Terms & Concepts

1. 12-tone equal temperament (12-tet, 12tet, 12-ET, etc.) {WP}
• See also: 12edo {XW}; Equal-step tuning {XW}
  
2. Absolute pitch {WP}
3. Acoustics {BA; HD; WP} & Psychoacoustics {WP}
• Beats {WP}
• Roughness {WP}
• Critical bandwidth {WP}
4. Ancient Greek genera {WP}, Gann, pp. 28-32 & Interlude A, pp. 42-47
• Genus {WP}
• Enharmonic
• Chromatic
• Diatonic
  
• Tetrachords {BA} (Chalmers 2006)
• Pitch nexus: 6:8:9:12
5. Aristoxenus, Elements of Harmonics (4th c. BC) {WP}
6. Auditory illusion {WP}
7. Auditory scene analysis {WP}
8. Barbour, Tuning and Temperament: A Historical Survey (Barbour 1951)
9. Benson, Music: A Mathematical Offering (Benson 2007)
10. Barbershop music {WP}
11. Blackwood, The Structure of Recognizable Diatonic Tunings (Blackwood 1985)
12. Boethius, Fundamentals of Music (1491) {WP}
13. Bohlen-Pierce scale {WP; XW}
• Tritave {XW}
14. Bosanquet, An Elementary Treatise on Musical Intervals and Temperament {IA} (Bosanquet 1876)
    
15. Carlos
• Alpha scale {XW}
• Beta scale {XW}
• Gamma scale {XW}
16. Carrillo, Sondio 13 {WP}
17. Chain-of-fifths notation {XW; Scholtz 1998)
18. Comma {BA; WP}
• Pythagorean comma {WP; XW}
  
• Syntonic comma {WP; XW}
• Diesis {WP; XW}
• Other commas, discrepancies, and small intervals
• Apotome {XW}
19. Comma pump {WP}
    
20. Consonance and dissonance {HD} (Helmholtz 1885; Campbell & Greated 1987)
• Tenney, A History of Consonance and Dissonance {Plainsound.org} (Tenney 1998)
• Doty, The Just Intonation Primer (Doty 2002)
• Dissonance curve
• See Sethares, Relating Tuning and Timbre {Wisc.edu} (Sethares 2005)
21. Cymatics {WP}
• Chiladni patterns {WP}
• Harmonograph {WP}
  
• Lissajous figures {WP}
• Various frequency and phase differences {WP}
• Rubens tube {WP}
  
22. Daniélou, Semantic system {WP}
23. Diatonic {XW}
• Regular diatonic tuning {WP}
• See also: Moment of symmetry (MOS) scale
24. Ear {WP}
25. 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:
• Equal-step tuning {XW}
• EDOs to ETs {XW}
• See also Regular temperament theory (RTT)
26. 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}
27. Expressive intonation (Sundberg et al. 1989)
28. Generated collection {WP}
29. Glissando {WP}
30. Harmonic series, or overtone series {Teoria; HD; WP; XW}
• Harmonics, partials, and overtones
31. Harmony of the spheres, see Musica universalis {WP}
32. HEJI microtonal notation, see Microtonal notation
33. Helmholtz, On the Sensations of Tone {WP} (Helmholtz 1885)
34. Historically informed performance {WP}
35. History of pitch standards {WP; EMS}
36. 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)
• Ch. 1 Introduction, pp. 1-8 {Doty.com}
• 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}
37. International Phonetic Alphabet (IPA) {WP}
38. Interval {WP}
• Complement
• Octave complement {XW}
• Fifth complement {XW}
• 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}
39. 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}
40. 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)
• Fokker organ
• Generalized keyboard (1873) {WP}
• R.H.M. Bosanquet (1841-1912) {WP}
• Erv Wilson (1928-2016) {WP}
• Siemen Terpstra (b. 1948) {Website}
• Microtonal keyboard designs by Erv Wilson at the The Wilson Archives
• Isomorphic keyboard layouts {WP} (Milne et al. 2007)
• See also: Learning Lumatone (LL) {YouTube Playlist}
• Harmonic table {WP; LL}
• Bosanquet-Wilson {LL}
• Wicki-Hayden {WP; LL}
41. Johnston notation, see Microtonal notation
42. Lambdoma, Pythagorean Lambdoma, or Lambdoma matrix
• Lambdoma Matrix {IEEE Xplore} (Hero and Foulkrod 1999)
• n=16, colorized {cymaticmusic.co.uk}
• The Lambdoma and the Farey sequence, see The Wilson Archives
• Farey sequence {WP}
• See also: Stern-Brocot tree {WP}
  
