TalksThe perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This can be shown by consistently applying results from psychophysics and neuroacoustics, namely that the just noticeable difference (JND) between pitches for humans is about 1% for the musically important low frequency range and that periodicities of complex chords can be detected in the human brain. Based thereon, the concepts of relative and logarithmic periodicity with smoothing can be introduced as measures of harmoniousness. In the auditory brainstem, the periodicity pitch frequency, which is not present in the input spectrum, occurs in addition in the response spectrum. To explain this, it can be argued that the most important factor during the neural processing is the highly non-linear transformation of the input signal into pulse trains (spikes) whose maximal amplitude is limited. This is can be demonstrated by a simple recurrent neural network model.
Talks
MaterialExtended Article Harmony Perception by Periodicity Detection (Frieder Stolzenburg, 2018)
Tables of computed harmoniousness values, in particular periodicity, for all 2048 possible harmonies consisting of up to 12 semitones (download)
| no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| chord | major | major | suspended | suspended | minor | minor | diminished | augmented | jazz | blues |
| melody | major | minor | major | minor | major | minor | minor | major | major | major |
ImplementationOctave code for the periodicity-based method, computing (smoothed) relative/logarithmic periodicity (2018) (download)
Prolog code for the periodicity-based method, computes also other measures of harmoniousness (2016) (download)
PublicationsMaria Heinze and Frieder Stolzenburg. Harmony cognition by neural transformation -- an analysis by EEG. In Proceedings of the ICMPC-ESCOM 2021 Joint Conference: 16th International Conference on Music Perception and Cognition and 11th Conference of the European Society for the Cognitive Sciences of Music, 2021. Abstract. [ http ]
Maria Heinze, Lars Hausfeld, Rainer Goebel, and Frieder Stolzenburg. Periodicity pitch detection in complex harmonies on EEG timeline data. CoRR -- Computing Research Repository abs/2002.04990, Cornell University Library, 2020. [ http ]
Frieder Stolzenburg. Harmoniewahrnehmung durch Periodizitätsdetektion. In Martin Ebeling and Morgana Petrik, editors, Harmonie -- musikalisch, philosophisch, psychologisch, neurologisch, volume 7 of Schriftenreihe der Carl Stumpf Gesellschaft, pages 57--84. Peter Lang, Berlin, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2019. [ DOI | http ]
Maria Heinze, Lars Hausfeld, Rainer Goebel, and Frieder Stolzenburg. Periodicity pitch detection in complex harmonies on EEG timeline data. In Axelle Calcus and Tim Schoof, editors, Frequency Following Response -- FFR Workshop 2019, London, 2019. Abstract Book. [ .pdf ]
Maria Heinze, Rainer Goebel, and Frieder Stolzenburg. Application of recurrent neural networks on fMRI and EEG timeline data in music cognition. In Constantin A. Rothkopf, Dirk Balfanz, Ralf Galuske, Frank Jäkel, Kristian Kersting, Jakob Macke, and Betty Mohler, editors, KogWis 2018: Computational Approaches to Cognitive Science -- 14th Biannual Conference of the German Society for Cognitive Science, page 22, Darmstadt, 2018. Abstract. [ .pdf ]
Frieder Stolzenburg. Periodicity detection by neural transformation. In Edith Van Dyck, editor, ESCOM 2017 -- 25th Anniversary Conference of the European Society for the Cognitive Sciences of Music, pages 159--162, Ghent, Belgium, 2017. IPEM, Ghent University. Proceedings. [ .pdf ]
Frieder Stolzenburg. Harmony perception by periodicity detection. Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance, 9(3):215--238, 2015. [ http ]
Frieder Stolzenburg. Harmony perception by periodicity detection. In Moo Kyoung Song, editor, Proceedings of the ICMPC-APSCOM 2014 Joint Conference: 13th International Conference on Music Perception and Cognition and 5th Conference of the Asian-Pacific Society for the Cognitive Sciences of Music, pages 27--31, Seoul, South Korea, 2014. College of Music, Yonsei University. [ .pdf ]
Frieder Stolzenburg. Harmony perception by periodicity detection. CoRR -- Computing Research Repository abs/1306.6458, Cornell University Library, 2013. Latest revision 2018. [ http ]
Frieder Stolzenburg. Harmony perception by periodicity and granularity detection. In Emilios Cambouropolos, Costas Tsougras, Panayotis Mavromatis, and Konstantinos Pastiadis, editors, Proceedings of 12th International Conference on Music Perception and Cognition and 8th Triennial Conference of the European Society for the Cognitive Sciences of Music, pages 958--959, Thessaloniki, Greece, 2012. [ .pdf ]
Frieder Stolzenburg. A periodicity-based approach on harmony perception including non-western scales. In Steven M. Demorest, Steven J. Morrison, and Patricia Sheehan Campbell, editors, Proceedings of 11th International Conference on Music Perception and Cognition, pages 683--687, Seattle, Washington, USA, 2010. [ .pdf ]
Frieder Stolzenburg. A periodicity-based theory for harmony perception and scales. In Keiji Hirata, George Tzanetakis, and Kazuyoshi Yoshii, editors, Proceedings of 10th International Society for Music Information Retrieval Conference, pages 87--92, Kobe, Japan, 2009. [ .pdf ]