Pythagoras 6th Century BC

treatises

None (Quasi Legendary)

contributions

believed that music is governed by simple ratios.
discovered simple ratios of perfect fourth, fifth and octave.

Aristoxenus 375-? BC

treatises

Harmonic Elements
Rhythmical Elements

contributions

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

treatises

The Harmonics

contributions

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

treatises

De istitutione musica

contributions

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

treatises

Alia Musica

contributions

Misinterpretation of the Greek modes, as described by Boethius, resulting in the Greek names for Ecclesiastic modes.

pseudo-Odo of Cluny 878/9-942 AD

treatises

Enchiridion Musices
Intonarium (various attributions)

contributions

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

treatises

Micrologus
Prologus Antiphonani
Epistolo de ignoto cantu

contributions

Invention of solmisation syllables.
Codified the use of the musical staff.
Expert in training singers.

Anonymous IV 13th C.

treatises

De Mensuris et Discantu

contributions

Extensive discussion of the rhythmic modes.
Extensive discussion of Notre-Dame polyphony, mentions Leonin and Pèrotin.

pseudo-Hucbald 9th C.

treatises

Musica Enchiriadis
Scolica Enchiriadis

contributions

Earliest known discussion of polyphony (organum, specifically).

Franco of Cologne Late 13th C.

treatises

Ars Cantus Mensurabilis

contributions

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

treatises

Ars Nova

contributions

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

treatises

Notitia Artis Musicæ (AKA Summa Musice)
Compendium Musicæ Practicæ
Musica Speculativa Secundum Boetium
Libellus Cantus Mensurabilis
Ars Contrapuncti

contributions

Imperfect division of the breve.
Extensive discussion of chromatic alterations in 'Musica Falsa'

Marchetto da Padua Early 14th C.

treatises

Lucidarium in Arte Musicæ Planæ
Pomerium in Arte Musicæ Mensuratæ

contributions

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

treatises

Speculum Musicæ
Tractus de consonantiis musicalibus
Tractus de intonatione tonarum
Compendium de muisca

contributions

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

treatises

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

contributions

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

treatises

Theoria Musicæ
Practica Musicæ
De harmonica instrumentorum opus

contributions

comissioned translations of Greek sources.
Accurately describes music of his contemporaries.
Referrd to Giovanni Spataro as 'Vaginarius' (sheath-maker).

Pietro of Aaron c1480-c1550

treatises

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.

contributions

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

treatises

Isagoge in musicen
Dodecachordon
Musicæ epitome sive conpendium ex Glareani Dodecachordo

contributions

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

treatises

Musica Practica

contributions

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

treatises

L'Antica musica ridotta alla Moderna Prattica

contributions

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

treatises

Syntagma Musicum (in three volumes)

contributions

Extensive descriptions of musical instruments.
First to write about figured-bass.

Thomas Morley c1557-1602

treatises

A Plaine and Easy Introduction to Practicall Musicke

contributions

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

treatises

Le istitutioni harmoniche (four volumes)
Dimonstrationi harmoniche
Sopplimenti musicali

contributions

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

treatises

Lux Bella
Comento Sobre Lux Bella
Sumúla de Canto de Organo

contributions

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!)

Marin Mersenne 1588-1648

treatises

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

contributions

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

treatises

Gradus ad Parnassum

contributions

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

treatises

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...

contributions

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

treatises

Der Vollkommene Capellmeister
Grundlage einer Ehrenpforte
many, many others...

contributions

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

treatises

Neu erfundene und gründliche Anweisung ... zu Erlernun des General-Basses
der General-Bass in der Composition (revision of above)

contributions

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

treatises

Abhandlung von der Fuge
Handbuch bey dem Generalbasse und der komposition
Anleitung zur Singe-Composition
Anleitung zur Musik
Versuch über die musikalische Temperatur

contributions

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

treatises

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

contributions

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

treatises

Versuch einer Anweisung, die Flöte traversiere zu spielen

contributions

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

treatises

Versuch über de wahre Art das Clavier zu spielen

contributions

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

treatises

General-Bass in drey Accorden
Der Musikalische Dillettant
Anleitung zur Erfindung der Melodie und ihere Fortsetzung

contributions

important early discussion of the emerging sonata form.
interesting observations about musical life in Vienna.

Françios Joseph Fetis 1784-1871

treatises

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)

contributions

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

treatises

Lehre von den Tonempfindungen als Physiolgische Grundlage für die Theorie der Musik

contributions

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

treatises

Musiklexikon
Handbuch der Harmonielehre
Geschichte der Musictheorie im 9-19 Jarhundert
Grosse Kompositionslehre

contributions

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

treatises

Harmonielehre
Structural Fuctions of Harmony
Preliminary exercises in counterpoint
Fundamentals of musical composition
Style and Idea
numerous essays, letters, articles and lectures.

contributions

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

treatises

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

contributions

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

treatises

Unterweisung im Tonsatz
The Craft of Musical Composition

contributions

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

treatises

Technique de mon langage musical

contributions

very influential composer.
influenced by bird songs.
use of non-diatonic 'modes of limited transposition'.
use of 'non-retrogradable' rhythms.

Vincent Persichetti 1915-1987

treatises

Twentieth Century Harmony:Creative Aspects and Practice

contributions

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

treatises

Musique Formelles
Arts/Sciences: Alloys (transcription of his thesis defense)
Formalized Music
Musique, Architecture
Music and Architecture

contributions

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

treatises

The Structure of Atonal Music.
Contemporary Tone Structures
The Compositional Matrix
Tonal Harmony in Concept and Practice
Workbook in Harmonic Composition

contributions

pioneer and proponent of set-theory.
enumerated and named all possible pitch-class sets.

Selected Summary of Music Theorists

Mike Krzyzaniak