Math and Music, Microtonal Music Theory, Just Intonation

Encyclopedia of Microtonal Music Theory - Index

Symbols Numbers 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

Symbols

¢ / cent

Φ / phi

π / pi

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

19-edo / 19-ET / 19-tET

24-edo (quarter-tone / 1mu / enamu)

31-edo / 31-ET / 31-tET

43-edo (méride)

48-edo (2mu / doamu)

55-edo (Mozart's tuning)

72-edo

88-edo (LucyTuning)

96-edo (3mu / triamu)

144-edo

192-edo (4mu / tetramu)

384-edo (5mu / pentamu)

768-edo (6mu / hexamu)

1536-edo (7mu / heptamu)

3072-edo (8mu / oktamu)

6144-edo (9mu / enneamu)

12288-edo (10mu / dekamu)

24576-edo (11mu / endekamu)

49152-edo (12mu / dodekamu)

98304-edo (13mu / tridekamu)

196608-edo (14mu / tetradekamu)

------------

aristoxenean (temperament family)

articulate

atomic (temperament family)

atonal

augmented / diesic (temperament family)

augmented-prime / aug-1 / #1 / chromatic semitone

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

B

badness

barypyknon / barypykna

basis, lattice: TM-reduced

bass

Beardsley/Pagano 7...17-limit scale

E

echos

EDO (equal divisions of the octave)

EDO 11-odd-limit JI error

eleventh / 11th (interval)

enamu / 1mu

endekamu / 11mu

enharmonic

enharmonic equivalence

ennealimmal (temperament family)

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)

experimental intonation

exponent

extended reference

F

factor

family

farab

fifth / 5th (interval)

finity

flat, b

flu

Fokker periodicity-block

Fokker periodicity-blocks, Gentle introduction (by Paul Erlich)

fourth / 4th (interval)

fraction

framework / harmonic framework

frequency

freshman sum

fundamental

fundamental theorem of arithmetic

G

gamma

gammier

gamut

Ganassi's rational well temperament

Gene Ward Smith's old website

generator

genos

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

GPS, greater perfect system

grad

gradus suavitatis, GS

greater perfect system, GPS

Greek terms, index of

hyperbolaion / hyperboleon

hyperypate / hyperhypate

onomasia kata dynamin

spondeiakos tropos / spondeiazon

spondeiasmos

spondeiazon / spondeiakos tropos

H

heterophony, heterophonic

Hindemith: 5-limit JI derivation of 12-et

homonymous

homophony, homophonic

Hungarian minor scale

hypate

hypaton

hyperbolaion / hyperboleon

hyperenharmonic

hyperhypate / hyperypate

hyperypate / hyperhypate

hypophrygian

Hz, Hertz

i

ratios

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

parts of a tone

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

diatonic intervals

generic interval classes

eighth / octave / 8ve

specific diatonic intervals

augmented

diminished

diminished-4th / dim4 / -4 / b4

diminished-5th / dim5 / -5 / b5

diminished-7th / dim7 / o7

major

M13 / major thirteenth

minor

m13 / minor thirteenth

perfect

perfect-4th / perfect fourth

perfect-5th / perfect fifth

interval of equivalence

intervals, big list of 11-limit

interval matrix

interval symmetric sets, ISS

ISS, interval symmetric sets

J

Johnston notation

Jones, Marc -- definitions by

Jones, Marc -- list of EDOs

jot

just intonation

"just-about" intonation

K

kwazy (temperament family)

M

magic (temperament family)

magnitude

major (mode / scale)

major diatonic intervals

M13 / major thirteenth

map / mapping / prime-mapping

marvel (temperament family)

matrix

maximal evenness

M.D., modal determinant

meantone (temperament family)

meantone error from just intonation

microtone, microtonal

midipu

millioctave / m8ve

minerva (temperament)

minimax

Minkowski-Tenney-reduced lattice basis

minor

minor diatonic intervals

m13 / minor thirteenth

minor mode, minor scale

minor scale, minor mode

miracle (temperament family)

mixolydian

mod, modulo

modal determinant, M.D.

