---
{
  "layout": "glossary.njk",
  "title": "glossary",
  "curr": "glossary"
}
---

{% glosslist %}
  <dt>AKA</dt>
  <dd>Initialism of <i><b>a</b>lso <b>k</b>nown <b>a</b>s</i>.</dd>

  <dt>c.</dt>
  <dd>Abbreviation of <i><b>c</b>entury</i>.</dd>

  <dt>ca.</dt>
  <dd>Abbreviation of <i><b>c</b>irc<b>a</b></i>.</dd>

  <dt>ff.</dt>
  <dd>Abbreviation meaning &ldquo;and following&rdquo;, typically used for pages. To refer to just one page, <dfn>f.</dfn> is used. In music, this is used for {% gloss "meter", "measures" %}.</dd>
{% endglosslist %}

{% h2 %}Linguistics{% endh2 %}

{% glosslist %}
  <dt>ENE</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/Early_Modern_English"><i><b>E</b>arly <b>N</b>ew <b>E</b>nglish</i></a>.</dd>

  <dt>ME</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/Middle_English"><i><b>M</b>iddle <b>E</b>nglish</i></a>.</dd>

  <dt>NE</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/Modern_English"><i><b>N</b>ew <b>E</b>nglish</i></a>.</dd>

  <dt>NP</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/Noun_phrase"><i><b>n</b>oun <b>p</b>hrase</i></a>.</dd>

  <dt>OE</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/Old_English"><i><b>O</b>ld <b>E</b>nglish</i></a>.</dd>

  <dt>OH</dt>
  <dd>Abbreviation meaning &ldquo;<a href="https://en.wikipedia.org/wiki/Ancient_Greek">Ancient Greek</a>&rdquo;, from <i><b>O</b>ld <a href="https://en.wikipedia.org/wiki/Hellenic_languages"><b>H</b>ellenic</a></i>.</dd>

  <dt>phonetic transcription</dt>
  <dd>
    <p>
      A way of notating how something is pronounced. Transcriptions here adhere closely to the official latest revision of the <a href="https://en.wikipedia.org/wiki/International_Phonetic_Alphabet">International Phonetic Alphabet</a> (<abbr title="International Phonetic Alphabet"><dfn>IPA</dfn></abbr>), but with the addition of characters from the <a href="https://en.wikipedia.org/wiki/Extensions_to_the_International_Phonetic_Alphabet">extIPA</a> as necessary.
    </p>

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

    <dl>
      <dt class="ipa">[&#x22ef;]</dt>
      <dd>Narrow transcription. At the level of actual speech production, <a href="https://en.wikipedia.org/wiki/Idiolect">idiolect</a>, or small <a href="https://en.wikipedia.org/wiki/Variety_(linguistics)">lect</a>.</dd>

      <dt class="ipa">/&#x22ef;/</dt>
      <dd>Broad transcription. At the <a href="https://en.wikipedia.org/wiki/Phoneme">phonemic</a> level.</dd>

      <dt class="ipa">&parsl;&#x22ef;&parsl;</dt>
      <dd>At the <a href="https://en.wikipedia.org/wiki/Morphophonology">morphophonologic</a> or <a href="https://en.wikipedia.org/wiki/Diaphoneme">diaphonemic</a> level.</dd>
    </dl>
  </dd>
{% endglosslist %}

{% h2 %}Mathematics{% endh2 %}

{% glosslist %}
  <dt>duodecimal</dt>
  <dd>
    <p>
      The <a href="https://en.wikipedia.org/wiki/Duodecimal">base-twelve numeral system</a>.
    </p>

    <p>
      The familiar <a href="https://en.wikipedia.org/wiki/Arabic_numerals">Hindu&ndash;Arabic numerals</a> used for <a href="https://en.wikipedia.org/wiki/Decimal">decimal</a> are also used for duodecimal; however, the necessary two additional digits are not always agreed upon. For convenience, the two digits have often been &lang;T, E&rang;, from the English words <i><b>t</b>en</i> and <i><b>e</b>leven</i>; or &lang;A, B&rang;, as in <a href="https://en.wikipedia.org/wiki/Hexadecimal">hexadecimal</a>.
    </p>

    <p>
      Unfortunately, &lang;A, B, E&rang; all overlap with the names for pitches &amp; {% gloss "pitchclasses" %} in music (see: <i>{% gloss "integer notation" %}</i>, for the use of duodecimal), and the use of &lang;T, E&rang; is regrettably language-specific. The use of letters in general is also problematic, causing numbers to be more easily confused with letters or words.
    </p>

    <p>
      For these reasons, I use the {% personage "Pitman", "Sir Isaac Pitman", "https://en.wikipedia.org/wiki/Isaac_Pitman", "Person" %} digits &lang;&#x218a;, &#x218b;&rang;; <code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>218a</code> &amp; <code>U+218b</code>, respectively.
    </p>
  </dd>
{% endglosslist %}

{% h2 %}Music{% endh2 %}

{% glosslist %}
  <dt style="font-style: normal; font-synthesis: none;">&#x2258; (<code>U+2258</code>)</dt>
  <dd>
    <p>
      &ldquo;Corresponds to&rdquo;. Used for connecting a concrete object to its counterpart that&rsquo;s relative to the surrounding context:
    </p>

    <ul>
      <li>In the key of {% m "C" %} major, we have {% m "D" %} &#x2258; {% m "2^" %}. (See: {% gloss "mode" %}.)</li>
      <li>In the key of {% m "C" %} major, we have {% m "D-7", "chord" %} &#x2258; {% m "ii7" %}. (See: {% gloss "Roman numeral analysis" %}.)</li>
    </ul>
  </dd>

  <dt>c-pitch</dt>
  <dd>Abbreviation of <i>{% gloss "contour space", "contour pitch" %}</i>.</dd>

  <dt>c-seg</dt>
  <dd>Abbreviation of <i>{% gloss "contour space", "contour segment" %}</i>.</dd>

  <dt>c-space</dt>
  <dd>Abbreviation of <i>{% gloss "contour space" %}</i>.</dd>

  <dt>collection</dt>
  <dd>
    <p>
      The word <dfn>collection</dfn> 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 <dfn>uniform</dfn> means that the collection&rsquo;s elements are all of the same type):
    </p>

    <table>
      <thead>
        <tr>
          <th scope="col">no&shy;ta&shy;tion</th>
          <th scope="col">col&shy;lec&shy;tion type</th>
          <th scope="col">or&shy;dered</th>
          <th scope="col">du&shy;pli&shy;cates</th>
          <th scope="col">uni&shy;form</th>
          <th scope="col">may con&shy;tain</th>
          <th scope="col">com&shy;ments</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td class="music center">(&#x22ef;)</td>
          <td><a href="https://en.wikipedia.org/wiki/Tuple">tuple</a></td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x274c;</td>
          <td>any&shy;thing</td>
          <td></td>
        </tr>
        <tr>
          <td class="music center">[&#x22ef;]</td>
          <td><a href="https://en.wikipedia.org/wiki/Row_and_column_vectors">row vector, column vector</a>, <a href="https://en.wikipedia.org/wiki/List_(abstract_data_type)">list</a>, <a href="https://en.wikipedia.org/wiki/Sequence">se&shy;quence</a></td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "pc", "pcs" %}, {% gloss "integer notation", "in&shy;te&shy;ger pitch&shy;es" %}, {% gloss "motion", "motions" %}</td>
          <td>Or&shy;der&shy;ing is not nec&shy;es&shy;sar&shy;i&shy;ly tem&shy;po&shy;ral.</td>
        </tr>
        <tr>
          <td class="music center">&lang;&#x22ef;&rang;</td>
          <td>se&shy;quence, vector</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "c-pitch", "c-pitch&shy;es" %} ({% gloss "c-seg" %}), {% gloss "ic", "ics" %} ({% gloss "ic-vector", "ic-vec&shy;tor" %}), notes &amp; rests ({% gloss "rhythm" %}), {% gloss "meter", "me&shy;ters" %} ({% gloss "hypermeter", "hy&shy;per&shy;meter" %})</td>
          <td>C-segs (and in&shy;di&shy;vid&shy;ual c-pitch&shy;es) also end with a sub&shy;script <sub class="music" style="font-weight: 700;">c</sub>.</td>
        </tr>
        <tr>
          <td class="music center">&Lang;&#x22ef;&Rang;</td>
          <td>{% gloss "schema" %}</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "section", "sections" %}</td>
          <td></td>
        </tr>
        <tr>
          <td class="music center">&#x27c5;&#x22ef;&#x27c6;</td>
          <td><a href="https://en.wikipedia.org/wiki/Multiset">bag (AKA <i>mul&shy;ti&shy;set</i>)</a></td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x2705;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "motion", "motions" %}</td>
          <td>Mul&shy;ti&shy;plic&shy;i&shy;ties de&shy;not&shy;ed by su&shy;per&shy;script num&shy;bers.</td>
        </tr>
        <tr>
          <td class="music center">{&#x22ef;}</td>
          <td><a href="https://en.wikipedia.org/wiki/Set_(mathematics)">set</a></td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "pc", "pcs" %}, {% gloss "integer notation", "in&shy;te&shy;ger pitch&shy;es" %}</td>
          <td></td>
        </tr>
        <tr>
          <td class="music center"><span class="piggpar">&#x2045;</span>&#x22ef;<span class="piggpar">&#x2046;</span></td>
          <td>{% gloss "setclass", "set&shy;class" %} (sans {% gloss "inversional equivalence", "in&shy;ver&shy;sion&shy;al equiv&shy;a&shy;lence" %})</td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "pc" %}-sets</td>
          <td></td>
        </tr>
        <tr>
          <td class="music center">&lobrk;&#x22ef;&robrk;</td>
          <td>{% gloss "setclass", "set&shy;class" %} (with {% gloss "inversional equivalence", "in&shy;ver&shy;sion&shy;al equiv&shy;a&shy;lence" %})</td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x274c;</td>
          <td class="center">&#x2705;</td>
          <td>{% gloss "pc" %}-sets</td>
          <td></td>
        </tr>
      </tbody>
    </table>
  </dd>

  <dt>contour space</dt>
  <dd>
    <p>
      A <a href="https://en.wikipedia.org/wiki/Space_(mathematics)">space</a> into which things from another one-dimensional space are mapped, for the purpose of preserving the points&rsquo; order relative to one another, while also abstracting away from exact &ldquo;distances&rdquo;.
    </p>

