![\"FMP\"](\"../data/FMP_Teaser_Cover.png\")
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"![\"AudioLabs\"](\"../data/Logo_AudioLabs_Long.png\"){kind=logo}
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"\n",
"\n",
"![\"C5\"](\"../data/C5_nav.png\")
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"\n", "Following Section 5.3.4 of [Müller, FMP, Springer 2015], we discuss in this notebook an HMM-based approach for chord recognition. The idea of using HMMs for chord recognition was originally introduced by Sheh and Ellis. \n", "
![\"FMP_C5_20a\"](\"../data/C5/FMP_C5_F20a.png\")
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"\n",
"![\"FMP_C5_F29-30-32\"](\"../data/C5/FMP_C5_F29-30-32.png\")
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"\n",
"![\"FMP_C5_F13\"](\"../data/C5/FMP_C5_F13.png\")
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Further Notes\n",
"\n",
"In this notebook, we introduced a basic HMM-based approach for chord recognition. In our simplistic model, we used $24$ states that correspond to the $12$ major and $12$ minor triads and fixed the HMM parameters explicitly using musical knowledge. \n",
"\n",
"* In the application to chord labeling, the HMM was then used to uncover the most likely chord labeling sequence that generates a given sequence of chroma features—an idea originally introduced by [Sheh and Ellis](https://www.ee.columbia.edu/~dpwe/pubs/ismir03-chords.pdf). \n",
"\n",
"* In general, there is a delicate interplay of the various feature extraction, filtering, and pattern matching components composing a chord recognition system. In this context, we refer to the excellent overview paper [On the Relative Importance of Individual Components of Chord Recognition Systems](https://ieeexplore.ieee.org/document/6691936) by Cho and Bello. \n",
"\n",
"* In the article [Analyzing Chroma Feature Types for Automated Chord Recognition](https://secure.aes.org/forum/pubs/conferences/?elib=15943) by Jiang et al., the importance of the input representation is investigated.\n",
"\n",
"In this book, we have only considered a basic HMM variant. There are many more variants and extensions of HMMs including continuous HMMs and HMMs with specific state transition topologies. Rather than fixing the model parameters manually, the power of general HMMs is to automatically learn the free parameters based on training examples (e.g., using the [Baum-Welch Algorithm](../C5/C5S3_HiddenMarkovModel.html)). The estimation of the model parameters can become very intricate, leading to challenging and deep mathematical problems. For an excellent textbook on the classical theory of HMMs, including the discrete as well as the continuous case, we refer to the excellent book on [Hidden Markov Models for Speech Recognition](https://dl.acm.org/doi/book/10.5555/575447) by Huang et al. (1990). We close this notebook with an overview of a typical HMM-based chord recognition approach consisting of a training and an evaluation stage.\n",
"\n",
"![\"FMP_C5_F33.png\"](\"../data/C5/FMP_C5_F33.png\")
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]
},
{
"cell_type": "markdown",
"metadata": {},
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"![\"C0\"](\"../data/C0_nav.png\") | \n",
" ![\"C1\"](\"../data/C1_nav.png\") | \n",
" ![\"C2\"](\"../data/C2_nav.png\") | \n",
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