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       M U S I C          T H E O R Y         O N L I N E

                     A Publication of the
                   Society for Music Theory
          Copyright (c) 2000 Society for Music Theory
+-------------------------------------------------------------+
| Volume 6, Number 4     October, 2000     ISSN:  1067-3040   |
+-------------------------------------------------------------+

  All queries to: mto-editor@smt.ucsb.edu or to
                  mto-manager@smt.ucsb.edu
+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
AUTHOR: Harrison, Daniel
TITLE: Tolling Time
KEYWORDS: clock chimes, bells, time, carillon, Westminster 
Quarters, Rochester Quarters, Magdalen Chimes, Parisfal Chimes, 
Guildford Chimes 
 
Daniel Harrison
University of Rochester
Department of Music
205 Todd
Rochester, New York 14627-0052
hrsn@mail.rochester.edu

ABSTRACT: Five clock chimes (Parsifal, Guildford, Magdalen,
Westminster, and Rochester) are analyzed to show how they
communicate specific values about time. These chimes are shown to
have two design elements, "distinctiveness" and "emergence," that
provide for particular kinds of temporal commentary.

ACCOMPANYING FILES:
ex1_Parsifal_1.gif
ex2_Parsifal_2.gif
ex3_Guildford.gif
ex4_Magdalen_1.gif
ex5_Magdalen_2.gif
ex6_Westminster_1.gif
ex7_Westminster_2.gif
ex8_Rochester.gif
ex9_Cartoon.gif

[1] It is a commonplace that music can be made out of any variety
of sounds, including those not originally intended for music-
making. I am concerned here, however, with a different case:
situations in which sounds with explicit pitch are neither meant
nor heard primarily as music. Car horns, doorbells, buzzers, and
other purely functional yet (proto-)musical sounds are--in this
present culture, at least--not much more than acoustic
signifiers, and arouse no one's aesthetic appreciation save
perhaps that of a composer inspired to use them. But I am
concerned here with an even more specialized case, one in which
acoustic signification is artistically grounded, where the sign
feigns a pure functionality, the import of which apparently can
be extracted casually by the observer (like a road sign), but
which also--and even really--expresses a subtle bit of art. My
object here is clock chimes.

[2] Are chimes amenable to musical analysis? This question would
not have occurred to me until a short time ago, as I--like
everyone else--heard mostly their functional message. To be sure,
they have bits of tune, and one of the five chimes that I will
discuss in detail here, the Westminster Quarters, actually forms
quite a pleasant and memorable collection of tones, so much so
that composers have used this collection as the motivic basis of
an extended composition.(1) But I found myself in the position of
having to write (compose? design?) a chime tune, and had
therefore to consider whatever musical principles there happened
to be in this apparently simple art. This article results from
this unusual experience, and it is partly an analysis of existent
clock chimes, partly a report on a model-compositional procedure
for a new chime that resulted from this analysis, and partly a
commentary on a music so regularly heard (like clockwork!) that
it becomes part of the acoustic landscape of a particular place
and eventually loses some of its quality as music. 
 
============================== 
1. See, for example, Louis Vierne, "Carillon de Westminster," 
from *Pieces de Fantaisie* for organ. 
============================== 
 
                    * * * * * * * * * *

[3] The Hopeman Memorial Carillon is installed at the top of Rush
Rhees Library at the University of Rochester, 189 feet above the
main campus quadrangle. Although it has fifty bells, played from
a mechanical-action console inside the tower, only five are
equipped with electric-action strikers activated by an electronic
clock. Every quarter hour, the clock triggers the strikers in a
melodic sequence, and the bells sound out over the campus.
Depending on wind and ambient noise conditions, they can be heard
up to half a mile from the tower. Several thousand people are
within earshot of the clock chimes.(2) 
 
============================== 
2. For more information about the instrument, consult its web 
site: http://www.cc.rochester.edu/College/MUR/carillon.html. 
==============================

[4] Since the original installation of bells in the library tower
in 1930, the clock has chimed the Westminster Quarters, so named
because of its adoption on the tower clock at Westminster Palace,
where the British Houses of Parliament meet. (The lowest bell
there, which tolls the hours and weighs thirteen and a half tons,
is the famous "Big Ben.") Having been reproduced in clocks both
large and small all over the world, the Westminster Quarters is a
well-known chime tune--perhaps the only tune people think of when
the subject of clock chimes is broached. Its popularity certainly
owes much to the attractive melodic sequence, but perhaps more to
sentimental associations of British imperial pomp and
circumstance, reinforced by the use of the Westminster Quarters
by the BBC World Service for many years to preface the
top-of-the-hour world news report on short-wave radio.