    <p>
      This notion was originally applied to pitches: in a finite piece of music, a finite number of pitches occur, and they can be <a href="https://en.wikipedia.org/wiki/Well-order">well-ordered</a> <abbr title="with respect to">w.r.t.</abbr> one another in the usual way. We can thus assign the <dfn>contour-pitch</dfn> (abbreviated as <dfn>{% gloss "c-pitch" %}</dfn>) {% m "<0>" %} to the lowest pitch that occurs, the c-pitch {% m "<1>" %} to the second-lowest pitch that occurs, and so on. This allows us to express {% gloss "melodic contour" %} by reducing the pitch of every note in a melody to its corresponding c-pitch &mdash; within the {% gloss "c-space" %} that represents exactly (&amp; only) those pitches that occur within said melody.
    </p>

    <p>
      For example, the melody (all within a single octave) {% m "C--D--F--D--C--F--D--F" %} gets the c-space representation {% m "<01210212>" %}. Such a path through c-space may be called a <dfn>{% gloss "c-seg" %}</dfn>.
    </p>

    <p>
      However, c-spaces can be applied to any number of things that aren&rsquo;t pitches. Even so, in a musical context, the term <i>c-<b>pitch</b></i> is still used to refer to the points in the space.
    </p>

    <p>
      <i>C-space</i> is taken from {% cite "ContourSpace", true %}. However, I don&rsquo;t have access to this book, so I have taken this description from {% cite "StructDist", true %}.
    </p>
  </dd>

  <dt>drum notation</dt>
  <dd>The percussion notation used here is based on {% personage "Audio Graffiti" %}&rsquo;s adaptation of {% cite "StdDrumNotation", true %}, which can be found at: <code><a href="https://web.mit.edu/merolish/Public/drums.pdf">https://web.mit.edu/merolish/Public/drums.pdf</a></code>.</dd>

  <dt>m.</dt>
  <dd>Abbreviation of <i>{% gloss "meter", "measure" %}</i>. Plural <dfn>mm.</dfn>.</dd>

  <dt>percussion notation</dt>
  <dd>See: <i>{% gloss "drum notation" %}</i>.</dd>

  <dt>progression</dt>
  <dd>
    <p>
      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 <a href="https://en.wikipedia.org/wiki/Dash#En_dash">en dashes</a> (<code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>2013</code>). Typical uses include:
    </p>

    <ul>
      <li>{% gloss "chord", "Chord" %} progressions, e.g. {% m "D-7--G7--C" %} {% gloss "U+2258", "&#x2258;" %} {% m "ii7--V7--I" %}.</li>
      <li>Melodies with unspecified rhythm, e.g. {% m "F--F--E--D#--B--C--C" %}.</li>
    </ul>
  </dd>
{% endglosslist %}

{% h3 %}Dynamics{% endh3 %}

{% glosslist %}
  <dt>dist-pitch</dt>
  <dd>A {% gloss "c-pitch" %} within {% gloss "dist-space" %}.</dd>

  <dt>dist-space</dt>
  <dd>{% gloss "contour space", "Contour space" %} as applied to levels of <a href="https://en.wikipedia.org/wiki/Distortion_(music)">distortion</a>; defined in {% cite "StructDist", true %}. A location ({% gloss "c-pitch" %}) within this space is called a {% gloss "dist-pitch" %}.</dd>

  <dt>dynamic range</dt>
  <dd>The range of {% gloss "dynamics" %} between the loudest &amp; softest parts of a piece, typically with consideration for dynamics in between.</dd>

  <dt>dynamics</dt>
  <dd>The &ldquo;loudness&rdquo; or &ldquo;softness&rdquo; of music, both through time, and between different simultaneous parts.</dd>
{% endglosslist %}

{% h3 %}Form &amp; structure{% endh3 %}

{% glosslist %}
  <dt>form</dt>
  <dd>The overall structure of a full musical piece, typically understood in terms of {% gloss "section", "sections" %} and their interrelations.</dd>

  <dt><i lang="fr">petite reprise</i></dt>
  <dd>A {% gloss "reprise" %} that is somehow partial &amp;/or truncated, reproducing only some of the original material &mdash; while still being recognizable.</dd>

  <dt>reprise</dt>
  <dd>{% ipa "en" %}&#x279;&#x26a;&#x2c8;p&#x279;i&#x2d0;z{% endipa %}. The return of a {% gloss "section" %} &mdash; especially {% m "A", "form" %} &mdash; later on in the piece, after one or more intervening sections, and with little (e.g. a change in <a href="https://en.wikipedia.org/wiki/Key_(music)">key</a>) or no variation.</dd>

  <dt>schema</dt>
  <dd>
    <p>
      An outline of a {% gloss "form", "musical form" %} in terms of its {% gloss "section", "sections" %}, with each section represented by an uppercase Latin letter starting from {% m "A", "form" %}.
    </p>

    <p>
      I use <span class="music">&Lang;&#x22ef;&Rang;</span> (<code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>27ea</code>&hellip;<code>U+27eb</code>; &ldquo;mathematical double angle brackets&rdquo;) to delineate schemata or individual sections within them. Sections that are repeated with significant variation get prime symbols, e.g. a variation of {% m "A", "form" %} may be written {% m "A'", "form" %}, another variation may be written {% m "A''", "form" %}, and so on. Different occurences of the same section with no significant variation may be distinguished with subscript numbers, e.g. {% m "A'1BA'2", "form" %} for two instances of {% m "A'", "form" %} separated by an instance of {% m "B", "form" %}.
    </p>
  </dd>

  <dt>section</dt>
  <dd>
    <p>
      A contiguous temporal segment of a musical piece that is demarcated from what comes before &amp; after it by an overall change in the musical materials used. A section generally lasts for numerous {% gloss "meter", "measures" %}, and contains significantly more than one complete phrase.
    </p>

    <p>
      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&rsquo;s sectioning may be captured with a {% gloss "schema" %}.
    </p>
  </dd>

  <dt>through-composition</dt>
  <dd>A {% gloss "form", "musical form" %} of the general {% gloss "schema" %} <span class="music">&Lang;A&ic;B&ic;C&ic;D&ic;E&ic;&#x22ef;&Rang;</span>, with no meaningfully repeated material nor {% gloss "reprise", "reprises" %}.</dd>
{% endglosslist %}

{% h3 %}Meter, rhythm, &amp; timing{% endh3 %}

{% glosslist %}
  <dt>beat</dt>
  <dd>A grouping of one or more contiguous {% gloss "pulse", "pulses" %}; specifically a grouping whose onset is intended to correspond to where a listener might tap their foot. Contiguous beats are grouped by the {% gloss "meter" %}.</dd>

  <dt>counting</dt>
  <dd>
    <p>
      A way of labelling {% gloss "timing", "timings" %} in a {% gloss "meter", "measure" %} at the {% gloss "beat" %} level, and at certain divisions of the beat.
    </p>

    <p>
      The method used here counts the first beat as &ldquo;1&rdquo;, the second beat as &ldquo;2&rdquo;, and so on. Then, the midpoint of each beat is counted as &ldquo;&amp;&rdquo; {% ipa "en" %}&aelig;nd{% endipa %}; for example, the midpoint of the second beat is the &ldquo;&amp; of 2&rdquo;.
    </p>

    <p>
      The point &frac14; of the way through the beat is &ldquo;e&rdquo; {% ipa "en" %}i{% endipa %}, and the point &frac34; of the way through is &ldquo;a&rdquo; {% ipa "en" %}&#x259;{% endipa %}. <a href="https://en.wikipedia.org/wiki/Metre_(music)#Compound_metre">Compound meter</a> and <a href="https://en.wikipedia.org/wiki/Tuplet#Triplet">triplets</a> are less commonly agreed upon, but here I use &ldquo;la&rdquo; {% ipa "en" %}l&#x251;{% endipa %} for the &frac13; point, and &ldquo;li&rdquo; {% ipa "en" %}li{% endipa %} for the &frac23; point.
    </p>
  </dd>

  <dt>hypermeter</dt>
  <dd>
    <p>
      Regular sequencing that occurs above the {% gloss "meter", "metric" %} level; that is, in terms of sequences of measures. A unit of hypermeter is a <dfn>hypermeasure</dfn> (AKA <dfn>hyperbar</dfn>). In this context, the constituent measures of a hypermeasure may be called <dfn>hyperbeats</dfn>.
    </p>

    <p>
      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 &ldquo;<dfn>hyperpulses</dfn>&rdquo; &mdash; although this term is not widely used.
    </p>
  </dd>

  <dt>meter</dt>
  <dd>
    <p>
      A regular sequence of {% gloss "beat", "beats" %} &mdash; typically, but not always, of the same kind &mdash; along with a system of accents; accented beats are <dfn>onbeats</dfn>, and other (unaccented) beats are <dfn>offbeats</dfn>. A unit of meter is a <dfn>measure</dfn> (also called a <dfn>bar</dfn>). Contiguous measures are grouped by {% gloss "hypermeter" %}, if at all. The overall duration of a measure is the meter&rsquo;s <dfn>extent</dfn> (e.g. {% m "4/4" %} and {% m "2/2" %} are <dfn>co&euml;xtensive</dfn>).
    </p>

    <p>
      The use of <a href="https://en.wikipedia.org/wiki/Time_signature">time signatures</a> to denote meters is potentially confusing, as the notation itself only specifies the nominal(!) length of a {% gloss "pulse" %}, and how many nominal pulses there are in each measure. Generally speaking:
    </p>

    <details>
      <summary>Full description of how to conventionally read time signatures as meters</summary>

