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Pitch Detection with SPICE

View on TensorFlow.org Run in Google Colab View on GitHub Download notebook See TF Hub model

This colab will show you how to use the SPICE model downloaded from TensorFlow Hub.

sudo apt-get install -q -y timidity libsndfile1
Reading package lists...
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libsndfile1 is already the newest version (1.0.28-7ubuntu0.1).
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  libblockdev-part2 libblockdev-swap2 libblockdev-utils2 libblockdev2 libnuma1
  libparted-fs-resize0
Use 'sudo apt autoremove' to remove them.
The following additional packages will be installed:
  fluid-soundfont-gm libao-common libao4
Suggested packages:
  fluid-soundfont-gs fluidsynth libaudio2 libsndio6.1 freepats pmidi
  timidity-daemon
The following NEW packages will be installed:
  fluid-soundfont-gm libao-common libao4 timidity
0 upgraded, 4 newly installed, 0 to remove and 95 not upgraded.
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# All the imports to deal with sound data
pip install pydub numba==0.48 librosa music21
import tensorflow as tf
import tensorflow_hub as hub

import numpy as np
import matplotlib.pyplot as plt
import librosa
from librosa import display as librosadisplay

import logging
import math
import statistics
import sys

from IPython.display import Audio, Javascript
from scipy.io import wavfile

from base64 import b64decode

import music21
from pydub import AudioSegment

logger = logging.getLogger()
logger.setLevel(logging.ERROR)

print("tensorflow: %s" % tf.__version__)
#print("librosa: %s" % librosa.__version__)
tensorflow: 2.9.0-rc1
/tmpfs/src/tf_docs_env/lib/python3.7/site-packages/pydub/utils.py:170: RuntimeWarning: Couldn't find ffmpeg or avconv - defaulting to ffmpeg, but may not work
  warn("Couldn't find ffmpeg or avconv - defaulting to ffmpeg, but may not work", RuntimeWarning)

The audio input file

Now the hardest part: Record your singing! :)

We provide four methods to obtain an audio file:

  1. Record audio directly in colab
  2. Upload from your computer
  3. Use a file saved on Google Drive
  4. Download the file from the web

Choose one of the four methods below.

[Run this] Definition of the JS code to record audio straight from the browser

Select how to input your audio

You selected https://storage.googleapis.com/download.tensorflow.org/data/c-scale-metronome.wav
--2022-04-27 12:02:29--  https://storage.googleapis.com/download.tensorflow.org/data/c-scale-metronome.wav
Resolving storage.googleapis.com (storage.googleapis.com)... 108.177.111.128, 172.217.212.128, 108.177.112.128, ...
Connecting to storage.googleapis.com (storage.googleapis.com)|108.177.111.128|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 384728 (376K) [audio/wav]
Saving to: ‘c-scale.wav’

c-scale.wav         100%[===================>] 375.71K  --.-KB/s    in 0.003s  

2022-04-27 12:02:29 (131 MB/s) - ‘c-scale.wav’ saved [384728/384728]

Preparing the audio data

Now we have the audio, let's convert it to the expected format and then listen to it!

The SPICE model needs as input an audio file at a sampling rate of 16kHz and with only one channel (mono).

To help you with this part, we created a function (convert_audio_for_model) to convert any wav file you have to the model's expected format:

# Function that converts the user-created audio to the format that the model 
# expects: bitrate 16kHz and only one channel (mono).

EXPECTED_SAMPLE_RATE = 16000

def convert_audio_for_model(user_file, output_file='converted_audio_file.wav'):
  audio = AudioSegment.from_file(user_file)
  audio = audio.set_frame_rate(EXPECTED_SAMPLE_RATE).set_channels(1)
  audio.export(output_file, format="wav")
  return output_file
# Converting to the expected format for the model
# in all the input 4 input method before, the uploaded file name is at
# the variable uploaded_file_name
converted_audio_file = convert_audio_for_model(uploaded_file_name)
# Loading audio samples from the wav file:
sample_rate, audio_samples = wavfile.read(converted_audio_file, 'rb')

# Show some basic information about the audio.
duration = len(audio_samples)/sample_rate
print(f'Sample rate: {sample_rate} Hz')
print(f'Total duration: {duration:.2f}s')
print(f'Size of the input: {len(audio_samples)}')

# Let's listen to the wav file.
Audio(audio_samples, rate=sample_rate)
Sample rate: 16000 Hz
Total duration: 11.89s
Size of the input: 190316

First thing, let's take a look at the waveform of our singing.

