Selected Summary of Music Theorists

Mike Krzyzaniak

Pythagoras 6th Century BC
  • None (Quasi Legendary)
  • believed that music is governed by simple ratios.
  • discovered simple ratios of perfect fourth, fifth and octave.
Aristoxenus 375-? BC
  • Harmonic Elements
  • Rhythmical Elements
  • Discussion of 'Greater Perfect System', Genera, Shades of Tuning;
  • Believed that the ear, not ratios, should be used to divide the intervals.
Ptolemy ?-161 AD
  • The Harmonics
  • Discussion of the Greek modes, 'Greater Perfect System', Genera, and Greek music in general.
  • Believed that music theory could be expressed precisely with mathematics, and that observation should corroborate the theory.
  • Criticizes Pythagoras and and Aristoxenus.
Boethus c. 480-524 AD
  • De istitutione musica
  • Transmission of ancient Greek music theory to the middle ages.
  • Transmission of Ptolemy's ideas, specifically.
  • Music, arithmetic, astronomy and geometry comprise the Quadrivium
  • Uses letters A-P to represent note names.
Anonymous 10th C. AD
  • Alia Musica
  • Misinterpretation of the Greek modes, as described by Boethius, resulting in the Greek names for Ecclesiastic modes.
Early Mediæval
pseudo-Odo of Cluny 878/9-942 AD
  • Enchiridion Musices
  • Intonarium (various attributions)
  • Discussed divion of the monochord.
  • Assigns letter names A-G to the notes, so that successive octaves have the same letter.
Guido d'Arezzo c991-c1033
  • Micrologus
  • Prologus Antiphonani
  • Epistolo de ignoto cantu
  • Invention of solmisation syllables.
  • Codified the use of the musical staff.
  • Expert in training singers.
Anonymous IV 13th C.
  • De Mensuris et Discantu
  • Extensive discussion of the rhythmic modes.
  • Extensive discussion of Notre-Dame polyphony, mentions Leonin and Pèrotin.
pseudo-Hucbald 9th C.
  • Musica Enchiriadis
  • Scolica Enchiriadis
  • Earliest known discussion of polyphony (organum, specifically).
Later Mediæval
Franco of Cologne Late 13th C.
  • Ars Cantus Mensurabilis
  • Introduces the concept of 'Mensurable Music'.
  • Assigned relative durations to notes based on their shape.
  • Introduced rests with unique durations.
  • Defined 'Copula' and 'Hocket'.
Philippe di Vitri 1291-1361
  • Ars Nova
  • Describes the mensuration symbols that became standard.
  • Describes 'perfect' and 'imperfect' tempus.
  • Describes red notes.
  • Attributed composer of 'Roman de Fauvel'
Jean de Muris ca 1300-1351
  • Notitia Artis Musicæ (AKA Summa Musice)
  • Compendium Musicæ Practicæ
  • Musica Speculativa Secundum Boetium
  • Libellus Cantus Mensurabilis
  • Ars Contrapuncti
  • Imperfect division of the breve.
  • Extensive discussion of chromatic alterations in 'Musica Falsa'
Marchetto da Padua Early 14th C.
  • Lucidarium in Arte Musicæ Planæ
  • Pomerium in Arte Musicæ Mensuratæ
  • Extensive discussion of notation particular to Italian Music of the time.
  • Discussion of 'chromaticism', first person to call it that.
  • Division of the whole-tone into five 'equal' parts, whatever that means.
Jacobus of Liège c1260-c1330
  • Speculum Musicæ
  • Tractus de consonantiis musicalibus
  • Tractus de intonatione tonarum
  • Compendium de muisca
  • introduced the term 'Cadence' to describe an imperfect interval moving to a perfect one.
  • ideological debate over the rhythmic innovations of the 'Ars Nova'.
Johannes Tinctoris c1435-1511
  • Liber de Arte Contrapuncti
  • Liber de Nature et Proptietate Tonorum
  • Proportionale Musices
  • Terminorum Musicæ Diffinitorum
  • De Inventione et Usu Musice
  • Speculum Musices (does not survive)
  • Exposito Manus
  • Complexus Effectuum Musices
  • Liber Imperfectionum Notarum Musicalium
  • Tractus de Regulari Valor Notarium
  • Tractus de Notis et Pausis
  • Tractus Alteratonum
  • Scriptum Super Punctis Musicalibus
  • Accurate description of musical techniques of early Franco-Flemish composers.