      <ul>
        <li>1 in the numerator implies no particular internal metric structure: 1&it;&nbsp;measure &equiv; 1&it;&nbsp;onbeat &equiv; 1&it;&nbsp;beat &equiv; 1&it;&nbsp;pulse.</li>
        <li>A positive <a href="https://en.wikipedia.org/wiki/Power_of_two">power of 2</a> (2, 4, 8, etc.) in the numerator implies that there are that many beats per measure (<a href="https://en.wikipedia.org/wiki/Duple_and_quadruple_metre"><dfn>duple meter</dfn>, <dfn>quadruple meter</dfn></a>, <dfn>octuple meter</dfn>, etc.), and that the beat may naturally divide into two pulses (<a href="https://en.wikipedia.org/wiki/Metre_(music)#Simple_metre"><dfn>simple meter</dfn></a>). Then, the odd-numbered beats (the 1<sup>st</sup> beat, 3<sup>rd</sup> beat, etc.) are typically the onbeats.</li>
        <li>3 in the numerator implies that there are 3 beats per measure (<a href="https://en.wikipedia.org/wiki/Triple_metre"><dfn>triple meter</dfn></a>), and that the beat may naturally divide into two pulses (<i>simple meter</i>). Then, the 1<sup>st</sup> beat is generally the sole onbeat.</li>
        <li><math><mn>3</mn><mo>&sdot;</mo><msup><mn>2</mn><mi>n</mi></msup></math> in the numerator, for <math><mi>n</mi><mo>&ge;</mo><mn>1</mn></math> (6, 12, 24, etc.), implies that there are <math><msup><mn>2</mn><mi>n</mi></msup></math> beats per measure (<i>duple meter</i>, <i>quadruple meter</i>, <i>octuple meter</i>, etc.), and so each beat is naturally composed of 3 pulses (<a href="https://en.wikipedia.org/wiki/Metre_(music)#Compound_metre"><dfn>compound meter</dfn></a>). Then, the odd-numbered beats are generally the onbeats.</li>
        <li>Any other 3-<a href="https://en.wikipedia.org/wiki/Smooth_number">smooth</a> number in the numerator (9, 18, 27, etc.) implies <i>compound meter</i> (and so <i>triple meter</i>, <a href="https://en.wikipedia.org/wiki/Sextuple_metre"><dfn>sextuple metre</dfn></a>, <dfn>nonuple meter</dfn>, etc.), with onbeats being of the form <math><mn>1</mn><mo>+</mo><mrow><mn>3</mn><mo>&it;</mo><mi>n</mi></mrow></math>.</li>
        <li>Any other even number <math><mn>2</mn><mo>&it;</mo><mi>n</mi></math> in the numerator (10, 14, 20, etc.) likely implies that there are <math><mi>n</mi></math> beats per measure (<a href="https://en.wikipedia.org/wiki/Quintuple_meter"><dfn>quintuple meter</dfn></a>, <a href="https://en.wikipedia.org/wiki/Septuple_meter"><dfn>septuple meter</dfn></a>, <dfn>decuple meter</dfn>, etc.), and thus <i>simple meter</i>. No particular system of accents is implied.</li>
        <li>Any other single number in the numerator (5, 7, 11, etc.) implies that there are that many beats per measure (<i>quintuple meter</i>, <i>septuple meter</i>, <a href="https://en.wikipedia.org/wiki/Undecuple_meter"><dfn>undecuple meter</dfn></a>, etc.), and presumably implies <i>simple meter</i>. No particular system of accents is implied.</li>
        <li>A sum in the numerator (as in e.g. {% m "3+3+2/8" %}) explicitly divides the measure. Whether this division is in terms of accents (in the example, 8 beats per bar, with the 1<sup>st</sup>, 4<sup>th</sup>, &amp; 7<sup>th</sup> beats accented), or in terms of beats (in the example, 3 beats per bar, with the beats consisting of 3, 3, &amp; 2 pulses, respectively), is ambiguous. Nevertheless, in such cases, the distinction is typically not particularly useful anyway.</li>
      </ul>
    </details>
  </dd>

  <dt>polymeter</dt>
  <dd>
    <p>
      The simultaneous use of two or more distinct {% gloss "meter", "meters" %} such that the meters&rsquo; extents are mutually in<a href="https://en.wikipedia.org/wiki/Divisor">divisible</a>. For example, simultaneous {% m "6/8" %} and {% m "4/4" %} produces polymeter, as 6&times;{% m "n8" %} does not divide 8&times;{% m "n8" %}, nor does 8 divide 6. Simultaneous {% m "6/8" %} and {% m "3/4" %} does <strong>not</strong> produce polymeter, as the two meters are co&euml;xtensive, and thus trivially divide one another &mdash; this would be an example of {% gloss "polyrhythm", "poly<em>rhythm</em>" %}.
    </p>

    <p>
      Note that the notion of &ldquo;polymeter&rdquo; implies a shared stream of {% gloss "pulse", "pulses" %}. When there is no such shared stream, or that stream would be unacceptably fine-grained, then the music may be analyzed as being <a href="https://en.wikipedia.org/wiki/Polytempo"><dfn>polytempic</dfn></a> (=&nbsp;multiple mutually-indivisible tempi), or perhaps as exhibiting both polymeter <em>and</em> polyrhythm simultaneously.
    </p>
  </dd>

  <dt>polyrhythm</dt>
  <dd>
    <p>
      The simultaneous use of two or more distinct {% gloss "meter", "meters" %} such that the meters disagree on where the {% gloss "beat", "beats" %} lie &mdash; &amp; may also disagree on the {% gloss "pulse" %} &mdash; but without being of mutually in<a href="https://en.wikipedia.org/wiki/Divisor">divisible</a> extents. For example, simultaneous {% m "6/8" %} and {% m "3/4" %} produces polyrhythm, as the former divides the meter into two beats {% m "[n4. n4.]" %}, whereas the latter divides it into three beats {% m "[n4 n4 n4]" %}. Simultaneous {% m "5/4" %} and {% m "4/4" %}, however, would instead be analyzed as {% gloss "polymeter", "poly<em>meter</em>" %}.
    </p>

    <p>
      By definition, <a href="https://en.wikipedia.org/wiki/Tuplet">tuplets</a> 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.
    </p>

    <p>
      When the meters&rsquo; extents are mutually indivisible, &amp;/or their pulse streams are more-or-less irreconcilable, the music is likely better analyzed as <a href="https://en.wikipedia.org/wiki/Polytempo"><dfn>polytempic</dfn></a> (=&nbsp;multiple mutually-indivisible tempi), or perhaps as exhibiting both polymeter <em>and</em> polyrhythm simultaneously.
    </p>
  </dd>

  <dt>pulse</dt>
  <dd>
    <p>
      The most basic regular unit of musical {% gloss "timing" %}. Any {% gloss "voice" %} that &mdash; in a given section of music &mdash; has regular timing necessarily has an underlying pulse; however, the notion is abstract enough that &ldquo;<em>the</em> pulse&rdquo; of said voice is not uniquely defined, although reasonable definitions are typically morally equivalent.
    </p>

    <p>
      Not every pulse is actually sounded in some way, thus making it more of an abstract notion. Pulses are often grouped into {% gloss "beat", "beats" %}, albeit not always uniquely. The denominator of a <a href="https://en.wikipedia.org/wiki/Time_signature">time signature</a> specifies the nominal(!) length of a pulse, e.g. the &ldquo;<span class="music"><span class="time-sig-denom">4</span></span>&rdquo; in &ldquo;{% m "3/4" %}&rdquo; implies that the nominal pulse is a quarter-note. For more on time signatures, see {% gloss "meter" %}.
    </p>
  </dd>

  <dt>rhythm</dt>
  <dd>A sequence &mdash; particularly, one of some regularity &amp;/or recurrence &mdash; of {% gloss "timing", "timings" %} that are actually sounded (rather than being notional, as in e.g. {% gloss "meter" %}). The use of rhythm generally implies the existence of an underlying {% gloss "pulse" %}.</dd>

  <dt>syncopation</dt>
  <dd>The use of {% gloss "rhythm", "rhythms" %} &amp; {% gloss "timing", "timings" %} that are unexpected at the {% gloss "meter", "metric" %} &amp;/or {% gloss "beat" %} level.</dd>

  <dt>timing</dt>
  <dd>
    <p>
      As a singular noun, a <dfn>timing</dfn> is a temporal location; an abstract point within a one-dimensional timeline. An event &mdash; e.g. the onset of a note &mdash; that occurs at &ldquo;a certain time&rdquo; has a timing: its &ldquo;certain time&rdquo;!
    </p>

    <p>
      More broadly, the (collective) <dfn>timing</dfn> of some collection of events is the collection of those events&rsquo; timings, considered as a kind of distribution. This leads to notions such as {% gloss "pulse" %} and {% gloss "rhythm" %}.
    </p>
  </dd>
{% endglosslist %}

{% h3 %}Pitch{% endh3 %}

{% glosslist %}
  <dt>12&nbsp;EDO</dt>
  <dd>Abbreviation of <a href="https://en.wikipedia.org/wiki/12_equal_temperament"><i><b>12 e</b>qual <b>d</b>ivisions of the <b>o</b>ctave</i></a>.</dd>

  <dt>added-tone</dt>
  <dd>Any {% gloss "pc" %} that is analyzed as part of a {% gloss "chord" %}, but that is not the 1<sup>st</sup>, 3<sup>rd</sup>, 5<sup>th</sup>, nor 7<sup>th</sup> <a href="https://en.wikipedia.org/wiki/Factor_(chord)">factor</a>. A chord with one or more added-tones is called an <dfn>added-tone chord</dfn>. The term <i>added-tone</i> is exclusively used with reference to <a href="https://en.wikipedia.org/wiki/Tertian">tertian</a> harmony.</dd>

  <dt>chord</dt>
  <dd>A collection of pitches that represents at least two distinct {% gloss "pitchclass", "pitchclasses" %}, and that is thought of as being essentially {% gloss "vertical" %}, even if <em>not necessarily</em> sounded as such (e.g. it may be <a href="https://en.wikipedia.org/wiki/Arpeggio">arpeggiated</a>). For the notation used here for chords, see {% gloss "chord notation", "the entry on chord notation" %}.</dd>

  <dt>chord alteration</dt>
  <dd>
    <p>
      A <a href="https://en.wikipedia.org/wiki/Factor_(chord)">factor</a> of a chord whose quality must be explicitly specified because it is otherwise &ldquo;unexpected&rdquo;. For less exotic chord extensions, see {% gloss "chord extension" %}. In {% gloss "chord notation", "the chord notation used here" %}, the following notations are used to indicate alterations:
    </p>

    <dl>
      <dt style="font-style: normal;">[<i>nothing</i>]</dt>
      <dd>No alterations.</dd>

      <dt class="music">&flat;5</dt>
      <dd>Having a diminished fifth factor, instead of a perfect one.</dd>

      <dt class="music">&sharp;5</dt>
      <dd>Having an augmented fifth factor, instead of a perfect one.</dd>

      <dt class="music">&flat;9</dt>
      <dd>Having a minor ninth factor, instead of a major one.</dd>

      <dt class="music">&sharp;9</dt>
      <dd>Having an augmented ninth factor, instead of a major one.</dd>

      <dt class="music">&sharp;11</dt>
      <dd>Having an augmented eleventh factor, instead of a perfect one.</dd>

      <dt class="music">&flat;13</dt>
      <dd>Having a minor thirteenth factor, instead of a major one.</dd>

      <dt class="music">alt</dt>
      <dd>Shorthand for an <a href="https://en.wikipedia.org/wiki/Altered_chord#Altered_dominant_chord">altered dominant seventh-chord</a> with otherwise unspecified construction. More-or-less any of the above alterations may be applicable, and at least one of them is.</dd>
    </dl>
  </dd>