[5] As University Carilloneur, I am steward of the bells and the
clock mechanism. Over the years, I had become curious about the
practice of chiming quarter hours, and wondered to what extent
this musical pronouncement of time--as opposed to the occasional
passive glance at a watch or clock--might affect the life of the
campus community. I had resolved in the summer of 1999 to see
about changing the chime tune, partly to mark the
sesquicentennial of the University of Rochester in 2000, but also
partly to respect the wishes of the composer Sir John Stainer,
who, in 1895, was quoted as remarking to a friend that "you will
be doing a kindness in turning out the Westminster Chimes, of
which everybody is heartily sick."(3) 
 
============================== 
3. Quoted in W. W. Starmer, "Chimes," *Proceedings of the 
Musical Association* 34th session, (1907-8): 8. 
==============================

[6] I therefore looked at some existing chime tunes in order to
learn the style, such as it was. I anticipated that the
analytical work would be simple, quick, and of no lasting
interest. I was surprised that it turned out differently. 
 
                    * * * * * * * * * *

[7] A useful feature of clock chimes is that each announcement of
time within the hour have a unique melodic sequence. In this way,
quarter past the hour, for example, can be distinguished by sound
alone from half past, a useful advantage when one is not in the
line of sight of a tower clock, or when (as is the case at the
University of Rochester) there is no visible tower clock at all.
I will call this rather elementary design feature of clock chimes
"distinctiveness." Another design feature, characteristic of
English-style clock chimes, I will call "emergence." Emergent
chimes are marked by progressive lengthening of the melodic
sequence during the course of the hour, with the shortest melodic
sequence at fifteen past the hour (the "first quarter") and the
longest on the hour (followed by a tolling of the hour).
Emergence can impart a definite temporal teleology, marking each
hour as a culmination and not a beginning, as sixty minutes past
a previous hour and not zero minutes of a new hour. This
acoustical sensibility contrasts markedly with a visual one
(reinforced by digital clocks) in which the hour is experienced
as ":00." Emergence thus is able to cloak the modular quality of
time by depicting linear rather than circular motion within the
hour, celebrating the arrival of the new hour both by completing
the melodic sequence and by striking the lowest bell in the peal
for the hour.

[8] Clock chimes can be composed to emphasize either
distinctiveness or emergence. While one quality cannot eradicate
the other, one can be so pronounced that the other becomes
secondary unto accidental. A chime tune emphasizing emergence is
shown in Ex. 1, the so-called Parsifal Chimes as they sound at
Riverside Church in New York.(4) Using only four melody bells
plus the hour strike, this chime adds a new four-note melodic
pattern to each quarter hour. Distinctiveness thus results both
from the number of bells struck at each quarter hour and from the
unique four-note pattern that concludes each quarter-hour chime.
While these unique patterns are a subset of the twenty-four
distinct permutations of the four bells, the emergent structure
can be modeled better by a different permutational design. Let
each quarter phrase be composed of two ordered intervals of a
perfect fourth, f1 = <C,G> and f2 = <A,E>, and let these two sets
of ordered intervals themselves be ordered. Considering pitch
succession alone, the chime pattern resolves thusly: 
 
1st quarter: Q1 = <f1,f2> 
2nd quarter: Q2 = <f2,f1> = R<f1,f2> 
3rd quarter: R(Q2) = <R(f1),R(f2)> 
4th quarter: R(Q1) = <R(f2),R(f1)> 
 
