http dmitri tymoczko com A STUDY ON THE

http: //dmitri. tymoczko. com A STUDY ON THE ORIGINS OF HARMONIC TONALITY Dmitri Tymoczko Princeton University

http: //dmitri. tymoczko. com WHEN DID FUNCTIONAL TONALITY ARISE? • Lowinsky: early 16 th century (Frottola, etc. ) • Fetis, Dalhaus: early 17 th century (Monteverdi) • Bukofzer: late 17 th century (Corelli) • Gauldin: sometime after Bach • Answers span more than 200 years!

http: //dmitri. tymoczko. com SOURCES OF DISAGREEMENT • Functional 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. com A CORPUS-BASED APPROACH • Roughly 1, 000 pieces from 1450 -1850 – Dufay to Brahms (plus rock) – Approximately 120 chords/piece (120, 000 total) • “Roman. Text” files and XML scores – Using Myke Cuthbert’s (very cool) music 21 • Balance of breadth and depth • Mostly Ionian mode

http: //dmitri. tymoczko. com A CORPUS-BASED APPROACH

http: //dmitri. tymoczko. com IMPORTANT METHDOLOGICAL POINTS (IMPs) • In my work, I use symbols like I or I 6 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 sonorities – Hardly ever label something a “passing chord” • I try to be stingy about identifying modulations – Require any key changes be accompanied by an explicit cadence

http: //dmitri. tymoczko. com OTHER IMPS • All analyses can be automatically redone to check for analyst bias – e. g. by counting every triad as a chord – Eliminating modulations altogether • We 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. com FINDINGS I • Purely “modal” music (e. g. Josquin) already exhibits several features of what we think of as functional tonality. – Preference for I and V • Including a relative favoring of I 6 and fairly strong disfavoring of vi 6 – proto “rule of the octave” • Signs that I 6 is considered closely related to I. – Inversions are leapt-to and leapt-from only in the context of progressions like I-I 6 -V (or IV-IV 6 -I …) – Origins of root functionality? – Preference for fourth motion in the bass – Preference for “strong” progressions

http: //dmitri. tymoczko. com FINDINGS I

http: //dmitri. tymoczko. com FINDINGS I

http: //dmitri. tymoczko. com FINDINGS I

http: //dmitri. tymoczko. com FINDINGS I • Early on, cadential formulae strongly resemble important functional progressions – Very robust preference for ending on root 3 position chords – 6 chords are less stable than ! chords – Bass voice is not “inessential” • There is no “pure modality”

http: //dmitri. tymoczko. com FINDINGS II • Functionality is originally an Ionian mode idiom – Early functionality features the subdominant (IV-I) and dominant (V-I) cycles. – Often involves IV as a predominant – Eventually becomes highly complex. ii IV or IV

http: //dmitri. tymoczko. com FINDINGS II • “Rudimentary tonality” – Appears in popular, homophonic genres. • Frottola, Dalza, Encina, etc. (Petrucci, 1504– 1508) – Mostly root position chords – Strong sense of tonal center – I, IV, and V by far the most prevalent sonorities • IV and the subdominant/predominant continuum – No distinctively functional ii or vi – No obvious signs of inversional equivalence – Not so dissimilar from Carter family • Appears alongside other, less functional organizational schemes. – Willaert as case study

http: //dmitri. tymoczko. com FINDINGS II Frottole I, 48, Micha (Petrucci, 1504)

http: //dmitri. tymoczko. com FINDINGS II (Petrucci, 1508)

http: //dmitri. tymoczko. com FINDINGS III • From 1500 -1680 one sees an extremely gradual transition toward functional tonality – Not possible to draw a sharp line between “tonality” and “modality” • Corollary: there is no unified language called “modality” – Instead a continuous shading between more and less functional procedures – Different idioms in different modes! • In particular, functional practices begin to influence Ionian mode polyphonic music by the mid-16 th century (esp. Palestrina, Lassus, Victoria). – – IV appears as a distinguished third sonority I 6 increasingly becomes the default harmonization of ^3 V tends more and more to go to I Often pieces will be fairly functional in their Ionian-mode sections, but less so when they emphasize other scale degrees.

