# Chroma feature

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{{Short description|Graphical representation of music}}
thumb|400px|right|(a) Musical score of a C-major scale. (b) Chromagram obtained from the score. (c) Audio recording of the C-major scale played on a piano. (d) Chromagram obtained from the audio recording.

In Western [music](/source/music), the term '''''chroma feature''''' or '''''chromagram''''' closely relates to twelve different [pitch classes](/source/pitch_classes). Chroma-based features, which are also referred to as "[pitch class profiles](/source/Harmonic_pitch_class_profiles)", are a powerful tool for analyzing music whose pitches can be meaningfully categorized (often into twelve categories) and whose tuning approximates to the [equal-tempered scale](/source/Equal_temperament). One main property of chroma features is that they capture harmonic and melodic characteristics of music, while being robust to changes in [timbre](/source/timbre) and instrumentation.

==Definition==

The underlying observation is that humans perceive two musical pitches as similar in color if they differ by an octave. Based on this observation, a pitch can be separated into two components, which are referred to as ''tone height'' and ''chroma''.<ref name=Shepard64_pitch_ASA>
{{cite journal
|last=Shepard
|first=Roger N.
|title=Circularity in judgments of relative pitch
|journal=Journal of the Acoustical Society of America
|volume=36
|issue=212
|date=1964
|pages=2346–2353|doi=10.1121/1.1919362
|bibcode=1964ASAJ...36.2346S
}}
</ref> Assuming the [equal-tempered scale](/source/Equal_temperament), one considers twelve chroma values represented by the set

:{C, C{{music|#}}, D, D{{music|#}}, E, F, F{{music|#}}, G, G{{music|#}}, A, A{{music|#}}, B}

that consists of the twelve pitch spelling attributes as used in Western music notation. Note that in the equal-tempered scale different pitch spellings such
C{{music|#}} and D{{music|b}} refer to the same chroma. Enumerating the chroma values, one can identify the set of chroma values with the set of integers {1,2,...,12}, where 1 refers to chroma C, 2 to C{{music|#}}, and so on. A [pitch class](/source/pitch_class) is defined as the set of all pitches that share the same chroma. For example, using the [scientific pitch notation](/source/scientific_pitch_notation), the pitch class corresponding to the chroma C is the set

:{..., C<sub>−2</sub>, C<sub>−1</sub>, C<sub>0</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> ...}

consisting of all pitches separated by an [integer](/source/integer) number of octaves. Given a music representation (e.g. a musical score or an audio recording), the  main idea of chroma features is to aggregate for a given local time window (e.g. specified in beats or in seconds) all information that relates to a given chroma into a single coefficient. Shifting the time window across the music representation results in a sequence of chroma features each expressing how the representation's pitch content within the time window is spread over the twelve chroma bands. The resulting time-chroma representation is also referred to as chromagram. The figure above shows chromagrams for a C-major scale, once obtained from a musical score and once from an audio recording. Because of the close relation between the terms chroma and pitch class, chroma features are also referred to as [pitch class profiles](/source/Harmonic_pitch_class_profiles).

