A way of notating how something is pronounced. Transcriptions here adhere closely to the official latest revision of the International Phonetic Alphabet (IPA), but with the addition of characters from the extIPA as necessary.

Transcriptions come in three flavors, depending on the conceptual level at which they exist:

[⋯]

Narrow transcription. At the level of actual speech production, idiolect, or small lect.

/⋯/

Broad transcription. At the phonemic level.

⫽⋯⫽

At the morphophonologic or diaphonemic level.

The base‐twelve numeral system.

The familiar Hindu–Arabic numerals used for decimal are also used for duodecimal; however, the necessary two additional digits are not always agreed upon. For convenience, the two digits have often been ⟨T, E⟩, from the English words ten and eleven; or ⟨A, B⟩, as in hexadecimal.

Unfortunately, ⟨A, B, E⟩ all overlap with the names for pitches & pitchclasses in music (see: integer notation, for the use of duodecimal), and the use of ⟨T, E⟩ is regrettably language‐specific. The use of letters in general is also problematic, causing numbers to be more easily confused with letters or words.

For these reasons, I use the Pitman digits ⟨↊, ↋⟩; U+218a & U+218b, respectively.

“Corresponds to”. Used for connecting a concrete object to its counterpart that’s relative to the surrounding context:

• In the key of C major, we have D ≘ 2̂. (See: mode.)
• In the key of C major, we have D−7 ≘ ii⁷. (See: Roman numeral analysis.)

The word collection itself is used very generically, to refer to any number of items considered together in an otherwise unspecified way. More precise notions are summarized in the following table (where uniform means that the collection’s elements are all of the same type):

A space into which things from another one‐dimensional space are mapped, for the purpose of preserving the points’ order relative to one another, while also abstracting away from exact “distances”.

This notion was originally applied to pitches: in a finite piece of music, a finite number of pitches occur, and they can be well‐ordered w.r.t. one another in the usual way. We can thus assign the contour‐pitch (abbreviated as c‐pitch) ⟨0⟩ to the lowest pitch that occurs, the c‐pitch ⟨1⟩ to the second‐lowest pitch that occurs, and so on. This allows us to express melodic contour by reducing the pitch of every note in a melody to its corresponding c‐pitch — within the c‐space that represents exactly (& only) those pitches that occur within said melody.

For example, the melody (all within a single octave) C–D–F–D–C–F–D–F gets the c‐space representation ⟨0⁣1⁣2⁣1⁣0⁣2⁣1⁣2⟩_c. Such a path through c‐space may be called a c‐seg.

However, c‐spaces can be applied to any number of things that aren’t pitches. Even so, in a musical context, the term c‐pitch is still used to refer to the points in the space.

C‐space is taken from [Mor87]. However, I don’t have access to this book, so I have taken this description from [Sco16].

A chronologic progression of musical objects that implies a lack of overlap between those objects, and that is typically actually sounded (rather than being purely notional). Notated by separating the objects with en dashes (U+2013). Typical uses include:

• Chord progressions, e.g. D−7–G7–C ≘ ii⁷–V⁷–I.
• Melodies with unspecified rhythm, e.g. F–F–E–D♯–B–C–C.

An outline of a musical form in terms of its sections, with each section represented by an uppercase Latin letter starting from ⟪A⟫.

I use ⟪⋯⟫ (U+27ea…U+27eb; “mathematical double angle brackets”) to delineate schemata or individual sections within them. Sections that are repeated with significant variation get prime symbols, e.g. a variation of ⟪A⟫ may be written ⟪A′⟫, another variation may be written ⟪A″⟫, and so on. Different occurrences of the same section with no significant variation may be distinguished with subscript numbers, e.g. ⟪A′₁⁣B⁣A′₂⟫ for two instances of ⟪A′⟫ separated by an instance of ⟪B⟫.

A contiguous temporal segment of a musical piece that is demarcated from what comes before & after it by an overall change in the musical materials used. A section generally lasts for numerous measures, and contains significantly more than one complete phrase.

A full piece of music may have any number of sections (including 1), and the demarcation of those sections may be fairly arbitrary. The structure of a piece’s sectioning may be captured with a schema.

