{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cacophony for the whole family\n",
"==============================\n",
"\n",
"Allen Downey\n",
"\n",
"This is an example that demonstrates some of the features in the *Think DSP* library.\n",
"\n",
"It is inspired by the performance of a grade school band I witnessed recently. My goal is to simulate the sound of a beginner band.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Get thinkdsp.py\n",
"\n",
"import os\n",
"\n",
"if not os.path.exists('thinkdsp.py'):\n",
" !wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/thinkdsp.py"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, a function that translates from a MIDI number to a frequency:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def midi_to_freq(midi_num):\n",
" \"\"\"Converts MIDI note number to frequency.\n",
"\n",
" midi_num: int MIDI note number\n",
" \n",
" returns: float frequency in Hz\n",
" \"\"\"\n",
" x = (midi_num - 69) / 12.0\n",
" freq = 440.0 * 2**x\n",
" return freq"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now here's a randomized version that simulates three kinds of errors: poor tuning, playing the wrong note, and [popping an overtone](https://en.wikipedia.org/wiki/Overtone). Notice that it is possible to make all three errors."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"\n",
"def random_freq(midi_num):\n",
"\n",
" # simulate poor tuning by adding gaussian noise to the MIDI number\n",
" midi_num += random.gauss(0, 0.5)\n",
" \n",
" # one kid out of 10 plays the wrong note\n",
" if random.random() < 0.1:\n",
" midi_num += random.randint(-5, 5)\n",
" \n",
" freq = midi_to_freq(midi_num)\n",
" \n",
" # and one kid in 10 pops an overtone\n",
" if random.random() < 0.1:\n",
" freq *= random.randint(2, 5)\n",
"\n",
" return freq"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This function takes a MIDI number and duration and makes a Wave:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from thinkdsp import SawtoothSignal\n",
"\n",
"def make_note(midi_num, duration, framerate=22050):\n",
" \"\"\"Make a MIDI note with the given duration.\n",
"\n",
" midi_num: int MIDI note number\n",
" duration: float seconds\n",
" sig_cons: Signal constructor function\n",
" framerate: int frames per second\n",
"\n",
" returns: Wave\n",
" \"\"\"\n",
" freq = random_freq(midi_num)\n",
" signal = SawtoothSignal(freq)\n",
" wave = signal.make_wave(duration, framerate=framerate)\n",
" wave.apodize()\n",
" return wave"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test make_note. MIDI number 60 is middle C."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"note = make_note(60, 1.0)\n",
"note.make_audio()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sounds good.\n",
"\n",
"Now we can make 10 notes and play them at the same time. Since Wave provides `__add__`, we can use `sum`:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def make_ensemble(midi_num, duration):\n",
" notes = [make_note(midi_num, duration) for i in range(10)]\n",
" ensemble = sum(notes)\n",
" ensemble.make_audio()\n",
" return ensemble"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can test it with a middle C:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = make_ensemble(60, 1.0)\n",
"c.make_audio()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Good, sounds like angry bees.\n",
"\n",
"And now, a rousing chorus of that old crowd favorite, _Hot Cross Buns_.\n",
"\n",
"Wave provides `__or__`, which concatenates notes, so we can use `reduce`:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from thinkdsp import Wave\n",
"from functools import reduce\n",
"\n",
"midi_nums = [64, 62, 60, 64, 62, 60, 60, 60, 60, 60, 62, 62, 62, 62, 64, 62, 60]\n",
"durations = [0.5, 0.5, 1.0, 0.5, 0.5, 1.0, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 1.0]\n",
"\n",
"waves = [make_ensemble(midi_num, duration) for midi_num, duration in zip(midi_nums, durations)]\n",
"wave = reduce(Wave.__or__, waves)\n",
"wave.make_audio()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And that brings a tear of pride to any parent's eye.\n",
"\n",
"On a more serious note, this example tells us something about how the ear interprets complex sounds with many tones and harmonics.\n",
"\n",
"Let's take a look at the spectrum of that middle C:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from thinkdsp import decorate\n",
"\n",
"spectrum = c.make_spectrum()\n",
"spectrum.plot()\n",
"decorate(xlabel='Frequency (Hz)', ylabel='Amplitude')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can zoom in on the first few harmonics:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"spectrum.plot(high=4000)\n",
"decorate(xlabel='Frequency (Hz)', ylabel='Amplitude')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A few observations: \n",
"\n",
"1. The kids playing out of tune have a bigger effect on the harmonics, and less effect on the fundamental, so the ear can still pick out a clear pitch, and\n",
"\n",
"2. Some of the unintentional overtones overlap with the harmonics, so they change the timbre, but don't stick out as much as you might expect, \n",
"\n",
"3. The high harmonics are so spread out that they basically contribute white noise and don't affect the perceived pitch."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}