==Applications==
Identifying pitches that differ by an octave, chroma features show a high degree of robustness to variations in timbre and closely correlate to the musical aspect of harmony. This is the reason why chroma features are a well-established tool for processing and analyzing music data.<ref name=Mueller15_FundamentalsMusicProcessig_SPRINGER>
{{cite book
| last = Müller
| first = Meinard
| title = Fundamentals of Music Processing
| url = http://www.music-processing.de
| publisher = Springer
| year = 2015
| doi = 10.1007/978-3-319-21945-5
| isbn = 978-3-319-21944-8| s2cid = 8691186
}}
</ref> For example, basically every chord recognition procedure relies on some kind of chroma representation.<ref name=ChoB14_Chord_IEEE-TASLP>
{{cite journal
|last1=Cho
|first1=Taemin
|last2=Bello
|first2=Juan Pablo 
|title=On the Relative Importance of Individual Components of Chord Recognition Systems
|journal=IEEE/ACM Transactions on Audio, Speech, and Language Processing
|volume=22
|issue=2
|year=2014
|pages=477–4920|doi=10.1109/TASLP.2013.2295926
|bibcode=2014ITASL..22..477C
|s2cid=16434636
}}</ref><ref name=MauchD10_SimultaneousEstimation_TASLP>
{{cite journal
|last1=Mauch
|first1=Matthias
|last2=Dixon
|first2=Simon
|title=Simultaneous estimation of chords and musical context from audio
|journal=IEEE Transactions on Audio, Speech, and Language Processing
|volume=18
|issue=6
|year=2010
|pages=138–153|doi=10.1109/TASL.2009.2032947
|bibcode=2010ITASL..18.1280M
|citeseerx=10.1.1.414.7800
|s2cid=15866073
}}
</ref><ref name=Fujishima99_ChordRecognition_ICMC>
{{cite journal
|last=Fujishima
|first=Takuya
|title=Realtime Chord Recognition of Musical Sound: a System Using Common Lisp Music
|journal=Proceedings of the International Computer Music Conference
|year=1999
|pages=464–467}}
</ref><ref name=JiangGKM11_Chord_AES>
{{cite journal
|last1=Jiang
|first1=Nanzhu 
|last2=Grosche
|first2=Peter
|last3=Konz
|first3=Verena
|last4=Müller
|first4=Meinard
|title=Analyzing Chroma Feature Types for Automated Chord Recognition
|url = https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/03-publications/2011_JiangGroscheKonzMueller_ChordRecognitionEvaluation_AES42-Ilmenau.pdf 
|journal=Proceedings of the AES Conference on Semantic Audio
|year=2011}}
</ref> Also, chroma features have become the de facto standard for tasks such as [music alignment](/source/music_alignment) and synchronization<ref name=HuDT03_audiomatching_WASPAA>
{{cite journal
|last1=Hu
|first1=Ning  
|last2=Dannenberg
|first2=Roger B. 
|last3=Tzanetakis
|first3=George 
|title=Polyphonic Audio Matching and Alignment for Music Retrieval
|journal=Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics
|year=2003}}
</ref><ref name=EwertMG09_HighResAudioSync_ICASSP>
{{cite book
|last1= Ewert 
|first1=Sebastian 
|last2=Müller 
|first2=Meinard
|last3=Grosche
|first3=Peter
|title=2009 IEEE International Conference on Acoustics, Speech and Signal Processing 
|chapter=High resolution audio synchronization using chroma onset features 
|chapter-url = https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/03-publications/2009_EwertMuellerGrosche_HighResAudioSync_ICASSP.pdf 
|year=2009
|pages=1869–1872|doi=10.1109/ICASSP.2009.4959972 
|isbn=978-1-4244-2353-8 
|s2cid=16952895 
}}
</ref> as well as audio structure analysis.<ref name=PaulusMK10_MusicStructure-STAR_ISMIR>
{{cite journal
|last1=Paulus
|first1=Jouni  
|last2=Müller
|first2=Meinard
|last3=Klapuri
|first3=Anssi  
|title=Audio-based Music Structure Analysis
|url = https://ismir2010.ismir.net/proceedings/ismir2010-107.pdf 
|journal=Proceedings of the International Conference on Music Information Retrieval
|year=2010
|pages=625–636}}
</ref> Finally, chroma features have turned out to be a powerful mid-level feature representation in content-based audio retrieval such as cover song
identification,<ref name=EllisP07_CoverSong_ICASSP>
{{cite journal
|last1=Ellis
|first1=Daniel P.W.
|last2=Poliner
|first2=Graham  
|title=Identifying 'Cover Songs' with Chroma Features and Dynamic Programming Beat Tracking
|journal=Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
|year=2007}}</ref><ref name=SerraGHS08_CoverSong_IEEE-TASLP>
{{cite journal
|last1=Serrà
|first1=Joan
|last2=Gómez
|first2=Emilia
|last3=Herrera
|first3=Perfecto
|last4=Serra
|first4=Xavier 
|title=Chroma Binary Similarity and Local Alignment Applied to Cover Song Identification
|journal=IEEE Transactions on Audio, Speech, and Language Processing
|volume=16
|issue=6
|year=2008
|pages=1138–1151|doi=10.1109/TASL.2008.924595
|bibcode=2008ITASL..16.1138S
|hdl=10230/16277
|s2cid=10078274
|hdl-access=free
}}
</ref> audio matching<ref name=MuellerKC05_ChromaFeatures_ISMIR>
{{cite journal
|last1=Müller
|first1=Meinard
|last2=Kurth
|first2=Frank
|last3=Clausen
|first3=Michael
|title=Audio Matching via Chroma-Based Statistical Features
|url = https://ismir2005.ismir.net/proceedings/1019.pdf
|journal=Proceedings of the International Conference on Music Information Retrieval 
|year=2005
|pages=288–295}}
</ref><ref name=KurthM08_IndexBasedAudioMatching_TASLP>
{{cite journal
|last1=Kurth
|first1=Frank
|last2=Müller
|first2=Meinard
|title=Efficient Index-Based Audio Matching
|journal=IEEE Transactions on Audio, Speech, and Language Processing
|volume=16
|issue=2
|year=2008
|pages=382–395|doi=10.1109/TASL.2007.911552
|bibcode=2008ITASL..16..382K
|s2cid=206601781
}}
</ref><ref name="Mueller15_Chapter3FMP_SPRINGER2">{{cite book|url=http://www.music-processing.de|title=Music Synchronization. In Fundamentals of Music Processing, chapter 3, pages 115-166|last=Müller|first=Meinard|publisher=Springer|year=2015|isbn=978-3-319-21944-8}}</ref><ref name="KurthM08_IndexBasedAudioMatching_TASLP3">{{cite journal|last1=Kurth|first1=Frank|last2=Müller|first2=Meinard|year=2008|title=Efficient Index-Based Audio Matching|journal=IEEE Transactions on Audio, Speech, and Language Processing|volume=16|issue=2|pages=382–395|doi=10.1109/TASL.2007.911552|bibcode=2008ITASL..16..382K |s2cid=206601781 }}</ref> or
audio hashing.<ref name="YY10">{{cite book |last1=Yu |first1=Yi |title=Proceedings of the international conference on Multimedia - MM '10 |last2=Crucianu |first2=Michel |last3=Oria |first3=Vincent |last4=Damiani |first4=Ernesto |chapter=Combining multi-probe histogram and order-statistics based LSH for scalable audio content retrieval |publisher=Proceedings of the 18th International Conference on Multimedia 2010 |pages=381–390 |ref=YY10|doi=10.1145/1873951.1874004 |year=2010 |isbn=9781605589336 |s2cid=9033525 }}</ref><ref name="YY09">{{cite book |last1=Yu |first1=Yi |title=Proceedings of the seventeen ACM international conference on Multimedia - MM '09 |last2=Crucianu |first2=Michel |last3=Oria |first3=Vincent |last4=Chen |first4=Lei |chapter=Local summarization and multi-level LSH for retrieving multi-variant audio tracks |publisher=Proceedings of the 17th International Conference on Multimedia 2009 |pages=341–350 |ref=YY09|doi=10.1145/1631272.1631320 |year=2009 |isbn=9781605586083 |s2cid=816862 }}</ref>

