Download Meter as Rhythm - Christopher F. Hasty. PDF

TitleMeter as Rhythm - Christopher F. Hasty.
File Size1.9 MB
Total Pages329
Table of Contents
                            Contents
PART I: METER AND RHYTHM OPPOSED
	ONE: General Characterization of the Opposition
		Periodicity and the Denial of Tense
		Rhythmic Experience
		Period versus Pattern; Metrical Accent versus Rhythmic Accent
	TWO: Two Eighteenth-Century Views
	THREE: Evaluations of Rhythm and Meter
	FOUR: Distinctions of Rhythm and Meter in Three Influential American Studies
	FIVE: Discontinuity of Number and Continuity of Tonal “Motion”
PART II: A THEORY OF METER AS PROCESS
	SIX: Preliminary Definitions
		Beginning, End, and Duration
		“Now”
		Durational Determinacy
	SEVEN: Meter as Projection
		"Projection” Defined
		Projection and Prediction
	EIGHT: Precedents for a Theory of Projection
	NINE: Some Traditional Questions of Meter Approached from the Perspective of Projective Process
		Accent
		Division
		Hierarchy
		Anacrusis
		Pulse and Beat
		Metrical Types — Equal/Unequal
	TEN: Metrical Particularity
		Particularity and Reproduction
		Two Examples
	ELEVEN: Obstacles to a View of Meter as Process
		Meter as Habit
		“Large-Scale” Meter as Container (Hypermeter)
	TWELVE: The Limits of Meter
		The Durational “Extent” of Projection
		The Efficacy of Meter
		Some Small Examples
	THIRTEEN: Overlapping, End as Aim, Projective Types
		Overlapping
		End as Aim
		Projective Types
	FOURTEEN: Problems of Meter in Early-Seventeenth-Century and Twentieth-Century Music
		Monteverdi, “Oimé, se tanto amate” (First Phase)
		Schütz, “Adjuro vos, filiae Jerusalem”
		Webern, Quartet, op. 22
		Babbitt, Du
	FIFTEEN: Toward a Music of Durational Indeterminacy
	SIXTEEN: The Spatialization of Time and the Eternal “Now Moment”
References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	P
	R
	S
	T
	V
	W
	Y
	Z
                        
Document Text Contents
Page 2

METER as
RHYTHM

Page 164

where, even while trying to realize the deferred
S and trying to hear the beginning, *, as inter-
ruptive, it will be difficult to avoid feeling the
“retrospective” formation of a triple, C – D – E,
with the beginning, *. It may be possible to sup-
press to some extent this triple and its realized
deferral by concentrating our attention on the
denied deferral L –M –N; however, to the ex-
tent we are able to do this, we will have had to
suppress T and, consequently, T'.

It must be said that the preceding demonstra-
tions concerning example 9.27 are circular, since
deferral has been defined precisely to account
for the feeling of triple unequal measure. In-
deed, it is my hope that they are circular, because
if this circle is truly closed, deferral will distin-
guish triple measure from all other varieties of
unequal measure, and the distinction will be one
of kind and not merely one of degree. Certainly,
there is a clear difference in feeling—quintuple
sounds more unequal than triple. If triple sounds
lilting, quintuple sounds limping. Thus, I would
like to suggest a division of metrical types into
three categories: equal, mediated unequal (3/4,
for example), and nonmediated or “pure” un-
equal (5/4, for example). By the term “mediated
unequal” I mean to suggest an accommodation
of inequality to a demand of equality or repro-
duction. Through deferral, a third beat extends a
unitary duration by becoming assimilated to a
projective potential created by an initial two
beats. The third beat, although it does not im-
mediately succeed the first beat, nevertheless
draws on the projective potential of the first beat
(or, more accurately, the projective potential of
what becomes the first beat) by reproducing the
first beat’s immediate successor, a reproduction
in which the dual function of the second beat
for the first is repeated: the function of continu-
ation (whereby a first beat was created) and the
function of realizing a projection (whereby the
projective potential of the first beat became ac-
tual ). Or, from a different perspective, it might
be said that in reproducing the second beat, the
third beat inherits the particular relevance the
first has for the second.

Although, for convenience, I have used (and,
for convenience, will continue to use) the terms
“duple,” “triple,” and “quintuple,” such terms are
not appropriate for the distinctions I have made.

As was noted in connection with example 9.27b,
a measure of 5/4 can take the form of duple un-
equal. Likewise, a nonmediated triple might be
represented by 8/8 as 3+3+2, for example.
“Oneness,” “twoness,” “threeness,” “fourness,”
“fiveness,” et cetera, are real properties that can-
not be detached from metrical formation, but I
do not believe that the feeling of meter is the
feeling of these numerical quantities per se, but
rather the projective possibilities that such quan-
tities offer. Indeed, these projective possibilities,
special for each cardinality, may be involved in
feeling the distinctiveness of various numerical
quantities.