A way of labelling timings in a measure at the beat level, and at certain divisions of the beat.

The method used here counts the first beat as “1”, the second beat as “2”, and so on. Then, the midpoint of each beat is counted as “&” /ænd/; for example, the midpoint of the second beat is the “& of 2”.

The point ¼ of the way through the beat is “e” /i/, and the point ¾ of the way through is “a” /ə/. Compound meter and triplets are less commonly agreed upon, but here I use “la” /lɑ/ for the ⅓ point, and “li” /li/ for the ⅔ point.

Regular sequencing that occurs above the metric level; that is, in terms of sequences of measures. A unit of hypermeter is a hypermeasure (AKA hyperbar). In this context, the constituent measures of a hypermeasure may be called hyperbeats.

Sometimes, it is convenient to have an additional hypermetric layer, so that a hyperbeat may encompass more than one measure. I use this convention, so that individual measures may be thought of as “hyperpulses” — although this term is not widely used.

A regular sequence of beats — typically, but not always, of the same kind — along with a system of accents; accented beats are onbeats, and other (unaccented) beats are offbeats. A unit of meter is a measure (also called a bar). The last beat is the upbeat, and the first beat of the following measure is the downbeat. Contiguous measures are grouped by hypermeter, if at all. The overall duration of a measure is the meter’s extent (e.g. 4⁄4 and 2⁄2 are coëxtensive).

The use of time signatures to denote meters is potentially confusing, as the notation itself only specifies the nominal(!) length of a pulse, and how many nominal pulses there are in each measure. Generally speaking:

The simultaneous use of two or more distinct meters such that the meters’ extents are mutually indivisible. For example, simultaneous 6⁄8 and 4⁄4 produces polymeter, as 6×𝅘𝅥𝅮 does not divide 8×𝅘𝅥𝅮, nor does 8 divide 6. Simultaneous 6⁄8 and 3⁄4 does not produce polymeter, as the two meters are coëxtensive, and thus trivially divide one another — this would be an example of polyrhythm.

Note that the notion of “polymeter” implies a shared stream of pulses. When there is no such shared stream, or that stream would be unacceptably fine‐grained, then the music may be analyzed as being polytempic (= multiple mutually‐indivisible tempi), or perhaps as exhibiting both polymeter and polyrhythm simultaneously.

The simultaneous use of two or more distinct meters such that the meters disagree on where the beats lie — & may also disagree on the pulse — but without being of mutually indivisible extents. For example, simultaneous 6⁄8 and 3⁄4 produces polyrhythm, as the former divides the meter into two beats ⟨⁠𝅘𝅥𝅭𝅘𝅥𝅭⁠⟩, whereas the latter divides it into three beats ⟨⁠𝅘𝅥𝅘𝅥𝅘𝅥⁠⟩. Simultaneous 5⁄4 and 4⁄4, however, would instead be analyzed as polymeter.

By definition, tuplets are an inherently polyrhythmic notation. However, care must be taken not to confuse the use of tuplets as a convenient notational device with the actual sounding of polyrhythm in the music itself.

When the meters’ extents are mutually indivisible, &/or their pulse streams are more‐or‐less irreconcilable, the music is likely better analyzed as polytempic (= multiple mutually‐indivisible tempi), or perhaps as exhibiting both polymeter and polyrhythm simultaneously.

The most basic regular unit of musical timing. Any voice that — in a given section of music — has regular timing necessarily has an underlying pulse; however, the notion is abstract enough that “the pulse” of said voice is not uniquely defined, although reasonable definitions are typically morally equivalent.

Not every pulse is actually sounded in some way, thus making it more of an abstract notion. Pulses are often grouped into beats, albeit not always uniquely. The denominator of a time signature specifies the nominal(!) length of a pulse, e.g. the “4” in “3⁄4” implies that the nominal pulse is a quarter‐note. For more on time signatures, see meter.

As a singular noun, a timing is a temporal location; an abstract point within a one‐dimensional timeline. An event — e.g. the onset of a note — that occurs at “a certain time” has a timing: its “certain time”!

More broadly, the (collective) timing of some collection of events is the collection of those events’ timings, considered as a kind of distribution. This leads to notions such as pulse and rhythm.

