Math and Music, Microtonal Music Theory, Just Intonation
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Encyclopedia of Microtonal Music Theory
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Math and Music
Microtonal, Just Intonation Theory
Just intonation and microtonal music theory form the basis of all musical scales and musical tuning systems. From the ancient Greeks and Sumerians right through the middle ages, musicians have studied math and music, and they were inseparable topics. Unfortunately, Western music has ignored its own math-and-music foundations for the last 100 years. Composers, theorists, and instrumentalists have completely ignored the fundamental relationship between math and music, and instead have focused on the rote learning of unchangable symbolic rules and musical scales.
Microtonal and just intonation composers and theorists have recently been working to re-establish the connection between math and music through the development of microtonal music theory. This vibrant, growing community of microtonal music theorists has been making tremendous contributions to our knowledge and understanding of a variety of topics in contemporary and historic music theory:
Just intonation scales, chords, and chord progressions
New musical scales and tuning-systems based on the expanded resources of musical pioneers such as Partch, Fokker, and Wilson.
Equal temperaments, unequal temperaments and how they relate to just-intonation music theory
The application of advanced mathematics such as group theory, integer programming, and N-dimensional Grassmann Algebra for the development and categorization of musical scales (tuning systems).
This Encyclopedia of Microtonal Music Theory is a group project and a work in progress. It contains entries, data, clarifications, and corrections from dozens of direct contributors, and includes thousands of direct and indirect contributions. If you would like to contribute to the encyclopedia or ask a question, please don't hesitate to contact us.
We hope you can fulfill your needs for information about just intonation and microtonal music theory right here in the encyclopedia. If there's something you can't find, check out the latest encyclopedia entries and the latest essays on microtonal and just intonation music theory at the inTune news column, right here on the Tonalsoft site.
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¢ / cent
Φ / phi
π / pi
edo
intervals
meantones
MIDI-resolution units (mu)
----------------
a&b temperament [a&b are numbers]
0 modulo n
3/2 complement
4/3 complement
5-limit ET consistency
7-nominal-staff notation
8ve (octave)
8ve-complement
8ve-species
12-edo / 12-EQ / 12-ET / 12-tET
12-edo-staff notation
12-tone method / serialism
88-cet
12-edo / 12-EQ / 12-ET / 12-tET (semitone)
12-edo, Sumerian base-60 approximation to
19-edo / 19-ET / 19-tET (third-tone)
24-edo (quarter-tone / 1mu / enamu)
31-edo / 31-ET / 31-tET (diesis / fifth-tone)
43-edo (méride)
48-edo (2mu / doamu)
55-edo (comma) (Mozart's tuning)
72-edo (morion)
88-edo (LucyTuning)
96-edo (3mu / triamu)
144-edo (farab)
192-edo (4mu / tetramu)
205-edo (mem)
300-edo (savart)
384-edo (5mu / pentamu)
730-edo (woolhouse-unit)
768-edo (6mu / hexamu)
