Hypotheses About Music

• Musicality is a one-dimensional quantity

  "Musicality" is that quality of music that distinguishes music from all things which are not musical. Assuming that musicality is one-dimensional gives rise to several conclusions:

  • If musicality is one-dimensional, then all other qualities of music other than musicality must be determined by factors that also apply to non-musical sounds. So, for example, if minor chords sound "sad", and major chords "happy", then this must be for some reason other than the musicality.
  • The greater the musicality of music, the "better" or "stronger" the music is. The judgement of musical strength is known to be subjective, but of course the perception of musicality occurs within the brain, so different brains may have similar but not exactly the same perception of musicality.
  • If musicality is one-dimensional, it is possible, that the percepion of musicality involves a non-neural mechanism. In particular, a non-neural mechanism may represent a one-dimensional quantity by the concentration of some molecular species over a large area of the brain. Also, there is a minimum time required for musicality to be perceived (at least a few seconds), so there is no need for the ultra-fast signalling capabilities of neurons to achieve the transmission of information about musicality.
• Every symmetry of music perception is either functional – serving a direct purpose – or, it arises as a trade-off against another function.

  A symmetry of music perception means that music can be transformed in some way, and some or all of the musical qualities remain unchanged. (The symmetries of musical perception are not exact, which requires one to develop a theory of "inexact" symmetries, however I will ignore this issue for the moment.)

  The two alternatives of function and trade-off can also be explained as follows, assuming that music perception is actually perception of an aspect of speech:

  • A symmetry of music perception is functional, if there is a reason why speech transformed according to the corresponding transformation should be perceived as the "same".
  • A symmetry of music perception is a trade-off, if not perceiving the corresponding component of speech improves the perception of some other component of speech.

  To see how this might apply in practice, we need to look at each symmetry of music perception in turn.

• To fully explain perceptions of music symmetry, we must also consider the cost of the symmetry, and whether we get it "for free" as a consequence of how sound perception works in general.
• Time-translation invariance is a general property of sound perception that enables the "same" sound to be perceived occurring at different times.

  Time-translation invariance is a general symmetry of all sound perception, so it does not require any special explanation with regard to speech or music perception. However, time-translation invariance of sound perception may not be completely trivial to implement, and the specific mechanisms of trim-translation invariance, to detect similarity between segments of sound occurring within some interval in time, may be relevant to the occurrence of phrasal repetition within musical items.

• Amplitude-scaling is a general property of sound perception that enables the "same" sound to be perceived whether occurring near or far (and also some sounds vary in amplitude when some dependent variable other than distance is varied).
• Pitch-translation invariance serves the purpose that the same speech melody can be generated by speakers with different pitch ranges, and perceived as such.
• Time-scaling invariance serves the purpose that the same speech rhythm can be generated independently of the speed of speech, and perceived as such.
• Octave-scaling invariance may serve as a trade-off to increase the accurate perception of very small pitch differences.

  A model for this is a cortical map which perceives very small changes in pitch via very small changes in the frequencies of harmonic frequencies. A feature of such a map is that pitch values an octave apart will seem very "close", because they have many matching harmonics.

  A second advantage of octave invariance is that if a cortical map represents pitch values modulo octaves, then that map can represent more precise information about pitch than a cortical map which represented all perceivable pitch values directly (consisting of 6 to 8 octaves).

• Pitch-reversal invariance, is an invariance that applies to perception of consonance, i.e. the relationship between two pitch values that are consonantly related..

  A model for this is a cortical map where neurons respond to pitch values when they occur and for some time afterwards – consonance is recognise when neurons representing pitch values consonantly related to each other are concurrently active. A consequence of this model is that information about which pitch value in a pair of consonantly related values occurred first is lost, so the perceived relationship is necessarily symmetric between the two values. (This model also explains how harmony can be a component of the perception of a "melody" which consists of only pitch value at any given time, yet is perceived more strongly when consonantly related pitch values occur simultaneously.)

• Rhyming emphasizes the approximately balanced binary structure of music.

  Rhyming is a ubiquitous feature of modern popular music. The hypothesis here is that rhyming is not intrinsically musical, but it enforces the perception of the balanced binary structure of music, and it is this perceived balanced binary structure which has musicality.

• Rhyming scanning poetry shares features with music. Therefore it probably is a form of music.

  Those features being:

  • Rhyming
  • Balanced binary structure
  • Regular beat
• Some aspects of our enjoyment of watching dance are actually the perception of musicality.

  Most if not all perceived aspects of music have analogs with perceived aspects of speech. But perception of speech is not purely aural – we also perceive gestures, facial expressions and body language of the speaker. It follows that there could exist musical analogs of these visual aspects of speech.

  Apart from the obvious association of the the timing of music and dance, and the very fact that people usually dance to music, dance has the following aspects which are plausibly interpreted as being super-stimuli for some aspect of visual perception of non-dance (i.e. "ordinary") human motion:

  • The emotional effect of dance is greater when a group of dancers simultaneously perform the same dance moves.
  • Dance motion has an intrinsic "smoothness" not generally found in non-dance motion.