A collection of pitches that represents at least two distinct pitchclasses, and that is thought of as being essentially vertical, even if not necessarily sounded as such (e.g. it may be arpeggiated). For the notation used here for chords, see the entry on chord notation.

A chord whose members are all struck more‐or‐less simultaneously, and all have more‐or‐less the same duration, is called a block‐chord.

A factor of a chord whose quality must be explicitly specified because it is otherwise “unexpected”. For less exotic chord extensions, see chord extension. In the chord notation used here, the following notations are used to indicate alterations:

[nothing]

No alterations.

♭5

Having a diminished fifth factor, instead of a perfect one.

♯5

Having an augmented fifth factor, instead of a perfect one.

♭9

Having a minor ninth factor, instead of a major one.

♯9

Having an augmented ninth factor, instead of a major one.

♯11

Having an augmented eleventh factor, instead of a perfect one.

♭13

Having a minor thirteenth factor, instead of a major one.

alt

Shorthand for an altered dominant seventh‐chord with otherwise unspecified construction. More‐or‐less any of the above alterations may be applicable, and at least one of them is.

A factor of a chord that goes beyond its basic quality, but in a way that is otherwise “expected”, given its quality. For more exotic extensions, see chord alteration. In the chord notation used here, the following notations are used to indicate extensions:

[nothing]

No extensions.

add2, add4

Added major second or perfect fourth factor, respectively, but without the presence of a seventh factor.

6

Added major sixth factor, but without the presence of a seventh factor.

°7

Fully‐diminished seventh‐chord, with diminished triad quality & diminished seventh factor.

𝆩7

Half‐diminished seventh‐chord. Has a minor seventh factor, rather than a diminished one.

alt7

Shorthand for an altered dominant seventh‐chord with otherwise unspecified construction. For more on alterations, see chord alteration.

∆7

Major seventh factor. Depending on the quality, this may be a major seventh‐chord, an augmented major seventh‐chord, or a minor major seventh‐chord.

7

By default, the seventh factor is minor.

9

Same as 7, but with a major ninth extension.

11

Same as 7, but with a perfect eleventh extension.

13

Same as 7, but with a major thirteenth extension.

Which factor of a chord is in the bass; that is, lowest in pitch. In the chord notation used here, the following notations are used to indicate inversion:

[nothing]

The default inversion is root position (≝ root in the bass).

◌⁶

First inversion (≝ third factor in the bass) of a tertian chord with no seventh factor.

◌⁶₅

First inversion of a seventh‐chord.

◌⁶₄

Second inversion (≝ fifth factor in the bass) of a tertian chord with no seventh factor.

◌⁴₃

Second inversion of a seventh‐chord.

◌⁴

Second inversion of a power‐chord.

◌⁴₂

Third inversion (≝ seventh factor in the bass).

◌/p

The pitch p is in the bass.

The name of a chord begins with the name of its root in uppercase; this may be followed by some symbols that give more information about the rest of the chord. For Roman numeral analysis notation, see the relevant entry.

By default, a named chord is a major triad in root position (e.g. the chord “B♭” is a B♭ major triad with B♭ in the bass). This basis in triads inherently biases the notation toward tertian constructions, so other notation may be used for other kinds of chords.

Poly­chords & other chord–chord hybrids are written as multiple chords connected with ⊔ (U+2294 “square cup; disjoint union”). The constituent chords are arranged in ascending order of pitch, if applicable.

Any added symbols can be broadly classified into about five categories, in the following order:

1. Quality.
2. Extension.
3. Alteration.
4. Omission.
5. Inversion.

The most fundamental part of a chord’s structure; in tertian harmony, this is the triad’s quality, ignoring other aspects of the chord like e.g. its other factors or its inversion. In the chord notation used here, the following notations are used to indicate quality:

[nothing]

The default quality is a major triad.

−

Minor triad.

⊟

Split‐third chord: superimposed major & minor triads, resulting in two distinct third factors within the same chord.

+

Augmented triad.

±

Augmented triad with a split third.

°

Diminished triad.

𝆩

Half‐diminished. A variant of the symbol for diminished triad that implies a minor seventh factor (rather than a diminished or missing seventh factor). For more seventh‐chords, see chord extension.

sus2, sus4

Suspended second or fourth chord, respectively.