Before leaving the topic of inequality, I
would like to consider briefly the projective
shortcoming of “pure” unequal measure com-
pared to the other two types. In example 9.27 I
placed question marks beneath the projective
potentials indicated for 5/4 measures to suggest
projective indeterminacy in these cases—that
with the beginning of a second bar measure (at
*) the projective potential for a definite duration
is not very clearly felt. Obviously, nonmediated
inequality detracts from projective potential. In
examples 9.27b and 9.27c the continuations M
do not realize the projected potentials Q' and
R', respectively, and thus do not complete a pro-
jection. The new beginnings with N complete a
previous measure, but this measure itself is not
composed of a completed projection above the
level of individual beats. In the case of 3/4, I
have argued that although the measure is un-
equal, it is nevertheless composed of a com-
pleted projection. One of my reasons for intro-
ducing the notion of deferral is to offer an ac-
count of why metrical types such as 2/4, 3/4,
4/4, 6/8, and 9/8 seem (at appropriate tempi) to
have similarly strong projective potential, where-
as metrical types such as 5/4, 7/8, and 3+3+2/8
are projectively much less determinate. Example
9.28 points to a further complication that can
arise in “pure unequal” projective types.

From a reproductive standpoint, a second
measure of 5/4 demands considerable reinter-
pretation, especially if, as in examples 9.28c and
9.28d, the tempo is slow enough to open the
possibility for the emergence of a smaller projec-
tive potential, R. If there is any ambiguity in the
projective “hierarchy” (S versus R), realized pro-

The Perspective of Projective Process 145

Page 165

jective potentials (Q and R) will issue in failed
projections (Q–Q' and R–R'). In the case of 3/4
or 2/4, et cetera, no such reinterpretation need
arise—all realized projective potentials result in
completed projections. This is not to say that
5/4, 7/8, and so on are unnatural or confused. It
is to say that such measures are complex. They
are in a sense underdetermined and in a sense
overdetermined—underdetermined in that the
smaller projections involved in the two-measure
projection are unrealized or denied and so do

not enhance the determinacy of the larger pro-
jection, and overdetermined in that within each
measure decisions among equally possible alter-
natives (in the case of 5/4, 2+3, or 3+2) must
be made. For this reason, 5/4 is not as flexible
as 3/4 or 4/4. If we are to feel quintuple mea-
sures, we will not be able to depart very far
from an explicit presentation of five appropri-
ately grouped beats. Due to their greater deter-
minacy, measures of 3/4, 4/4, and so on can sup-
port a greater variety of patterns and can with-

146 A Theory of Meter as Process

a) 43
Q

(S

W

W

œ
––

œ œ
|
(|

\ \

Q'
R W

œ
––

œ œ
|
\

\ \

R'
S'

œ
––

œ œ
|
|

\ \

œ
––

œ
)

œ
|
\

\ \
)

b) 42
Q

(S

W

W

œ œ
|
(|

\

Q'
R W

œ œ
|
\

\

R'
S'

œ œ
|
|

\

œ
)

œ
|
\

\
)

b) 42
Q

(S

∑  √±´ †√

W

W

c) œ œ
|
(|

Q'
R W

œ œ œ
|
\

R'
S'

?

œ œ
|
|

œ œ
)

œ
|
\ )

b) 43
Q

(S

´´  √±∑ †√

d)

W

W

œ œ œ
|
(|

Q'
R W

œ œ
|
\

R'
S'

?

œ œ œ
|
|

œ
)

œ
|
\ )

EXAMPLE 9.28 Contrasting projective potentials for “mediated unequal,” “equal,”
and “pure unequal” measure

Page 328

Fraisse, Paul, 92, 108 n.2

Galileo, 10 n.2
Georgiades, Thrasybulos, 43–47, 257, 298
Gibson, J. J., 94 n.1
goal, 219, 221–222, 225
Goethe, Johann Wolfgang von, 48, 266
Guarini, Giovanni Battista, 241

Halm, August, 41–42
Handel, Stephen, 124–125, 173
Hasty, Christopher, F., 283
Hauptmann, Moritz, 34–35, 36, 38, 100–102,

135, 197
Hauser, Franz, 35
Haydn, Franz Joseph, 43 n.2, 44; Symphony no.

