science

Harmonic pitch class profiles

Harmonic pitch class profiles is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Harmonic pitch class profiles rather than just read about it. In short: Harmonic pitch class profiles (HPCP) is a group of features that a computer program extracts from an audio signal, based on a pitch class profile—a descriptor proposed in the context of a chord recognition system. HPCP are an enhanced pitch distribution feature that are sequences of feature vectors that, to a certain extent, describe tonality, measuring the relative intensity of each of the 12 pitch classes of the e…

Key takeaways

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Connect Harmonic pitch class profiles to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Harmonic pitch class profiles from memory before moving on to harder problems.

Reference excerpt

Harmonic pitch class profiles (HPCP) is a group of features that a computer program extracts from an audio signal, based on a pitch class profile—a descriptor proposed in the context of a chord recognition system. HPCP are an enhanced pitch distribution feature that are sequences of feature vectors that, to a certain extent, describe tonality, measuring the relative intensity of each of the 12 pitch classes of the equal-tempered scale within an analysis frame. Often, the twelve pitch spelling attributes are also referred to as chroma and the HPCP features are closely related to what is called chroma features or chromagrams. By processing musical signals, software can identify HPCP features and use them to estimate the key of a piece, to measure similarity between two musical pieces (cover version identification), to perform content-based audio retrieval (audio matching), to extract the musical structure (audio structure analysis), and to classify music in terms of composer, genre or mood. The process is related to time-frequency analysis. In general, chroma features are robust to noise (e.g., ambient noise or percussive sounds), independent of timbre and instrumentation and independent of loudness and dynamics. HPCPs are tuning independent and consider the presence of harmonic frequencies, so that the reference frequency can be different from the standard A 440 Hz. The result of HPCP computation is a 12, 24, or 36-bin octave-independent histogram depending on the desired resolution, representing the relative intensity of each 1, 1/2, or 1/3 of the 12 semitones of the equal tempered scale.

General HPCP feature extraction procedure

The block diagram of the procedure is shown in Fig.1 and is further detailed in. The General HPCP feature extraction procedure is summarized as follows:

Input musical signal. Do spectral analysis to obtain the frequency components of the music signal. Use Fourier transform to convert the signal into a spectrogram. (The Fourier transform is a type of time-frequency analysis.) Do frequency filtering. A frequency range of between 100 and 5000 Hz is used. Do peak detection. Only the local maximum values of the spectrum are considered. Do reference frequency computation procedure. Estimate the deviation with respect to 440 Hz. Do Pitch class mapping with respect to the estimated reference frequency. This is a procedure for determining the pitch class value from frequency values. A weighting scheme with cosine function is used. It considers the presence of harmonic frequencies (harmonic summation procedure), taking account a total of 8 harmonics for each frequency. To map the value on a one-third of a semitone, the size of the pitch class distribution vectors must be equal to 36. Normalize the feature frame by frame dividing through the maximum value to eliminate dependency on global loudness. This results in a HPCP sequence like the one shown in Fig.2.

System of measuring similarity between two songs

After getting the HPCP feature, the pitch of the signal in a time section is known. The HPCP feature has been used to compute similarity between two songs in many research papers. A system of measuring similarity between two songs is shown in Fig.3. First, time-frequency analysis is needed to extract the HPCP feature. And then set two songs' HPCP feature to a global HPCP, so there is a standard of comparing. The next step is to use the two features to construct a binary similarity matrix. Smith–Waterman algorithm is used to construct a local alignment matrix H in the Dynamic Programming Local Alignment. Finally, after doing post processing, the distance between two songs can be computed.

See also Time-frequency analysis Time-frequency analysis for music signal Pitch (music) Musical theory

References

External links HPCP - Harmonic Pitch Class Profile plugin available for download http://mtg.upf.edu/technologies/hpcp Chroma Toolbox Free MATLAB implementations of various chroma types of pitch-based and chroma-based audio features

Illustrations

Worked examples

Example 1 — a first encounter with Harmonic pitch class profiles

Start with the simplest possible case. Write down what Harmonic pitch class profiles claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Harmonic pitch class profiles before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Harmonic pitch class profiles ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Harmonic pitch class profiles

In research: Harmonic pitch class profiles appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Harmonic pitch class profiles in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Harmonic pitch class profiles is common in secondary-school and first-year university syllabi. It links to neighbouring topics Music information retrieval, Time–frequency analysis, so understanding it makes those chapters shorter.
In everyday life: Look for Harmonic pitch class profiles outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Harmonic pitch class profiles in 20 minutes

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Close the page and write down what Harmonic pitch class profiles means in your own words.
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Frequently asked questions

What is Harmonic pitch class profiles in simple terms?

Why does Harmonic pitch class profiles matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Harmonic pitch class profiles?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Harmonic pitch class profiles.