1000-edo (millioctave)
1200-edo (cent)
1536-edo (7mu / heptamu)
2460-edo (mina)
3072-edo (8mu / oktamu)
6144-edo (9mu / enneamu)
8539-edo (tina)
10600-edo (turk-sent)
12288-edo (10mu / dekamu)
24576-edo (11mu / endekamu)
30103-edo (jot)
46032-edo (flu)
49152-edo (12mu / dodekamu)
98304-edo (13mu / tridekamu)
196608-edo (14mu / tetradekamu)
ratios
parts of a tone
diatonic intervals
----------------
big list of 11-limit intervals
1/1 or 1:1 (ratio)
2/1 or 2:1 (ratio)
1/2-tone / semitone
1/3-tone / third-tone
1/4-tone / quarter-tone
1/5-tone / fifth-tone
1/6-tone / sixth-tone
1/8-tone / eighth-tone (2mu)
1/12-tone / twelfth-tone
2/3-tone
3/4-tone
5/6-tone
5/12-tone
7/12-tone
11/12-tone
generic
augmented
diminished
major
minor
perfect
----------------
chromatic-semitone
diatonic-semitone
semitone
tone
2nd / second
3rd / third
4th / fourth
5th / fifth
6th / sixth
7th / seventh
8ve / octave
9th / ninth
10th / tenth
11th / eleventh
12th / twelfth
13th / thirteenth
----------------
eighth / octave / 8ve
eleventh / 11th
fifth / 5th
fourth / 4th
ninth / 9th
octave / 8ve
second / 2nd
seventh / 7th
sixth / 6th
third / 3rd
tenth / 10th
thirteenth / 13th
twelfth / 12th
augmented-prime / aug1 / #1 / chromatic-semitone
augmented-2nd / aug2 / #2 / +2
augmented-4th / aug4 / #4 / +4
augmented-5th / aug5 / #5 / +5
augmented-6th / aug6 / #6 / +6
augmented-9th / aug9 / sharp-9 / #9 / +9
augmented-11th / aug11 / sharp-11 / #11 / +11
diminished-4th / dim4 / -4 / b4
diminished-5th / dim5 / -5 / b5
diminished-7th / dim7 / o7
major-2nd / major second / maj2 / M2
major-3rd / major third / maj3 / M3
major-6th / major sixth / maj6 / M6
major-7th / major seventh / maj7 / M7
major-9th / major ninth / maj9 / M9
major-10th / major tenth / maj10 / M10
major-13th / major thirteenth / maj13 / M13
minor-2nd / minor second / m2 / diatonic-semitone
minor-3rd / minor third / m3 / -3
minor-6th / minor sixth / m6 / -6
minor-7th / minor seventh / m7 / -7
minor-9th / minor ninth / m9 / -9
minor-10th / minor tenth / m10 / -10
minor-13th / minor thirteenth / m13 / flat-13 / b13 / -13
perfect-4th / perfect fourth
perfect-5th / perfect fifth
1/3-comma meantone
1/4-comma meantone
2/7-comma meantone
7/26-comma meantone
3/10-comma meantone (LucyTuning)
1mu / enamu (24-edo)
2mu / doamu (48-edo)
3mu / triamu (96-edo)
4mu / tetramu (192-edo)
5mu / pentamu (384-edo)
6mu / hexamu (768-edo)
7mu / heptamu (1536-edo)
8mu / oktamu (3072-edo)
9mu / enneamu (6144-edo)
10mu / dekamu (12288-edo)
11mu / endekamu (24576-edo)
12mu / dodekamu (49152-edo)
13mu / tridekamu (98304-edo)
14mu / tetradekamu (196608-edo)
a&b temperament [a&b are numbers]
accidental
accordance
adaptive-JI
adaptive-tuning
aeolian
affect
algebraic-number
alpha
ampersand-comma
anomaly
aperiodic
apotome (Greek interval)
apyknon
Arab lute frettings
aristoxenean (temperament family)
Aristoxenos: divisions of the tetrachord
articulate
atomic (temperament family)
atonal
augmented / diesic (temperament family)
augmented-prime / aug-1 / #1 / chromatic semitone (interval)
augmented-2nd / aug-2 / #2 (interval)
augmented-4th / aug-4 / #4 (interval)
augmented-5th / aug-5 / #5 (interval)
augmented-6th / aug-6 / #6 (interval)
augmented-9th / aug-9 / #9 (interval)
augmented-11th / aug-11 / #11 (interval)
