kennethreitz/pytheory
1
0
Fork 0
mirror of https://github.com/kennethreitz/pytheory.git synced 2026-06-05 14:50:18 +00:00
Code Issues Packages Projects Releases Wiki Activity

Saxophone synth overhaul: reed clipping, formants, breath noise — v0.40.5

Browse Source 
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
This commit is contained in:
Kenneth Reitz
2026-04-01 00:38:10 -04:00
parent 755b33a63b
commit 63362df697
5 changed files with 113 additions and 37 deletions
Download Patch File Download Diff File Expand all files Collapse all files
CHANGELOG.md
+7
View File
@@ -2,6 +2,13 @@
All notable changes to PyTheory are documented here.
## 0.40.5
- **Saxophone synth overhaul** — reed nonlinearity (asymmetric soft clipping),
conical bore formant resonances, breath noise with attack envelope, separate
reed buzz, key click transient, and sub-harmonic warmth. Vibrato dialed back
to subtle, delayed onset.
## 0.40.4
- **Distortion overhaul** — multi-stage clipping (preamp → power amp →
pyproject.toml
+1 -1
View File
@@ -1,6 +1,6 @@
[project]
name = "pytheory"
version = "0.40.4"
version = "0.40.5"
description = "Music Theory for Humans"
readme = "README.md"
license = "MIT"
pytheory/__init__.py
+1 -1
View File
@@ -1,6 +1,6 @@
"""PyTheory: Music Theory for Humans."""
__version__ = "0.40.4"
__version__ = "0.40.5"
from .tones import Tone, Interval
from .systems import System, SYSTEMS, TET
pytheory/play.py
+103 -34
View File
@@ -1187,62 +1187,131 @@ def timpani_wave(hz, peak=SAMPLE_PEAK, n_samples=SAMPLE_RATE):
def saxophone_wave(hz, peak=SAMPLE_PEAK, n_samples=SAMPLE_RATE):
"""Saxophone — single reed through a conical brass bore.
"""Saxophone — single reed driving a conical brass bore.
The conical bore produces all harmonics (like oboe), but the
brass body and larger mouthpiece give a warmer, fatter, more
vocal quality. The reed adds a slight buzz. Saxophone is
between clarinet (odd harmonics) and oboe (nasal even+odd) —
it has everything, with a strong fundamental and rich mids.
Models the key acoustic properties of a saxophone:
1. Reed-bore interaction — nonlinear clipping creates the characteristic
bright, edgy tone (not just additive sines)
2. Conical bore formants — vocal-like resonances at ~500, ~1400, ~2300,
~3200 Hz that give sax its singing quality
3. Breath noise — turbulent airflow through the mouthpiece, strongest
at attack and blending into sustained tone
4. Sub-harmonic warmth — the conical bore's coupling creates warmth
below the fundamental
5. Vibrato — delayed onset, ~5 Hz, characteristic of jazz/classical sax
"""
import scipy.signal as _sig
t = numpy.arange(n_samples, dtype=numpy.float64) / SAMPLE_RATE
rng = numpy.random.default_rng(int(hz * 100) % 2**31)
# Vibrato — develops after ~250ms, wider than flute
vib_onset = numpy.clip(t / 0.25, 0.0, 1.0)
vib = hz * 0.0012 * vib_onset * numpy.sin(2 * numpy.pi * 5.2 * t)
# --- Vibrato: delayed onset, subtle depth ---
vib_onset = numpy.clip((t - 0.3) / 0.3, 0.0, 1.0)
vib_rate = 5.0 + 0.15 * numpy.sin(2 * numpy.pi * 0.4 * t)
vib = hz * 0.0006 * vib_onset * numpy.sin(2 * numpy.pi * vib_rate * t)
# --- Core tone: sawtooth-like waveform with reed clipping ---
# Real sax reed creates a quasi-sawtooth pressure wave, not pure sines.
# Build from harmonics with sax-specific spectral envelope, then clip.
wave = numpy.zeros(n_samples, dtype=numpy.float64)
n_harmonics = min(20, int((SAMPLE_RATE / 2) / hz))
n_harmonics = min(25, int((SAMPLE_RATE / 2) / hz))
for n in range(1, n_harmonics + 1):
f_n = hz * n
if f_n >= SAMPLE_RATE / 2:
