dmitritymoczkocom A STUDY ON THE ORIGINS OF HARMONIC TONALITY Dmitri Tymoczko Princeton University WHEN DID FUNCTIONAL TONALITY ARISE Lowinsky early 16 th century Frottola etc ID: 371557
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Slide1
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dmitri.tymoczko.com
A STUDY ON THE ORIGINS OF HARMONIC TONALITY
Dmitri Tymoczko
Princeton UniversitySlide2
WHEN DID FUNCTIONAL TONALITY ARISE?
Lowinsky: early 16
th century (Frottola, etc.)Fetis, Dalhaus
: early 17
th
century (Monteverdi)Bukofzer: late 17th century (Corelli)Gauldin: sometime after BachAnswers span more than 200 years!
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dmitri.tymoczko.comSlide3
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.
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A CORPUS-BASED APPROACH
Roughly 1,000 pieces from 1450-1850
Dufay to Brahms (plus rock)Approximately 120 chords/piece (120,000 total)“RomanText” files and XML scores
Using
Myke
Cuthbert’s (very cool) music21Balance of breadth and depthMostly Ionian mode
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A CORPUS-BASED APPROACH
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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 modulationsRequire any key changes be accompanied by an explicit cadence
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OTHER IMPS
All analyses can be automatically redone to check for analyst bias
e.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)
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FINDINGS I
Purely “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 vi
6
proto “rule of the octave”
Signs 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-IV
6-I …)Origins of root functionality?Preference for fourth motion in the bassPreference for “strong” progressions
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FINDINGS I
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FINDINGS I
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FINDINGS I
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FINDINGS I
Early on, cadential
formulae strongly resemble important functional progressionsVery robust preference for ending on root position chords
6
chords
are less stable than ! chordsBass voice is not “inessential”There is no “pure modality”
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3Slide13
FINDINGS II
Functionality 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.
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IV
ii
or
IVSlide14
FINDINGS II
“Rudimentary tonality”
Appears in popular, homophonic genres.Frottola, Dalza, Encina, etc. (
Petrucci
, 1504–1508)
Mostly root position chordsStrong sense of tonal centerI, IV, and V by far the most prevalent sonorities
IV and the subdominant/predominant continuumNo distinctively functional ii or viNo obvious signs of inversional equivalenceNot so dissimilar from Carter family
Appears
alongside other,
less functional organizational
schemes
.
Willaert
as case study
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FINDINGS II
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Frottole
I, 48,
Micha
(Petrucci, 1504)Slide16
FINDINGS II
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(
Petrucci
, 1508)Slide17
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 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 sonority
I6 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
.
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FINDINGS III
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FINDINGS III
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SUMMARY
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THE TENDENCY HISTOGRAM
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FINDINGS IV
The 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-) 17
th
-century.
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I
[
vi
(IV or ii)
]
vii° or V
I
vii° or V
I
ii
)
]
vii° or V
I Slide23
FINDINGS IV
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FINDINGS IV
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FINDINGS IV
The 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 17
th
-century.The vi chord emerges as a pre-predominant only in the 18th-century.
http://dmitri.tymoczko.com
I
[
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 Slide26
FINDINGS IV
The 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 17
th
-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.com
I
[
vi
(IV or ii)
]
vii° or V
I Slide27
FINDINGS IV
Lots of other 17th
-century developmentsBeginning of the vi-I6 idiom
^
1–^2–^3 gets harmonized as I-vii°6-I6
In Monteverdi, Morley, etc., it is still I-ii-I6i6 replaces III in minorDevelopment of sequencesEtc.
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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 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
predominants
Idioms
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WHAT DOES IT MEAN FOR ANALYSIS?
Don’t be afraid to draw on tonal concepts when looking at 16
th-century music!
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Lassus
,
Lamentationes
Hieremiae
Prophetae
(5v
) Slide30
WHAT DOES IT MEAN FOR ANALYSIS?
Don’t be afraid to draw on tonal concepts when looking at 16
th-century music!
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Palestrina
,
Tu Es Petrus (5v)Slide31
PEDAGOGY
A big subject!
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ANSWERING DIFFERENT QUESTIONS
When 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
pre
dominant?Fetis, Dalhaus: late 16th/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
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Thank you!
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/
OriginsOfTonality.pptx