# We can visualize the audio as a waveform.
_ = plt.plot(audio_samples)

png

A more informative visualization is the spectrogram, which shows frequencies present over time.

Here, we use a logarithmic frequency scale, to make the singing more clearly visible.

MAX_ABS_INT16 = 32768.0

def plot_stft(x, sample_rate, show_black_and_white=False):
  x_stft = np.abs(librosa.stft(x, n_fft=2048))
  fig, ax = plt.subplots()
  fig.set_size_inches(20, 10)
  x_stft_db = librosa.amplitude_to_db(x_stft, ref=np.max)
  if(show_black_and_white):
    librosadisplay.specshow(data=x_stft_db, y_axis='log', 
                             sr=sample_rate, cmap='gray_r')
  else:
    librosadisplay.specshow(data=x_stft_db, y_axis='log', sr=sample_rate)

  plt.colorbar(format='%+2.0f dB')

plot_stft(audio_samples / MAX_ABS_INT16 , sample_rate=EXPECTED_SAMPLE_RATE)
plt.show()

png

We need one last conversion here. The audio samples are in int16 format. They need to be normalized to floats between -1 and 1.

audio_samples = audio_samples / float(MAX_ABS_INT16)

Executing the Model

Now is the easy part, let's load the model with TensorFlow Hub, and feed the audio to it. SPICE will give us two outputs: pitch and uncertainty

TensorFlow Hub is a library for the publication, discovery, and consumption of reusable parts of machine learning models. It makes easy to use machine learning to solve your challenges.

To load the model you just need the Hub module and the URL pointing to the model:

# Loading the SPICE model is easy:
model = hub.load("https://tfhub.dev/google/spice/2")
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'global_step:0' shape=() dtype=int64_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/conv2d/kernel:0' shape=(1, 3, 1, 64) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/gamma:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/beta:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().
WARNING:tensorflow:Unable to create a python object for variable <tf.Variable 'encoder/batch_normalization/moving_mean:0' shape=(64,) dtype=float32_ref> because it is a reference variable. It may not be visible to training APIs. If this is a problem, consider rebuilding the SavedModel after running tf.compat.v1.enable_resource_variables().

With the model loaded, data prepared, we need 3 lines to get the result:

# We now feed the audio to the SPICE tf.hub model to obtain pitch and uncertainty outputs as tensors.
model_output = model.signatures["serving_default"](tf.constant(audio_samples, tf.float32))

pitch_outputs = model_output["pitch"]
uncertainty_outputs = model_output["uncertainty"]

# 'Uncertainty' basically means the inverse of confidence.
confidence_outputs = 1.0 - uncertainty_outputs

fig, ax = plt.subplots()
fig.set_size_inches(20, 10)
plt.plot(pitch_outputs, label='pitch')
plt.plot(confidence_outputs, label='confidence')
plt.legend(loc="lower right")
plt.show()

png

Let's make the results easier to understand by removing all pitch estimates with low confidence (confidence < 0.9) and plot the remaining ones.

confidence_outputs = list(confidence_outputs)
pitch_outputs = [ float(x) for x in pitch_outputs]

indices = range(len (pitch_outputs))
confident_pitch_outputs = [ (i,p)  
  for i, p, c in zip(indices, pitch_outputs, confidence_outputs) if  c >= 0.9  ]
confident_pitch_outputs_x, confident_pitch_outputs_y = zip(*confident_pitch_outputs)

fig, ax = plt.subplots()
fig.set_size_inches(20, 10)
ax.set_ylim([0, 1])
plt.scatter(confident_pitch_outputs_x, confident_pitch_outputs_y, )
plt.scatter(confident_pitch_outputs_x, confident_pitch_outputs_y, c="r")

plt.show()

png

The pitch values returned by SPICE are in the range from 0 to 1. Let's convert them to absolute pitch values in Hz.

