a study on the origins of harmonic tonality dmitri tymoczko princeton university

The Music of the Spherical Quotients

http://dmitri.tymoczko.comA STUDY ON THE ORIGINS OF HARMONIC TONALITYDmitri TymoczkoPrinceton University1WHEN DID FUNCTIONAL TONALITY ARISE?Lowinsky: early 16th century (Frottola, etc.)Fetis, Dalhaus: early 17th century (Monteverdi)Bukofzer: late 17th century (Corelli)Gauldin: sometime after BachAnswers span more than 200 years!

http://dmitri.tymoczko.com2SOURCES OF DISAGREEMENTFunctional tonality is not as a single unified system, but a complex array of idiomatic features that developed extremely gradually.Contemporary theorists resist using later (anachronistic) theoretical terms to describe earlier music.Functionality was developed by composers in an implicit and embodied way, long before it was explicitly described by theorists.

http://dmitri.tymoczko.com3A CORPUS-BASED APPROACHRoughly 1,000 pieces from 1450-1850Dufay to Brahms (plus rock)Approximately 120 chords/piece (120,000 total)RomanText files and XML scoresUsing Myke Cuthberts (very cool) music21Balance of breadth and depthMostly Ionian mode

http://dmitri.tymoczko.com4A CORPUS-BASED APPROACH

http://dmitri.tymoczko.com

5IMPORTANT METHDOLOGICAL POINTS (IMPs)In my work, I use symbols like I or I6 as uninterpreted primitives identifying harmonic structures and a bass:There is no implication that these sonorities are the same or even related.In Renaissance music I try to identify almost all triadic vertical sonoritiesHardly ever label something a passing chordI try to be stingy about identifying modulationsRequire any key changes be accompanied by an explicit cadence

http://dmitri.tymoczko.com6OTHER IMPSAll analyses can be automatically redone to check for analyst biase.g. by counting every triad as a chordEliminating modulations altogetherWe might be interested in a tonal center that is different from that intended by the composer or experienced by contemporaneous listeners.e.g. it might be that the Phrygian tonic gradually started to act like the dominant-in-Aeolian, but that the behavior predated the conceptual recognition of the change.A phrygian tonic that (a) always appears as a major triad, and (b) always moves downward by fifth is acting like a dominant.Zarlino (IV:30)

http://dmitri.tymoczko.com7FINDINGS IPurely modal music (e.g. Josquin) already exhibits several features of what we think of as functional tonality.Preference for I and VIncluding a relative favoring of I6 and fairly strong disfavoring of vi6proto rule of the octaveSigns that I6 is considered closely related to I.Inversions are leapt-to and leapt-from only in the context of progressions like I-I6-V (or IV-IV6-I )Origins of root functionality?Preference for fourth motion in the bassPreference for strong progressions

http://dmitri.tymoczko.com8FINDINGS I


9FINDINGS I


10FINDINGS I


11FINDINGS IEarly on, cadential formulae strongly resemble important functional progressionsVery robust preference for ending on root position chords6 chords are less stable than ! chordsBass voice is not inessentialThere is no pure modality

http://dmitri.tymoczko.com312FINDINGS IIFunctionality is originally an Ionian mode idiomEarly functionality features the subdominant (IV-I) and dominant (V-I) cycles.Often involves IV as a predominantEventually becomes highly complex.


IViiorIV13FINDINGS IIRudimentary tonalityAppears in popular, homophonic genres.Frottola, Dalza, Encina, etc. (Petrucci, 15041508)Mostly root position chordsStrong sense of tonal centerI, IV, and V by far the most prevalent sonoritiesIV and the subdominant/predominant continuumNo distinctively functional ii or viNo obvious signs of inversional equivalenceNot so dissimilar from Carter familyAppears alongside other, less functional organizational schemes.Willaert as case study

http://dmitri.tymoczko.com14FINDINGS II


Frottole I, 48, Micha (Petrucci, 1504)

15FINDINGS II


(Petrucci, 1508)

