below[0]:].max(), 0.0)))
|
||||
return np.array(out), lags
|
||||
|
||||
|
||||
def fatness(spl, hr):
|
||||
l = 10 / (1 + 4.5487 * np.exp(0.13 * (62.9366 - spl)))
|
||||
h = 10 / (1 + 1.4317 * np.exp(2.5575 * (0.3299 - hr)))
|
||||
return 0.14689 * l * h
|
||||
|
||||
|
||||
def measure(path, offset):
|
||||
x = load(path)
|
||||
lufs = integrated_lufs(x)
|
||||
x = x * 10 ** ((-23 - lufs) / 20)
|
||||
low = band_below(x, 200.)
|
||||
mono = low.mean(axis=0)
|
||||
# HR on a 4 kHz copy; the band is below 200 Hz, so nothing aliases.
|
||||
hr, skip = harmonic_ratio(mono[::RATE // HR_RATE], HR_RATE)
|
||||
weighted = filtered(low, c_weight_db)
|
||||
n = int(WINDOW_S * RATE)
|
||||
first = skip * (RATE // HR_RATE)
|
||||
sq = (weighted * weighted).sum(axis=0) / 2
|
||||
frames = len(hr)
|
||||
spl = np.array([10 * np.log10(sq[first + i * n:first + (i + 1) * n].mean() + 1e-30)
|
||||
for i in range(frames)]) + offset
|
||||
times = (first + np.arange(frames) * n) / RATE
|
||||
return lufs, times, spl, hr, fatness(spl, hr)
|
||||
|
||||
|
||||
def main():
|
||||
parser = argparse.ArgumentParser(description=__doc__.split('\n\n')[0])
|
||||
parser.add_argument('files', nargs='*', type=Path)
|
||||
parser.add_argument('--folder', type=Path, default=Path('references/devath'))
|
||||
parser.add_argument('--offset', type=float, default=100.0,
|
||||
help='dB(C) for a 0 dBFS RMS signal (default 100)')
|
||||
parser.add_argument('--output', type=Path, required=True,
|
||||
help='folder for fatness.png and fatness.json')
|
||||
args = parser.parse_args()
|
||||
files = args.files or sorted(args.folder.glob('*.flac'))
|
||||
if not files:
|
||||
parser.error('no audio files')
|
||||
args.output.mkdir(parents=True, exist_ok=True)
|
||||
import matplotlib
|
||||
matplotlib.use('Agg')
|
||||
import matplotlib.pyplot as plt
|
||||
fig, axes = plt.subplots(len(files), 1, squeeze=False, figsize=(15, 2.2 * len(files)),
|
||||
constrained_layout=True)
|
||||
summary = []
|
||||
for ax, path in zip(axes[:, 0], files):
|
||||
lufs, t, spl, hr, fat = measure(path, args.offset)
|
||||
smooth = np.convolve(fat, np.ones(8) / 8, mode='same') # 400 ms
|
||||
pct = lambda v: {str(p): round(float(np.percentile(v, p)), 3) for p in (10, 50, 90)}
|
||||
row = {'file': path.name, 'lufs': round(float(lufs), 2), 'spl_c_below_200': pct(spl),
|
||||
'hr_below_200': pct(hr), 'fatness': pct(fat),
|
||||
'share_spl_70_80': round(float(np.mean((spl >= 70) & (spl <= 80))), 3)}
|
||||
summary.append(row)
|
||||
print(json.dumps(row))
|
||||
ax.plot(t, fat, color='#ccc', lw=0.5)
|
||||
ax.plot(t, smooth, color='#e0115f', lw=1.2)
|
||||
ax.set_ylim(0, 14.7)
|
||||
ax.set_xlim(0, t[-1] if len(t) else 1)
|
||||
ax.set_title(f'{path.stem} ({lufs:.1f} LUFS, normalised to -23)', loc='left', fontsize=9)
|
||||
ax.set_ylabel('Fat_mom')
|
||||
axes[-1, 0].set_xlabel('seconds')
|
||||
fig.savefig(args.output / 'fatness.png', dpi=110)
|
||||
(args.output / 'fatness.json').write_text(json.dumps(
|
||||
{'offset_db': args.offset, 'window_s': WINDOW_S, 'tracks': summary}, indent=2))
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Reference in new issue
Block a user