5

Power‐chord. No third factor, perfect fifth factor.

alt

Shorthand for an altered dominant seventh‐chord with otherwise unspecified construction. May or may not affect the quality of the chord, as its third & fifth factors may still form a major triad. For more seventh‐chords, see chord extension.

A short­hand notation for harmonic function. Uses en­circled upper­case Latin letters:

Ⓣ

Tonic.

Ⓢ

Sub­dominant &/or pre‐dominant.

Ⓟ

Sub­dominant used cadentially. So named for the plagal cadence.

Ⓓ

Dominant.

Abbreviation of intervalclass vector. Enumerates how many times each nonzero ic is represented within a setclass — or more generally, within any arbitrary set of pitches or pitchclasses — by counting pairwise. Notated as a row vector of six natural numbers within angle brackets, representing ics 1 through 6 from left to right.

For example, a root‐position major triad might be represented in integer notation as {0⁣4⁣7}. The interval between 0 & 4 represents ic 4, between 4 & 7 represents ic 3, and between 0 & 7 represents ic 5. Thus, the ic‐vector is ⟨0⁣0⁣1⁣1⁣1⁣0⟩. Because a minor triad is the inversion of a major triad, repeating the same analysis with {0⁣3⁣7} results in the same ic‐vector, and indeed both are members of the same setclass ⟦0⁣3⁣7⟧_3‐11. However, in general, two setclasses may have the same ic‐vector in spite of being otherwise distinct; this is called the Z‐relation.

The total number of ics (counting duplicates) is the sum of the ic‐vector’s entries. In the example, this number is 3, because $\left(\genfrac{}{}{0ex}{}{3}{2}\right)=3$. In general, the number of ics is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ (a triangular number), where $n$ is the cardinality of a candidate underlying set (not setclass) of pitches.

A way of representing pitches (or pitchclasses) as numbers. An ad hoc origin is chosen, and is assigned the number 0. Then, each pitch is assigned a number — which may be negative in some cases — equal to its distance, in semitones, away from the origin.

When dealing with nonnegative integers less than twelve, duodecimal is used. This allows for each number to be represented as a single digit, so that visible separators (e.g. spaces or commas) are unnecessary. Instead, U+2063 “invisible separator” is used. In other cases, decimal can be assumed.

The distance between two pitches, considered in any of various ways. At its most basic, an interval is a ratio between two fundamental frequencies (although some tuning systems have intervals that are mathematically irrational, so this is not true sensu stricto). See the relevant English Wikipedia article.

For ratios, I use the notation n∶d (U+2236 “ratio”). For cents, I use the unit symbol ¢ (U+00a2 “cent sign”). For named intervals, I use the following shorthands:

P

Perfect. For example, P1 = “perfect unison” = 1∶1.

m

Minor. For example, m2 = “minor second” (in 12 EDO: 1⁢ semitone).

M

Major. For example, M2 = “major second” (in 12 EDO: 2⁢ semitones).

d

Diminished. For example, d4 = “diminished fourth” (in 12 EDO: 4⁢ semitones).

A

Augmented. For example, A5 = “augmented fifth” (in 12 EDO: 8⁢ semitones).

TT

Tritone = 6⁢ semitones.

The equivalence‐class of intervals under both octave equivalence and inversional equivalence. Expressed in semitones. Any ic falls within the range $0\le \mathrm{ic}\le 6$.

For example, in 12 EDO, all of the following intervals — regardless of whether they’re ascending or descending — are members of ic 4: M3, m6, d4, d11, m13, M10, etc..

See also: ic‐vector.

Equivalence under inversion around any axis. Always used in combination with transpositional equivalence, although the converse is not necessarily true. See also: intervalclass.

To get from the prime form of a setclass to the prime form of its inversion (or vice versa), count intervals from the highest number downward. For example, ⁅0⁣1⁣6⁆_3‐5A can be read right‐to‐left as 6 − 6 = 0, 6 − 1 = 5, and 6 − 0 = 6; so its inverse is ⁅0⁣5⁣6⁆_3‐5B.