def output2hz(pitch_output):
  # Constants taken from https://tfhub.dev/google/spice/2
  PT_OFFSET = 25.58
  PT_SLOPE = 63.07
  FMIN = 10.0;
  BINS_PER_OCTAVE = 12.0;
  cqt_bin = pitch_output * PT_SLOPE + PT_OFFSET;
  return FMIN * 2.0 ** (1.0 * cqt_bin / BINS_PER_OCTAVE)

confident_pitch_values_hz = [ output2hz(p) for p in confident_pitch_outputs_y ]

Now, let's see how good the prediction is: We will overlay the predicted pitches over the original spectrogram. To make the pitch predictions more visible, we changed the spectrogram to black and white.

plot_stft(audio_samples / MAX_ABS_INT16 , 
          sample_rate=EXPECTED_SAMPLE_RATE, show_black_and_white=True)
# Note: conveniently, since the plot is in log scale, the pitch outputs 
# also get converted to the log scale automatically by matplotlib.
plt.scatter(confident_pitch_outputs_x, confident_pitch_values_hz, c="r")

plt.show()

png

Converting to musical notes

Now that we have the pitch values, let's convert them to notes! This is part is challenging by itself. We have to take into account two things:

  1. the rests (when there's no singing)
  2. the size of each note (offsets)

1: Adding zeros to the output to indicate when there's no singing

pitch_outputs_and_rests = [
    output2hz(p) if c >= 0.9 else 0
    for i, p, c in zip(indices, pitch_outputs, confidence_outputs)
]

2: Adding note offsets

When a person sings freely, the melody may have an offset to the absolute pitch values that notes can represent. Hence, to convert predictions to notes, one needs to correct for this possible offset. This is what the following code computes.

A4 = 440
C0 = A4 * pow(2, -4.75)
note_names = ["C", "C#", "D", "D#", "E", "F", "F#", "G", "G#", "A", "A#", "B"]

def hz2offset(freq):
  # This measures the quantization error for a single note.
  if freq == 0:  # Rests always have zero error.
    return None
  # Quantized note.
  h = round(12 * math.log2(freq / C0))
  return 12 * math.log2(freq / C0) - h


# The ideal offset is the mean quantization error for all the notes
# (excluding rests):
offsets = [hz2offset(p) for p in pitch_outputs_and_rests if p != 0]
print("offsets: ", offsets)