============================== 
4. The melodic sequence from *Parsifal* upon which the chime is
based is found at the end of the "Good Friday" scene in the third
act. According to Percival Price (*Bells and Man* [Oxford: Oxford
University Press, 1983], 182), this sequence ". . . is associated
with the Benedictine Abbey of Beuron, Germany, which in 1869
installed a swinging peal of four bells sounding, in descending
order, the notes B-flat, G, F, and D above middle C. Wagner
wanted the bells sounding a minor seventh lower in order to
suggest the solemnity of the Monastery of the Holy Grail. . . .
The only place where the Parsifal Quarters may be heard complete
and on bells of the deep pitches that Wagner envisioned is at the
Riverside Church." For more information about the carillon at
Riverside, consult its web site:
http://theriversidechurchny.org/about_carillon.html
==============================

[9] The sophisticated emergent effect that this structure creates
is illustrated in Ex. 2. Two time spans are especially marked:
the sixty-minute whole and two thirty-minute segments. The
sixty-minute span is conveyed by a climax figure created by
dotted-half notes that end each quarter-phrase. Counterpointing
this rising line is its retrograde on the first quarter-note of
each quarter-phrase. Upon completion of both lines at the fourth
quarter, the hour is tolled on the lowest and heaviest bell in
the instrument, a twenty-ton C2 that is the largest bell ever
cast for a carillon. The hour strike thus "turns over" the
modulus, transforming sixty-past into zero-hour, from which the
registral ascent of the dotted-halves begins again. Within this
sixty-minute span are two thirty-minute spans, the "outbound" and
"inbound" half hours. The outbound is created by falling fourths,
the last of which, f2, produces a half cadential effect at thirty
past. The inbound, a retrograde of the outbound, is created by
rising fourths and produces an authentic cadential effect at
sixty past. The association of retrogression with inbound effects
can be extended to the fifteen-minute spans as well, where the
retrograde affects the order of the two perfect-fourth intervals.
In this way, thirty-past is composed of an outbound quarter hour
and an inbound quarter hour. The inbound half hour is similarly
composed. 

[10] In comparison to the Parsifal Chimes, the Guildford Chimes,
shown in Ex. 3, emphasize distinctiveness, and what emerges over
the course of the hour is not a single melodic entity, but rather
something more abstract: a "compositional" sensibility that
progressively displaces what might be called a "sound design"
sensibility. The Parsifal Chimes has a limited number of
available bells, and, as a result, it displays its design
elements as the main feature of its art. In contrast, the
Guildford Chimes has a peal of eight bells forming a major scale
and thus offers opportunity for rudimentary tonal composition.
Because of emergence, it takes advantage of this opportunity only
gradually during the course of the hour. The first quarter, like
that of the Parsifal Chimes, is a melodic sequence without much
cohesion as a musical phrase. The second quarter presents a
minimal phrase involving a tonic-dominant-tonic harmonic
progression as well as polyphonic melody, thereby introducing an
elementary tonal-compositional feature. A measure longer than the
first, it concludes with an imperfect authentic cadence,
appropriately signaling a conventionally important segment of the
hour. The third quarter adds another measure, continues the
polyphonic-melody technique, and presents in addition a definite
melodic contour that strengthens the compositional sensibility at
the expense of the design sensibility. Interestingly, the third
quarter concludes with a perfect authentic cadence on the
downbeat of the fourth measure, creating thereby a strong closing
effect before the hour is up.

[11] The fourth quarter has a number of striking features. While
the second and third quarters each added a single measure to the
total, the fourth doubles the length of the third to cover eight
measures. These eight measures contain four phrases that--save
for a missing anacrusis in the first phrase--could set a typical
English ballad text in an iambic common (86.86.) meter, a
possibility shown by the phrasing marks in the example. The
fourth quarter thus sounds like a "real" piece of music,
something definitely composed rather than designed. Because of
its exceptional nature, the fourth quarter stands apart from the
previous three, and the curious closure effected in the third
quarter is, in effect, the cadence of the overture before the
main act commences on the hour. This idea of an hour "show,"
incidentally, is realized spectacularly in a number of
continental tower clocks, where cast metal puppets ("clock-
jacks") strike bells in full view of a presumably amused public.
A very elaborate clock-jack show at the Rathaus in Munich has
revolving multilevel stages on which dancers and jousting knights
cavort.(5) (The inspiration for any number of Disneyland effects
is obvious.) While no colorful clock-jacks emerge to ring the
hour on the Guildford Chimes, a complete if rudimentary
composition does. Perhaps the most unusual feature of the fourth
quarter is its cadence, which is strongly on the dominant. The
eight measures are thus tonally open and incomplete. It is the
hour strike on the tonic that closes and completes the piece,
conclusively resolving the dominant on which the fourth-quarter
chime rested. In this way, the hour strike becomes part of the
show--the denouement of it, actually--instead of being a event
separate from the tonal structure of the chime. 
 
