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• Vestibular system

  • https://en.wikipedia.org/wiki/Vestibular_system
  • Push-pull systems: The canals are arranged in such a way that each canal on the left side has an almost parallel counterpart on the right side. Each of these three pairs works in a push-pull fashion: when one canal is stimulated, its corresponding partner on the other side is inhibited, and vice versa. This push-pull system makes it possible to sense all directions of rotation: while the right horizontal canal gets stimulated during head rotations to the right, the left horizontal canal gets stimulated (and thus predominantly signals) by head rotations to the left.
    Vertical canals are coupled in a crossed fashion, i.e. stimulations that are excitatory for an anterior canal are also inhibitory for the contralateral posterior, and vice versa.

• Sound localization

  • https://en.wikipedia.org/wiki/Sound_localization
  • https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4769260/
  • Duplex theory: To determine the lateral input direction (left, front, right), the auditory system https://en.wikipedia.org/wiki/Auditory_system analyzes the following ear signal information: In 1907, Lord Rayleigh utilized tuning forks to generate monophonic excitation and studied the lateral sound localization theory on a human head model without auricle. He first presented the interaural clue difference based sound localization theory, which is known as Duplex Theory. Human ears are on different sides of the head, and thus have different coordinates in space. As shown in the duplex theory figure, since the distances between the acoustic source and ears are different, there are time difference and intensity difference between the sound signals of two ears. We call those kinds of differences as Interaural Time Difference (ITD) and Interaural Intensity Difference (IID) respectively.
  • Most mammals are adept at resolving the location of a sound source using interaural time differences and interaural level differences.
  • These ambiguities can be removed by tilting the head, which can introduce a shift in both the amplitude and phase of sound waves arriving at each ear.

• Binocular vision

  • https://en.wikipedia.org/wiki/Binocular_vision
  • In biology, binocular vision is a type of vision in which an animal has two eyes capable of facing the same direction to perceive a single three-dimensional image of its surroundings.
  • Stereopsis from Ancient Greek στερεός stereós 'solid' and ὄψις ópsis 'appearance, sight' is the component of depth perception retrieved through binocular vision. Stereopsis is not the only contributor to depth perception, but it is a major one. Binocular vision happens because each eye receives a different image because they are in slightly different positions on one’s head (left and right eyes). These positional differences are referred to as "horizontal disparities" or, more generally, "binocular disparities". Disparities are processed in the visual cortex of the brain to yield depth perception. While binocular disparities are naturally present when viewing a real three-dimensional scene with two eyes, they can also be simulated by artificially presenting two different images separately to each eye using a method called stereoscopy. The perception of depth in such cases is also referred to as "stereoscopic depth".

The duplex model measures consonance relative to reference pitches above and below the tonal center, or tonic pitch, of the musical context, which leads to major-minor and consonance-dissonance perception.

Traditional simplex models measure consonance relative to the tonic pitch, which is usually the bass pitch of a specific chord.

Duplex frequency ratios are not the same as the simplex ratios that have been studied since antiquity. For example, the simplex ratio for the Perfect Fifth is 3/2, whereas the duplex ratios for the Perfect Fifth are 3/1 and 3/4, from below and above, respectively. The key ratios from below are:

• Low Reference Pitch: 1/1
• Tonic: 2/1
• Perfect Fifth: 3/1
• Octave: 4/1
• Major 3rd (compound) : 5/1
• Perfect Fifth (compound): 6/1
• Double Octave: 8/1
• Major 2nd (double compound): 9/1
• Major 3rd (double compound): 10/1
• Perfect Fifth (double compound): 12/1
• Triple Octave: 16/1

If one wants to build a piano, one is going to need the simplex ratios: they originate in the study of string ratios and the production of musical instruments.

However, if one wants to build a model of music perception, the venerable simplex models and their enshrined ratios might be distracting us from how the brain processes frequency ratios from octaves above and below the tonal center.

Duplex periodicity
Duplex interference

More vertical lines
Centered
Add named intervals to plot

https://statisticsglobe.com/modify-major-and-minor-grid-lines-of-ggplot2-plot-in-r