ideal_offset = statistics.mean(offsets)
print("ideal offset: ", ideal_offset)
offsets:  [0.2851056911175931, 0.3700368844097355, 0.2861639241998972, 0.19609005646164235, 0.17851549283916768, 0.2733467103665532, -0.4475316266590852, -0.24651809109990808, -0.1796576844031108, -0.23060136331860548, -0.37826153113190486, -0.4725081829601976, -0.3457194541269999, -0.2436666886383776, -0.1818906877810207, -0.1348077739650435, -0.24551812662426897, -0.4454903457934165, -0.3126792745167535, -0.12241723670307181, -0.06614479972665066, -0.06702634735648871, -0.1744116301709866, -0.29365739389006507, -0.32520890458170726, -0.0564402572685907, 0.1470525135224534, 0.17167006002122775, 0.16529058740790248, 0.09569531546290477, -0.006323616641203955, -0.11799822075907684, -0.18835098459069144, -0.17934754504506145, -0.17215607120338916, -0.23695828034226452, -0.34594501002376177, -0.39380233241860907, -0.2528674895936689, -0.11009436621014146, -0.07118973328416445, -0.08042436762396932, -0.12799598588293293, -0.16227296366040633, -0.05931985421721464, 0.1066761283701112, 0.21044687793906292, 0.2931939382975841, -0.22329278631751492, -0.12365553720538713, -0.4571117360765271, -0.34864566459005175, -0.35947798653189267, -0.4313175396496476, -0.4818984494978622, 0.44220950977261, 0.45883109973128455, -0.47095710887258235, -0.3674495078498552, -0.3047186536962201, -0.310761672096902, -0.4501401792341895, 0.3966096259778311, 0.4238116671269694, 0.4982676686471237, -0.45931842459980743, -0.4890504510576079, 0.3836871527260044, 0.4441286145275285, -0.38787359430138935, -0.24855899466817277, -0.20666198684519088, -0.23811575664822726, -0.2760223047310504, -0.3641714288169524, -0.41670715643708434, -0.41009460939710607, -0.3340427999073796, -0.26122771753614416, -0.2232610212141708, -0.19940660549943345, -0.22528914465252825, -0.2780880208188776, -0.2744434134537457, -0.25655307157580154, -0.33068201704567457, -0.4678933079416083, -0.4695135511333177, -0.1648172314340286, -0.24618840082233362, -0.48052406086269883, -0.3771743489677135, -0.32261613680665846, -0.25560160024707557, -0.24629741950576545, -0.14035005553309787, -0.16659160448853783, -0.2442749349648139, -0.236978201704666, -0.20882882578912643, -0.22637331529204374, -0.2983651186401133, -0.39081296219175243, -0.3909896476442043, -0.3650093676025108, -0.2642347521955202, -0.13023199393098395, -0.18214744283501716, -0.3020849113041564, -0.33754229827467697, -0.34391425235812534, -0.31454499496763333, -0.26713314546887545, -0.2910458297902778, -0.11686573876684037, -0.1673094354445226, -0.24345710619036964, -0.30852622314040445, -0.35647376789395935, -0.37154654069487236, -0.3600187547380216, -0.2667062802488047, -0.21902000440899627, -0.2484456507736823, -0.2774107871825038, -0.2941432754570741, -0.31118778272216474, -0.32662896348779213, -0.3053947554403962, -0.2160201109821145, -0.17343703730647775, -0.17792559965198507, -0.19880643679444177, -0.2725030667955153, -0.3152120758468442, -0.28216813697164156, -0.11595223738495974, 0.0541883348053247, 0.11488166735824024, -0.2559698195630773, 0.019302356106599916, -0.002236352401425279, 0.4468796487277231, 0.15514959977323883, 0.4207713650291751, 0.3854474319642307, 0.4373497234409669, -0.4694994504625001, -0.3662756739431998, -0.20354085369650932, -0.015043790774988963, -0.4185651697093675, -0.17896653874461066, -0.032896162706066434, -0.061098168330843805, -0.1953772325689087, -0.2545161090666568, -0.3363741032654488, -0.39191536320988973, -0.36531668408458984, -0.3489657612020167, -0.35455202891175475, -0.38925192399566555, 0.48781259374078445, -0.2820884378129733, -0.241939488189864, -0.24987529649083484, -0.3034880535179809, -0.2910712014014081, -0.2783103765422581, -0.30017802073304267, -0.23735882385318519, -0.15802893533056306, -0.1688725350672513, 0.00533368216211727, -0.2545762573057857, -0.28210347487274845, -0.29791870250051034, -0.3228332309300086, -0.3895802937323367, 0.4323790387934068, 0.17438820408041522, -0.12961039467398905, -0.2236296109730489, -0.04022635205333813, -0.4264081214243589, -0.0019025255615048309, -0.07466309859101727, -0.08664951487129002, -0.08169104440753472, -0.31617519541327965, -0.47420548422877573, 0.1502044753855003, 0.30507923857624064, 0.031032583278971515, -0.17852388186996393, -0.3371385477358615, -0.41780861421172233, -0.2023970939094255, -0.10604901297633518, -0.10770872844999246, -0.16037790997569346, -0.18698222799842767, -0.17355977250879562, -0.008242337244190878, -0.011401999431292609, -0.18767393274848132, -0.360175323324853, 0.011681766969516616, -0.1931417836124183]
ideal offset:  -0.16889359351455108

We can now use some heuristics to try and estimate the most likely sequence of notes that were sung. The ideal offset computed above is one ingredient - but we also need to know the speed (how many predictions make, say, an eighth?), and the time offset to start quantizing. To keep it simple, we'll just try different speeds and time offsets and measure the quantization error, using in the end the values that minimize this error.

def quantize_predictions(group, ideal_offset):
  # Group values are either 0, or a pitch in Hz.
  non_zero_values = [v for v in group if v != 0]
  zero_values_count = len(group) - len(non_zero_values)