axis
badness
barypyknon / barypykna
base-60 approximation to 12-edo
basis, lattice: TM-reduced
bass
Beardsley/Pagano 7...17-limit scale
beta
bibreed / bival
bike-chain
bimonzo / bivector
bingo-card lattice
bipromo
bival
bivector / bimonzo
blackjack (tuning)
Boethius's Greek-letter notation
Bohlen-Pierce Tuning
breed
bridging
brinko
c - cn
co - cz
calculated optimum fixed tuning (COFT)
canasta
cardinality
cawapu
cent / ¢ (unit of interval measurement)
centitone / iring (unit of interval measurement)
chain
changeless-system
characteristic-interval
chord
chroai
chroma
chromatic
chromatic genus
chromatic scale
chromatic-semitone / augmented-prime (interval)
chronology of music-theory treatises
circle-of-5ths
circle-of-degrees
COFT (calculated optimum fixed tuning)
Colonna's Sambuca tuning
color / shade
Coltrane, John: Giant Steps
combination product set (CPS)
comma
comma-pump
commatic drift
common-practice
complement
complete
complexity
complex-tone
concord / concordance
conjugate
conjunct
consistent
consonant / consonance
constant-structure
contortion
contrary-motion
convex
copoptimal
c.p.s. / CPS
critical-band
crumpled-napkin
cycles-per-second
d - dia
dib - dz
daseian (musical notation)
decad / 10ad
deceptive diatonicity
decimal / 10al
degree
dekamu / 10mu (MIDI-unit)
dekatesserany / 14any (CPS)
delta
determinant
deviation
diad / dyad
"dialogus" of pseudo-Odo
diamond
diapason (Greek interval)
diapente (Greek interval)
diaphonic-cycle
diaschisma
diatessaron (Greek interval)
diatonic
diatonic genus
diatonic scale
diatonic semitone (minor-2nd) (interval)
diatonon
diesic (temperament family)
diesis
diezeugmenon (Greek tetrachord)
diminished-5th / dim5 / -5 / b5 (interval)
diminished-7th / dim7 / o7 (interval)
diminished-7th chord / dim7 / o7 chord
discord
disjunct
dissonance
distributional-evenness
ditone
ditoniaion
doamu / 2mu (MIDI-unit)
dodekamu / 12mu (MIDI-unit)
dominant
dominant-7th (dom-7, x7) (chord)
dorian (mode)
Dowland, John: lute fretting
drift
duodene
dyad / diad
dynamin
e - en
eo - ez
echos
EDO (equal division of the "octave")
EDO 11-odd-limit JI error
EDO pitch-height
EDO prime error
efficiency
eigenmonzo
eikosany
ekbole
eklysis
eleventh / 11th (interval)
enamu / 1mu (MIDI-unit)
endekamu / 11mu (MIDI-unit)
enharmonic
enharmonic equivalence
enharmonic genus
enharmonic semitone (interval)
enharmonicity
enharmonion
ennealimmal (temperament family)
enneamu / 9mu (MIDI-unit)
epimere
epimeris
epimore
epimorios
epimorphic
epsilon
equable diatonic
equal temperament (ET)
equal temperaments: gallery of lattices
equitone
equivalence interval
Erlich, Paul; writings by
error
error of EDOs from 11-odd-limit JI
ET (equal temperament)
Euler's music-theory
Euler-Fokker genus
Euler genus
Eulerian scale
even diatonic
even number
experimental intonation
exponent
exponent vector
extended reference
factor
family
farab (unit of interval measurement)
fifth / 5th (interval)
finity
flat, b
flu (unit of interval measurement)
Fokker periodicity-block
Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)
fourth / 4th (interval)
fraction
framework / harmonic framework
frequency
freshman sum
frettings, Arab lute
fundamental
fundamental theorem of arithmetic
part 1
part 2
an excursion
part 3
