BAIN MUSC 726T
Tuning Theory
Terms & Concepts
Acoustical Society of
America, Standard Term Database {
ASA}
Gann,
Glossary of Tuning Turning Terms (
Gann 2019, 227-282)
Wilson Archives, Glossary {
Anaphoria.com}
- 12-tone equal temperament (12-tet, 12tet, 12-ET, etc.) {WP}
- See also: 12edo {XW};
Equal-step tuning {XW}
- Absolute pitch {WP}
- Acoustics {BA;
HD;
WP} &
Psychoacoustics {WP} (Campbell & Greated 1987; Roederer 2008; Rossing et al. 2002)
- Doty, Musical Ratios {Sound
American 20} (Doty 2018;
Sabat and Schweinitz 2004)
- Beats {WP},
Roughness {WP},
and Critical bandwidth {WP}
- Combination tones {WP}
- Intervals and combined partial tones (Hindemith 1937)
- Periodicity pitch {WP}
- Sabat and Schweinitz, The Extended Helmholtz-Ellis JI Pitch
Notation (Sabat and Schweinitz 2004)
- Region of tolerance
- Tunability
- Ancient Greek music {WP;
Grove},
Gann, pp. 28-32 & Interlude A, pp.
42-47
- Aristides Quintilianus, On Music (3rd-4th c.) {WP;
Grove}
- Aristoxenus, Elements of Harmonics (4th c. BCE) {WP}
- Auditory illusion {WP}
- Auditory scene analysis {WP}
- Barbour, Tuning and Temperament: A Historical Survey
(Barbour 1951)
- Benson, Music: A Mathematical Offering (Benson 2007)
- Barbershop music {WP}
- Blackwood, The Structure of Recognizable Diatonic Tunings
(Blackwood 1985)
- Boethius, Fundamentals of Music (1491) {WP}
(Bower 1989)
- Bohlen-Pierce scale {WP;
XW}
- Bosanquet, An Elementary Treatise on Musical Intervals
and Temperament {IA}
(Bosanquet 1876)
- Carlos
- Alpha scale {XW}
- Beta scale {XW}
- Gamma scale {XW}
- Carrillo, Sondio 13 {WP}
- Chain-of-fifths notation {XW;
Scholtz
1998)
- Comma {BA;
WP}
- Pythagorean comma {WP;
XW}
- Syntonic comma {WP;
XW}
- Diesis {WP;
XW}
- Other commas, discrepancies, and small intervals
- Comma pump {WP}
- Consonance and dissonance {HD}
(Helmholtz 1885; Campbell & Greated 1987)
- Tenney, A History of Consonance and Dissonance {Plainsound.org}
(Tenney 1998)
- Dissonance curve
- Cymatics {WP}
- Chiladni patterns {WP}
- Harmonograph {WP}
- Lissajous figures {WP}
- Various frequency and phase differences {WP}
- Rubens tube {WP}
- Daniélou, Semantic system {WP}
- Diatonic {XW}
- Regular diatonic tuning {WP}
- See also: Moment of symmetry (MOS) scale
- Doty, The Just Intonation Primer (Doty 2002)
- Ear {WP}
- Equal division of the octave (EDO) {XW}
- Some EDOs with close approximations of JI intervals
n = 12, 19, 31, 53
- 19-edo {XW; JI
intervals approx. by 19ed2: XW;
svg}
- 31-edo {XW; JI
intervals approx. by 31ed2: XW;
svg}
- 53-edo {XW; JI
intervals approx. by 53ed2: XW;
svg}
- Some EDOs with close approximations of 3/2 fifths:
n = 12, 17, 19, 24, 29, 31, 36, 41, 43, 48 & 53,
Gann, p. 50
- See also: Scale tree {XW}
- Related topics:
- EDOs to ETs {XW}
- See also Regular temperament theory (RTT)
- Equal temperament (ET) {XW; WP},
see also EDO
- 12-tet/12-edo {XW;
WP;
JI intervals approximated by 12ed2: svg}
- Some twelve-divisible EDOs
- 24-tet/24-edo (1/4 tone) {XW; WP;
JI intervals approx. by 24ed2: svg}
- 36-tet/36-edo (1/6 tone) {XW}
- 48-tet/48-edo (1/8 tone) {XW}
- 72-tet/72-edo (1/12 tone) {XW; WP;
JI intervals approx. by 72ed2: svg}
