De juiste toon: had Pythagoras gelijk? [Dutch]

In muziek zijn vele wiskundige en natuurkundige wetten te vinden. Liggen die patronen aan de basis van wat we mooi vinden? Hebben onze hersenen een voorkeur voor bepaalde patronen? En hoe zit het met andere culturen, die weer andere patronen waarderen?

Over al deze zaken werd er stevig gediscussieerd tijdens de BètaBreak van 18 november j.l. met Michiel Schuijer (Muziektheoreticus, lector aan Conservatorium van Amsterdam), Henkjan Honing (hoogleraar Muziekcognitie aan de UvA) en Jan van de Craats (hoogleraar Wiskunde aan de UvA). Enkele van de referneties die genoemd worden staan hieronder (Plomp & Levelt, 1965; Savage et al., 2015).



De benadering van muziek als een natuurkundig of wiskundig verschijnsel heeft als mogelijke valkuil om naast geluidsleer een soort getallenleer te worden. Alsof harmonische, mooie of ‘juiste’ muziek door de natuur bepaald of zelfs afgedwongen wordt. Er klinkt iets in terug van het, in steeds wisselende gedaantes terugkerende Oudgriekse idee van een ‘harmonie der sferen’, het idee dat de wiskundige structuur van muziek iets zou kunnen onthullen over de natuur zelf. Of omgekeerd: dat een elegante formule die de code van de muziek van vermaarde componisten (denk aan Bach) weet te kraken en de onderliggende getallenstructuur ervan blootlegt, ons kan laten zien hoe mooi, hoe ‘natuurlijk’ die muziek is. Maar al Pythagoras’ ideeën over consonantie in termen van heeltallige ratio’s ten spijt: een hedendaagse, zorgvuldig maar allesbehalve heeltallig gestemde piano wordt door opvallend weinig mensen als ‘vals’ ervaren. Het is de eeuwenoude tegenstelling tussen muziek opgevat als getal en muziek als empirisch feit (cf. Pythagoras versus Aristoxenus). Muziek huist niet zozeer in het geluid of in het getal, maar eerder in het hoofd van de luisteraar (Honing, 2012).

Honing, H. (2012). Een vertelling. In S. van der Maas, C. Hulshof, & P. Oldenhave (Eds.), Liber Plurum Vocum voor Rokus de Groot (pp. 150-154). Amsterdam: Universiteit van Amsterdam (ISBN 978-90-818488-0-0)
Plomp R, & Levelt WJ (1965). Tonal consonance and critical bandwidth. The Journal of the Acoustical Society of America, 38 (4), 548-60 PMID: 5831012
Savage, P., Brown, S., Sakai, E., & Currie, T. (2015). Statistical universals reveal the structures and functions of human music Proceedings of the National Academy of Sciences, 112 (29), 8987-8992 DOI: 10.1073/pnas.1414495112

Does musicality have a biological foundation?

Genes with functions that are relevant to music aptitude such as hearing, cognitive performance and neurodegenerative functions are marked by triangles (From Liu et al., 2016).

A few days ago a study was published by the team of Irma Järvelä (University of Helsinki) on the identification of genetic variants underlying musical ability. They based their new study (Liu et al., 2016) on an existing database of ca. 150 unrelated Finnish subjects that were tested for their musical ability using a collection of pitch and pattern perception tests. In addition, for all participants genomic DNA was available (based on a blood sample). The participants were divided into two groups (low vs high musical aptitude), with the lower scoring individuals functioning as the control group.

The study focused on regions that can be associated with positive selection (Sabeti et al., 2006). Using genomic and bioinformatic techniques, the researchers were able to identify those regions that contain sets of variations in the DNA and show which regions are likely under positive selection.

The regions that were identified contained genes that are involved in auditory perception (e.g. GPR98, USH2A), cognition and memory (e.g. GRIN2B, IL1A, IL1B, RAPGEF5), reward mechanisms (RGS9), and song perception and production of songbirds (e.g. FOXP1, RGS9, GPR98, GRIN2B).

There are, of course, some drawbacks in this study that is largely exploratory. While the study was able to identify positively selected regions, the actual genes involved and their function remains unclear. Musicality is, obviously, a complex trait that likely has many contributing genes, and developing a proper phenomics is still quite a challenge (cf. Gingras et al., 2015). Nevertheless, the study suggests that several genes – that can be argued to be essential for musical aptitude (or musicality at large) – could well be under positive selection. The result hence supports the idea that musicality has a biological foundation that is necessary for the development of musical culture.