Greek terms, index of
----------------
gamma
gammier
gamut
Ganassi's rational well temperament
gene
generator
genos
Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)
genus
geometric complexity
German "H" note
Giant Steps (John Coltrane)
gipsy scale
gleichschwebende
golden meantone
GPS, greater perfect system
grad (unit of interval measurement)
gradus suavitatis, GS
Greek-letter notation of Boethius
greater perfect system, GPS
Groven's schismatic temperament
guide-tone
part 1
part 2
an excursion
part 3
a - g
h - m
n - t
apotome
apyknon
chroai
chroma / chromatikon
comma
diapason
diapente
diatessaron
diatonon
diesis
diezeugmenon
ditoniaion
dynamin
echos
ekbole
eklysis
enharmonion
epimeris
epimorios
genos
harmonia
harmonike
hemiolion
hestotes
homalon
hypate
hypaton
hyperbolaion / hyperboleon
hyperypate / hyperhypate
kata dynamin
kata thesin
katapyknosis
kinoumenoi
kithara
leimma / limma
lichanos
lyra / lyre
malakon
mese
meson
mesopyknon
metabole
morion
nete
onomasia kata dynamin
onomasia kata thesin
oxypyknon
paramese
paranete
parhypate
proslambanomenos
pyknon / pyknoma
skhisma
spondeiakos tropos / spondeiazon
spondeiasmos
spondeiazon / spondeiakos tropos
stasimon
synemmenon
syntonon
systema
thesin
tonos
trite
trochos
h - hep
heq - hz
Hába, Alois
Hahn metric
Halberstadt keyboard
half tone (interval)
Hamiltonian scale
Hammond Organ tuning
harmonia
harmonic / harmony
harmonic complexity
harmonic distance
harmonic entropy
harmonic framework
harmonic series
harmonicity
harmonike
harmony / harmonic
hemiolic
hemiolion
heptachord
heptameride (unit of interval measurement)
heptamu / 7mu (MIDI-unit)
heptatonic
Hertz / Hz
hestotes
heterophony, heterophonic
heuristic complexity
heuristic error
HEWM staff-notation
hexachord
hexad
hexagram
hexamu / 6mu (MIDI-unit)
hexany
hexatonic
hexenharmonic
Hindemith: 5-limit JI derivation of 12-et
homonymous
homophony, homophonic
Hucbald's "De harmonica institutione"
Hungarian minor scale
Hurrian Hymn (Monzo reconstruction)
hypate (Greek note)
hypaton (Greek tetrachord)
hyperbolaion / hyperboleon (Greek tetrachord)
hyperenharmonic
hyperhypate / hyperypate
hyperypate / hyperhypate
hypophrygian (Greek mode)
Hz, Hertz
intervals
----------------
ic / interval class
icon
identity
imperfect (interval quality)
improper
incomposite
Indian tuning
indexed genera
indigestibility
integer
intense
interval
interval of equivalence
interval class / ic
intervals, big list of 11-limit
interval matrix
interval-vector
interval symmetric sets, ISS
inversion
ionian
Iranian segah mode
iring / centitone (unit of interval measurement)
irrational
ISS, interval symmetric sets
Ives, Charles: a stretched-'octave' scale
ratios
parts of a tone
diatonic intervals
----------------
big list of 11-limit intervals
1/1 or 1:1 (ratio)
2/1 or 2:1 (ratio)
1/2-tone / semitone
1/3-tone / third-tone
1/4-tone / quarter-tone
1/5-tone / fifth-tone
1/6-tone / sixth-tone
1/8-tone / eighth-tone (2mu)
1/12-tone / twelfth-tone
2/3-tone
3/4-tone
5/6-tone
5/12-tone
7/12-tone
11/12-tone
generic
augmented
diminished
major
minor
perfect
----------------
chromatic-semitone
diatonic-semitone
semitone
tone
2nd / second
3rd / third
4th / fourth
5th / fifth
6th / sixth
7th / seventh
8ve / octave
9th / ninth
10th / tenth
11th / eleventh