16FINDINGS IIIFrom 1500-1680 one sees an extremely gradual transition toward functional tonalityNot possible to draw a sharp line between tonality and modalityCorollary: there is no unified language called modalityInstead a continuous shading between more and less functional proceduresDifferent idioms in different modes!In particular, functional practices begin to influence Ionian mode polyphonic music by the mid-16th century (esp. Palestrina, Lassus, Victoria).IV appears as a distinguished third sonorityI6 increasingly becomes the default harmonization of ^3 V tends more and more to go to IOften pieces will be fairly functional in their Ionian-mode sections, but less so when they emphasize other scale degrees.

http://dmitri.tymoczko.com17FINDINGS III


18FINDINGS III


19SUMMARY


20THE TENDENCY HISTOGRAM


21FINDINGS IVThe harmonic cycle is the default scheme:

The harmonic cycle gets built backward along the circle of fifths from dominant to predominant to pre-predominant.First, the dominant increasingly goes to I.Then ii chord emerges in the early (or mid-) 17th-century.

http://dmitri.tymoczko.comI [vi (IV or ii)] vii or V I vii or V I ii)] vii or V I 22FINDINGS IV


23FINDINGS IV


24FINDINGS IVThe harmonic cycle is the default scheme:

The harmonic cycle gets built backward along the circle of fifths from dominant to predominant to pre-predominant.First, the dominant increasingly goes to I.Then ii chord emerges in the early 17th-century.The vi chord emerges as a pre-predominant only in the 18th-century.

http://dmitri.tymoczko.comI [vi (IV or ii)] vii or V I vii or V I ii)] vii or V I I [vi (IV or ii)] vii or V I 25FINDINGS IVThe harmonic cycle is the default scheme:

The harmonic cycle gets built backward from dominant to predominant to pre-predominant.First, the dominant increasingly goes to I.Then ii chord emerges in the early 17th-century.The vi chord emerges as a pre-predominant only in the 18th-century.Prior to that, it often goes directly to V

http://dmitri.tymoczko.comI [vi (IV or ii)] vii or V I

26FINDINGS IVLots of other 17th-century developmentsBeginning of the vi-I6 idiom ^1^2^3 gets harmonized as I-vii6-I6In Monteverdi, Morley, etc., it is still I-ii-I6i6 replaces III in minorDevelopment of sequencesEtc.

http://dmitri.tymoczko.com27SUMMARYTransition to functionality is extremely gradual, taking ~200 yearsEvolution involves three processes:Loose statistical tendencies become much stricter rulesUnification of separate syntactical systems:Incorporation of popular Ionian-mode idiomsHomogenization of the cadential system and early phrase techniquesDisappearance of indigenous Phrygian, Mixolydian, Aeolian, Dorian, techniques in favor of patterns based on IonianExtension of proto-functional idiomsHarmonic cycles become more complexBegin with rudimentary I-IV-I, I-V-I, and are gradually embellished with secondary chords like predominantsIdioms

http://dmitri.tymoczko.com28WHAT DOES IT MEAN FOR ANALYSIS?Dont be afraid to draw on tonal concepts when looking at 16th-century music!


Lassus, Lamentationes Hieremiae Prophetae (5v)

29WHAT DOES IT MEAN FOR ANALYSIS?Dont be afraid to draw on tonal concepts when looking at 16th-century music!

http://dmitri.tymoczko.comPalestrina, Tu Es Petrus (5v)

30PEDAGOGYA big subject!

http://dmitri.tymoczko.com31ANSWERING DIFFERENT QUESTIONSWhen do we first find the subdominant and dominant cycles?Lowinsky: early 16th century (Frottola, etc.)

When do we start to see the disappearance of the modes, as well as the first appearance of the supertonic predominant?Fetis, Dalhaus: late 16th/early 17th centuries (Gastoldi, Cavalieri, Morley, etc.)NB: Monteverdi not exceptionally functional

When do we find the first thoroughly functional music (including sequences)?Bukofzer: late 17th century (Lully, Corelli)

When does modern textbook harmony (complete with the standard treatment of the vi chord) appear?Gauldin: sometime after Bach

http://dmitri.tymoczko.com32Thank you!


http://dmitri.tymoczko.com/OriginsOfTonality.pptx33

a study on the origins of harmonic tonality dmitri tymoczko princeton university

Documents

strong progressions

explicit cadence http

pure modality http

spherical quotients

depthmostly ionian mode

earlier music

renaissance music

origins of root functionality