The collection (or possibly, distribution) of pitches (usually pitchclasses — see the entry for scale) used throughout some music, considered at a broader scope than a scale. Essentially a generalization of the traditional notion of key, as well as an alternative way to understand “modal mixture”.

Macroharmony is especially relevant when certain alterations are commonly made to a scale or other source of pitches, or when scales alternate with each other as in e.g. classical minor‐key harmony (where natural minor, harmonic minor, & melodic minor coëxist). Another example is the so‐called blues “scale”, which is not a scale in the proper sense (although it could be forcibly & artificially turned into one), but can be a meaningful macroharmony in some cases.

This term is taken from [Tym11].

An abstraction of melody that considers only its general shape, to the exclusion of exact pitches, exact interval sizes, & timings.

One method of encoding contour is with the Parsons code. Every Parsons code begins with a * representing the first note, which is then followed by one additional character for each successive note in the melody: d “down” if lower in pitch than the previous note, r “repeat” if equal, or u “up” if higher.

Another method of encoding contour, which contains more information, is using contour space.

Music is described as modal when its dominant paradigm of arranging pitch‐material is one where a particular mode prevails at any given time, with harmonic changes being at the mode‐to‐mode level, rather than at the chord‐to‐chord &/or key‐to‐key level.

Indeed, by definition, the term key does not apply (sensu stricto) to modal music. Instead, each mode has its own bespoke — & typically, weak — center (or simply “1̂”), with one mode giving way to the next more‐or‐less freely, their 1̂s being more like roots than like tonics.

Even a piece with no changes of mode may be described as “modal”, simply because the mode in question is neither Ionian nor Aeolian, &/or because no tonic is established via the relevant idiom originating in Western classical music.

In the Occident, explicitly modal music is commonly associated with modal jazz. However, many other musical traditions — including several vernacular ones — can be described similarly.

A particular instantiation of a scale that endows it with a privileged member — a “first” pitch (which may be a “tonic” pitch). A scale (assuming symmetry of ascent & descent) with n distinct members has n possible modes.

For convenience, however, many scales are thought of as having a “default” mode that is implicit — thus blurring the distinction between the scale & its implicit mode. For example, the diatonic scale usually defaults to its major mode (AKA the modern Ionian mode).

A mode’s members may be labelled with numerals that have circumflexes upon them: the first degree of the mode is 1̂, the second degree is 2̂, and so on. The same notation, & use of the term degree, is also applied to keys, where the term tonic is more meaningful.

A factor of a chord that is absent, in spite of its presence being implied by the chord’s basic quality.

When the fifth factor is implied to be perfect, but is nonetheless absent, and the other expected factors are present, the fifth’s omission is usually considered unimportant, and is thus left unspecified. In some cases (especially in jazz), the root may be omitted, in which case its omission is typically unspecified as well.

In the chord notation used here, the following notations are used to specify omissions:

[nothing]

No omissions (or an unspecified omission of the fifth factor &/or root, if appropriate).

no1

Omitted root.

no3

Omitted third factor.

no5

Omitted fifth factor.

A traditional form of chordwise harmonic analysis that uses Roman numerals to represent each chord’s root as a degree of the key. See the relevant English Wikipedia article.

The notation used here for RNA is based closely upon that specified in the chord notation entry. However, there are some important differences:

• Rather than the default chord quality always being that of a major triad, an uppercase Roman numeral retains this default, while a lowercase numeral makes a minor triad (or more generally, a minor third factor) the default.
• An accidental (♭ or ♯) may appear before the Roman numeral, in which case the root’s relationship to the key’s tonic is shifted by semitone (down or up, respectively) relative to the major or perfect version of the tonic‐to‐root ascending interval. In other words, the Roman numerals & their accidentals are always relative to a major key based on the tonic, even when the key isn’t major. For example, the diatonic submediant triad in the key of A minor is F ≘ ♭VI (not VI, which would be F♯).
• A slash is used for applied chords (AKA secondary chords). This means that chord inversions that cannot be represented using figured‐bass‐style notation are either omitted, or else written with a circumflexed Hindu–Arabic numeral after the slash, instead of a Roman numeral. For example, in the key of C major, D9 ≘ V^7,9/V, but G9/A ≘ V^7,9/6̂ (or simply V^7,9).
• The seventh & higher factors — as well as the fifth factor of a power‐chord — may be given as superscripts, and may be separated with commas.

