Is melody dimensionality “4D” in the brain? I suspect “yes.”
Here is some related research.
REFERENCES AND QUOTES
Ambinder M. S., et al (2009). Human four-dimensional spatial intuition in virtual reality. Psychonomics Bulletin & Review, 16, 5, 818-823
http://link.springer.com/article/10.3758%2FPBR.16.5.818
Abstract
It is a long-lasting question whether human beings, who evolved in a physical world of three dimensions, are capable of overcoming this fundamental limitation to develop an intuitive understanding of four-dimensional space. Techniques of analogy and graphical illustration have been developed with some subjective reports of success. However, there has been no objective evaluation of such achievements. Here, we show evidence that people with basic geometric knowledge can learn to make spatial judgments on the length of, and angle between, line segments embedded in four-dimensional space viewed in virtual reality with minimal exposure to the task and no feedback to their responses. Their judgments incorporated information from both the three-dimensional (3-D) projection and the fourth dimension, and the underlying representations were not algebraic in nature but based on visual imagery, although primitive and short lived. These results suggest that human spatial representations are not completely constrained by our evolution and development in a 3-D world. Illustration of the stimuli and experimental procedure (as video clips) and the instruction to participants (as a pdf file) may be downloaded from http://pbr.psychonomic-journals.org/content/supplemental.
Trehub, A. (2014). ResearchGate Message to Herb Klitzner, Dec 2, 2014
Thanks for your interest. I’m not knowledgeable enough to respond to your detailed observations about music, but I must point out that all autaptic-cell activity in retinoid space is 4D because autaptic neurons have short-term memory. This means that there is always some degree of temporal binding of events that are “now” happening and events that happened before “now”. The temporal span of such binding probably varies as a function of diffuse activation/arousal. The temporal envelope of autaptic-cell excitation and decay defines our extended present. This enables us to understand sentences and tunes.
Trehub, A. (2007). Space, self, and the theater of consciousness. Concsciousness and cognition, 16, 310-330
http://people.umass.edu/trehub/YCCOG828%20copy.pdf
Trehub, A. (2013). Where Am I? Redux. J. of Consciousness Studies, 20, (1-2), 207-225
http://www.ingentaconnect.com/content/imp/jcs/2013/00000020/F0020001/art00011
Baroin, G. (2011). The Planet-4D Model: An Original Hypersymmetric Music Space Based on Graph Theory. Mathematics and Computation in Music, Lecture Notes in Computer Science Volume 6726, 2011, pp 326-329
http://link.springer.com/chapter/10.1007%2F978-3-642-21590-2_25
Published on Mar 14, 2012
Extract of the main movie:
From Circle to Hyperspheres, when Tonnetze go 4D
ACT 5 FOUR DIMENSIONS :
THE PLANET-4D PITCH AND CHORDAL SPACE
We now visualize the pitch space in a true four-dimensional space, by projecting it into our 3D space and letting it rotate around two 4D Axes. The same rotating ball that symbolize the current position, never moves while the models rotates. Thanks to this technique, the model appears to be deforming within a 3D sphere. That reinforces the feelings of symmetry for the spectator.
http://youtu.be/MGCIPZyaiuw
4D perceived space of musical key distances from each other:
Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial map of musical keys. Psychological Review, 89, 334-368
http://music.psych.cornell.edu/articles/tonality/1982K&KesslerPsychRevfromJournal.pdf
The Melody of the Text (Mike Mair)
“Even though the speech trajectories capture virtual world models rather than actual objects on four-dimensional trajectories (like a prey animal moving in the environment), I suggest that the trajectory of speech with movement [gesture, including ballistic and oral-facial] is non-verbal, the product of the core brain forming the core to the speech act. The ‘point’ is the point. A growth point is defined as the ‘initial form of thinking out of which speech-gesture organization emerges’. (McNeill) It might also be called the ‘projection point’.
The core brain mechanisms underlying human natural story telling can now be glimpsed. Damasio’s core brain text generator in action describes the nonverbal internal structure of gesturing behaviour in speech with movement. It may have functioned projectively on 4D-space time for probably billions of years. Additional control of outcomes is achieved by adding more dimensions or variables to the modeling process, up to our present limit of 7+/-2.”
Mike Mair
The Melody of the Text – Revisited (c. 2002-2014).
I-Ching Approach to Musical Harmony (Chung-Ling Cheng)
“This analytical reconstruction of the musical harmony, however, is not complete without also mentioning that: (4) Relating parts to totality in music is a dynamic process consummated in a process of movement of time. In mentioning time, one cannot ignore the spatial involvement inherent in a musical harmony either. The reason is that, in producing a piece of music, locations of the sound and relations of locations in space make a difference. Hence we must recognize musical harmony as a four-dimensional totality exhibiting an order of mutual support among its notes and realizing itself (the totality) in a specific process of time and implicit reference to space.”
Chung-Ling Cheng (2009)
On harmony as transformation: Paradigms from the Yiching.
In Philosophy of the Yi: Unity and Dialectics (2009)
Comment: “Implicit reference to space” can have several interpretations here, some not necessarily intended by the author. The author is speaking literally about the pattern of sound locations — this is acoustics (sound in an environment), not acousmatics (music in the brain). Music cognition researchers dealing with harmony speak of the construction in the brain of a virtual tonal space, likely generated by the processes of the parietal lobe in its finished 3D/4D display of perceived and imagined multisensory objects. So the spatial mechanism of representation is used to display melody and harmony — a virtual reality.
And this in turn could be influenced by, and have blended into its operation, some spatially-oriented available ancient animal and human processes regarding trajectory and emotion, as described by Mike Mair, Kevin Behan, Jaak Panksepp (and myself in this set of blog discussions).