#!/usr/bin/env python
# coding: utf-8

# Cacophony for the whole family
# ==============================
# 
# Allen Downey
# 
# This is an example that demonstrates some of the features in the *Think DSP* library.
# 
# 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.
# 

# In[1]:


# Get thinkdsp.py

import os

if not os.path.exists('thinkdsp.py'):
    get_ipython().system('wget https://github.com/AllenDowney/ThinkDSP/raw/master/code/thinkdsp.py')


# In[ ]:





# First, a function that translates from a MIDI number to a frequency:

# In[2]:


def midi_to_freq(midi_num):
    """Converts MIDI note number to frequency.

    midi_num: int MIDI note number
    
    returns: float frequency in Hz
    """
    x = (midi_num - 69) / 12.0
    freq = 440.0 * 2**x
    return freq


# 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.

# In[3]:


import random

def random_freq(midi_num):

    # simulate poor tuning by adding gaussian noise to the MIDI number
    midi_num += random.gauss(0, 0.5)
    
    # one kid out of 10 plays the wrong note
    if random.random() < 0.1:
        midi_num += random.randint(-5, 5)
        
    freq = midi_to_freq(midi_num)
    
    # and one kid in 10 pops an overtone
    if random.random() < 0.1:
        freq *= random.randint(2, 5)

    return freq


# This function takes a MIDI number and duration and makes a Wave:

# In[4]:


from thinkdsp import SawtoothSignal

def make_note(midi_num, duration, framerate=22050):
    """Make a MIDI note with the given duration.

    midi_num: int MIDI note number
    duration: float seconds
    sig_cons: Signal constructor function
    framerate: int frames per second

    returns: Wave
    """
    freq = random_freq(midi_num)
    signal = SawtoothSignal(freq)
    wave = signal.make_wave(duration, framerate=framerate)
    wave.apodize()
    return wave


# Let's test make_note.  MIDI number 60 is middle C.

# In[5]:


note = make_note(60, 1.0)
note.make_audio()


# Sounds good.
# 
# Now we can make 10 notes and play them at the same time.  Since Wave provides `__add__`, we can use `sum`:

# In[6]:


def make_ensemble(midi_num, duration):
    notes = [make_note(midi_num, duration) for i in range(10)]
    ensemble = sum(notes)
    ensemble.make_audio()
    return ensemble


# And we can test it with a middle C:

# In[7]:


c = make_ensemble(60, 1.0)
c.make_audio()


# Good, sounds like angry bees.
# 
# And now, a rousing chorus of that old crowd favorite, _Hot Cross Buns_.
# 
# Wave provides `__or__`, which concatenates notes, so we can use `reduce`:

# In[8]:


from thinkdsp import Wave
from functools import reduce

midi_nums = [64, 62, 60,     64, 62, 60,    60, 60, 60, 60,      62, 62, 62, 62,      64, 62, 60]
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]

waves = [make_ensemble(midi_num, duration) for midi_num, duration in zip(midi_nums, durations)]
wave = reduce(Wave.__or__, waves)
wave.make_audio()


# And that brings a tear of pride to any parent's eye.
# 
# On a more serious note, this example tells us something about how the ear interprets complex sounds with many tones and harmonics.
# 
# Let's take a look at the spectrum of that middle C:

# In[9]:


from thinkdsp import decorate

spectrum = c.make_spectrum()
spectrum.plot()
decorate(xlabel='Frequency (Hz)', ylabel='Amplitude')


# And we can zoom in on the first few harmonics:

# In[10]:


spectrum.plot(high=4000)
decorate(xlabel='Frequency (Hz)', ylabel='Amplitude')


# A few observations: 
# 
# 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
# 
# 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, 
# 
# 3. The high harmonics are so spread out that they basically contribute white noise and don't affect the perceived pitch.

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