  • First true European dictionary of musical terms.
  • Considered the fourth a dissonance for purposes of 2-voice counterpoint.
  • Suggests a pervasive use of imperfect consonance.
  • Rules of counterpoint set the tone for later theorists.
Franchino Gafori 1451-1522
  • Theoria Musicæ
  • Practica Musicæ
  • De harmonica instrumentorum opus
  • comissioned translations of Greek sources.
  • Accurately describes music of his contemporaries.
  • Referrd to Giovanni Spataro as 'Vaginarius' (sheath-maker).
Pietro of Aaron c1480-c1550
  • De institutione harmonica (Libri Tre)
  • Il Toscanello in Musica
  • Trattato della natura e cognizione di tutte gli toni di canto figurato
  • Lucidario in musica
  • Compendiolo de molti dubbi, secreti, et sentenze intorno al canto fermo, et figurato.
  • Thinks that composers should notate all accidentals and use uniform key signatures.
  • Describes the use of ♭ to avoid melodic tritones, even when not written.
  • Mentions tuning 5ths flat to obtain puer thirds.
Heinrich Glarean 1488-1563
  • Isagoge in musicen
  • Dodecachordon
  • Musicæ epitome sive conpendium ex Glareani Dodecachordo
  • Proposed a system of 12 modes, that added Ionian and Aeolian (and their Hypo versions) to the existing system.
Bartolomè Ramos de Pareia c1440-1500
  • Musica Practica
  • Scorned Guido, invented new 'hand' for solmization that had 8 syllables to the octave
  • Proposed a tuning system with pure M/m thirds at the expense of fourths and fifths.
  • Upheld equal length of the breve in either tempus.
Niccolo Vicentino 1511-1576
  • L'Antica musica ridotta alla Moderna Prattica
  • Divides whole-tone into 5 parts and gives solmization syllables for each part.
  • Composed microtonal music using the above principals.
  • Showed how to write modes with 4 flats.
  • Discusses 'musica ficta' in canons.
  • Thought that some chant was sung in the Greek chromatic genus.
Michael Prætorius 15 February 1571-15 February 1621
  • Syntagma Musicum (in three volumes)
  • Extensive descriptions of musical instruments.
  • First to write about figured-bass.
Thomas Morley c1557-1602
  • A Plaine and Easy Introduction to Practicall Musicke
  • Practical treatise on singing in English is still very useful.
  • responsible for the dispersion of 'light Italian genres' and Engilsh madrigals
Gioseffo Zarlino 1517-1590
  • Le istitutioni harmoniche (four volumes)
  • Dimonstrationi harmoniche
  • Sopplimenti musicali
  • Very important and extensive treatise on counterpoint.
  • Adopted the 12-mode System of Glarean (without crediting him).
  • Disagreed with Vicentino, Considered chromatic and enharmonic Greek 'genera' unsuitable.
Domingo Marcos Duràn c1465-1529
  • Lux Bella
  • Comento Sobre Lux Bella
  • Sumúla de Canto de Organo
  • First musical treatise in Castilian
  • Added two hexachords and one letter to ther Guidonian system, and overlaped hexachords to extend them indefinitely, which he demonstrated on a 'musical wheel'
  • Gives rules for singing chant written on a single line.
  • Gave Dr. Vogel a subject for his dissertation (hey, that's an important contribution!)
Common Practice
Marin Mersenne 1588-1648
  • Harmonie universelle
  • Quæstiones celeberrimæ in Genesim
  • Traitè de l'armonie universelle
  • Les prèludes de l'harmonie universelle
  • Les questions thèologiques physiques, morales, et mathèmatiques
  • Questions harmoniques
  • Questions inouyes ou Rècrèation des sçavans
  • Harmonicorum Libri
  • Cogitata physico-mathematica
  • Novarum observationum physico-mathematica
  • extensive epistolary writings
  • Study of physics and acoustics in describing sound.