==Computation of audio chromagrams==
There are many ways for converting an audio recording into a chromagram. For example, the conversion of an audio recording into a chroma representation (or chromagram) may be performed either by using short-time [Fourier transform](/source/Fourier_transform)s in combination with binning strategies<ref name=BartschW05_chroma_IEEEMULTIMEDIA>
{{cite journal
|last1=Bartsch
|first1=Mark A. 
|last2=Wakefield
|first2=Gregory H. 
|title=Audio thumbnailing of popular music using chroma-based representations
|journal=IEEE Transactions on Multimedia
|volume=7
|number=1
|year=2005
|pages=96–104|doi=10.1109/TMM.2004.840597 
|bibcode=2005ITMm....7...96B 
|citeseerx=10.1.1.379.3293 
|s2cid=12559221 
}}
</ref><ref name=Gomez06_PhD>
{{cite journal
|last=Gómez
|first=Emilia 
|title=Tonal Description of Music Audio Signals
|journal=PhD Thesis, UPF Barcelona, Spain
|year=2006}}
</ref><ref name=Mueller15_Chapter3FMP_SPRINGER>
{{cite book
| last = Müller
| first = Meinard
| title = Music Synchronization. In Fundamentals of Music Processing, chapter 3, pages 115-166
| url = http://www.music-processing.de
| publisher = Springer
| year = 2015
| isbn = 978-3-319-21944-8 }}
</ref> or by employing suitable multirate filter banks.<ref name=MuellerKC05_ChromaFeatures_ISMIR/>
Furthermore, the properties of chroma features can be significantly changed by
introducing suitable pre- and post-processing steps modifying spectral, temporal,
and dynamical aspects. This leads to a large number of chroma variants, which
may show a quite different behavior in the context of a specific music analysis scenario.<ref name=MuellerE11_ChromaToolbox_ISMIR>
{{cite journal
|last1=Müller
|first1=Meinard
|last2=Ewert
|first2=Sebastian  
|title=Chroma Toolbox: MATLAB Implementations For Extracting Variants of Chroma-Based Audio Features
|url = https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/03-publications/2011_MuellerEwert_ChromaToolbox_ISMIR.pdf
|journal=Proceedings of the International Society for Music Information Retrieval Conference
|year=2011
|pages=215–220}}</ref>

==See also==
*[Time-frequency analysis](/source/Time-frequency_analysis)
*[Time-frequency analysis for music signal](/source/Time-frequency_analysis_for_music_signal)
*[Pitch (music)](/source/Pitch_(music))
*[Musical theory](/source/Musical_theory)

==References==
{{Reflist|30em}}

== External links ==
*[https://www.audiolabs-erlangen.de/resources/MIR/chromatoolbox Chroma Toolbox] Free MATLAB implementations of various chroma types of pitch-based and chroma-based audio features
*[http://mtg.upf.edu/technologies/hpcp Harmonic Pitch Class Profile plugin]

Category:Music information retrieval
Category:Music technology
Category:Musicology
Category:Time–frequency analysis

---
Adapted from the Wikipedia article [Chroma feature](https://en.wikipedia.org/wiki/Chroma_feature) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Chroma_feature?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.