43. Lattice {WP}
• Harmonic lattice diagram {XW}
44. Line of fifths
• Blackwood 1985, p. 49;
  
• Scholtz 1997 {MTO}
• David Temperley, The Line of Fifths (Temperley 2000)
• Moss et al., The line of fifths and the coevolution of tonal pitch classes (Moss et al. 2021)
45. Lipps-Meyer law {WP}
46. Meantone temperament {WP; XW; Tonalsoft}
• 1/4 comma {XW}
• 1/5 comma {XW}
• 1/6 comma {XW}
• 2/7 comma {Tonalsoft}
47. Mersenne, Harmonie Universelle (1639) {WP}
48. Microtonal notation
    
49. Microtonality {HFF; XW}
50. Monochord {WP; Grove}
51. Multiphonic {WP}
52. Musical tone {WP}
• Pitch
• Intensity
• Duration
• Timbre {BA}
53. Music of the spheres, see Musica universalis {WP}
54. Newton's spectrum scale {Gencer 2020}
55. Number {WP}
56. Overtone {BA}
57. Partch,Genesis of a Music {WP} (Partch 1974/1949)
• 43-tone scale {WP}
• Otonality and utonality {WP}
• Tonality diamond {WP; Tonalsoft}
58. Pitch notation
• American Standard Pitch Notation (ASPN) {WP}
• Concert pitch {WP}
• ISO 16:1975 {ISO.org}
• Helmholtz Notation {WP}
• See also: Microtonal notation
59. Physics {WP}
• See also: Psychophysics {WP}
60. Physiology {WP}
61. Plato, Timeaus (c. 360 BC) {WP; Internet Classics Archive}
    
62. 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
63. Psychology {WP}
64. Ptolemy, Harmonics (2nd c.) {Chicago.edu; IA}, Gann, Ch. 3, pp. 42-47
65. Pythagoras {WP}
• Legend of the harmonious blacksmith {WP}
• Flood, Temple of Music {BibliOdyssey}
66. Quadrivium: arithmetic, geometry, music, and astronomy {WP}
    
67. Quarter tone {WP}, Gann, Ch. 13 (Skinner 2006)
• See also: 24edo {XW}
68. Ratio {XW}
• Gann, Just Intonation Explained {KyleGann.com} (Gann 1997)
• Johnston, Rational Structure in Music {Ebook Central} (Johnston 2006)
• Doty, Musical Ratios {Sound American} (Doty 2018)
69. 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)
  
70. Saggital notation, see Microtonal notation
71. Savart {WP}
72. Scale {BA; HD}
• Generated collection {WP}
• MOS scale {XW} (Milne et al. 2007)
• Period {XW}
• Pythagorean scale {WP; XW}, Gann, Ch. 4
• Scale tree {XW}
73. Scordatura {WP}
74. Sensory dissonance curve {Chromotone.center}
    
75. Solfège {WP}
    
76. Sethares, Tuning, Timbre, Spectrum, Scale (Sethares 2005)
• Relating Tuning and Timbre {Wisc.edu}
77. Spectralism {WP}, Gann, Ch. 13, pp. 214-217
78. Stretched tuning {WP}
79. Subharmonic series, or undertone series {WP}
80. Superparticular ratio {XW}
81. Temperament
• Tempered interval (Milne et al. 2007)
• Meantone (see Meantone temperament)
• Historical temperaments {XW}
• Temperly, Tuning and Temperament {BA}
82. Tetractys {WP}
83. Tone circles and spirals
• Chromatic circle {WP}
• 31-edo
• Fifths circle {WP}
• 19-edo
• Spiral of  fifths {WP}
84. Tonnetz {WP}
85. Tuning system {XW}
    
86. Unity (1/1)
87. Well Temperament {WP; XW}, Gann, Ch. 8
88. Well-formed scales (Carey and Clampitt 1989)
89. Xenharmonic music {WP}
90. Zarlino, De institutione musica (1558) {WP}
• Senario {MTO} (see Duffin 2006)

For citations, see BAIN MUSC 726T Bibliography | Articles

BA - Britannica Academic
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

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

References

Updated: November 30, 2025