  • Advocated equal temperament.
  • interested in psychological aspects of music
  • discussion of musical instruments from outside western Europe
  • Use of 7 solmization syllables (ci and bi)
Johann Fux 1660-1741
  • Gradus ad Parnassum
  • Most influential compositional treatise, used by Mozart, Beethoven, Hayden and others.
  • Focused on counterpoint and Fugue-writing in a (nominally) 16th century style.
  • Composed over 400 pieces of music.
Jean Rameau 1683-1764
  • Traité de l'harmonie réduite a ses principes naturels
  • Nouveau système de musique théorique
  • Génération harmonique, ou traité de musique théorique et pratique
  • many others...
  • Thought that all music had an implied 'Fundamental Bass', and that the actual music was a realization of the overtone series of that bass.
  • Recognized only two types of chords: Major and Minor.
  • Thought that melody arises from harmony and not vice versum.
Johann Mattheson 1681-1764
  • Der Vollkommene Capellmeister
  • Grundlage einer Ehrenpforte
  • many, many others...
  • believed that melody was the foundation of harmony, unlike Rameau.
  • Interesting views on the practice of music from the viewpoint of a music-director
Johann Heinichen 1683-1729
  • Neu erfundene und gründliche Anweisung ... zu Erlernun des General-Basses
  • der General-Bass in der Composition (revision of above)
  • Full description of figured-bass playing.
  • Understood of inversions of triads.
  • Summarizes variety of figures used in different countries to describe the same chords.
  • Treats the art of accompaniment.
Freidrich Wilhelm Marpurg 1718-1795
  • Abhandlung von der Fuge
  • Handbuch bey dem Generalbasse und der komposition
  • Anleitung zur Singe-Composition
  • Anleitung zur Musik
  • Versuch über die musikalische Temperatur
  • Important journal editor and writer. Geared his articles towards middle-class amateurs.
  • Many short, accessible reviews of books, biographies of musicians and discussions of theoretical topics.
  • believed that the point of art is to move the audience through the imitation of nature.
  • Composed lots of songs, 6 keyboard sonatas, a collection of fugues, and two collections of chorale preludes.
  • Theoretical discussion of fugues that was the forerunner to modern counterparts.
Giuseppe Tartini 1692-1770
  • Regole per arrivate a saper ben suonar il violino/Traité des Agréments
  • Trattato di musica secondo la vera scienza dell'armonia.
  • De' principi dell'armonia musicale contenuta nel diatonico genere dissertazione
  • Wrote over 135 violin concerti, and other works, mainly for violin.
  • extensive treatment of ornamentation and violin bowing.
  • Rejected Rameau's idea that frequency, not string length, determined pitch.
  • Discovered difference tones.
  • Disliked the idea of temparment, but admitted its necessity.
Johann Joachim Quantz 1697-1773
  • Versuch einer Anweisung, die Flöte traversiere zu spielen
  • Discussion of baroque flute playing and ornamentation.
  • Discussion of the rolse of the instruments in orchestras of his time.
Carl Philipp Emanuel Bach 1714-1788
  • Versuch über de wahre Art das Clavier zu spielen
  • Discussion of keyboard-playing, figured-bass, ornamentation.
  • Identifies different chords by their 'figure', thereby ignoring Rameau's theory that first and second position chords are the derived from root-position.
Daube c1730-1797
  • General-Bass in drey Accorden
  • Der Musikalische Dillettant
  • Anleitung zur Erfindung der Melodie und ihere Fortsetzung
  • important early discussion of the emerging sonata form.
  • interesting observations about musical life in Vienna.
Françios Joseph Fetis 1784-1871
  • Biographie universelle des musiciens (8 volumes)
  • Esquisse de l'historie de l'harmonie
  • Traite complete de la theorie et de la pratique de l'harmonie
  • Musique mise à la portée de tout le mond
  • Histoire général de la Musique (5 volumes)
  • Extensive source for bigraphies of contemporary French musicians
  • Music is made of major and minor triads, and dominant seventh chords. Other sonorities are the the result of non-chord tones.
