From Harmonic Structure to HCF to Sample Value, Part 3: Clarifying Terminology

This is very much a work in progress. No doubt the list will grow over time, as inspiration strikes and I have time to give to it. Some items link to Wikipedia (or other) articles, and some of those might not be included except that the articles they link too are so well done and include relevant material.

Array

A common way of structuring data, a list of items, usually all of the same type.

Big O notation

A standard method of expressing the computational complexity of an algorithm.

ADSR Envelope

Attack: the initial, usually abrupt escalation of volume at the beginning of a note.
Decay: the rapid loss of some of that volume immediately following the attack phase.
Sustain: a period of more stable volume following the decay phase.
Release: the final attenuation of volume to zero.

Anchor

My name for an intermediary object used to establish the frequencies of the fundamentals of the harmonic series composing a harmonic structure, and the frequency of their Highest Common Fundamental. The frequency of the Anchor is specified by the combination of two factors multiplied together, a scalar and an integer ratio.

Base Frequency

My name for an intermediary object which may be used in conjunction with the Anchor, providing the scalar factor.

Beat Frequency

A periodic variation in volume at a rate that is the difference between the frequencies of two simultaneous tones.

C-family Programming Languages

For the present purpose, C, C++, and Objective-C.

Callback

Code you provide to a framework which it calls when the conditions are right or when the time comes.

CD Quality

Two channels of 16-bit integer values at 44100 samples per channel per second.

Consonance

A quality of "simultaneous or successive sounds...associated with sweetness, pleasantness, and acceptability" best exemplified by chords composed of frequencies all related by ratios of small integers.

Consonant Transposition

Moving a harmonic structure up/down-scale as a unit, by an integer-ratio factor.

CPU Cycle

Not exactly a precise unit of measure, because various instructions take differing amounts of time to complete, because multiple instructions may be 'in-flight' simultaneously, and because it is becoming increasingly common to offload much of the work to coprocessors better adapted for particular classes of algorithms. Even so, it still works as a rough measure of computational effort.

Cycle

One repetition of a repeating pattern or event.

Cycles per Second

The number of repetitions of a repeating pattern or event with each passing second.

Digital Audio

The encoding of audio signals into or their synthesis in digital form, subsequent processing, and decoding to analog signals to drive speakers.

Double Precision

A floating point number with relatively high precision, usually occupying 64 bits.

Floating Point Number

A means of expressing very large, very small, and fractional values.

Frequency

The rate of repetition of a repeating pattern or event; for sound usually expressed in cycles per second (Hertz or Hz).

Fundamental

The lowest member of a harmonic series, every other member of the series being an integer multiple of the fundamental.

Harmonic

A member of a harmonic series, an integer multiple of the fundamental.

Harmonic Number

An integer representing both the factor by which the frequency of the fundamental of a harmonic series is multiplied to produce the frequency of a particular harmonic and the position of that harmonic within the series, where the fundamental itself is the first harmonic.

Harmonic Series

A sequence of integer multiples of a fundamental, of a fundamental frequency in the context of sound.

Harmonic Structure

Two or more harmonic series the fundamentals of which are related by integer ratios, having members with the same frequency at different harmonic numbers (although these may occur at harmonic numbers too high for inclusion in a given implementation).

Hertz (Hz)

Cycles per second.

Highest Common Fundamental (HCF)

The highest frequency which can serve as the fundamental of a harmonic series including every member of every harmonic series constituting a harmonic structure.

Index (plural: Indices)

A means of specifying a particular member of an array.

Integer

A whole number: ..., -3, -2, -1, 0, 1, 2, 3, ...

Integer Ratio

A ratio in which both the numerator and denominator are positive integers. In the context of ratio-based music, ratios composed of small integers are strongly preferred.

Intensity

An abstract representation of volume, which may or may not scale linearly.

Inverse (multiplicative)

The result of reversing the numerator and denominator of a ratio.

Modulo Division

Extraction of the remainder from a division, as opposed to its truncation or expression as a fractional result.

Note

An instance of a tone, generated either programmatically or in response to a user event.

Phase

The state of completion of the current cycle of a repeating pattern or event.

Phase Advancement

The amount by which the phase changes between one point in time (one sample) and the next.

Pi (𝜋)

The ratio between the circumference and the diameter of a circle.

Pitch

Used interchangeably with frequency, but occasionally with the suggestion of subjectivity.

Radian (rad)

The angle traversed by wrapping the radius of a circle around its circumference; commonly used as the unit for an argument in functions that calculate trigonometric values.

Ratio (fraction)

A proportionality between two quantities, calculated by dividing one (the numerator or dividend) by the other (the denominator or divisor), using a variation on division that preserves any remainder as a fractional component of the result, for example a quotient of type Double.

Real-time

Any computational context where both the initiation and completion of a sequence of operations are time-constrained to the extent that efficiency becomes a high priority.

Sample

A single value, representing a single instant, in a sequence of values composing a digital audio signal.

Sample Rate

The number of samples per second composing a digital audio signal.

Secondary Harmonics

The harmonics of a member of a harmonic structure.

Sine

A repeating trigonometric function.

Sine Wave

A graph of the sine function, and, by analogy, any phenomenon having a similar pattern, like sound.

Sound

The sensory experience of a sound wave.

Sound Wave

Propagating variations in air pressure, or a graph of those variations.

Table

An ordered list of values of the same type, frequently implemented as an array.

Tone

Used interchangeably with frequency, but occasionally with the implication of a voice being applied to that frequency.

Truncation

Discarding the fractional portion of a floating point value, as when performing conversion to an integer. Also discarding the remainder in integer division.

Unit Circle

A circle with a radius of 1.0, frequently centered on the origin of a two-dimensional coordinate system (x = 0.0 and y = 0.0); the foundational concept for much/most of trigonometry.

Unsigned Integer

An integer with no sign bit, representing a value that is greater than or equal to zero.

Voice

Any attributes in the synthesis of a note other than its basic frequency and the overall volume, for example the ADSR Envelope or emphasis on different harmonics as the note progresses.

Zero-based Indexing

The first element of an array has index 0.

Feel free to comment with suggestions, terms to include and/or definitions, or if you disagree with a definition I've supplied. If I use a definition that you've supplied, I'll provide attribution by linking to the comment, unless you specify that I should not do so.