12th / twelfth
13th / thirteenth
----------------
eighth / octave / 8ve
eleventh / 11th
fifth / 5th
fourth / 4th
ninth / 9th
octave / 8ve
second / 2nd
seventh / 7th
sixth / 6th
third / 3rd
tenth / 10th
thirteenth / 13th
twelfth / 12th
augmented-prime / #1
augmented-2nd / #2
augmented-4th / #4
augmented-5th / #5
augmented-6th / #6
augmented-9th / #9
augmented-11th / #11
----------------
#1 / augmented-prime
#2 / augmented-2nd
#4 / augmented-4th
#5 / augmented-5th
#6 / augmented-6th
#9 / augmented-9th
#11 / augmented-11th
----------------
sharp 5 / +5
sharp 9 / +9
sharp 11 / +11
diminished-4th / dim4 / -4 / b4
diminished-5th / dim5 / -5 / b5
diminished-7th / dim7 / o7
M2 / major second
M3 / major third
M6 / major sixth
M7 / major seventh
M9 / major ninth
M10 / major tenth
M13 / major thirteenth
----------------
major 2nd / M2
major 3rd / M3
major 6th / M6
major 7th / M7
major 9th / M9
major 10th / M10
major 13th / M13
m2 / minor second
m3 / minor third
m6 / minor sixth
m7 / minor seventh
m9 / minor ninth
m10 / minor tenth
m13 / minor thirteenth
----------------
minor-2nd / m2
minor-3rd / m3
minor-6th / m6
minor-7th / m7
minor-9th / m9
minor-10th / m10
minor-13th / m13
perfect-4th / perfect fourth
perfect-5th / perfect fifth
JI
Johnson, Robert: Drunken Hearted Man tuning
Johnston notation
Jones, Marc -- definitions by
Jones, Marc -- list of EDOs
jot (unit of interval measurement)
just intonation
"just-about" intonation
JustMusic: A New Harmony [Monzo's book]
JustMusic prime-factor notation [Monzo essay]
kata dynamin
katapyknosis
kata thesin
key
key-signature
kHz, kilohertz
kinoumenoi
Kirnberger
kithara
kleisma
kwazy (temperament family)
L (= Large)
lattice basis, TM-reduced
lattice diagram
LCD / lowest common divisor
LCM / least common multiple
least common multiple / LCM
leimma / limma (Greek interval)
lesser perfect system / LPS
lichanos (Greek note)
limit
limma / leimma (Greek interval)
limmatic
linear division
linear temperament
locrian (mode)
logflat badness
lowest common divisor / LCD
LPS / lesser perfect system
LucyTuning
Lumma impropriety
Lumma stability
lute fretting of John Dowland
lute frettings, Arab
lydian (mode)
lyra / lyre
lyre / lyra
ma - me
mi...
mo - my
----------------
major intervals
minor intervals
modes
magic (temperament family)
magnitude
Mahler 7th/1 [Monzo score and analysis]
major mode, major scale
major scale, major mode
malakon
Malcolm monochord
mandala
map / mapping / prime-mapping
Marchetto of Padua's "Fifth-Tones"
marvel (temperament family)
mars-pyramid tunings
matrix
maximal evenness
M.D., modal determinant
meantone (temperament family)
meantone error from just intonation
mediant
mediant averaging
mem (unit of interval measurement)
member
Mercator's comma
meride (unit of interval measurement)
mese (Greek note)
mesolabium
meson (Greek tetrachord)
mesopyknon
metabole
microtemperament
microtone, microtonal
MIDI Tuning Specification, A Gentle Introduction
midipu
millioctave / m8ve (unit of interval measurement)
mina (unit of interval measurement)
minerva (temperament family)
minimax
Minkowski-Tenney-reduced lattice basis
minor
minor mode, minor scale
minor scale, minor mode
miracle (temperament family)
mixolydian (mode)
mod, modulo
modal determinant, M.D.
