Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited

with contributions by:

  • John Chalmers
  • Paul Erlich
  • Charles Lucy
  • Margo Schulter
  • Brian McLaren
  • Kees van Prooijen
  • Kraig Grady
  • Jan Haluska
  • Gene Ward Smith
  • Marc Jones
  • Graham Breed
  • Carl Lumma

  • INDEX: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z, specific ratios, other numbers



    A

    accidental
    accordance
    adaptive JI
    adaptive tuning
    affect
    algebraic number
    alpha
    anomaly
    apotome
    aristoxenean
    augmented 4th


    B

    bass
    beta
    bike-chain
    bingo-card lattice
    blackjack scale
    bridging


    C

    Calculated Optimum Fixed Tuning (COFT)
    canasta scale
    cawapu
    cents,
    Changless System
    characteristic interval, C.I.
    chord
    chordoid
    chromatic
    COFT
    color, shade
    Combination Product Sets (CPS)
    comma
    comma pump
    commatic drift
    complement
    complete
    complex tone
    complexity
    concord, concordance
    conjugate
    conjunct
    constant structure
    consistent
    consonance, consonant
    convex
    cordance
    cps or c.p.s
    critical band


    D

    daseian notation
    decad
    deceptive diatonicity
    decimal notation
    degree
    dekamu, 10mu
    Dekatesserany
    delta
    determinant
    deviation
    diad, dyad
    diamond
    diapason
    diapente
    diaphonic Cycles
    diaschisma, diaskhisma
    diatessaron
    diatonic
    diatonon
    diesis
    diezeugmenon
    diminished 5th
    discord, discordance
    disjunct, disjunction
    dissonance, dissonant
    distributional evenness
    ditone
    ditoniaion
    doamu, 2mu
    dodekamu, 12mu
    dominant
    duodene
    dyad


    E


    echos
    EDO (equally-divided 'octave')
    efficiency, Rothenberg efficiency
    eikosany
    ekbole
    eklysis
    enamu, 1mu
    endekamu, 11mu
    enharmonic
    enharmonicity
    enharmonion
    enneamu, 9mu
    epimere
    epimeris
    epimore
    epimorios
    epimorphic
    epsilon
    equable diatonic
    equal temperament
    equivalence interval
    error
    ET
    Euler-Fokker genus
    Euler genus
    even number
    experimental intonation
    exponent
    extended reference


    F

    factor
    finity
    Fokker Periodicity Block, FPB
    FPB, Fokker Periodicity Block
    fraction
    framework, harmonic framework
    frequency
    fundamental
    Fundamental Theorem of Arithmetic


    G

    gamma
    gammier
    gamut
    generator
    genos
    genus
    geometric complexity
    German "H"
    gipsy scale
    gleichschwebende temperatur
    golden meantone
    GPS, greater perfect system
    grad
    gradus suavitatis, GS
    greater perfect system, GPS
    guide-tone


    H

    the "H" note in German musical notation
    Halberstadt keyboard
    half tone
    harmonia
    harmonic
    harmonic complexity
    harmonic distance
    harmonic entropy
    harmonic series
    harmonicity
    harmonike
    hemiolic
    hemiolion
    heptachord
    heptameride
    heptamu, 7mu
    heptatonic
    heterophony, heterophonic
    hexachord
    hexad
    hexagram
    hexamu, 6mu
    hexany
    hexatonic
    hexenharmonic
    HEWM
    homonymous
    homophony, homophonic
    Hungarian minor scale
    hyperenharmonic


    I

    identity
    incomposite
    indexed genera
    indigestibility
    integer
    intense
    interval
    interval matrix
    interval of equivalence
    interval of periodicity
    interval symmetric sets, ISS
    inversion
    irrational
    ISS, interval symmetric sets


    J

    JI
    Johnston notation
    jot
    just intonation
    just-about intonation


    K

    katapyknosis
    key-signature
    Kirnberger III tuning
    kleisma


    L

    L (= Large)
    lattice diagram
    LCD, lowest common divisor
    LCM, least common multiple
    lowest common divisor, LCD
    least common multiple, LCM
    leimma, limma
    lesser perfect system, LPS
    limit
    limma, leimma
    limmatic
    linear division
    linear temperament
    LPS, lesser perfect system
    LucyTuning
    Lumma impropriety
    Lumma stability


    M

    M2, major 2nd, major second
    m2, minor 2nd, minor second
    M3, major 3rd, major third
    m3, minor 3rd, minor third
    major mode, major scale
    major scale, major mode
    major second, major 2nd, M2
    major third, major 3rd, M3
    major 3rd, major third, M3
    mandala
    Marc Jones (Orphon Soul) definitions
    matrix
    maximal evenness
    member
    M.D., modal determinant
    meantone
    mediant
    mediant averaging
    meride
    mesolabium
    microtemperament
    microtone, microtonal
    midipu
    millioctave
    minor 2nd, m2
    minor 3rd, minor third, m3
    minor mode, minor scale
    minor scale, minor mode
    minor third, minor 3rd, m3
    MIRACLE
    mod, modulo
    modal determinant, M.D.
    modal octave
    mode
    modulation
    monochord
    Monophony (capital 'M')
    monophony (lower-case 'm'), monophonic
    monzisma
    monzo
    morion, moria
    morphological metric
    morphology
    MOS
    moment of symmetry
    mu
    mutation
    Myhill's property