- 96-tet/96-edo (1/16 tone) {XW;
WP;
JI intervals approx. by 96ed2: svg}
- A few interesting non-twelve-divisible EDOs
- 10-tet/10-edo {XW}
- 17-tet/17-edo {XW;
WP}
- 22-tet/22-edo {XW;
WP}
- Expressive intonation (Sundberg
et al. 1989)
- Generated collection {WP}
- Glissando {WP}
- Harmonic series, or overtone series {WP;
XW; HD;
Teoria}
- Harmonics, partials, and overtones
- Subharmonic series {WP;
XW}
- Harmony of the spheres, see Musica universalis {WP}
- HEJI microtonal notation, see Microtonal notation
- Helmholtz, On
the Sensations of Tone {WP}
(Helmholtz 1885)
- Historically informed performance {WP}
- History of pitch standards {WP;
EMS}
- History of tuning theory
- Barbour, Tuning and Temperament: A Historical Survey
(Barbour 1951)
- Christensen, The Cambridge History of Western Music
Theory (Christensen 2002)
- Doty, The Just Intonation Primer (Doty 2002)
- Gann, The Arithmetic of Listening (Gann 2019)
- Jorgensen, Tuning (Jorgensen
1991)
- Partch, Genesis of a Music (Partch 1974/1949)
- See also:
- Grove Music Online {Grove}
- International Phonetic Alphabet (IPA) {WP}
- Interval {WP}
- Complementary intervals
- Octave complement {XW}
- Fifth complement {XW}
- Etc.
- Gallery
- List of Octave-Reduced Harmonics {XW}
- List of Superparticular intervals {XW}
- Gallery of Just intervals {XW}
- Manuel Op de Coul, List of Intervals {HFF}
- Rational vs. ordinal identification (Milne et al. 2007)
- Octave reduction {XW}
- Harmonic space (Tenney 1983)
- Just intonation (JI) {BA;
HD;
XW} (Doty 2002; Nicholson and Sabat
2018)
- 5-limit, Gann Ch. 5
- Extended just intonation
- 7-limit, 11-limit, 13-limit, and beyond, Gann Ch. 9-11
- Adaptive just intonation {XW}
- Keyboards {WP}
- Halberstadt keyboard (1361) {WP;
Tonalsoft}
- Enharmonic Keyboards {WP}
- Nicola Vicentino (c1511-1575) {WP}
- Archicembalo (1555) {WP},
Gann
Interlude L, pp. 199-204
- Ivo Salzinger
- Tastatura Nova Perfecta (1721)
- Adriaan Fokker (1887-1972)
- Generalized keyboard (1873) {WP}
- R.H.M. Bosanquet (1841-1912) {WP}
- Erv Wilson (1928-2016) {WP}
- Siemen Terpstra (b. 1948) {Website}
- Isomorphic keyboard layouts {WP}
(Milne et al. 2007)
- Johnston notation, see Microtonal notation
- Lambdoma, Pythagorean Lambdoma, or Lambdoma matrix
- Lattice {WP}
- Harmonic lattice diagram {XW}
- Line of fifths
- Lipps-Meyer law {WP}
- Meantone temperament {WP;
XW; Tonalsoft}
- Mersenne, Harmonie Universelle (1639) {WP}
- Microtonal notation
- Microtonality {HFF;
XW}
- Monochord {WP;
Grove}
- Multiphonic {WP}
- Musical tone {WP}
- Pitch
- Intensity
- Duration
- Timbre {BA}
- Music of the spheres, see Musica universalis {WP}
- Number {WP}
- Overtone {BA}
- Partch,Genesis of a Music {WP}
(Partch 1974/1949)
- Pitch notation
- Physics {WP}
& Psychophysics {WP}
- Physiology {WP}
- Plato, Timeaus (c. 360 BC) {WP;
Internet
Classics Archive}
- Prime limit {WP;
XW}, Gann, pp. 36-37
- 3-limit {XW}, Gann, Ch. 4
- 5-limit {XW}, Gann, Ch. 5
- 7-limit {XW}, Gann, Ch. 9
- 11-limit {XW},
Gann, Ch. 10
- 13-limt and beyond, Gann, Ch. 11
- Psychology {WP}
- Ptolemy, Harmonics (2nd c.) {Chicago.edu;
IA},
Gann, Ch. 3, pp.