Liu, X., Kanduri, C., Oikkonen, J., Karma, K., Raijas, P., Ukkola-Vuoti, L., Teo, Y., & Järvelä, I. (2016). Detecting signatures of positive selection associated with musical aptitude in the human genome Scientific Reports, 6 DOI: 10.1038/srep21198

Sabeti, P. (2006). Positive Natural Selection in the Human Lineage Science, 312 (5780), 1614-1620 DOI: 10.1126/science.112430

Gingras, B., Honing, H., Peretz, I., Trainor, L., & Fisher, S. (2015). Defining the biological bases of individual differences in musicality Philosophical Transactions of the Royal Society B: Biological Sciences, 370 (1664), 20140092-20140092 DOI: 10.1098/rstb.2014.0092

Do songbirds perceive melody different from humans?

European Starling (Sturnus vulgaris)

Last week a fascinating study appeared in PNAS on melody (re)cognition in sparrows (Sturnus vulgaris). It provides an alternative interpretation to the widespread believe that songbirds have a strong bias to rely on absolute pitch (AP) for the recognition of melodies (e.g. Hulse et al., 1992).

In a series of behavioral experiments, Bregman et al. (2016) find that the human percepts of both pitch and timbre are poor descriptions of the perceptual cues used for melody recognition by the five sparrows that participated in the study. The results suggest that auditory sequence recognition in sparrows might be largely dependent on the perception of acoustic spectral shape, and not just AP. Sounds that preserve this shape, even in the absence of pitch cues, seem to be perceived as equivalent. The finding suggests that songbirds (unlike humans, for whom pitch plays a dominant role in the perception of melodic sequences) rely on a perceptual representation that is a combination of pitch and timbre. It suggests that the perceptual separability of pitch and timbre might also in humans be largely based on experience.

Hulse, S., Takeuchi, A., & Braaten, R. (1992). Perceptual Invariances in the Comparative Psychology of Music Music Perception: An Interdisciplinary Journal, 10 (2), 151-184 DOI: 10.2307/40285605

Bregman, M., Patel, A., & Gentner, T. (2016). Songbirds use spectral shape, not pitch, for sound pattern recognition Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1515380113

Abnormalities in later cognitive stages of beat processing?

Mathieu in 2012 (Dutch Tv).

A few years ago I reported on the start of a series of experiments with Mathieu, a case of congenital beat deafness (Phillips-Silver et al., 2011; see here). The paper reporting on that work just came out:

"Beat deafness, a recently documented form of congenital amusia, provides a unique window into functional specialization of neural circuitry for the processing of musical stimuli: Beat-deaf individuals exhibit deficits that are specific to the detection of a regular beat in music and the ability to move along with a beat. Studies on the neural underpinnings of beat processing in the general population suggest that the auditory system is capable of pre-attentively generating a predictive model of upcoming sounds in a rhythmic pattern, subserved largely within auditory cortex and reflected in mismatch negativity (MMN) and P3 event-related potential (ERP) components. The current study examined these neural correlates of beat perception in two beat-deaf individuals, Mathieu and Marjorie, and a group of control participants under conditions in which auditory stimuli were either attended or ignored. Compared to control participants, Mathieu demonstrated reduced behavioral sensitivity to beat omissions in metrical patterns, and Marjorie showed a bias to identify irregular patterns as regular. ERP responses to beat omissions reveal an intact pre-attentive system for processing beat irregularities in cases of beat deafness, reflected in the MMN component, and provide partial support for abnormalities in later cognitive stages of beat processing, reflected in an unreliable P3b component exhibited by Mathieu – but not Marjorie – compared to control participants. P3 abnormalities observed in the current study resemble P3 abnormalities exhibited by individuals with pitch-based amusia, and are consistent with attention or auditory-motor coupling accounts of deficits in beat perception." (Mathias et al., 2016)

Phillips-Silver, J., Toiviainen, P., Gosselin, N., Piché, O., Nozaradan, S., Palmer, C., & Peretz, I. (2011). Born to dance but beat deaf: A new form of congenital amusia Neuropsychologia DOI: 10.1016/j.neuropsychologia.2011.02.002

Mathias, B., Lidji, P., Honing, H., Palmer, C., & Peretz, I. (2016). Electrical brain responses to beat irregularities in two cases of beat deafness. Frontiers in Neuroscience. DOI: 10.3389/fnins.2016.00040.