  <dt>chord extension</dt>
  <dd>
    <p>
      A <a href="https://en.wikipedia.org/wiki/Factor_(chord)">factor</a> of a chord that goes beyond {% gloss "chord quality", "its basic quality" %}, but in a way that is otherwise &ldquo;expected&rdquo;, given its quality. For more exotic extensions, see {% gloss "chord alteration" %}. In {% gloss "chord notation", "the chord notation used here" %}, the following notations are used to indicate extensions:
    </p>

    <dl>
      <dt style="font-style: normal;">[<i>nothing</i>]</dt>
      <dd>No extensions.</dd>

      <dt><span class="music">add2</span>, <span class="music">add4</span></dt>
      <dd>Added major second or perfect fourth factor, respectively, but without the presence of a seventh factor.</dd>

      <dt class="music">6</dt>
      <dd>Added major sixth factor, but without the presence of a seventh factor.</dd>

      <dt class="music">&deg;7</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Diminished_seventh_chord">Fully-diminished seventh-chord</a>, with diminished triad quality &amp; diminished seventh factor.</dd>

      <dt class="music">&#x1d1a9;7</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Half-diminished_seventh_chord">Half-diminished seventh-chord</a>. Has a minor seventh factor, rather than a <a href="https://en.wikipedia.org/wiki/Diminished_seventh_chord">diminished</a> one.</dd>

      <dt class="music">alt7</dt>
      <dd>Shorthand for an <a href="https://en.wikipedia.org/wiki/Altered_chord#Altered_dominant_chord">altered dominant seventh-chord</a> with otherwise unspecified construction. For more on alterations, see {% gloss "chord alteration" %}.</dd>

      <dt class="music">&#x2206;7</dt>
      <dd>Major seventh factor. Depending on the {% gloss "chord quality", "quality" %}, this may be either a <a href="https://en.wikipedia.org/wiki/Major_seventh_chord">major seventh-chord</a> or an <a href="https://en.wikipedia.org/wiki/Augmented_major_seventh_chord">augmented major seventh-chord</a>.</dd>

      <dt class="music">7</dt>
      <dd>By default, the seventh factor is minor.</dd>

      <dt class="music">9</dt>
      <dd>Same as <span class="music">7</span>, but <a href="https://en.wikipedia.org/wiki/Ninth_chord">with a major ninth extension</a>.</dd>

      <dt class="music">11</dt>
      <dd>Same as <span class="music">7</span>, but <a href="https://en.wikipedia.org/wiki/Eleventh_chord">with a perfect eleventh extension</a>.</dd>

      <dt class="music">13</dt>
      <dd>Same as <span class="music">7</span>, but with a major <a href="https://en.wikipedia.org/wiki/Thirteenth">thirteenth</a> extension.</dd>
    </dl>
  </dd>

  <dt>chord inversion</dt>
  <dd>
    <p>
      Which <a href="https://en.wikipedia.org/wiki/Factor_(chord)">factor</a> of a {% gloss "chord" %} is in the bass; that is, lowest in pitch. In {% gloss "chord notation", "the chord notation used here" %}, the following notations are used to indicate inversion:
    </p>

    <dl>
      <dt style="font-style: normal;">[<i>nothing</i>]</dt>
      <dd>The default inversion is <a href="https://en.wikipedia.org/wiki/Root_position">root position</a> (&#x225d;&nbsp;root in the bass).</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">6</sup><span class="inversion-lower"></span></span></dt>
      <dd><a href="https://en.wikipedia.org/wiki/First_inversion">First inversion</a> (&#x225d;&nbsp;third factor in the bass) of a tertian chord with no seventh factor.</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">6</sup><sub class="inversion-lower">5</sub></span></dt>
      <dd>First inversion of a seventh-chord.</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">6</sup><sub class="inversion-lower">4</sub></span></dt>
      <dd><a href="https://en.wikipedia.org/wiki/Second_inversion">Second inversion</a> (&#x225d;&nbsp;fifth factor in the bass) of a tertian chord with no seventh factor.</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">4</sup><sub class="inversion-lower">3</sub></span></dt>
      <dd>Second inversion of a seventh-chord.</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">4</sup><span class="inversion-lower"></span></span></dt>
      <dd>Second inversion of a power-chord.</dd>

      <dt class="music">&#x25cc;<span class="inversion"><sup class="inversion-upper">4</sup><sub class="inversion-lower">2</sub></span></dt>
      <dd><a href="https://en.wikipedia.org/wiki/Third_inversion">Third inversion</a> (&#x225d;&nbsp;seventh factor in the bass).</dd>

      <dt class="music">&#x25cc;/<var>p</var></dt>
      <dd>The pitch <var>p</var> is in the bass.</dd>
    </dl>
  </dd>

  <dt>chord notation</dt>
  <dd>
    <p>
      The name of a {% gloss "chord" %} begins with the name of its <a href="https://en.wikipedia.org/wiki/Root_(chord)">root</a> 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 {% gloss "Roman numeral analysis", "the relevant entry" %}.
    </p>

    <p>
      By default, a named chord is a <a href="https://en.wikipedia.org/wiki/Major_chord">major triad</a> in <a href="https://en.wikipedia.org/wiki/Root_position">root position</a> (e.g. the chord &ldquo;{% m "Bb", "chord" %}&rdquo; is a {% m "Bb" %} major triad with {% m "Bb" %} in the bass). This basis in triads inherently biases the notation toward <a href="https://en.wikipedia.org/wiki/Tertian">tertian</a> constructions, so other notation may be used for other kinds of chords.
    </p>

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

    <ol>
      <li>{% gloss "chord quality", "Quality" %}.</li>
      <li>{% gloss "chord extension", "Extension" %}.</li>
      <li>{% gloss "chord alteration", "Alteration" %}.</li>
      <li>{% gloss "omitted factor", "Omission" %}.</li>
      <li>{% gloss "chord inversion", "Inversion" %}.</li>
    </ol>
  </dd>

  <dt>chord quality</dt>
  <dd>
    <p>
      The most fundamental part of a chord&rsquo;s structure; in <a href="https://en.wikipedia.org/wiki/Tertian">tertian</a> harmony, this is the triad&rsquo;s quality, ignoring other aspects of the chord like e.g. {% gloss "chord extension", "its other factors" %} or its {% gloss "chord inversion", "inversion" %}. In {% gloss "chord notation", "the chord notation used here" %}, the following notations are used to indicate quality:
    </p>

    <dl>
      <dt style="font-style: normal;">[<i>nothing</i>]</dt>
      <dd>The default quality is a <a href="https://en.wikipedia.org/wiki/Major_chord">major triad</a>.</dd>

      <dt class="music">&minus;</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Minor_chord">Minor triad</a>.</dd>

      <dt class="music">&#x229f;</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Added_tone_chord#Mixed_third_chords">Split-third</a> chord: superimposed major &amp; minor triads, resulting in two distinct third factors within the same chord.</dd>

      <dt class="music">+</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Augmented_triad">Augmented triad</a>.</dd>

      <dt class="music">&pm;</dt>
      <dd>Augmented triad with a split third.</dd>

      <dt class="music">&deg;</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Diminished_triad">Diminished triad</a>.</dd>

      <dt class="music">&#x1d1a9;</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Half-diminished_seventh_chord">Half-diminished</a>. A variant of the symbol for diminished triad that implies a minor seventh factor (rather than a <a href="https://en.wikipedia.org/wiki/Diminished_seventh_chord">diminished</a> or missing seventh factor). For more seventh-chords, see {% gloss "chord extension" %}.</dd>

      <dt><span class="music">sus2</span>, <span class="music">sus4</span></dt>
      <dd><a href="https://en.wikipedia.org/wiki/Suspended_chord">Suspended second or fourth chord</a>, respectively.</dd>

      <dt class="music">5</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Power_chord">Power-chord</a>. No third factor, perfect fifth factor.</dd>

      <dt class="music">alt</dt>
      <dd>Shorthand for an <a href="https://en.wikipedia.org/wiki/Altered_chord#Altered_dominant_chord">altered dominant seventh-chord</a> with otherwise unspecified construction. May or may not affect the quality of the chord, as its third &amp; fifth factors may still form a major triad. For more seventh-chords, see {% gloss "chord extension" %}.</dd>
    </dl>
  </dd>

  <dt>chord tone</dt>
  <dd>A pitch sounding concurrently with a {% gloss "chord" %}, which is analyzed as being {% gloss "pitchclass", "equivalent to" %} one of that chord&rsquo;s <a href="https://en.wikipedia.org/wiki/Factor_(chord)">factors</a>. Antonym of <i>{% gloss "non-chord tone" %}</i>.</dd>

  <dt>CT</dt>
  <dd>Initialism of <i>{% gloss "chord tone" %}</i>. Plural <dfn>CTs</dfn>.</dd>

  <dt>functional notation</dt>
  <dd>
    <p>
      A shorthand notation for <a href="https://en.wikipedia.org/wiki/Function_(music)">harmonic function</a>. Uses encircled uppercase Latin letters:
    </p>

    <dl>
      <dt class="sem-i">&#x24c9;</dt>
      <dd>Tonic.</dd>

      <dt class="sem-i">&#x24c8;</dt>
      <dd>Subdominant &amp;/or pre-dominant.</dd>

      <dt class="sem-i">&#x24b9;</dt>
      <dd>Dominant.</dd>

      <dt class="sem-i">&#x24c5;</dt>
      <dd>Used cadentially without having a &ldquo;dominant&rdquo; function. So named for the <a href="https://en.wikipedia.org/wiki/Cadence#Plagal_cadence"><i><b>p</b>lagal cadence</i></a>.</dd>
    </dl>
  </dd>

  <dt>ic</dt>
  <dd>Initialism of <i>{% gloss "intervalclass" %}</i>. Plural <dfn>ics</dfn>.</dd>

  <dt>ic-vector</dt>
  <dd>
    <p>
      Abbreviation of <dfn>{% gloss "intervalclass" %} vector</dfn>. Enumerates how many times each nonzero {% gloss "ic" %} is represented within a {% gloss "setclass" %} &mdash; or more generally, within any arbitrary <a href="https://en.wikipedia.org/wiki/Set_(mathematics)">set</a> of pitches or {% gloss "pitchclass", "pitchclasses" %} &mdash; by counting pairwise. {% gloss "collection", "Notated as" %} a <a href="https://en.wikipedia.org/wiki/Row_and_column_vectors">row vector</a> of six <a href="https://en.wikipedia.org/wiki/Natural_number">natural numbers</a> within <a href="https://en.wikipedia.org/wiki/Bracket#Angle_brackets">angle brackets</a>, representing ics 1 through 6 from left to right.
    </p>