A collection of pitches that typically repeats at the octave, and that is contrasted with a chord by usually having at least five members (rather than at least two), and most importantly, by being used as the primary source of horizontal pitch‐material (and often also of vertical). The distance from a scale member to the next‐higher or next‐lower scale member is called a step.

Some scales do not repeat at the octave, leading to the contrast of octave‐repeating vs. non‐octave‐repeating scales. Only in the former can the scale members be thought of as pitchclasses. Moreover, some scales — most notably melodic minor — may be different depending on whether they are ascended or descended.

When a scale has a privileged member — a “first” pitch (or “tonic” pitch) — it is actually instead a mode of the underlying scale. For convenience, however, many scales are thought of as having a “default” mode that is implicit.

Abbreviation of pc‐set class, which is in turn an abbreviation of pitchclass‐set equi­valence‐class: an equi­valence‐class of pc‐sets that are related by trans­pos­i­tion­al equi­valence, and often also by inversional equivalence. The term n‐setclass is used to refer to a setclass whose elements each have n pcs in them (e.g. ⟦0⁣1⁣6⟧_3‐5 is a 3‐setclass).

Equi­valence‐classes are conventionally denoted in mathematics by enclosing a representative element in square brackets. However, because square brackets are already overloaded in music notation, I instead use ⟦⋯⟧ (U+27e6…U+27e7; “mathematical white square brackets; doubled square brackets”) to enclose the prime form of the setclass. Moreover, I include the Forte number as a subscript immediately after the closing bracket. For example: ⟦0⁣1⁣6⟧_3‐5.

When inversional equi­valence is not observed, ⁅⋯⁆ (U+2045…U+2046; “square brackets with quill; spike parentheses; piggparenteser”) are used instead. Also in this case, the Forte number for invertible setclasses is suffixed with an “A” to denote the prime form, and a “B” for its inversion. For example: ⁅0⁣5⁣6⁆_3‐5B.

/ˌhoʊ̯.miˈɒ.fə.ni/. A texture defined in this essay. Not to be confused with homophony. May alternatively be spelt ⟨homoeophony⟩ or ⟨homœophony⟩, but here I prefer the spelling ⟨homeophony⟩.

Relative motion between two or more simultaneous pitched voices, typically understood in terms of contrapuntal motion. I use the following categories, in generally descending order of independence:

contrary

The voices move in opposite directions.

oblique

One voice moves while the other does not.

similar

The voices move in the same direction, but by different amounts. In music with meaningful macroharmony, the “amounts” are typically calculated scalewise; that is, in terms of scale steps.

imperfect parallel

The voices move in the same direction & by the same amount (scalewise, if applicable); but not in a way that qualifies as perfect parallel motion.

perfect parallel

The voices move in the same direction & by the same amount; furthermore, the starting & ending intervals are exactly (chromatically) identical, and that interval is perfect.

By acronymizing each of these five motion types to its initial letter, we get the mnemonic cosip. A simplification of cosip ignores oblique motion, dichotomizing into contrary & anticontrary motion.

When motions are normalized, they may be prefixed with ⇕ (U+21d5 “up down double arrow”).

An approach to analyzing melodic motion wherein the absolute magnitudes of melodic intervals are heard as no larger than a TT. This effectively treats pitches as pitch­classes, thus reflecting the “heard” voice‐leading from an octave‐equivalence perspective.

This is the same perspective from which (for example) two voices that move in the same direction, but by intervals of in­com­men­su­rate magnitudes, may be heard as moving in­de­pend­ent­ly; and two voices that move from unison to octave — one descending by P4, the other ascending by P5 — isn’t really meaning­fully “contrary” motion.

To normalize motion from one sonority to the next, each directed melodic interval — one per voice — is normalized individually. An octave (= 12 semitones) is repeatedly subtracted or added to each interval $i$ until the condition $\mathrm{-6}\le i\le \mathrm{+6}$ is satisfied. In the ambiguous case of $i\equiv \mathrm{\pm 6}$, the sign of the original interval is retained; for example, the interval −18 is normalized to −6, and the interval +6 is normalized to +6.