============================== 
5. For a useful web site (with bibliography) concerning clock 
jacks although not dealing with those in tower clocks, consult: 
http://www.msen.com/~lemur/dm-clock-jacks.html#southwold-jack1 
===============================

[12] The Parsifal and Guildford Chimes illustrate strong
tendencies towards emergence and distinctiveness respectively.
The Magdalen Chimes, shown in Ex. 4, has a more balanced
relationship of the two features. (To ease the analytic
discussion below, each quarter is denoted by thematic tokens.)
Emergence is a straightforward affair, as two notes are added at
each quarter hour. For the first two quarters, the chime seems to
be unfolding a single tune in the manner of the Parsifal Chimes:
A, A+B, and then possibly A+B+Y and A+B+Y+Z for the final two
quarters, with Y and Z each being putative two-note motives. The
third quarter, however, unexpectedly sounds a new melodic
pattern, C, while still striking the expected six times. The
fourth then takes C and, significantly, appends the two notes of
A to it, completing the emergent total of eight.

[13] The teleological character of the Magdalen Chimes is thus
quite different from that of either the Parsifal or the Guildford
Chimes. Although in different ways, those two chimes "build" the
hour and present the other quarters as supporting structures that
prepare the ultimate goal. The Magdalen Chimes has a more modular
character than the other two, and, while the fourth quarter is
still the longest sequence, it seems less climactic than those of
the other chimes. To be sure, it still presents something tonally
coherent, with complementary linear motions converging on the
tonic scale degree shown at B in Ex. 4. But this culminating
effect is less powerful than that of the Parsifal Chimes because
of the deployment of the motivic material.

[14] Ex. 5 maps the Magdalen Chimes onto an analog-clock grid
marked in quarters, showing the hour to be divided into two
distinct half hours. These time spans are different from the
inbound/outbound half hours of the Parsifal Chimes, which convey
a kind of pendular oscillation. The Magdalen half hours, as Ex. 5
suggests, are experienced as two different entities because
motive C--the irruptive event of the third quarter--dramatically
separates the first from the second half. Both half hours are
further marked by other features. The second and fourth quarters
(the concluding segments of each half hour) use the lowest bell
in the peal to create cadential effects appropriate to the time
spans in question. In the second quarter, this tonic precedes a
dominant one, producing a half-cadential effect, whereas in the
fourth quarter, the low bell reinforces the authentic-cadential
effect of the concluding motive A of the chime. Reinforcing these
tonal signals of conclusion is the use of compound motivic
figures at the second and fourth quarters: AB at the second and
CA for the fourth.

[15] To some extent, motive A cuts against the half-hour
division. By recapitulating A from the first half hour, the
fourth quarter creates a liaison between the ending of the second
half and the beginning of a new first half, so that the hour
event is experienced less as a culmination and more as an
anticipation of the following hour segment. In other words, the
motivic combination CA in the fourth quarter defines the hour as
the median between the third quarter of the present hour (C) and
the first quarter of the hour to come (A). In this way, the first
quarter can be heard as an echo of the previous hour; it looks
backwards rather than forwards.

[16] Like the Magdalen Chimes, the more famous Westminster
Quarters (Ex. 6) balances distinctiveness and emergence. The fame
of these chimes is such that its origins are well documented. The
composer William Crotch (1775-1847), while a student at Cambridge
in 1794, was asked to write a chime tune for a new clock at the
university. He took the fifth and sixth measures of Handel's "I
know that my Redeemer liveth" from *Messiah* as his inspiration,
and--considering them somewhat as a designer of a change-ringing
method--produced four sets of permutations on the four bells
{G,C,D,E}.(6) Each permutation is shown below as ordered sets of
quarter-phrases, which are defined by the rhythmic signature of
the Westminster Quarters: three quarter notes followed by a
dotted half. Note that the second quarter-phrase of the second
quarter is a "malformed" permutation due to the absence of the G
bell:

