Frequently abbreviated math term

Usage examples of modulo.

Any computation that starts with absolute pitch values and results in a pitch translation invariant output will still be pitch translation invariant if the input values are first reduced to a value modulo octaves.

I will use the simpler terminology that the map represents pitch values modulo octaves.

For example, two numbers are equal modulo 10 if they have the same last digit.

Two musical notes are equal modulo octaves if the interval between them is a whole number of octaves.

Both maps represent pitch modulo octaves, both have an activation of neurons that persists after the occurrence of the relevant pitch, and both have mutual reinforcement between consonantly related notes and mutual inhibition between notes not consonantly related.

In fact they all process pitch information modulo octaves, and an interval between two pitch values considered modulo octaves may be considered as either an interval going up or an interval going down.

In particular, the brain separates each pitch value into a precise pitch value modulo octaves and an imprecise absolute value, and performs subtraction separately on each of these components.

We might suppose that something similar is going on with pitch: a separation into a component modulo octaves and a component that retains octave information.

However, compared to other decompositions of information that occur in the brain, this particular decomposition has a rather unusual mathematical nature: an apparently simple continuum of possible pitch values is decomposed into a modulo value and a non-modulo value.

As a result, the absolute frequency of the sound is ambiguous, even though its value modulo octaves is unambiguous.

Diana Deutsch, which is that the ambiguity in perception of direction of tritone intervals between Shepard tones is a function of absolute pitch modulo octaves, with the function being different for different individuals.

Taking into account all sets of pitch values related in this way, and even after reduction by means of splitting pitch into absolute and modulo octaves components, such an implementation would require a large number of connections.

The split of pitch values into imprecise absolute pitch value and pitch value modulo octaves necessarily requires an accurate determination of the octave relationships between frequency values.

The scale map responds to pitch values modulo octaves that have occurred in the immediate past.

The harmonic map responds to pitch values modulo octaves in the current chord.