modal octave

mode

modes: the various Western modes

moment of symmetry (MOS)

monochord

Monophony (Partch: capital 'M')

monophony (lower-case 'm'), monophonic

monzisma

monzo

Monzo, Joe (music-theorist)

morion / moria

morphological metric

morphology

MOS (moment of symmetry)

MT-reduced lattice basis

multibreed

multimonzo

multival

music-theory treatises, chronology of

mutation

mutt (temperament family)

Myhill's property

mystery (temperament family)

N

neutral 3rd, neutral third

nexus

ninth / 9th (interval)

O

octachord

octagram

octamu / oktamu / 8mu

oktamu / octamu / 8mu

onomasia kata dynamin

onomasia kata thesin

orwell (temperament family)

otonality

oxypyknon

P

p4, perfect 4th, perfect fourth

p5, perfect 5th, perfect fifth

pentachordal interval, P.I.

perfect 4th, perfect fourth, p4

perfect 5th, perfect fifth, p5

perfect fifth, perfect 5th, p5

perfect fourth, perfect 4th, p4

perfect immutable system (PIS)

Philolaus, tuning theory of

phonic

phrygian

pi / π

P.I., pentachordal interval

PIS (perfect immutable system)

polyphony, polyphonic

Ptolemaic interpretation

Q

R

ratio

ratio-of

real-space

reduced lattice basis, TM

rational intonation (RI)

reduplicated, reduplication

RI (rational intonation)

rms

root

Rothenberg efficiency

Rothenberg redundancy

Rothenberg stability

roughness

S

s (= small)

sagittal staff-notation

schismic tuning / schismatic tuning

schismic / skhismic (temperament family)

schismic major 3rd, skhismic major 3rd

schismina, skhismina

Schlesinger harmoniai

second / 2nd (interval)

semisixths (temperament family)

septimal schisma as xenharmonic bridge?

serialism / 12-tone method

seventh / 7th (interval)

shade, color

sharp, #

simplicity

sixth / 6th (interval)

sixth-tone

skhisma / schisma

skhismic / schismic (temperament family)

skhismic major 3rd

skhismina / schismina

skip

s (small)

Smith, Gene Ward, definitions

Smith's old website, Gene Ward

spondeiakos tropos / spondeiazon

spondeiasmos

spondeiazon / spondeiakos tropos

stellated / stellation

T

taxicab metric

temper

temperament

temperament-unit / tu

temperament ordinaire

Tenney-Minkowski-reduced lattice basis

tenth / 10th (interval)

third / 3rd (interval)

third-tone, 1/3-tone

thirteenth / 13th (interval)

three-quarter-tone

timbre

time-line of music-theorists

tina (unit of interval measurement)

TM-reduced lattice basis

transcendental number

transformation

transpose, transposition

treatises, chronology of music-theory

tu / temperament-unit

tuning by concords

tuning-map

Türk sent

twelfth / 12th (interval)

U

V

W

Wendell well-temperaments

X

xenharmonic

xenharmonic bridge

Y

yamaha-unit

yantra

yantgen (yantra-genus)

Z

Zalzal, wosta of

Encyclopedia of Microtonal Music Theory - Index

Symbols

Numbers

ratios

parts of a tone

generic diatonic interval names

fraction-of-a-comma meantone names

MIDI pitch-bend resolution units

A

B

C

D

E

F

Fokker periodicity-blocks, Gentle introduction (by Paul Erlich)

G

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

Greek terms, index of

H

i

ratios

parts of a tone

diatonic intervals

generic interval classes

specific diatonic intervals

augmented

diminished

major

minor

perfect

J

K

L

M

major diatonic intervals

minor diatonic intervals

modes: the various Western modes

N

O

P

Q

R

S

T

U

V

W

X

Y

Z