First quarter:  <E,D,C,G> 
Second quarter: <C,E,D,G> <C,D,E,C> 
Third quarter:  <E,C,D,G> <G,D,E,C> <E,D,C,G> 
Fourth quarter: <C,E,D,G> <C,D,E,C> <E,C,D,G> <G,D,E,C> 
 
The relationship between the permutational and temporal 
structures can best be illustrated by recourse to the following 
abbreviations:

Q1 = <E,D,C,G> 
Q2 = <C,E,D,G> 
Q3 = <E,C,D,G> 
Q4 = <G,D,E,C> 
MQ = <C,D,E,C> 

First quarter:  Q1 
Second quarter: Q2 MQ 
Third quarter:  Q3 Q4 Q1 
Fourth quarter: Q2 MQ Q3 Q4

==============================
6. See Starmer, "Chimes," p. 9. Starmer quotes a "Dr. Raven," to
whom was written a letter by a "Mr. Amps," who apparently knew
the origination story of the chime. Dr. Raven notes that Crotch's
permutations show evidence of a systematic order ". . . not
unworthy of Fabian Stedman." Stedman was the author of
*Campanologia* (Cambridige, 1677), the first thorough examination
of change ringing and its permutational nature. *Campanologia*
can fairly be said to be the first work of in which group theory
was applied to a musical situation.
==============================

[17] As was the case with the previous chimes, cadential effects
are coordinated with quarter-hour segments. In the Westminster
Quarters, however, these are prominent and may even be said to be
paramount. But other forces are at work here as well, and these
endow this chime with different levels of structural cohesion.
Like the Parsifal chimes, the Westminster Quarters builds the
hour from quarter phrases, but there is no rigid assignment of a
particular phrase to a particular quarter hour in this case. All
odd quarters (i.e., the first and third) use quarter-phrases with
half-cadential effects (Q1, Q2, Q3), while even quarters use
phrases with authentic effects (Q4, MQ). The odd quarters thus
conclude with a G, and the even with a C. This observation
suggests that Crotch's permutational design has at least some
partial ordering constraints. These are explored further in Ex.
7, which adopts a "node & arrow" system from David Lewin to show
a left-to-right ordering of events.(7) Those events in squares
have fixed precedence, while those in circles are movable,
appearing in the sequence at the indicated quarter. Thus, in the
half-cadential quarters, E is always before D, which is always
before G; C--to use the parlance of change ringing--"hunts" in
the order, moving about the other, fixed bells. Further, it hunts
in a consistent way. The three half-cadential quarter-phrases
are heard six times during the course of the hour, proceeding
from Q1 at the first quarter, through Q2 at the second, to Q3 and
back to Q1 at the third, and finally to Q2 and Q3 at the fourth. 
 
============================== 
7. See David Lewin, *Generalized Musical Intervals and
Transformations* (New Haven: Yale University Press, 1987), 134-5,
209 ff. For a more concise treatment, see David Lewin, "On
Partial Ordering," *Perspectives of New Music* 14-15 (1976): 252-
59. 
==============================

[18] The authentic-cadential phrases, as Ex. 7 shows, have a
different ordering design. To be sure, C no longer hunts but is
fixed as the cadential end. Yet D and E exchange precedence as
well, as the dashed lines indicate. It is this change that gives
the Westminster Quarters a pleasing balance and symmetry more
subtle than that created by the alternation of cadential effects.
These effects are obvious; the change of {E,D} precedence is less
so. (Yet, as an experiment, create for yourself an authentic-
cadence permutation in which E precedes D and substitute it for
either MQ or Q4. The effect is surprisingly dramatic.) Just as
the six half-cadential opportunities are parceled out to three
different quarter-phrases, the four authentic-cadential
opportunities are sounded by two different quarter-phrases, MQ
and Q4, that alternate consistently--MQ being heard first and
then Q4, followed by MQ and the final Q4.

[19] The cumulative effect of the design is multilayered. The
consistent rotation of quarter-phrases over the course of the
hour provides a subtle sense of modularity to the hour while not
interfering with the teleology of emergence. Moreover, this
rotation allows the astute listener to tell what time it is by
hearing the first quarter-phrase alone, the one exception being
the fourth quarter. At a middle and more easily-heard level, the
alternation of precedence for E and D creates a pleasing balance
and undulation to the unfolding chime tune. And at the surface,
the cadential effects create half-hour units from rudimentary
quarter-hour antecedent & consequent constructions.