  • 4 periods in music history: unitonique, transitonique, pluritonique, and omnitonique.
  • Harmony is approached form the standpoint of practice rather than acoustic laws or theories.
Hermann Helmholtz 1821-1894
  • Lehre von den Tonempfindungen als Physiolgische Grundlage für die Theorie der Musik
  • Applied empirical science to human perception.
  • explained the role of overtones in timbre using Ohm's Acoustic Law, Fourier analysis and Helmholtz resonators.
  • Founded the study of the physiology of hearing
  • explained combination tones (aka "Tartini Tones"), and discovered summation tones, which founded the basis for his theory of non-lineararity of the ear
  • invented a microscope to study sound waves
  • discussed beats, and their role in consonance and dissonance
  • Formulated the law of conservation of energy
  • Disagreed with Rameau, thinks that music is the result of human creativity, not physics
Hugo Rieman 1849-1919
  • Musiklexikon
  • Handbuch der Harmonielehre
  • Geschichte der Musictheorie im 9-19 Jarhundert
  • Grosse Kompositionslehre
  • Father of modern musicology.
  • Thought that musical tones had 'undertones', like overtones but below. Later admitted that he was smoking crack on that one.
  • Used a 'Tonnets' to show that keys related by thirds are closely related.
  • 'Functional' view of harmony.
Arnie Schoenberg 1874-1951
  • Harmonielehre
  • Structural Fuctions of Harmony
  • Preliminary exercises in counterpoint
  • Fundamentals of musical composition
  • Style and Idea
  • numerous essays, letters, articles and lectures.
  • Extremely infulential as a composer
  • Believed that dissonances were just more remote consonances (as opposed to, for instance, Tinctoris, who considered them polar opposites, as vice and virtue)
  • Credited with the invention of serialism.
  • Interesting perspectives on tonal theory. 'Fluctuating/Suspended Tonality', 'Developing Variation'.
  • Extensive rant about how the streets in his town go circuitously.
Heinrich Schenker 1865-1868
  • Neue Musikalische Theorien und Phantasien (Three Volumes)
  • Fünf Urline-Tafen
  • Ein Beitrag zur Ornamentik asl Einführung zu Ph. Em. Bachs Klavierwerken.
  • Beethovens neunte Sinfonie
  • Der Tonwille
  • Das Masterwerk in der Musik
  • Looked at music theory from the perspective of human perception.
  • First to discuss hierarchy in music.
  • Propsed concept of unerlying structure (Ursatz) in music.
  • Intend his theories to be beneficial to performers.
Paul Hindemith 1895-1963
  • Unterweisung im Tonsatz
  • The Craft of Musical Composition
  • uses the harmonic series and combination tones as a basis for his theories.
  • measured the 'distance' from any pitch to a tonal center.
  • analysis of non-triadic chords.
  • used the chromatic scale as the basis of his theories.
Olivier Messiaen 1908-1992
  • Technique de mon langage musical
  • very influential composer.
  • influenced by bird songs.
  • use of non-diatonic 'modes of limited transposition'.
  • use of 'non-retrogradable' rhythms.
Vincent Persichetti 1915-1987
  • Twentieth Century Harmony:Creative Aspects and Practice
  • Discussion of the non-serial harmonic techinques of first half of the twentieth century, like unusual scales, non-traiadic chords, polytonality, pan-diatonicism.
  • Prolific composer, numerous large compositions.
Iannis Xenakis 1922–2001
  • Musique Formelles
  • Arts/Sciences: Alloys (transcription of his thesis defense)
  • Formalized Music
  • Musique, Architecture
  • Music and Architecture
  • Important architect, working on high profile projects for Le Corbusier's, culminating in the design of the Philips Pavillion in Bruxels.
  • Research in computer generated music.
  • used complex scales called "Sieves" which, unlike Messian's modes of limited transposition, are asymmetric and reject octave equivalence.
Alan Forte b.1926
  • The Structure of Atonal Music.
  • Contemporary Tone Structures
  • The Compositional Matrix
  • Tonal Harmony in Concept and Practice
  • Workbook in Harmonic Composition
  • pioneer and proponent of set-theory.
  • enumerated and named all possible pitch-class sets.