88 in G Major, 205–206; Symphony
no.101 in D Major, 128–129

hiatus, 88, 129, 170, 191
hierarchy: extensive, 18–19, 49–50, 56,

115–118, 175; projective, 151
hypermeasure, 49, 51, 175, 179–183, 196–197

Imbrie, Andrew W., 17–18, 19
indifference point, 108 n.2
inertia, 168
instant, 7, 16–19, 38, 56–57, 70–71, 73, 301
internal clock, 170
interruption, 138
intrinsic quantity (quantitas intrinsica), 27–28,

105

James,William, 31–32, 286, 302
Jone, Hildegard, 266
Joyce, James, 46, 298

Kant, Immanuel, 45
Koch, Christoph Heinrich, 21, 26–32, 50, 69,

83, 105, 106, 116
Kramer, Jonathan, 16–17
Kuba, Fritz, 42

laws of material and laws of presentation,
266–267

Lerdahl and Jackendoff, 20, 56–59, 63 n.3, 129,
176

Lewin, David, 277
Lieb, Irwin C., 7 n.1
Ligeti, György, 297
Lorenz, Alfred, 34, 48, 175
Lussy, Mathis, 16 n.4
Lutosrawski,Witold, Jeux Venitiens, 293–295,

296

Mattheson, Johann, 21, 22–26, 28, 30–31, 32,
69, 116, 302

Mead, Andrew, 262 n.2
Meister Eckhart, 298
memory, 12, 81, 94 n.1, 283–284, 299, 301
mensural determinacy, 80–83, 95
Messiaen, Olivier, 297
Meyer, Leonard B., 197. See also Cooper and

Meyer
Miller, G. A., 283–284
Moldenhauer, Hans, 267
Monteverdi, Claudio, “Ohimè, se tanto amate,”

237–243
motion, 12, 20–25, 37, 49, 57–59, 62–63, 175
Mozart, 43, 44; Piano Concerto in C Major,

K.467, 179–181; Piano Sonata in D
Major, K.311, 203–204; Symphony no. 35
in D Major (Haffner), K.385, 177–178,
184–191, 194–196, 198–200, 201, 220;
Symphony no. 40 in G Minor, K.550,
53–54; Symphony no. 41 in C Major
( Jupiter), K.551, 53

Narmour, Eugene, 111
Neisser, Ulric, 94, n.1, 283, 286
Neumann, Friedrich, 38–41, 48, 96–100
Newton, Sir Isaac, 9–10
now, 43–46, 72, 76–78, 151
number, 9–10, 16–19, 30, 38–39, 60

pedagogy, 5, 130, 152
performance, 48, 130, 152, 209, 260, 293
phrase constituent, 283
Piaget, Jean, 67 n.1
Plato, 10–11, 26, 35
Pollock, Jackson, 68
Printz,Wolfgang Caspar, 105, 135

Index 309

Page 329

Ratz, Erwin, 198
Reich, Steve, 296
Reich,Willi, 266, n.4
reinterpretation, 119, 218
relevance, 77, 81, 84, 93–95, 110, 150–151,

169–173
reproduction, 80–82, 92, 94, 150–152, 184
rhuthmos, 10–11, 20
Riemann, Hugo, 35–38, 39, 44, 50, 98, 100,

129, 191, 302
Rochberg, George, 297
Ross, Christopher, 11 n.3
Rothstein,William, 176, 177, 179–181, 211
Rousseau, Jean, 23–24, 31
row structure, 265

Schachter, Carl, 17, 176–179, 180, 182, 198
Schenker, Heinrich, 61–61, 63 n.3, 176–177,

179, 195
Schönberg, Arnold, 68 n.2, 113, 267
Schütz, Heinrich: “Adjoro vos, filiae Jerusalem,”

243–257
segmentation, 283–284
Seidel,Wilhelm, 24–25, 26–27, 35
sentence, 113, 230
silence, 75–76, 78–79, 90, 169–170, 184
simultaneity, 75
Smalley, Roger, 267, 273
sono-mama, 298
space, 7, 38 n.1
Stockhausen, Karlheinz, 46, 68, 296, 297, 299
Stramm, August, 278
structure, 4, 64, 67
subjective grouping, 27–28, 131–132, 141, 147

Sulzer, Johann-Georg, 26–27, 30, 32, 106
suspense, projective, 127, 136–137, 157
Suzuki, D. T., 298, 300
syncopation, 119, 152. See also suspense, projective

tactus, 23
time: absolute, 7 n.1, 9–10, 59, 98; relational, 7

n.1; smooth and striated, 286, 293
timelessness, 9, 24–25, 46, 61 n.2, 257,

297–298, 300
timepoint. See instant
time sense, 169
time signatures, 5, 26, 129
Toch, Ernst, 42–43

virtual articulation, 89, 110, 120, 130, 152–154
visual experience, 12
Vivaldi, Antonio: “Spring” Concerto from The

Four Seasons, 201–204

Webern, Anton, 261–262, 266–267; Quartet,
op. 22, 257–265; sketches for op. 22,
267–275

Whitehead, Alfred North, 65, 69
Whitrow, G. J., 7 n.1, 10 n.2
Wiehmeyer, Theodor, 102, 227 n.2
Wolpe, Stefan: Piece in Two Parts for Violin

Alone, 169–174, 244

Yeston, Maury, 69, 106
Yudkin, Jeremy, 227

Zeno, 60
Zuber, Barbara, 266 n.4

310 Index

Similer Documents