    <p>
      For example, a <a href="https://en.wikipedia.org/wiki/Root_position">root-position</a> <a href="https://en.wikipedia.org/wiki/Major_chord">major triad</a> might be represented in {% gloss "integer notation" %} as {% m "{0,4,7}" %}. The interval between {% m "0", 0 %} &amp; {% m "4", 0 %} represents ic&nbsp;4, between {% m "4", 0 %} &amp; {% m "7", 0 %} represents ic&nbsp;3, and between {% m "0", 0 %} &amp; {% m "7", 0 %} represents ic&nbsp;5. Thus, the ic-vector is {% m "<001110>", "icv" %}. Because a <a href="https://en.wikipedia.org/wiki/Minor_chord">minor triad</a> is {% gloss "inversional equivalence", "the inversion of" %} a major triad, repeating the same analysis with {% m "{0,3,7}" %} results in the same ic-vector, and indeed both are members of the same {% gloss "setclass" %} {% m "3-11" %}. However, in general, two setclasses may have the same ic-vector in spite of being otherwise distinct; this is called the <a href="https://en.wikipedia.org/wiki/Interval_vector#Z-relation"><dfn>Z-relation</dfn></a>.
    </p>

    <p>
      The total number of ics (counting duplicates) is the sum of the ic-vector&rsquo;s entries. In the example, this number is 3, because <math>
        <mrow>
          <mo>(</mo>
          <mfrac linethickness="0">
            <mn>3</mn>
            <mn>2</mn>
          </mfrac>
          <mo>)</mo>
        </mrow>
        <mo>=</mo>
        <mn>3</mn>
      </math>. In general, the number of ics is <math>
        <mrow>
          <mo>(</mo>
          <mfrac linethickness="0">
            <mi>n</mi>
            <mn>2</mn>
          </mfrac>
          <mo>)</mo>
        </mrow>
      </math> (a <a href="https://en.wikipedia.org/wiki/Triangular_number">triangular number</a>), where <math><mi>n</mi></math> is the <a href="https://en.wikipedia.org/wiki/Cardinality">cardinality</a> of a candidate underlying set (<strong>not</strong> setclass) of pitches.
    </p>
  </dd>

  <dt>integer notation</dt>
  <dd>
    <p>
      A way of representing pitches (or {% gloss "pitchclass", "pitchclasses" %}) as numbers. An <i>ad hoc</i> <a href="https://en.wikipedia.org/wiki/Origin_(mathematics)">origin</a> is chosen, and is assigned the number 0. Then, each pitch is assigned a number &mdash; which may be negative in some cases &mdash; equal to its distance, in <a href="https://en.wikipedia.org/wiki/Semitone">semitones</a>, away from the origin.
    </p>

    <p>
      When dealing with <a href="https://en.wikipedia.org/wiki/Natural_number">nonnegative integers</a> less than twelve, {% gloss "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, <code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>2063</code> &ldquo;invisible separator&rdquo; is used. In other cases, <a href="https://en.wikipedia.org/wiki/Decimal">decimal</a> can be assumed.
    </p>
  </dd>

  <dt>interval</dt>
  <dd>
    <p>
      The distance between two pitches, considered in any of various ways. At its most basic, an interval is a ratio between two {% gloss "fundamental", "fundamental frequencies" %} (although some <a href="https://en.wikipedia.org/wiki/Musical_tuning#Tuning_systems">tuning systems</a> have intervals that are <a href="https://en.wikipedia.org/wiki/Irrational_number">mathematically irrational</a>, so this is not true <i>sensu stricto</i>). See <a href="https://en.wikipedia.org/wiki/Interval_(music)">the relevant English Wikipedia article</a>.
    </p>

    <p>
      For ratios, I use the notation <var>n</var>&ratio;<var>d</var> (<code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>2236</code>; &ldquo;ratio&rdquo;). For <a href="https://en.wikipedia.org/wiki/Cent_(music)">cents</a>, I use the unit symbol <span class="music">&cent;</span> (<code>U+00a2</code>; &ldquo;cent sign&rdquo;). For <dfn>named intervals</dfn>, I use the following shorthands:
    </p>

    <dl>
      <dt class="music">P</dt>
      <dd>Perfect. For example, {% m "P1" %} = &ldquo;perfect <a href="https://en.wikipedia.org/wiki/Unison">unison</a>&rdquo; = 1&ratio;1.</dd>

      <dt class="music">m</dt>
      <dd>Minor. For example, {% m "m2" %} = &ldquo;<a href="https://en.wikipedia.org/wiki/Semitone#Minor_second">minor second</a>&rdquo; (in {% gloss "12 EDO", "12&nbsp;EDO" %}: 1&it;&nbsp;<a href="https://en.wikipedia.org/wiki/Semitone">semitone</a>).</dd>

      <dt class="music">M</dt>
      <dd>Major. For example, {% m "M2" %} = &ldquo;<a href="https://en.wikipedia.org/wiki/Major_second">major second</a>&rdquo; (in 12&nbsp;EDO: 2&it;&nbsp;semitones).</dd>

      <dt class="music">d</dt>
      <dd>Diminished. For example, {% m "d4" %} = &ldquo;<a href="https://en.wikipedia.org/wiki/Diminished_fourth">diminished fourth</a>&rdquo; (in 12&nbsp;EDO: 4&it;&nbsp;semitones).</dd>

      <dt class="music">A</dt>
      <dd>Augmented. For example, {% m "A5", "inter" %} = &ldquo;<a href="https://en.wikipedia.org/wiki/Augmented_fifth">augmented fifth</a>&rdquo; (in 12&nbsp;EDO: 8&it;&nbsp;semitones).</dd>

      <dt class="music">TT</dt>
      <dd><a href="https://en.wikipedia.org/wiki/Tritone">Tritone</a> = 6&it;&nbsp;semitones.</dd>
    </dl>
  </dd>

  <dt>intervalclass</dt>
  <dd>
    <p>
      The <a href="https://en.wikipedia.org/wiki/Equivalence_class">equivalence-class</a> of {% gloss "interval", "intervals" %} under both {% gloss "pitchclass", "octave equivalence" %} <em>and</em> {% gloss "inversional equivalence" %}. Expressed in <a href="https://en.wikipedia.org/wiki/Semitone">semitones</a>. Any {% gloss "ic" %} falls within the range <math><mn>0</mn><mo>&le;</mo><mi>ic</mi><mo>&le;</mo><mn>6</mn></math>.
    </p>

    <p>
      For example, in {% gloss "12 EDO", "12&nbsp;EDO" %}, all of the following intervals &mdash; regardless of whether they&rsquo;re ascending or descending &mdash; are members of ic&nbsp;4: {% m "M3" %}, {% m "m6" %}, {% m "d4" %}, {% m "d11" %}, {% m "m13" %}, {% m "M10" %}, etc..
    </p>

    <p>
      See also: <i>{% gloss "ic-vector" %}</i>.
    </p>
  </dd>

  <dt>interval quality</dt>
  <dd>The quality of an {% gloss "interval" %} is perfect, or major, or minor, or augmented, or diminished, etc.; as opposed to its {% gloss "interval quantity", "quantity" %}.</dd>

  <dt>interval quantity</dt>
  <dd>The quantity of an {% gloss "interval" %} is a unison, or a second, or a third, or a fourth, etc.; as opposed to its {% gloss "interval quality", "quality" %}.</dd>

  <dt>inversional equivalence</dt>
  <dd>
    <p>
      Equivalence under <a href="https://en.wikipedia.org/wiki/Inversion_(music)#Inversional_equivalency_and_symmetry">inversion</a> around any axis. Always used in combination with <a href="https://en.wikipedia.org/wiki/Transposition_(music)#Transpositional_equivalence">transpositional equivalence</a>, although the converse is not necessarily true. See also: <i>{% gloss "intervalclass" %}</i>.
    </p>

    <p>
      To get from the <a href="https://en.wikipedia.org/wiki/Set_(music)#Non-serial">prime form</a> of a {% gloss "setclass" %} to the prime form of its inversion (or vice versa), count {% gloss "interval", "intervals" %} from the highest number downward. For example, {% m "3-5A" %} can be read right-to-left as 6&nbsp;&minus;&nbsp;6 = <b>0</b>, 6&nbsp;&minus;&nbsp;1 = <b>5</b>, and 6&nbsp;&minus;&nbsp;0 = <b>6</b>; so its inverse is {% m "3-5B" %}.
    </p>
  </dd>

  <dt>macroharmony</dt>
  <dd>
    <p>
      The collection (or possibly, distribution) of pitches (usually {% gloss "pitchclass", "pitch<em>classes</em>" %} &mdash; see {% gloss "scale", "the entry for <i>scale</i>" %}) used throughout some music, considered at a broader scope than a {% gloss "scale" %}. Essentially a generalization of the traditional notion of <a href="https://en.wikipedia.org/wiki/Key_(music)">key</a>, as well as an alternative way to understand &ldquo;<a href="https://en.wikipedia.org/wiki/Borrowed_chord">modal mixture</a>&rdquo;.
    </p>

    <p>
      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 <a href="https://en.wikipedia.org/wiki/Minor_scale#Natural_minor_scale">natural minor</a>, <a href="https://en.wikipedia.org/wiki/Harmonic_minor_scale">harmonic minor</a>, &amp; <a href="https://en.wikipedia.org/wiki/Jazz_minor_scale">melodic minor</a> co&euml;xist). Another example is the so-called <a href="https://en.wikipedia.org/wiki/Blues_scale"><i>blues &ldquo;scale&rdquo;</i></a>, which is <em>not</em> a scale in the proper sense (although it could be forcibly &amp; artificially turned into one), but <em>can</em> be a meaningful macroharmony in some cases.
    </p>

    <p>
      This term is taken from {% cite "GeomMusic", true %}.
    </p>
  </dd>

  <dt>melodic contour</dt>
  <dd>
    <p>
      An abstraction of melody that considers only its general shape, to the exclusion of exact pitches, exact {% gloss "interval" %} sizes, &amp; {% gloss "timing", "timings" %}.
    </p>

    <p>
      One method of encoding contour is with the <a href="https://en.wikipedia.org/wiki/Parsons_code"><dfn>Parsons code</dfn></a>. Every Parsons code begins with a <code>*</code> representing the first note, which is then followed by one additional character for each successive note in the melody: <code>d</code> &ldquo;down&rdquo; if lower in pitch than the previous note, <code>r</code> &ldquo;repeat&rdquo; if equal, or <code>u</code> &ldquo;up&rdquo; if higher.
    </p>

    <p>
      Another method of encoding contour, which contains more information, is using {% gloss "contour space" %}.
    </p>
  </dd>

