### Crossword clues for modulo

##### Wiktionary

**modulo**

n. (context computing English) the operation or function that returns the remainder of one number divided by another prep. 1 (context mathematics English) Given a specified modulus of. 2 (context jargon or colloquial English) Except for differences accounted for by. 3 (rfquote-sense: en) (context extended use English) With due allowance for (a specified exception or particular detail).

##### Wikipedia

**Módulo**

**Módulo** is a Brazilian company with international operations specializing in technology for Governance, Risk and Compliance. It operates in areas of software, consulting and education, offering, since 1985, security solutions. The company has offices in Brazil, United States, Europe, United Kingdom and operates throughout Latin America through a network of partners.

Since 1998, Módulo has customers from all sectors, and has participated in projects internationally recognized as the Brazilian electronic elections, the delivery of income tax via the Internet, the Brazilian Payment System (SPB) and the Pan American Games Rio 2007 (edition held in Rio de Janeiro, Brazil), and provider of software with technology for Risk Management, incidents and events.

**Modulo (jargon)**

The word ** modulo** (Latin, with respect to a modulus of ___) is the Latin ablative of

*modulus*which itself means "a small measure." It was introduced into mathematics in the book

*Disquisitiones Arithmeticae*by Carl Friedrich Gauss in 1801. Ever since, however, "modulo" has gained many meanings, some exact and some imprecise. Generally, to say:

*A*is the same as

*B*modulo

*C*

means

*A*and

*B*are the same except for differences accounted for or explained by

*C*.

#### 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.