Glossary#

sample#: A single value in a time series. In audio, this corresponds to the amplitude of the waveform at a given point in time.
sampling rate#: The number of samples per second of a time series. This is denoted by a positive number sr.
time series#: Typically an audio signal, denoted by y, and represented as a one-dimensional numpy.ndarray of floating-point values. y[t] corresponds to amplitude of the waveform at sample t.
frame#: A short slice of a time series used for analysis purposes. This usually corresponds to a single column of a spectrogram matrix.
window#: A vector or function used to weight samples within a frame when computing a spectrogram.
frame length#: The (positive integer) number of samples in an analysis window (or frame). This is denoted by an integer variable n_fft.
hop length#: The number of samples between successive frames, e.g., the columns of a spectrogram. This is denoted as a positive integer hop_length.
window length#: The length (width) of the window function (e.g., Hann window). Note that this can be smaller than the frame length used in a short-time Fourier transform. Typically denoted as a positive integer variable win_length.
Fourier transform#
DFT#
FFT#: A mathematical operation that transforms a time-domain signal into a frequency-domain representation. The discrete Fourier transform (DFT) is typically computed using the fast Fourier transform (FFT) algorithm.
STFT#: The short-time Fourier transform (STFT) is a sequence of Fourier transforms of windowed frames of a time series. The STFT is typically represented as a complex-valued matrix D, where the rows index frequency bins, and the columns index frames (time).
spectrogram#: A matrix S where the rows index frequency bins, and the columns index frames (time). Spectrograms can be either real-valued or complex-valued. By convention, real-valued spectrograms are denoted as numpy.ndarrays S, while complex-valued STFT matrices are denoted as D.
magnitude#: A complex number z can be expressed as a combination of real and imaginary parts, \(z = a + jb\) (where j represents the imaginary unit). The magnitude of z is the distance from the origin as computed by the Pythagorean theorem: \(|z| = \sqrt{a^2 + b^2}\).
phase#: The phase of a complex number \(z = a + jb\) is the angle between the positive real axis and the line connecting the origin to the point (a, b) in the complex plane. The phase is computed as \(\phi = \arctan(b / a)\).
decibel#
dB#: A logarithmic unit used to express the ratio of two values, typically power or intensity. In audio, decibels are often used to represent the amplitude of a signal relative to a reference level.
dBFS#: Decibels relative to full scale (dBFS) is a unit of measurement for amplitude levels in digital audio systems. 0 dBFS represents the maximum possible digital level, while negative values indicate lower amplitudes.
frequency bin#: In a discrete Fourier transform (DFT) representation, the signal is represented as a combination of sinusoidal components at a finite set of frequencies. Each frequency index k corresponds to a frequency bin.
fundamental frequency#
f0#: The fundamental frequency (f0) is the lowest frequency of a periodic waveform, and is often perceived as the pitch of the sound. Note that not all waveforms are periodic.
pitch#: The perceived frequency of a sound, which is often associated with the fundamental frequency (f0) of a periodic waveform. In music, pitch is typically represented as a note name (e.g., A4, C#5) or as a MIDI note number.
pitch class#: A pitch class is a set of all pitches that are a whole number of octaves apart. For example, the pitch classes for the note C include C, C1, C2, C3, etc. In Western music, there are 12 pitch classes corresponding to the 12 notes in the chromatic scale.
chroma#
pitch class profile#: Chroma representations measure the amount of relative energy in each pitch class (e.g., the 12 notes in the chromatic scale) at a given frame/time.
onset#: The beginning time of a musical note or sound event.
onset (strength) envelope#
novelty function#
novelty curve#: An onset envelope onset_env[t] measures the strength of note onsets at frame t. Typically stored as a one-dimensional numpy.ndarray of floating-point values onset_envelope.
tempo#: The speed of a piece of music, typically measured in beats per minute (BPM).
beat#: A beat is a basic unit of time in music, often corresponding to a regular pulse that listeners can tap their foot to.
cqt#: The constant-Q transform (CQT) is a time-frequency representation of a signal that uses logarithmically spaced frequency bins with window lengths scaled inversely with frequency.
mel scale#: The mel scale is a perceptual scale of pitches that approximates the human ear’s response to different frequencies. The mel scale is approximately linear below 1 kHz and logarithmic above 1 kHz.
mel spectrogram#: A mel spectrogram is a time-frequency representation of a signal where the frequency axis is transformed to the mel scale.
mel frequency cepstral coefficient#
MFCC#: Mel-frequency cepstral coefficients (MFCCs) are a representation of the short-term power spectrum of a sound, based on a linear cosine transform of a log power mel spectrogram. MFCCs are commonly used as features in speech and audio processing.
tempogram#: A representation of the rhythmic structure of a piece of music over time. It measures the strength of periodicities in the onset envelope, using either autocorrelation or Fourier analysis.
recurrence matrix#
self-similarity matrix#: A square matrix that measures the similarity between features at all pairs (i, j) of time or frame indices.
beat synchronous features#: Beat-synchronous features are computed by aligning and aggregating features over detected inter-beat intervals.
multi-channel audio#: Audio signals that contain more than one channel, such as stereo (2 channels) or surround sound (5.1 channels). Multi-channel audio is typically represented as a two-dimensional numpy.ndarray of shape (n_channels, n_samples).
MIDI#: Musical Instrument Digital Interface (MIDI) is a technical standard that describes a protocol, digital interface, and connectors for communicating musical performance data between electronic musical instruments, computers, and other related devices.
MIDI number#: A MIDI number is an integer value that represents a specific musical note in the MIDI standard. For example, the MIDI number for middle C (C4) is 60. This is sometimes extended to fractional values to allow representation of all frequencies.
Scientific Pitch Notation#
SPN#: Scientific Pitch Notation (SPN) is a standardized system for naming musical notes based on their pitch class and octave number.
accidental#: An accidental is a musical notation symbol that indicates the alteration of a pitch. Common accidentals include sharps (#), flats (b), and naturals (♮).
cent#: One one-hundredth (1/100) of a semitone in the 12-tone equal temperament scale.
A440#: A tuning standard that defines the pitch of the musical note A4 (the A above middle C) as 440 Hz.
12TET#: A musical tuning system that divides the octave into 12 equal parts (semitones), commonly used in Western scales.
Just intonation#: A musical tuning system that uses simple whole-number ratios to determine the frequencies of notes, resulting in consonant intervals.
svara#: A pitch in Indian classical music, which can be thought of as a note in the context of a raga.
Sa#: The tonic svara in Indian classical music.
thaat#: A system of classifying ragas in Hindustani classical music based on their scale and note patterns.
melakarta#
mela#: A system of classifying ragas in Carnatic classical music based on their scale and note patterns.