modal octave
mode
modulation
moment of symmetry (MOS)
monochord
Monophony (Partch: capital 'M')
monophony (lower-case 'm'), monophonic
monzisma
monzo (prime-exponent vector)
Monzo, Joe (music-theorist)
morion / moria (unit of interval measurement)
morphological metric
morphology
MOS (moment of symmetry)
Mozart's tuning: 55-edo
MT-reduced lattice basis
mu
multibreed
multimonzo
multival
music-theory treatises, chronology of
mutation
mutt (temperament family)
Myhill's property
mystery (temperament family)
M2 / major 2nd / maj 2
M3 / major 3rd / maj 3
M6 / major 6th / maj 6
M7 / major 7th / maj 7
M9 / major 9th / maj 9
M10 / major 10th / maj 10
M13 / major 13th / maj 13
----------------
major 2nd / maj 2 / M2
major 3rd / maj 3 / M3
major 6th / maj 6 / M6
major 7th / maj 7 / M7
major 9th / maj 9 / M9
major 10th / maj 10 / M10
major 13th / maj 13 / M13
m2 / minor-2nd / minor second (diatonic semitone)
m3 / minor-3rd / minor third
m6 / minor-6th / minor sixth
m7 / minor-7th / minor seventh
m9 / minor-9th / minor ninth
m10 / minor-10th / minor tenth
m13 / minor-13th / minor thirteenth
----------------
minor-2nd / minor second / m2 (diatonic semitone)
minor-3rd / minor third / m3
minor-6th / minor sixth / m6
minor-7th / minor seventh / m7
minor-9th / minor ninth / m9
minor-10th / minor tenth / m10
minor-13th / minor thirteenth / m13
aeolian
dorian
hypermixolydian
hyperphrygian
hypodorian
hypolydian
hypophrygian
ionian
locrian
lydian
mixolydian
phrygian
nanisma
napkin, crumpled
natural
negative system
neo-Aristoxenian
nete (Greek note)
neutral 3rd, neutral third (interval)
nexus
ninth / 9th (interval)
node
nominal
non-just non-equal
no syntonic comma
notation
numerary nexus
octachord
octagram
octamu / oktamu / 8mu (MIDI-unit)
octatonic
octave (interval)
octave complement
octave-equivalence
octave species
octony / 8ony (CPS)
odd number
odentity
pseudo-Odo's "dialogus"
oktamu / octamu / 8mu (MIDI-unit)
onomasia kata dynamin
onomasia kata thesin
orwell (temperament family)
otonality
oxypyknon
p - pen
peo - pol
pom - pz
p4, perfect 4th, perfect fourth (interval)
p5, perfect 5th, perfect fifth (interval)
pain
pantonal
pantonality of Schoenberg [Monzo essay]
parachromatic
paramese (Greek note)
paranete (Greek note)
paratactical
parhypate (Greek note)
Partch, Harry
partial
patent val
pc / pitch-class
pc-set / pitch-class set
pentachord
pentachordal family
pentachordal interval, P.I.
pentachromatic
pentad
pentamu / 5mu (MIDI-unit)
pentatonic
pentatriadic
pentenharmonic
perfect (interval quality)
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
phi / φ
Philolaus, tuning theory of
phinocchio tuning
phonic
phrygian (mode)
pi / π
P.I., pentachordal interval
PIS (perfect immutable system)
pitch
pitch-class / pc
pitch-class set / pc-set
pivot-ET
planar temperament
polychordal
polymicrotonality
polyphony, polyphonic
polytriadic
Poole just-intonation keyboard
poptimal
positive
prime
prime-exponent vector; monzo
prime-factor notation (JustMusic) [Monzo essay]
prime form
prime limit
prime-mapping
prime-space
promo
proper, propriety
proslambanomenos (Greek note)
Ps., pseudo
pseudo-Odo's "dialogus"
Ptolemaic interpretation
Ptolemy, Claudius
pump / comma-pump
pyknon
pyramid on mars symmetry
pythagorean
pythagorean-comma
quartal
quarter-tone (unit of interval measurement)
quarter-tone staff
quasi-just
quintal
quomma
Ramos's divisions of the monochord
ratio
ratio-of
real-space
reduced lattice basis, TM
rational intonation (RI)
reduplicated, reduplication
ri
RI (rational intonation)
rms
root
Rothenberg efficiency
Rothenberg redundancy
Rothenberg stability
roughness
s - se
sh - sr
st - sz
s (= small)
sagittal staff-notation
Salinas
Sambuca tuning [Colonna]
saturated
savart (unit of interval measurement)
scale
schisma / skhisma
schismic tuning / schismatic tuning
schismic / skhismic (temperament family)
schismic major 3rd, skhismic major 3rd
schismina, skhismina
Schlesinger harmoniai
Schoenberg's pantonality [Monzo essay]
second / 2nd (interval)
secondary ratios
secor
segah mode, Iranian
semicomma
semisixths (temperament family)
semi-tempered
semitone (unit of interval measurement)
septendecimal
septimal
septimal comma
septimal schisma as xenharmonic bridge?