  # Create a rest if 80% is silent, otherwise create a note.
  if zero_values_count > 0.8 * len(group):
    # Interpret as a rest. Count each dropped note as an error, weighted a bit
    # worse than a badly sung note (which would 'cost' 0.5).
    return 0.51 * len(non_zero_values), "Rest"
  else:
    # Interpret as note, estimating as mean of non-rest predictions.
    h = round(
        statistics.mean([
            12 * math.log2(freq / C0) - ideal_offset for freq in non_zero_values
        ]))
    octave = h // 12
    n = h % 12
    note = note_names[n] + str(octave)
    # Quantization error is the total difference from the quantized note.
    error = sum([
        abs(12 * math.log2(freq / C0) - ideal_offset - h)
        for freq in non_zero_values
    ])
    return error, note


def get_quantization_and_error(pitch_outputs_and_rests, predictions_per_eighth,
                               prediction_start_offset, ideal_offset):
  # Apply the start offset - we can just add the offset as rests.
  pitch_outputs_and_rests = [0] * prediction_start_offset + \
                            pitch_outputs_and_rests
  # Collect the predictions for each note (or rest).
  groups = [
      pitch_outputs_and_rests[i:i + predictions_per_eighth]
      for i in range(0, len(pitch_outputs_and_rests), predictions_per_eighth)
  ]

  quantization_error = 0

  notes_and_rests = []
  for group in groups:
    error, note_or_rest = quantize_predictions(group, ideal_offset)
    quantization_error += error
    notes_and_rests.append(note_or_rest)

  return quantization_error, notes_and_rests


best_error = float("inf")
best_notes_and_rests = None
best_predictions_per_note = None

for predictions_per_note in range(20, 65, 1):
  for prediction_start_offset in range(predictions_per_note):

    error, notes_and_rests = get_quantization_and_error(
        pitch_outputs_and_rests, predictions_per_note,
        prediction_start_offset, ideal_offset)

    if error < best_error:      
      best_error = error
      best_notes_and_rests = notes_and_rests
      best_predictions_per_note = predictions_per_note

# At this point, best_notes_and_rests contains the best quantization.
# Since we don't need to have rests at the beginning, let's remove these:
while best_notes_and_rests[0] == 'Rest':
  best_notes_and_rests = best_notes_and_rests[1:]
# Also remove silence at the end.
while best_notes_and_rests[-1] == 'Rest':
  best_notes_and_rests = best_notes_and_rests[:-1]

Now let's write the quantized notes as sheet music score!

To do it we will use two libraries: music21 and Open Sheet Music Display

# Creating the sheet music score.
sc = music21.stream.Score()
# Adjust the speed to match the actual singing.
bpm = 60 * 60 / best_predictions_per_note
print ('bpm: ', bpm)
a = music21.tempo.MetronomeMark(number=bpm)
sc.insert(0,a)

for snote in best_notes_and_rests:   
    d = 'half'
    if snote == 'Rest':      
      sc.append(music21.note.Rest(type=d))
    else:
      sc.append(music21.note.Note(snote, type=d))
bpm:  78.26086956521739

[Run this] Helper function to use Open Sheet Music Display (JS code) to show a music score

# rendering the music score
showScore(sc)
print(best_notes_and_rests)
/tmpfs/src/tf_docs_env/lib/python3.7/site-packages/music21/musicxml/m21ToXml.py:478: MusicXMLWarning: <music21.stream.Score 0x7f93a8080dd0> is not well-formed; see isWellFormedNotation()
  category=MusicXMLWarning)
<IPython.core.display.Javascript object>
['C3', 'D3', 'E3', 'F3', 'G3', 'A3', 'B3', 'C4']

Let's convert the music notes to a MIDI file and listen to it.

To create this file, we can use the stream we created before.

# Saving the recognized musical notes as a MIDI file
converted_audio_file_as_midi = converted_audio_file[:-4] + '.mid'
fp = sc.write('midi', fp=converted_audio_file_as_midi)
wav_from_created_midi = converted_audio_file_as_midi.replace(' ', '_') + "_midioutput.wav"
print(wav_from_created_midi)
converted_audio_file.mid_midioutput.wav

To listen to it on colab, we need to convert it back to wav. An easy way of doing that is using Timidity.

timidity $converted_audio_file_as_midi -Ow -o $wav_from_created_midi
Playing converted_audio_file.mid
MIDI file: converted_audio_file.mid
Format: 1  Tracks: 2  Divisions: 1024
Track name: 
Playing time: ~16 seconds
Notes cut: 0
Notes lost totally: 0

And finally, listen the audio, created from notes, created via MIDI from the predicted pitches, inferred by the model!

Audio(wav_from_created_midi)