  <dt>modal</dt>
  <dd>
    <p>
      Music is described as <dfn>modal</dfn> when its dominant paradigm of arranging {% gloss "pitch-material" %} is one where a particular {% gloss "mode" %} prevails at any given time, with harmonic changes being at the mode-to-mode level, rather than at the {% gloss "chord" %}-to-chord &amp;/or <a href="https://en.wikipedia.org/wiki/Key_(music)">key</a>-to-key level.
    </p>

    <p>
      Indeed, by definition, the term <i>key</i> does not apply (<i>sensu stricto</i>) to modal music. Instead, each mode has its own bespoke &mdash; &amp; typically, weak &mdash; center (or simply &ldquo;{% m "1^" %}&rdquo;), with one mode giving way to the next more-or-less freely, their {% m "1^" %}s being more like <a href="https://en.wikipedia.org/wiki/Root_(chord)"><em>roots</em></a> than like <a href="https://en.wikipedia.org/wiki/Tonality">tonics</a>.
    </p>

    <p>
      Even a piece with no changes of mode may be described as &ldquo;modal&rdquo;, simply because the mode in question is neither <a href="https://en.wikipedia.org/wiki/Ionian_mode">Ionian</a> nor <a href="https://en.wikipedia.org/wiki/Aeolian_mode">Aeolian</a>, &amp;/or because no tonic is established via the relevant idiom originating in {% gloss "Western classical", "Western classical music" %}.
    </p>

    <p>
      In the Occident, explicitly modal music is commonly associated with <a href="https://en.wikipedia.org/wiki/Modal_jazz">modal jazz</a>. However, many other musical traditions &mdash; including several vernacular ones &mdash; can be described similarly.
    </p>
  </dd>

  <dt>mode</dt>
  <dd>
    <p>
      A particular instantiation of a {% gloss "scale" %} that endows it with a privileged member &mdash; a &ldquo;first&rdquo; pitch (which may be a &ldquo;tonic&rdquo; pitch). A scale (assuming symmetry of ascent &amp; descent) with <var>n</var> distinct members has <var>n</var> possible modes.
    </p>

    <p>
      For convenience, however, many scales are thought of as having a &ldquo;default&rdquo; mode that is implicit &mdash; thus blurring the distinction between the scale &amp; its implicit mode. For example, the <a href="https://en.wikipedia.org/wiki/Diatonic_scale">diatonic scale</a> usually defaults to its <a href="https://en.wikipedia.org/wiki/Major_scale">major</a> mode (AKA the modern <a href="https://en.wikipedia.org/wiki/Ionian_mode"><i>Ionian</i> mode</a>).
    </p>

    <p>
      A mode&rsquo;s members may be labelled with numerals that have <a href="https://en.wikipedia.org/wiki/Circumflex">circumflexes</a> upon them: the first <a href="https://en.wikipedia.org/wiki/Degree_(music)"><dfn>degree</dfn></a> of the mode is {% m "1^" %}, the second degree is {% m "2^" %}, and so on. The same notation, &amp; use of the term <i>degree</i>, is also applied to <a href="https://en.wikipedia.org/wiki/Key_(music)">keys</a>, where the term <i>tonic</i> is more meaningful.
    </p>
  </dd>

  <dt>NCT</dt>
  <dd>Initialism of <i>{% gloss "non-chord tone" %}</i>. Plural <dfn>NCTs</dfn>.</dd>

  <dt>non-chord tone</dt>
  <dd>A pitch sounding concurrently with a {% gloss "chord" %}, but that is not a {% gloss "chord tone" %}.</dd>

  <dt>omitted factor</dt>
  <dd>
    <p>
      A factor of a chord that is absent, in spite of its presence being implied by {% gloss "chord quality", "the chord&rsquo;s basic quality" %}.
    </p>

    <p>
      When the fifth factor is implied to be perfect, but is nonetheless absent, and the other expected factors are present, the fifth&rsquo;s omission is usually considered unimportant, and is thus left unspecified. In some cases (especially in <a href="https://en.wikipedia.org/wiki/Jazz">jazz</a>), the root may be omitted, in which case its omission is typically unspecified as well.
    </p>

    <p>
      In {% gloss "chord notation", "the chord notation used here" %}, the following notations are used to specify omissions:
    </p>

    <dl>
      <dt style="font-style: normal;">[<i>nothing</i>]</dt>
      <dd>No omissions (or an unspecified omission of the fifth factor &amp;/or root, if appropriate).</dd>

      <dt class="music">no1</dt>
      <dd>Omitted root.</dd>

      <dt class="music">no3</dt>
      <dd>Omitted third factor.</dd>

      <dt class="music">no5</dt>
      <dd>Omitted fifth factor.</dd>
    </dl>
  </dd>

  <dt>pc</dt>
  <dd>Initialism of <i>{% gloss "pitchclass" %}</i>. Plural <dfn>pcs</dfn>.</dd>

  <dt>pitch-material</dt>
  <dd>The pitches used by a piece of music. Encompasses {% gloss "vertical" %} &amp; {% gloss "horizontal" %} {% gloss "interval", "intervals" %}, {% gloss "pitchclass", "pitchclasses" %}, {% gloss "setclass", "setclasses" %}, {% gloss "chord", "chords" %}, {% gloss "scale", "scales" %}, {% gloss "mode", "modes" %}, {% gloss "macroharmony", "macroharmonies" %}, etc..</dd>

  <dt>pitchclass</dt>
  <dd>The <a href="https://en.wikipedia.org/wiki/Equivalence_class">equivalence-class</a> of all pitches whose {% gloss "fundamental" %} frequencies are related by an integer number of <a href="https://en.wikipedia.org/wiki/Octave">octaves</a> (including 0&it;&nbsp;octaves &mdash; that is, a unison); this equivalence is called <dfn>octave equivalence</dfn>. For example, in {% gloss "12 EDO", "12&nbsp;EDO" %}, {% m "C2" %}, {% m "C5" %}, &amp; {% m "B#3" %} are all members of the pitchclass typically referred to as {% m "C" %}.</dd>

  <dt>RNA</dt>
  <dd>Initialism of <i>{% gloss "Roman numeral analysis" %}</i>.</dd>

  <dt>Roman numeral analysis</dt>
  <dd>
    <p>
      A traditional form of {% gloss "chord" %}wise harmonic analysis that uses <a href="https://en.wikipedia.org/wiki/Roman_numerals">Roman numerals</a> to represent each chord&rsquo;s <a href="https://en.wikipedia.org/wiki/Root_(chord)">root</a> as a {% gloss "mode", "degree" %} of the <a href="https://en.wikipedia.org/wiki/Key_(music)">key</a>. See <a href="https://en.wikipedia.org/wiki/Roman_numeral_analysis">the relevant English Wikipedia article</a>.
    </p>

    <p>
      The notation used here for {% gloss "RNA" %} is based closely upon that specified in {% gloss "chord notation", "the chord notation entry" %}. However, there are some important differences:
    </p>

    <ul>
      <li>Rather than the default {% gloss "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.</li>
      <li>An accidental (<span class="music">&flat;</span> or <span class="music">&sharp;</span>) may appear before the Roman numeral, in which case the root&rsquo;s relationship to the key&rsquo;s tonic is shifted by semitone (down or up, respectively) relative to the {% gloss "interval quality", "major or perfect" %} version of the tonic-to-root ascending {% gloss "interval" %}. In other words, the Roman numerals &amp; their accidentals are <em>always relative to a major key</em> based on the tonic, even when the key isn&rsquo;t major. For example, the diatonic <a href="https://en.wikipedia.org/wiki/Submediant">submediant</a> triad in the key of {% m "A" %} minor is {% m "F", "chord" %} {% gloss "U+2258", "&#x2258;" %} {% m "bVI" %} (<strong>not</strong> {% m "VI" %}, which would be {% m "F#", "chord" %}).</li>
      <li>A slash is used for <a href="https://en.wikipedia.org/wiki/Secondary_chord">applied chords (AKA <i>secondary chords</i>)</a>. This means that {% gloss "chord inversion", "chord inversions" %} that cannot be represented using <a href="https://en.wikipedia.org/wiki/Figured_bass">figured-bass</a>-style notation are either omitted, or else written with a <a href="https://en.wikipedia.org/wiki/Circumflex">circumflexed</a> <a href="https://en.wikipedia.org/wiki/Arabic_numerals">Hindu&ndash;Arabic numeral</a> after the slash, instead of a Roman numeral. For example, in the key of {% m "C" %} major, {% m "D9", "chord" %} &#x2258; {% m "V9/V" %}, but {% m "G9/A" %} &#x2258; {% m "V9/6" %} (or simply {% m "V9" %}).</li>
      <li>The seventh &amp; higher factors &mdash; as well as the fifth factor of a power-chord &mdash; may be given as <a href="https://en.wikipedia.org/wiki/Subscript_and_superscript">superscripts</a>, and may be separated with commas.</li>
    </ul>
  </dd>

  <dt>scale</dt>
  <dd>
    <p>
      A collection of pitches that <em>typically</em> repeats at the octave, and that is contrasted with a {% gloss "chord" %} by usually having at least five members (rather than at least two), and most importantly, by being used as the primary source of {% gloss "horizontal" %} {% gloss "pitch-material" %} (and often also of {% gloss "vertical" %}). The distance from a scale member to the next-higher or next-lower scale member is called a <dfn>step</dfn>.
    </p>

    <p>
      Some scales do not repeat at the octave, leading to the contrast of <dfn>octave-repeating</dfn> vs. <dfn>non-octave-repeating</dfn> scales. Only in the former can the scale members be thought of as {% gloss "pitchclass", "pitchclasses" %}. Moreover, some scales &mdash; most notably <a href="https://en.wikipedia.org/wiki/Minor_scale#Melodic_minor_scale">melodic minor</a> &mdash; may be different depending on whether they are ascended or descended.
    </p>

    <p>
      When a scale has a privileged member &mdash; a &ldquo;first&rdquo; pitch (or &ldquo;tonic&rdquo; pitch) &mdash; it is actually instead a <em>{% gloss "mode" %}</em> of the underlying scale. For convenience, however, many scales are thought of as having a &ldquo;default&rdquo; mode that is implicit.
    </p>
  </dd>

  <dt>setclass</dt>
  <dd>
    <p>
      Abbreviation of <dfn>{% gloss "pc" %}-<a href="https://en.wikipedia.org/wiki/Set_(mathematics)">set</a> class</dfn>, which is in turn an abbreviation of <dfn>{% gloss "pitchclass" %}-set <a href="https://en.wikipedia.org/wiki/Equivalence_class">equivalence-class</a></dfn>: an equivalence-class of pc-sets that are related by <a href="https://en.wikipedia.org/wiki/Transposition_(music)#Transpositional_equivalence">transpositional equivalence</a>, and often also by {% gloss "inversional equivalence" %}. The term <dfn><var>n</var>-setclass</dfn> is used to refer to a setclass whose elements each have <var>n</var> pcs in them (e.g. {% m "3-5" %} is a 3-setclass).
    </p>