http: //dmitri. tymoczko. com FINDINGS III

http: //dmitri. tymoczko. com FINDINGS III

http: //dmitri. tymoczko. com SUMMARY

http: //dmitri. tymoczko. com THE TENDENCY HISTOGRAM

http: //dmitri. tymoczko. com FINDINGS IV • The harmonic cycle is the default scheme: I [vi (IV or ii)] vii° or V I • The harmonic cycle gets built backward along the circle of fifths from dominant to prepredominant. – First, the dominant increasingly goes to I. – Then ii chord emerges in the early (or mid-) 17 th-century. vii° or V I ii)] vii° or V I

http: //dmitri. tymoczko. com FINDINGS IV

http: //dmitri. tymoczko. com FINDINGS IV

http: //dmitri. tymoczko. com FINDINGS IV • The harmonic cycle is the default scheme: I [vi (IV or ii)] vii° or V I • The harmonic cycle gets built backward along the circle of fifths from dominant to prepredominant. – First, the dominant increasingly goes to I. – Then ii chord emerges in the early 17 th-century. – The vi chord emerges as a pre-predominant only in the 18 th-century. vii° or V I ii)] vii° or V I I [vi (IV or ii)] vii° or V I

http: //dmitri. tymoczko. com FINDINGS IV • The harmonic cycle is the default scheme: I [vi (IV or ii)] vii° or V I • The harmonic cycle gets built backward from dominant to pre-predominant. – First, the dominant increasingly goes to I. – Then ii chord emerges in the early 17 th-century. – The vi chord emerges as a pre-predominant only in the 18 th-century. • Prior to that, it often goes directly to V

http: //dmitri. tymoczko. com FINDINGS IV • Lots of other 17 th-century developments – Beginning of the vi-I 6 idiom – ^1–^2–^3 gets harmonized as I-vii° 6 -I 6 • In Monteverdi, Morley, etc. , it is still I-ii-I 6 – i 6 replaces III in minor – Development of sequences – Etc.

http: //dmitri. tymoczko. com SUMMARY • Transition to functionality is extremely gradual, taking ~200 years • Evolution involves three processes: – Loose statistical tendencies become much stricter rules – Unification of separate syntactical systems: • Incorporation of popular Ionian-mode idioms • Homogenization of the cadential system and early phrase techniques • Disappearance of indigenous Phrygian, Mixolydian, Aeolian, Dorian, techniques in favor of patterns based on Ionian – Extension of proto-functional idioms • Harmonic cycles become more complex – Begin with rudimentary I-IV-I, I-V-I, and are gradually embellished with secondary chords like predominants • Idioms

http: //dmitri. tymoczko. com WHAT DOES IT MEAN FOR ANALYSIS? • Don’t be afraid to draw on tonal concepts when looking at 16 th-century music! Lassus, Lamentationes Hieremiae Prophetae (5 v)

http: //dmitri. tymoczko. com WHAT DOES IT MEAN FOR ANALYSIS? • Don’t be afraid to draw on tonal concepts when looking at 16 th-century music! Palestrina, Tu Es Petrus (5 v)

http: //dmitri. tymoczko. com PEDAGOGY • A big subject!

http: //dmitri. tymoczko. com ANSWERING DIFFERENT QUESTIONS • When do we first find the subdominant and dominant cycles? – Lowinsky: early 16 th 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 16 th/early 17 th centuries (Gastoldi, Cavalieri, Morley, etc. ) – NB: Monteverdi not exceptionally functional • When do we find the first thoroughly functional music (including sequences)? – Bukofzer: late 17 th 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. com/Origins. Of. Tonality. pptx Thank you!