42-47
- Pythagoras {WP}
- Legend of the harmonious blacksmith {WP}
- Quadrivium: arithmetic, geometry, music, and astronomy {WP}
- Quarter tone {WP}, Gann, Ch. 13 (Skinner
2006)
- Ratio {XW}
- Regular temperament theory (RTT) {XW}, Gann, pp. 214-217
- Paul Erlich, A Middle Path Between Just Intonation and the
Equal Temperaments (Erlich 2015/2004)
{XW}
- Dave Keenan & Douglas Blumeyer's guide to RTT (2021) {XW}
(Keenan and Blumeyer 2024)
- Saggital notation, see Microtonal notation
- Savart {WP}
- Scale {BA;
HD}
- Generated collection {WP}
- MOS scale {XW}
(Milne et al. 2007)
- Period {XW}
- Scale tree {XW}
- Scordatura {WP}
- Solfège {WP}
- Sethares, Tuning, Timbre, Spectrum, Scale (Sethares 2005)
- Spectralism {WP}, Gann, Ch. 13, pp. 214-217
- Stretched tuning {WP}
- Subharmonic series, see Harmonic series
- Superparticular ratio {XW}
- Temperament {WP;
XW}
- Tempered interval (Milne et
al. 2007)
- Meantone {WP;
XW}
- Historical temperaments {XW}
- Temperley, Tuning and Temperament {BA}
- Tetractys {WP}
- Tone circles and spirals
- Fifths circle {WP}
- Spiral of fifths {WP}
- Tonnetz {WP}
- Tuning system {XW}
- Unity (1/1)
- Well Temperament {WP;
XW}, Gann, Ch. 8
- Well-formed scales (Carey and
Clampitt 1989)
- Xenharmonic music {WP}
- Zarlino, De institutione musica (1558) {WP}
- Senario {MTO}
(see Duffin 2006)
For citations, see BAIN MUSC 726T Bibliography | Articles
LEGEND
Britannica Academic {TCL}
HD - Harvard
Dictionary
HFF - Huygens-Fokker
Foundation
IA – Internet
Archive
Ebook Central - ProQuest
Ebook Central
Grove - Grove
Music Online
MTO - Music Theory Online
SA - Sound American
TCL - Thomas Cooper Library, FindIt
@ USC
WP - WP - Wikipedia
XW - Xenharmonic Wiki
Links
Acoustical Society
of America (ASA) – https://acousticalsociety.org
Chromotone.center –
https://chromatone.center
Grove Music Online –
https://www-oxfordmusiconline-com.pallas2.tcl.sc.edu/grovemusic/
Huygens-Fokker
Foundation – https://www.huygens-fokker.org
Monzo, Tonalsoft Encyclopedia of
Microtonal Music Theory – http://www.tonalsoft.com/enc/encyclopedia.aspx
Plainsound Music
Edition: Just Intonation and Microtonal Resources – https://www.plainsound.org
Sabat, Music and Writings – https://masa.plainsound.org
Wilson Archives –
https://www.anaphoria.com/wilson.html
Xenharmonic Wiki (XW) – https://en.xen.wiki/w/Main_Page
Textbook
Gann, Kyle. 2019. The Arithmetic of
Listening: Tuning Theory and History for the Impractical
Musician. Urbana: University of Illinois Press. {GB;
TCL;
Audio
Examples}
References
Updated:
January 19, 2025