    <p>
      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 <span class="music">&lobrk;&#x22ef;&robrk;</span> (<code><a href="https://en.wikipedia.org/wiki/Unicode#Codespace_and_code_points">U+</a>27e6</code>&hellip;<code>U+27e7</code>; &ldquo;mathematical white square brackets&rdquo;, AKA &ldquo;doubled square brackets&rdquo;) to enclose the <a href="https://en.wikipedia.org/wiki/Set_(music)#Non-serial">prime form</a> of the setclass. Moreover, I include the <a href="https://en.wikipedia.org/wiki/Forte_number">Forte number</a> as a subscript immediately after the closing bracket. For example: {% m "3-5" %}.
    </p>

    <p>
      When inversional equivalence is not observed, <span class="music"><span class="piggpar">&#x2045;</span>&#x22ef;<span class="piggpar">&#x2046;</span></span> (<code>U+2045</code>&hellip;<code>U+2046</code>; &ldquo;square brackets with quill&rdquo;, AKA &ldquo;spike parentheses&rdquo; or &ldquo;<i lang="sv">piggparenteser</i>&rdquo;) are used instead. Also in this case, the Forte number for invertible setclasses is suffixed with an &ldquo;<span class="music">A</span>&rdquo; to denote the prime form, and a &ldquo;<span class="music">B</span>&rdquo; for its inversion. For example: {% m "3-5B" %}.
    </p>
  </dd>

  <dt>sonority</dt>
  <dd>The collection of all pitched sounds audible at a particular moment in time. Contrasted with its more inclusive counterpart, the {% gloss "simultaneity" %}. Less abstract than a {% gloss "chord" %}, because it&rsquo;s tied to a particular moment.</dd>
{% endglosslist %}

{% h3 %}Texture{% endh3 %}

{% glosslist %}
  <dt>anticontrary</dt>
  <dd>A type of {% gloss "motion" %} that encompasses both similar &amp; parallel motion. Opposed to contrary motion, to the exclusion of oblique motion (which is neither contrary nor anticontrary).</dd>

  <dt>cosip</dt>
  <dd>{% ipa "en" %}&#x2c8;ko&#x28a;&#x32f;.s&#x26a;p{% endipa %}. Acronym of <i><b>c</b>ontrary, <b>o</b>blique, <b>s</b>imilar, <b>i</b>mperfect parallel, &amp; <b>p</b>erfect parallel</i> {% gloss "motion", "motions" %}.</dd>

  <dt>horizontal</dt>
  <dd>Arranged throughout time, as opposed to {% gloss "vertical", "vertically" %}. Pitchwise, the archetypal horizontal construction is a melody.</dd>

  <dt>homeophony</dt>
  <dd>
    <p>
      {% ipa "en" %}&#x2cc;ho&#x28a;&#x32f;.mi&#x2c8;&#x252;.f&#x259;.ni{% endipa %}. A {% gloss "texture" %} defined in <a href="/post/turtlelephant/#a-texture">this essay</a>. <strong>Not</strong> to be confused with <a href="https://en.wikipedia.org/wiki/Homophony"><i>homophony</i></a>. May alternatively be spelt &lang;homoeophony&rang; or &lang;hom&oelig;ophony&rang;, but here I prefer the spelling &lang;homeophony&rang;.
    </p>
  </dd>

  <dt>motion</dt>
  <dd>
    <p>
      Relative motion between two or more simultaneous pitched {% gloss "voice", "voices" %}, typically understood in terms of <a href="https://en.wikipedia.org/wiki/Contrapuntal_motion">contrapuntal motion</a>. I use the following categories, in generally descending order of independence:
    </p>

    <dl>
      <dt>contrary</dt>
      <dd>The voices move in opposite directions.</dd>

      <dt>oblique</dt>
      <dd>One voice moves while the other does not.</dd>

      <dt>similar</dt>
      <dd>The voices move in the same direction, but by different amounts. In music with meaningful {% gloss "macroharmony" %}, the &ldquo;amounts&rdquo; are typically calculated {% gloss "scale" %}wise; that is, in terms of scale steps.</dd>

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

      <dt>perfect parallel</dt>
      <dd>The voices move in the same direction &amp; by the same amount; furthermore, the starting &amp; ending {% gloss "interval", "intervals" %} are exactly (chromatically) identical, and that {% gloss "interval quality", "interval is perfect" %}.</dd>
    </dl>

    <p>
      By acronymizing each of these five motion types to its initial letter, we get the mnemonic <i>{% gloss "cosip" %}</i>. A simplification of cosip ignores oblique motion, dichotomizing into contrary &amp; <i>{% gloss "anticontrary" %}</i> motion.
    </p>
  </dd>

  <dt>simultaneity</dt>
  <dd>The collection of all sounds &mdash; pitched &amp; unpitched alike &mdash; audible at a particular moment in time. Contrasted with its pitched counterpart, the {% gloss "sonority" %}.</dd>

  <dt>texture</dt>
  <dd>
    <p>
      The way in which {% gloss "voice", "musical voices" %} are combined to produce a segment (small or large) of music.
    </p>

    <p>
      Traditionally focuses on pitched voices, but can generally include any sounds. Common concerns include how voices move relative to one another, which voices are &ldquo;melodic&rdquo; &amp; which are &ldquo;accompaniment&rdquo;, how many voices are present &amp; in what registers, which voices are made to &ldquo;blend&rdquo; together or not, etc..
    </p>
  </dd>

  <dt>vertical</dt>
  <dd>Arranged atemporally &mdash; that is, in terms of sounds occurring simultaneously &mdash; as opposed to {% gloss "horizontal", "horizontally" %}. Pitchwise, the archetypal vertical construction is a {% gloss "chord" %}.</dd>

  <dt>voice</dt>
  <dd>
    <p>
      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.
    </p>

    <p>
      When otherwise distinct voices {% gloss "motion", "move" %} together in lockstep, they lose their aural <dfn>independence</dfn>, thus becoming (at least for that time) effectively a single voice for many purposes.
    </p>

    <p>
      In the particular case of pitched voices, the part played by a single voice is called a <dfn>melody</dfn>. However, in general, a voice needn&rsquo;t be pitched at all.
    </p>
  </dd>
{% endglosslist %}

{% h3 %}Timbre{% endh3 %}

{% glosslist %}
  <dt>attack</dt>
  <dd>The noisy onset of certain {% gloss "timbre", "timbres" %}. Some timbres have little or no attack, others are totally dominated by attack, and yet others are somewhere in between.</dd>

  <dt>fundamental</dt>
  <dd>The lowest-frequency {% gloss "partial" %} of a sound; that is, the 1<sup>st</sup> partial (=&nbsp;1<sup>st</sup> {% gloss "harmonic" %}).</dd>

  <dt>harmonic</dt>
  <dd>
    <p>
      A {% gloss "partial" %} that is a member of the <a href="https://en.wikipedia.org/wiki/Harmonic_series_(music)">harmonic series</a> of the {% gloss "fundamental" %}, meaning that its frequency is an integer multiple of the fundamental frequency.
    </p>

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

  <dt>harmonicity</dt>
  <dd>A property of a sustained sound: that its {% gloss "partial", "partials" %} are predominantly {% gloss "harmonic", "harmonics" %}.</dd>

  <dt>inharmonicity</dt>
  <dd>The opposite of harmonicity: many of the sound&rsquo;s {% gloss "partial", "partials" %} are not {% gloss "harmonic", "harmonics" %}.</dd>

  <dt>partial</dt>
  <dd>
    <p>
      Any <a href="https://en.wikipedia.org/wiki/Frequency">frequency</a> component of a sound, regardless of its {% gloss "harmonicity" %}.
    </p>

    <p>
      Partials are numbered from the 1<sup>st</sup> being the {% gloss "fundamental" %}, the 2<sup>nd</sup> being the next-highest audible partial, and so on, with no regard for harmonicity.
    </p>
  </dd>

  <dt>timbre</dt>
  <dd>
    <p>
      The quality of a sound, as considered apart from any pitch that it might have. A primary point of differentiation between musical instruments.
    </p>

    <p>
      In spite of its foundational nature, timbre &mdash; especially how humans perceive it &mdash; remains poorly understood. Basic explanations appeal to the <a href="https://en.wikipedia.org/wiki/Spectral_density">power spectrum</a> (including {% gloss "partial", "partials" %} {% gloss "harmonicity", "harmonic" %} or not), the nature of a note&rsquo;s {% gloss "attack" %}, and more generally its <a href="https://en.wikipedia.org/wiki/Envelope_(music)">envelope</a>.
    </p>
  </dd>
{% endglosslist %}

{% h3 %}Tradition, genre, &amp; style{% endh3 %}

{% glosslist %}
  <dt>emocore</dt>
  <dd>
    <p>
      A retrospective term (the earliest emocore bands would have been simply &ldquo;hardcore&rdquo;) blending <i><b>emo</b>tive</i> + <i>hard<b>core</b></i>. 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, {% gloss "dynamic range" %}, and introspectively emotional lyrics. Exemplars include {% band "Rites of Spring" %} and {% band "Moss Icon" %}.
    </p>

    <p>
      Although the historic activity of &ldquo;emocore proper&rdquo; was limited &amp; didn&rsquo;t last long, this was arguably because it almost immediately gave rise to manifold new scenes &amp; styles, the umbrella of which is sometimes simply called <dfn>emo</dfn> (although this term has seen mild abuse as a result of its commercialization). Nevertheless, the use of the term <i>emocore</i> always refers <em>strictly</em> to this particular style, rather than any of its more or less distant descendants.
    </p>
  </dd>

  <dt>mathcore</dt>
  <dd>
    <p>
      A subgenre of {% gloss "metalcore" %} that emerged in the 1990s, defined by its jarring {% gloss "rhythm", "rhythms" %} &amp; {% gloss "meter", "meters" %}, use of unusual or dissonant {% gloss "pitch-material" %}, and focus on instrumental partwriting. Some mathcore is also structured around the brief, violent bursts of <a href="https://en.wikipedia.org/wiki/Grindcore">grindcore</a>. Exemplars include {% band "Deadguy" %}, {% band "Botch" %}, {% band "Converge" %}, {% band "The Dillinger Escape Plan" %}, {% band "Coalesce" %}, and {% band "The Sawtooth Grin" %}.
    </p>

    <p>
      Mathcore is primarily dif&shy;fer&shy;en&shy;ti&shy;a&shy;ted from its etymon {% gloss "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&ndash;punk distinctions.
    </p>
  </dd>