break
# Sax spectral shape: strong fundamental, broad mid peak (3-6),
# slower rolloff than oboe (brass body carries harmonics further)
# Saxophone spectral envelope from acoustic measurements:
# Strong fundamental, nearly-as-strong 2nd and 3rd harmonics,
# broad energy peak around harmonics 4-8 (the "body"), then
# gradual rolloff — but slower than other woodwinds (brass bore
# sustains upper partials).
if n == 1:
amp = 1.0
elif n <= 3:
amp = 0.6
elif n <= 6:
amp = 0.4 * numpy.exp(-0.1 * (n - 4) ** 2)
elif n == 2:
amp = 0.85
elif n == 3:
amp = 0.7
elif n <= 8:
# Broad mid peak — this is the sax "meat"
amp = 0.55 * numpy.exp(-0.06 * (n - 5) ** 2)
else:
amp = 0.2 / n
# Slower rolloff than oboe/clarinet
amp = 0.35 / (n ** 0.7)
# Slight even/odd asymmetry — conical bore has all harmonics
# but evens are ~10% weaker (midway between cylinder and cone)
if n % 2 == 0:
amp *= 0.9
phase = rng.uniform(0, 2 * numpy.pi)
wave += amp * numpy.sin(2 * numpy.pi * (f_n + vib * n) * t + phase)
# Reed buzz — more present than oboe but still warm
reed = rng.normal(0, 0.07, n_samples)
# Bandpass the reed noise around 1-3kHz (the "honk" range)
import scipy.signal as _sig
reed_lo = max(20, int(hz * 2))
reed_hi = min(SAMPLE_RATE // 2 - 1, int(hz * 6))
# --- Reed nonlinearity: soft clipping ---
# The reed closes against the mouthpiece, creating asymmetric clipping
# that adds brightness and "edge". This is what makes sax sound like
# sax and not a flute.
wave_max = numpy.abs(wave).max()
if wave_max > 0:
wave /= wave_max
# Asymmetric soft clip: positive peaks clip harder (reed closure)
wave = numpy.tanh(1.8 * wave) * 0.7 + numpy.tanh(2.5 * wave) * 0.3
# --- Formant resonances: conical bore creates vocal quality ---
# These fixed resonances are what make sax sound "vocal" — they
# emphasize certain frequency bands regardless of the note played.
formant_freqs = [520, 1380, 2300, 3200]
formant_bws = [120, 200, 280, 350]
formant_gains = [0.25, 0.18, 0.12, 0.08]
formant_sum = numpy.zeros(n_samples, dtype=numpy.float64)
for fc, bw, gain in zip(formant_freqs, formant_bws, formant_gains):
lo = max(20, int(fc - bw))
hi = min(SAMPLE_RATE // 2 - 1, int(fc + bw))
if lo < hi:
bf, af = _sig.butter(2, [lo, hi], btype='band', fs=SAMPLE_RATE)
formant_sum += _sig.lfilter(bf, af, wave) * gain
wave = wave * 0.7 + formant_sum
# --- Breath noise: turbulent air through the mouthpiece ---
# Strongest at the attack, then settles to a subtle constant hiss
# that gives the tone "life" and prevents it from sounding synthetic.
breath = rng.normal(0, 1.0, n_samples)
# Shape breath noise into the sax's "hiss" band (2-6 kHz)
breath_lo = max(20, 2000)
breath_hi = min(SAMPLE_RATE // 2 - 1, 6000)
if breath_lo < breath_hi:
bb, ab = _sig.butter(2, [breath_lo, breath_hi], btype='band', fs=SAMPLE_RATE)
breath = _sig.lfilter(bb, ab, breath)
# Attack envelope for breath — strong at onset, then quiet
breath_env = 0.15 * numpy.exp(-8.0 * t) + 0.03
wave += breath * breath_env
# --- Reed buzz: low-frequency interaction noise ---
# Different from breath — this is the "buzz" from reed vibration
# against the mouthpiece, centered around the playing frequency.
reed_noise = rng.normal(0, 1.0, n_samples)
reed_lo = max(20, int(hz * 0.8))
reed_hi = min(SAMPLE_RATE // 2 - 1, int(hz * 4))
if reed_lo < reed_hi:
br, ar = _sig.butter(2, [reed_lo, reed_hi], btype='band', fs=SAMPLE_RATE)
reed = _sig.lfilter(br, ar, reed).astype(numpy.float64) * 2.0
wave += reed
reed_noise = _sig.lfilter(br, ar, reed_noise) * 0.06
wave += reed_noise
# Brass body warmth — low-mid boost
center = min(1500, hz * 4)
bw = 500
lo = max(20, int(center - bw))
hi = min(SAMPLE_RATE // 2 - 1, int(center + bw))
if lo < hi:
bp, ap = _sig.butter(2, [lo, hi], btype='band', fs=SAMPLE_RATE)
body = _sig.lfilter(bp, ap, wave) * 0.2
wave += body
# --- Attack transient: key click + breath burst ---
attack_len = min(int(SAMPLE_RATE * 0.015), n_samples)
if attack_len > 0:
click = rng.uniform(-1.0, 1.0, attack_len)
click *= numpy.exp(-numpy.linspace(0, 8, attack_len))
wave[:attack_len] += click * 0.12
# --- Sub-harmonic warmth ---
# Conical bore coupling produces energy slightly below fundamental
if hz > 80: # only if there's room
sub = numpy.sin(2 * numpy.pi * (hz * 0.5) * t) * 0.04
sub *= numpy.clip(t / 0.1, 0.0, 1.0) # fade in gently
wave += sub
# --- Final shaping ---
mx = numpy.abs(wave).max()
if mx > 0:
wave /= mx
uv.lock
Generated
+1 -1
View File
@@ -690,7 +690,7 @@ wheels = [
[[package]]
name = "pytheory"
version = "0.40.4"
version = "0.40.5"
source = { editable = "." }
dependencies = [
{ name = "rich" },