serialism / 12-tone method
sexagesimal approximation to 12-edo
seventh / 7th (interval)
shade, color
sharp, #
simplicity
sixth / 6th (interval)
sixth-tone; 1/6-tone
sk (unit of interval measurement)
skhisma / schisma
skhismic / schismic (temperament family)
skhismic major 3rd
skhismina / schismina
skip
s (small)
Smith, Gene Ward, definitions
soft
sonance
span
specific harmonicity
spondeiakos tropos / spondeiazon
spondeiasmos
spondeiazon / spondeiakos tropos
spring
sruti
sruti tuning [Monzo essay]
stability
staff
standard val
stasimon
stella octangula
stellated / stellation
step
Stopper Tuning
strictly proper
strong
studloco (tuning)
subcommatic
subdominant
subgenus / subgenera
subharmonic
submediant
subminor 3rd (interval)
subtonic
Sumerian tuning [speculations by Monzo]
superparticular
supertonic
synemmenon (Greek tetrachord)
syntonic
syntonic comma
syntonon
system
systema
t - tm
to...
tr - tz
taxicab metric
temper
temperament
temperament-unit / tu (unit of interval measurement)
temperament ordinaire
Tenney-Minkowski-reduced lattice basis
tenth / 10th (interval)
tertian harmony
tetrachord
tetrachord-theory tutorial [by Monzo]
tetrad
tetradekany / 14any
tetradekamu / 14mu (MIDI-unit)
tetramu / 4mu (MIDI-unit)
tetraphonic cycle
thesin
third / 3rd (interval)
third-tone; 1/3-tone
thirteenth / 13th (interval)
three-quarter-tone; 3/4-tone
timbre
time-line of music-theorists
tina (unit of interval measurement)
TM-reduced lattice basis
tolerance
tonality
tonality diamond
tonal lattice
tonalness
tone (interval, and other definitions)
tone of disjunction
tone-space
tonic
Tonnetz
tonos
tonus
TOP (temperament)
torsion
transcendental number
transformation
transpose, transposition
treatises, chronology of music-theory
triad
triamu / 3mu (MIDI-unit)
triaphonic cycle
tricesimoprimal
trichord
trichromatic
tricomma
tridecimal
tridekamu / 13mu (MIDI-unit)
trihemitone (Greek interval)
triprime-comma
trite (Greek note)
tritone
tritriadic
trochos
trumpet, intonation of the valve
tu / temperament-unit (unit of interval measurement)
tuning
tuning by concords
tuning-map
Türk sent (unit of interval measurement)
twelfth / 12th (interval)
units of interval measurement
----------------
udentity
um
undecimal
unequal temperaments
unique
unison
unison vector
unit-proportion (UP)
unit of interval measurement
UP (unit-proportion)
utonality
cent
centitone / iring
diesis
farab
flu
gene
grad
heptameride
iring / centitone
jot
mem
meride
millioctave
mina
morion
quarter-tone
savart
semitone
sk
sruti
tina
tuning-unit
türk-sent
woolhouse-unit
yamaha-unit
val
vanish
vapro
vector
Vicentino's adaptive-JI of 1555
Vienna, A Century of New Music in
vum
wafso-just
waveform
weak
wedge-product
wedgie
weighting
well-temperament
Wendell well-temperaments
Werckmeister tunings
whole-tone (interval)
wolf
Woolhouse: Essay on musical intervals
woolhouse-unit (unit of interval measurement)
wosta of Zalzal
xenharmonic
xenharmonic bridge
yamaha-unit (unit of interval measurement)
yantra
yantgen (yantra-genus)
Zalzal, wosta of
Zarlino's description of 2/7-comma meantone
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