  <dt>mathpop</dt>
  <dd>A subgenre of {% gloss "mathrock" %} defined by its unexpected use of features characteristic of pop (or {% gloss "pop-punk" %}) music, especially catchy vocal melodies and identifiable chorus {% gloss "section", "sections" %}. Exemplars include {% band "Heavy Vegetable" %}, {% band "The Dismemberment Plan" %}, {% band "TTNG" %}, {% band "The Brave Little Abacus" %}, {% band "tubelord" %}, and {% band "Feed Me Jack" %}.</dd>

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

    <p>
      Although originally a misnomer &mdash; as &ldquo;mathrock&rdquo; has no more to do with mathematics than any other style of music &mdash; this term is widely recognized to the point that it has terminologic descendants: <dfn>mathy</dfn> may be used as an adjective, and the genre of <i>mathcore</i> is similarly named, albeit not closely related.
    </p>
  </dd>

  <dt>metalcore</dt>
  <dd>
    <p>
      A <a href="https://en.wikipedia.org/wiki/Blend_word#Total_blends">total blend</a> of <i><b>metal</b>lic</i> + <i>hard<b>core</b></i>, a phrase which is synonymous with <i>metalcore</i>. This style emerged ca. <time datetime="1990">1990</time> as a fusion of hardcore punk with extreme metal (e.g. death metal), the extremeness of which is a primary point of dif&shy;fer&shy;en&shy;ti&shy;a&shy;tion from other punk&ndash;metal fusions like e.g. <a href="https://en.wikipedia.org/wiki/Crossover_thrash">crossover thrash</a>. Metalcore is also typically distinguished from <a href="https://en.wikipedia.org/wiki/Grindcore">grindcore</a> and <a href="https://en.wikipedia.org/wiki/Crust_punk">crust punk</a>, as a result of those genres&rsquo; independent &amp; earlier inceptions.
    </p>

    <p>
      Musically, metalcore is defined by its use of primarily unclean vocals borrowing freely from both post-hardcore &amp; extreme metal styles, its <a href="https://en.wikipedia.org/wiki/Breakdown_(music)#Heavy_metal_and_punk_rock">breakdowns</a>, its extensive use of <a href="https://en.wikipedia.org/wiki/Bass_drum">kickdrum</a> &amp; sometimes of <a href="https://en.wikipedia.org/wiki/Blast_beat">blastbeats</a>, its focus on low-pitched distorted guitar riffs, and its intermingling of {% gloss "pitch-material" %} r&eacute;gimes from post-hardcore &amp; extreme metal. Exemplars include {% band "Rorschach" %}, {% band "Earth Crisis" %}, {% band "Deadguy" %}, {% band "Converge" %}, and {% band "Botch" %}.
    </p>

    <p>
      As the style diversified, several generally-recognized subgenres emerged. {% gloss "mathcore", "Mathcore" %} is defined by its jarring {% gloss "rhythm", "rhythms" %} &amp; {% gloss "meter", "meters" %}, use of unusual or dissonant pitch-material, and focus on instrumental partwriting. <dfn>Deathcore</dfn> is defined by its explicit fusion with death metal, <dfn>melodic metalcore</dfn> with melodic death metal (AKA <i><abbr title="melodic death metal">melodeath</abbr></i>), and <dfn>easycore</dfn> with {% gloss "pop-punk" %}.
    </p>
  </dd>

  <dt>midwest emo</dt>
  <dd>
    <p>
      A infusion of &ldquo;indie rock&rdquo; into post-hardcore, so named for its debt to {% gloss "emocore" %} in particular. Emerged in the mid-1990s.
    </p>

    <p>
      Defined by its often melodramatic {% gloss "dynamics", "dynamic" %} contrasts (borrowed from emocore), its ambivalent relationship to traditional well-tuned &amp; clearly-pitched vocal styles (in its most extreme manifestations, leading to {% gloss "midwest screamo" %}), and its characteristic &ldquo;twinkly&rdquo; guitar parts that combine clean (or mostly clean) electric guitars with <a href="https://en.wikipedia.org/wiki/Close_and_open_harmony">open-voiced</a> <a href="https://en.wikipedia.org/wiki/Arpeggio">arpeggi</a>. Has affinities with {% gloss "mathrock" %}. Exemplars include {% band "Sunny Day Real Estate" %}, {% band "Cap&rsquo;n Jazz" %}, {% band "American Football" %}, {% band "Mineral" %}, and {% band "The Brave Little Abacus" %}.
    </p>

    <p>
      The term itself is something of a misnomer, as the genre neither originated in, nor is exclusive to, the <a href="https://en.wikipedia.org/wiki/Midwestern_United_States">Midwestern U.S.</a>; nevertheless, some of its exemplars have hailed from there.
    </p>
  </dd>

  <dt>midwest screamo</dt>
  <dd>The fusion of {% gloss "midwest emo" %} with {% gloss "screamo" %}. Exemplars include {% band "The Little Explorer" %}, {% band "the cabs" %}, {% band "Merchant Ships" %}, {% band "William Bonney" %}, and {% band "Foxtails" %}.</dd>

  <dt>pop-punk</dt>
  <dd>A subgenre of punk that is defined by its focus on the primary thrust of pop music: catchy melodies &amp; singable harmonies. Has considerable overlap with <a href="https://en.wikipedia.org/wiki/Skate_punk">skate-punk</a>; also includes a handful of bands sometimes referred to as &ldquo;emo&rdquo;. Exemplars include {% band "Ramones" %}, {% band "Green Day" %}, {% band "Blink-182" %}, and {% band "My Chemical Romance" %}.</dd>

  <dt>popular music</dt>
  <dd>
    <p>
      The broad tradition of music that emerged at the turn of the 19<sup>th</sup> to the 20<sup>th</sup> <abbr title="century">c.</abbr> in the <abbr title="United States of America">U.S.A.</abbr> &mdash; but that is now thoroughly global &mdash; as an alloy of <a href="https://en.wikipedia.org/wiki/Tin_Pan_Alley">Tin Pan Alley</a> music, <a href="https://en.wikipedia.org/wiki/Blues">the blues</a>, &amp; local <a href="https://en.wikipedia.org/wiki/Country_music">country</a> &amp; <a href="https://en.wikipedia.org/wiki/American_folk_music">folk music traditions</a>, and that was subsequently launched by the advent of radio broadcasting.
    </p>

    <p>
      Strongly distinguished from <dfn>pop music</dfn>, which is a specific (albeit loosely-defined) genre <em>within</em> popular music.
    </p>
  </dd>

  <dt>post-rock</dt>
  <dd>
    <p>
      A subgenre of rock music defined by its explicit abandonment of rock (&amp; generally {% gloss "popular music" %}) {% gloss "form", "song structure" %}, its emphasis on {% gloss "timbre" %} &amp; {% gloss "texture" %}, and its frequently lengthy, meandering, &amp;/or atmospheric compositions that draw focus away from vocals (or lack vocals entirely). Exemplars include {% band "Talk Talk" %}, {% band "Slint" %}, {% band "Tortoise" %}, and {% band "Do Make Say Think" %}.
    </p>
  </dd>

  <dt>powerviolence</dt>
  <dd>An intensification of hardcore punk characterized by even more extreme tempi, breakneck transitions, sporadic use of <a href="https://en.wikipedia.org/wiki/Blast_beat">blastbeats</a>, sporadic slower but bass-heavy breaks, and occasional experimentation with electronics or sampling. Closely related to <a href="https://en.wikipedia.org/wiki/Thrashcore">thrashcore</a>, and fused with <a href="https://en.wikipedia.org/wiki/Metalcore">metalcore</a> to form <a href="https://en.wikipedia.org/wiki/Grindcore">grindcore</a>. Exemplars include {% band "Siege" %}, {% band "Man Is The Bastard" %}, {% band "Charles Bronson" %}, and {% band "Gasp" %}.</dd>

  <dt>PV</dt>
  <dd>Initialism of <i>{% gloss "powerviolence" %}</i>.</dd>

  <dt>screamo</dt>
  <dd>
    <p>
      A subgenre of post-hardcore that emerged in <a href="https://en.wikipedia.org/wiki/California">California</a> in the early 1990s, defined by its typically screamed vocal technique, its oblique or abrupt {% gloss "form", "song structures" %}, its melodramatic juxtaposition of heavily-distorted &amp; dissonant sections with quiet &amp; peaceful sections, and its aggressive tempi that sometimes reach beyond those of its hardcore punk forebears. Exemplars include {% band "Portraits of Past" %}, {% band "Orchid" %}, {% band "Saetia" %}, {% band "City of Caterpillar" %}, and {% band "Da&iuml;tro" %}.
    </p>

    <p>
      Sometimes referred to by the neologism <dfn>skramz</dfn>. The term <i>screamo</i> has been subject to some abuse as a result of its apparent (but false) etymologic suggestion of &ldquo;any music with screamed or otherwise unclean vocals&rdquo;.
    </p>
  </dd>

  <dt>Western classical</dt>
  <dd>
    <p>
      The Western written music tradition generally considered to have begun some time <a href="https://en.wikipedia.org/wiki/Medieval_music">during the medieval period</a>, and stretching through the present day. Defined musically by its strong focus on {% gloss "pitch-material" %}; particularly the historic development of, use of, &amp; subsequent reaction against, the <a href="https://en.wikipedia.org/wiki/Tonality">tonality</a> of so-called <a href="https://en.wikipedia.org/wiki/Common_practice_period">Common Practice</a>.
    </p>

    <p>
      Some writers object to the use of the word <i>classical</i>, on account of the <a href="https://en.wikipedia.org/wiki/Classical_period_(music)"><dfn>Classical period</dfn></a> referring more specifically to the period of the Western classical tradition from <abbr title="circa">ca.</abbr> <time datetime="1750">1750</time>&ndash;<time datetime="1820">1820</time>, and also because Western classical music cannot be &ldquo;classical&rdquo; insofar as it continues to be practiced in very modern times. For these reasons, the term <dfn>Western art music</dfn> is frequently employed.
    </p>

    <p>
      However, I make the distinction between the <i>Western classical tradition</i> and the <i>Classical period</i> based partly on capital&shy;ization (of the &lang;c&rang; vs. &lang;C&rang;), and partly on <a href="https://en.wikipedia.org/wiki/Collocation">the other words used</a>. Moreover, just because something is &ldquo;classical&rdquo; &mdash; in the context of music, or in any other context &mdash; does not imply that it can&rsquo;t continue to be practiced (or revived, or what have you). I avoid *<i>art music</i> as a term in any context, as the word <i>art</i> here is nonoperative: all (or at least most) music is art, arguably by definition.
    </p>
  </dd>
{% endglosslist %}

{% refs %}