Normalized motions may be denoted by the prefix ⇕ (U+21d5 “up down double arrow”).

The way in which musical voices are combined to produce a segment (small or large) of music.

Traditionally focuses on pitched voices, but can generally include any sounds. Common concerns include how voices move relative to one another, which voices are “melodic” & which are “accompaniment”, how many voices are present & in what registers, which voices are made to “blend” together or not, etc..

In this abstract sense, a voice is the smallest unit of temporal continuity in music. Parts played on separate instruments are typically distinct voices on some level, but a single instrument (e.g. a piano or a drumkit) may produce multiple voices concurrently. The production of more than one distinct note at a given time implies the existence of more than one voice at that time.

When otherwise distinct voices move together in lockstep, they lose their aural independence, thus becoming (at least for that time) effectively a single voice for many purposes.

In general, a voice needn’t be pitched at all. In the particular case of pitched voices, the part played by a single voice is called a melody. The relative motion & inter­action of voices to produce harmonies (read: chords) is called voice‐leading. The way in which a chord’s factors are distributed among voices is that chord’s voicing.

A partial that is a member of the harmonic series of the fundamental, meaning that its frequency is an integer multiple of the fundamental frequency.

Harmonics are numbered from the 1^st being the fundamental, the 2^nd being twice that frequency, and so on, with no regard for which harmonics are actually present in the sound.

Any frequency component of a sound, regardless of its harmonicity.

Partials are numbered from the 1^st being the fundamental, the 2^nd being the next‐highest audible partial, and so on, with no regard for harmonicity.

The quality of a sound, as considered apart from any pitch that it might have. A primary point of differentiation between musical instruments.

In spite of its foundational nature, timbre — especially how humans perceive it — remains poorly understood. Basic explanations appeal to the power spectrum (including partials harmonic or not), the nature of a note’s attack, and more generally its envelope.

A retrospective term (the earliest emocore bands would have been simply “hardcore”) blending emotive + hardcore. This splinter of post‐hardcore emerged in the mid‐1980s, defining itself in opposition to its hardcore parents by its greater use of (relatively) slow tempi, explicitly melodic material, dynamic range, and introspectively emotional lyrics. Exemplars include Rites of Spring and Moss Icon.

Although the historic activity of “emocore proper” was limited & didn’t last long, this was arguably because it almost immediately gave rise to manifold new scenes & styles, the umbrella of which is sometimes simply called emo (although this term has seen mild abuse as a result of its com­mercial­iz­a­tion). Nevertheless, the use of the term emocore always refers strictly to this particular style, rather than any of its more or less distant descendants.

A subgenre of metalcore that emerged in the 1990s, defined by its jarring rhythms & meters, its use of unusual or dissonant pitch‐material, and its focus on instrumental part­writing. Some mathcore is also structured around the brief, violent bursts of grindcore. Exemplars include Deadguy, Botch, Converge, The Dillinger Escape Plan, Coalesce, and The Sawtooth Grin.

Mathcore is primarily dif­fer­en­ti­a­ted from its etymon mathrock by the influence of extreme metal, rather than solely of post‐hardcore. Both genres commonly feature unclean vocal styles (with the caveat that mathrock frequently lacks vocals entirely), but the two are divided along much the same lines as other metal–punk distinctions.

Originally a subgenre of post‐hardcore, this style of rock music emerged in the late 1980s & early 1990s as a result of punk‐driven experimentation with songwriting. The genre is defined by its focus on the primary instruments of rock — guitars & drumkit — sometimes to the exclusion of vocals, its complete freedom of musical form, its difficult melodies (& not infrequently, harmonies), its punk‐rock attitude, and its complex uses of rhythms, syncopation, & meter. Mathrock has affinities with post‐rock, although the two are not closely related. Exemplars include Ruins, Slint, Don Caballero, Cheval de Frise, Hella, and TTNG.

Although originally a misnomer — as “mathrock” has no more to do with mathematics than any other style of music — this term is widely recognized to the point that it has terminologic descendants: mathy may be used as an adjective, and the genre of math­core is similarly named, albeit not closely related.