    N

    nanisma
    natural
    neo-Aristoxenian
    neutral 3rd, neutral third
    negative system
    non-just non-equal
    notation
    Numerary Nexus


    O

    octachord
    octagram
    octatonic
    octave, octave-equivalence
    octave complement
    octave species
    Octony
    odd number
    odentity
    oktamu, 8mu
    Orphon Soul (Marc Jones) definitions
    orwell
    otonality


    P

    p4, perfect 4th, perfect fourth
    p5, perfect 5th, perfect fifth
    pain
    parachromatic
    paratactical
    partial
    pentachord
    pentachordal family
    pentachordal interval, P.I.
    pentachromatic
    pentamu, 5mu
    pentatonic
    pentatriadic
    pentenharmonic
    perfect 4th, perfect fourth, p4
    perfect 5th, perfect fifth, p5
    perfect fifth, perfect 5th, p5
    perfect fourth, perfect 4th, p4
    Perfect Immutable System, PIS
    period
    periodicity
    periodicity block
    periodicity interval
    phonic
    pi, π
    P.I., pentachordal interval
    PIS, Perfect Immutable System
    pitch
    pitch-class
    planar temperament
    polychordal
    polymicrotonality
    polyphony, polyphonic
    polytriadic
    poptimal
    positive system
    prime
    prime form
    prime limit
    prime-space
    proper, propriety
    Ps., pseudo
    Ptolemaic interpretation
    pyknon
    Pythagorean
    Pythagorean Comma


    Q

    quartal
    quarter-tone
    quarter-tone staff
    quasi-just
    quintal


    R

    ratio
    rational intonation, RI
    reduplicated, reduplication
    ri
    RI, rational intonation
    root
    Rothenberg efficiency
    Rothenberg redundancy
    Rothenberg stability
    roughness


    S


    s (= small)
    saturated
    savart
    scale
    schisma, skhisma
    schismatic tuning
    schismic, skhismic
    schismic major 3rd, skhismic major 3rd
    Schlesinger harmoniai
    second, 2nd
    secondary ratios
    secor
    semicomma
    semi-tempered
    Semitone
    septendecimal
    septimal
    Septimal Comma
    shade, color
    simplicity
    sixth-tone
    skhisma, schisma
    skhismic, schismic
    skhismic major 3rd
    skip
    s (small)
    soft
    sonance
    span
    specific harmonicity
    spring
    stability
    stella octangula
    Stellated, Stellation
    step
    strictly proper
    strong
    studloco, StudLoco
    subcommatic
    subdominant
    subgenus, subgenera
    subharmonic
    submediant
    subminor 3rd
    subtonic
    superparticular
    supertonic
    syntonic
    syntonic comma
    syntonic comma, tempering out the
    system


    T

    taxicab metric
    temper
    temperament
    temperament ordinaire
    tempering out the syntonic comma
    tertian harmony
    Tetrachord
    Tetrad
    tetradekamu, 14mu
    tetradekany
    tetramu, 4mu
    tetraphonic cycle
    third-tone, 1/3-tone
    three-quarter-tone
    tolerance
    tonal lattice
    tonality
    tonalness
    Tonality Diamond
    tone
    tonic
    torsion
    transcendental number
    transformation
    triad
    triamu, 3mu
    triaphonic cycle
    trichord
    trichromatic
    tricomma
    tridecimal
    tridekamu, 13mu
    trihemitone
    tritone
    tritriadic
    tuning unit, TU


    U

    udentity
    undecimal
    unequal temperaments
    unique
    unison
    unison vector
    unit-proportion, UP
    UP, unit-proportion
    utonality


    V

    val
    vector


    W

    wafso-just
    weak
    well temperament
    Werckmeister temperaments
    whole tone
    wolf
    Wosta of Zalzal


    X

    xenharmonic
    xenharmonic bridge


    Y


    Z


    Zalzal, Wosta of


    specific ratios


    3:2
    4:3
    7:5
    10:7
    27:22
    45:32
    64:45
    81:80
    128:125
    256:243
    2048:2025
    2187:2048
    15625:15552
    32805:32768
    531441:524288
    2109375:2097152


    other numbers

    , cents
    π, pi
    0 modulo n
    1/1
    1/12-tone
    1/3-tone
    1/4-comma meantone
    1/4-tone
    1/6-tone
    1mu, enamu
    10mu, dekamu
    11mu, endekamu
    12edo, 12-EQ
    12mu, dodekamu
    13mu, tridekamu
    14mu, tetradekamu
    144-EDO
    19edo
    2/1
    2/7-comma meantone
    2mu, doamu
    2nd, second
    3/2 complement
    3/4-tone
    3mu, triamu
    3rd-tone
    4/3 Complement
    4mu, tetramu
    5mu, pentamu
    6mu, hexamu
    6th-tone
    7mu, heptamu
    72-EDO
    8mu, oktamu
    8ve
    88CET
    9mu, enneamu



    (to download a zip file of the entire Dictionary, click here)

  • For many more diagrams and explanations of historical tunings, see my book.
  • If you don't understand my theory or the terms I've used, start here
  • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.


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