[20] The Westminster Quarters seems to comment on the passing of 
quarter hours in the following way: A short quarter-phrase ending 
half-cadentially signifies the first quarter, which seems an 
obvious incomplete section of time.  The second quarter, which 
ends authentically, seems more complete yet not whole. The 
obvious incompleteness of the first quarter (marked by Q1) is 
avoided by the use of a "new" quarter-phrase Q2.  But the use of 
the "malformed" permutation, MQ, lessens the cadential strength.  
The second quarter is thus not heard as the first quarter plus 
another, but rather as an original half.  For the third quarter, 
a completely new representation of the first half hour (Q3+Q4 
instead of Q2+MQ) is followed by the original marker of 
incomplete quarter time, Q1. In a literal sense, the third 
quarter does not "contain" the previous two but is a new entity 
that, by concluding with Q1, recapitulates that quarter's message 
of incompleteness.  This situation becomes clearer at the fourth 
quarter, where two equal segments make up a satisfying whole: an 
outbound "malformed" 30-minute segment (Q2+MQ) and inbound "well-
formed" 30-minute segment (Q3+Q4), previously heard in the third 
quarter satisfactorily to "seal" the outbound half. In this 
light, 45 past does not resolve to 30+15, but rather to 60-15. 
The third quarter thus looks forward to and anticipates the hour 
to come.

	                    * * * * * * * * * *
	                    
[21] In composing a new chime for the Hopeman Carillon, a number
of novel ideas occurred to me, such as designing "third-hour"
chimes that would sound every twenty minutes, or (and this was
admittedly impish) having chimes sound, say, every eighteen
minutes on a six-hour modulus. But I was restrained by a
sympathetic consideration for the "user community"--for the
people who might possibly rely on the clock chimes to regulate
their lunch hour, to gauge their arrival time at class, or simply
to order their day in a traditional quarter-hour rhythm. This was
not a matter of artistic composition, but of maintaining the
integrity of a publically-traded signifier. An eighteen-minute
interval, for example, would no doubt force people always to look
at their watch to figure out what time it was, which could be a
continual annoyance. Moreover, it would defeat the original
mission of the clock chimes to tell time using sound alone. While
entertaining these notions, I was also reminded of the reception
that Richard Serra's "Tilted Arc" received when installed at the
Federal Building plaza in New York; what had been a bland but
functional space for unfettered human movement become blocked by
a 120-foot length of worked steel, twelve feet high. An outcry
ensued and, after a highly publicized lawsuit, the sculpture was
removed.(8) A similar point for modernist aesthetics I did not
care to make. Nor, in the end, did I want to trouble the
engineers at the Verdin Company, the manufacturers of the clock
chime mechanism, with my whimsy. So I resolved to maintain the
quarter-hour chiming. As it was, a new logic chip would have to
be manufactured for the quartz clock that triggers the strikers,
and this would strain my limited budget. To avoid the expense of
additional strikers, which would have created opportunities for a
more expansive, Guildford-style composition, I decided to use the
same bells as those used for the Westminster Quarters. 
 
==============================
8. For more information about "Tilted Arc," including
bibliography, consult:
http://www.arts.arizona.edu/are476/files/tilted_arc.htm 
==============================

[22] The first problem was thus composing a chime tune that
sounded manifestly different from the Westminster Quarters, whose
bells and timing it would nonetheless share. Seeing little
opportunity for emphasizing distinctiveness under these
conditions, I opted for an emergent design (Ex. 8A) like that of
the Parsifal Chimes.(9) The main innovation of the Rochester
Quarters is its phrase structure. Whereas both the Westminster
Quarters and Parsifal Chimes have distinct quarter-phrases,
emphasizing the quarter hour as the unit of measure, the
Rochester Quarters presents a new segment of a single if
miniature tonal structure at each quarter hour. This structure is
best explained in Schenkerian terms, as seen in Ex. 8B. The chime
marks each quarter-hour segment with a report of progress towards
completion of the fundamental 3-line. A major interruption occurs
at the second quarter, which effectively couples the half hour
with an important structural event. At the third quarter, the
Kopfton is regained and the line begins a descent in double time,
clearly aiming towards arrival on ^1 at the downbeat of m. 4
(=fourth quarter). The interruption at the third quarter (marked
by breaking the beam) disrupts this motion dramatically--marking
the third quarter as the point of greatest tonal and temporal
tension within the hour. At the fourth quarter, this interruption
disappears as ^3 progresses to ^1 without pause.