A total blend of metallic + hardcore, a phrase which is synonymous with metalcore. This style emerged ca. 1990 as a fusion of hardcore punk with extreme metal (e.g. death metal), the extremeness of which is a primary point of dif­fer­en­ti­a­tion from other punk–metal fusions like e.g. crossover thrash. Metalcore is also typically distinguished from grindcore and crust punk, as a result of those genres’ independent & earlier inceptions.

Musically, metalcore is defined by its use of primarily unclean vocals borrowing freely from both post‐hardcore & extreme metal styles, its breakdowns, its extensive use of kickdrum & sometimes of blastbeats, its focus on low‐pitched distorted guitar riffs, and its intermingling of pitch‐material régimes from post‐hardcore & extreme metal. Exemplars include Rorschach, Earth Crisis, Deadguy, Converge, and Botch.

As the style diversified, several generally‐recognized subgenres emerged. Mathcore is defined by its jarring rhythms & meters, its use of unusual or dissonant pitch‐material, and its focus on instrumental part­writing. Deathcore is defined by its explicit fusion with death metal, melodic metalcore with melodic death metal (AKA melodeath), and easycore with pop‐punk.

An infusion of “indie rock” into post‐hardcore, so named for its debt to emo­core in particular. Emerged in the mid‐1990s.

Defined by its often melodramatic dynamic contrasts (borrowed from emocore), its ambivalent relationship to traditional well‐tuned & clearly‐pitched vocal styles (in its most extreme manifestations, leading to midwest screamo), and its characteristic “twinkly” guitar parts that combine clean (or mostly clean) electric guitars with open‐voiced arpeggi. Has affinities with mathrock. Exemplars include Sunny Day Real Estate, Cap’n Jazz, Braid, American Football, Mineral, and The Brave Little Abacus.

The term itself is something of a misnomer, as the genre neither originated in, nor is exclusive to, the Midwestern U.S.; nevertheless, some of its exemplars have hailed from there.

The broad tradition of music that emerged at the turn of the 19^th to the 20^th c. in the U.S.A. — but that is now thoroughly global — as an alloy of Tin Pan Alley music, the blues, & local country & folk music traditions, and that was subsequently launched by the advent of radio broadcasting.

Strongly distinguished from pop music, which is a specific (albeit loosely‐defined) genre within popular music.

A subgenre of rock music defined by its explicit abandonment of rock (& generally popular music) song structure, its emphasis on timbre & texture, and its frequently lengthy, meandering, &/or atmospheric compositions that draw focus away from vocals (or lack vocals entirely). Exemplars include Talk Talk, Slint, Tortoise, and Do Make Say Think.

A subgenre of post‐hardcore that emerged in California in the early 1990s, defined by its typically screamed vocal technique, its oblique or abrupt song structures, its melodramatic juxtaposition of heavily‐distorted & dissonant sections with quiet & peaceful sections, and its aggressive tempi that sometimes reach beyond those of its hardcore punk forebears. Exemplars include Portraits of Past, Orchid, Saetia, City of Caterpillar, and Daïtro.

Sometimes referred to by the neologism skramz. The term screamo has been subject to some abuse as a result of its apparent (but false) etymologic suggestion of “any music with screamed or otherwise unclean vocals”.

The Western written music tradition generally considered to have begun some time during the medieval period, and stretching through the present day. Defined musically by its strong focus on pitch‐material; particularly the historic development of, use of, & subsequent reaction against, the tonality of so‐called Common Practice.

Some writers object to the use of the word classical, on account of the Classical period referring more specifically to the period of the Western classical tradition from ca. 1750–1820, and also because Western classical music cannot be “classical” insofar as it continues to be practiced in very modern times. For these reasons, the term Western art music is frequently employed.

However, I make the distinction between the Western classical tradition and the Classical period based partly on capital­ization (of the ⟨c⟩ vs. ⟨C⟩), and partly on the other words used. Moreover, just because something is “classical” — in the context of music, or in any other context — does not imply that it can’t continue to be practiced (or revived, or what have you). I avoid *art music as a term in any context, as the word art here is nonoperative: all (or at least most) music is art, arguably by definition.