==============================
9. The hour strike on G is correct, despite the obvious clash
with the remainder of the chime. This G is the lowest bell in the
Hopeman Carillon, and it also struck the hours when the
Westminster Quarters (also set in F major) chimed from that
instrument. Many chimes lack a bell large enough to act as a
suboctave tonic for hour strikes, so hour strikes often occur on
whatever the largest bell is regardless of key.
==============================
	
[23] The chime at the first quarter points out a defect in the
fundamental structure: there is no apparent tonic support for the
Kopfton ^3. Given the length of the piece, and given that there
is only one bell sounding ^1, there was no way to put that scale
degree in service of both the upper voice and the bass. To have
put ^1 in the first-quarter chime would have suggested a downward
bass arpeggiation to ^5, or would have created some other
registral confusion as to what was upper voice and what was bass.
Despite this issue, the absence of a ^1 support for the Kopfton
actually enhances the effect of the chime by making the first
quarter a decidedly incomplete structure. As the hour passes and
the tune unfolds, the attainment of ^1 and of an attendant
structural "repair" becomes apparent. That is, the final ^1,
while appearing within the upper voice-leading, also creates the
heretofore missing bass line; a single note (C as ^5) cannot be a
line, but two (CF as ^5-^1) can. Although the bass arpeggiation
is truncated, it occurs nonetheless as part of the last event in
the structure. With some imagination, it is not hard to hear the
first two ^1s as upper-voice pitches, and the last two as bass
voice, as Ex. 8B graphs. 
 
                    * * * * * * * * * *

[24] The Rochester Quarters debuted on January 31, 2000, the
sesquicentennial anniversary of the signing of the university
charter. I did some advance publicity for the change, so that the
community was somewhat prepared, but it was not extensive.
Reaction was largely positive, which has been gratifying because,
in truth, what I composed is not as deeply interesting as the
Westminster Quarters from the theoretical perspective; given four
bells, a lick from Handel, and the reflected glory from most
famous and prestigious bell tower in Western culture, it is hard
to improve upon the Westminster Quarters. The student newspaper
did find cause for complaint; I had tampered with one of the few
venerable traditions the campus had, and the new chime sounded
like ". . . the pounding of a kindergartener on a xylophone." An
editorial cartoon that linked the new chime with an unwelcome
innovation in student dining (Ex. 9) underlined the point.(10) 
 
==============================
10. University of Rochester *Campus Times*, Februrary 3, 2000.
==============================

[25] All reactions, whether positive or negative, seemed to
comment not so much on the chime tune itself, but rather on a
renewed appreciation for being called to note the passing of
time, and to note it with some pleasure. Buzzers, electronic
beeps, and other assorted chirps also mark time, but crudely and
without intelligence. Moreover, many are meant as private signals
(e.g., the watch alarm), which makes their public impact one of
inadvertent rudeness. The clock chime, in contrast, is a
courteous public service. It asks to be appreciated rather than
merely noted. The examples analyzed here also communicate
something about the passage of time, and not just about a
particular time point. They all use musical means to comment
about what time it is or what part of the hour it is, and the
consistent repetition of these comments throughout the day
encourages one to transfer characteristics of a particular chime
pattern to a particular quarter-hour segment. Fifteen past sounds
different--and therefore feels different when heard--from
forty-five past. Gradually, like all things that repeat
mechanically for an indefinite term, these feelings aroused by
the clock chime, as well as the attention paid to the chimes
themselves, blend into the background of daily routine. The
chimes will be heard instead of listened to, and the time points
they mark will sound dull instead of sharp. But there will still
be yet a unique and intrinsically musical sense of time in the
place wherein they sound, a sense its denizens will share for as
long as the bells continue to toll their particular story.

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