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Tone color and bells

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The tone color of a sound is its personality, a defining trait independent of pitch and volume. Tone color, also known as timbre, is what makes a flute, cello, and human voice sound like different instruments, even at the same pitch. Somewhat intangible, timbre is described by words like warm, round, dark, shrill, thin, bright, nasal, dull, brilliant, etc.

Musical sounds are made up of many different pitches. Tone color is determined by the frequency (pitch) and intensity (volume) of these constituent pitches, known as partials or overtones. On most instruments, the lowest pitch is strongest and perceived by the ear and brain to be the note. The higher overtones color the sound, and are usually integer multiples of the base frequency, corresponding to the natural harmonic series (see diagrams below). The term fundamental is usually used to describe the lowest pitch of a series. For carillon bells, though, the 'fundmental,' or prime, is one octave above the lowest pitch, and is the perceived note.

The left diagram gives the first five overtones for the harmonic series (most instruments) and a carillon bell. Many overtones exist above these, though the ear is not able to distinguish between those pitches higher than about the seventh partial. The right diagram shows the overtone spectrum of Denver's C3 Eijsbouts bell. Horizontal bands represent each overtone as it decays over 3 seconds, the intensity indicated by brightness. Clearly, the hum, prime, and tierce continue to sound as the upper overtones fade.

Instruments such as bells and strings vibrate at many different frequencies simultaneously, and for a bell, both horizontally and vertically (see diagrams below). Bells' characteristic somber tone is the result of a unique overtone profile, most notably the prominent minor-third overtone. This overtone is unusual among musical instruments in that it is non-harmonic—it vibrates at 2.4 times the base frequency, outside of the natural harmonic series. In its most basic vibrational modes, the circular bell struck by the clapper deforms to an ellipse, then returns to the circle and further to the perpendicular ellipse. The frequency of these alternating mis-shapings is the pitch of the overtone.

Percy Scholes writes, "The one and only factor in sound production which conditions timbre is the presence or absence, or relative strength or weakness, of overtones."¹

Controlling tone color

Many instruments allow a player to manipulate timbre in performance. A violin player can use different parts of the bow, or play nearer the fingerboard or bridge to produce contrasting tone colors. Wind players can change their embouchure or volume of air. In these cases, the variations in tone color are used to better express the music.

Though it currently cannot be proven outright, the carillonneur most likely has no means for controlling timbre. Clapper shape and material, strike location, and clapper-bell contact time can all change a bell's timbre, but they are not of use to the performer.

This can be difficult to accept, especially since many players are taught that they can control tone color with the proper keyboard technique. It is only natural to believe that the very different key attacks and wrist actions used in carillon playing should evoke different sounds from the bells. It is important to avoid this tempting belief, though, and focus on those factors that the carillonneur actually controls: when the note sounds, and how loud. Just the feeling of using a different attack on the key can actually make a player (or viewer) perceive the sound differently, even though nothing has changed. The nature of sound perception is highly psychological.

I will discuss two explanations for why timbre control is probably not possible on the carillon. A third method would be to hold blind listening tests of the same bells played using different touches. I am working to set up such a test on this website in the coming months.

1. The mechanism

As described in the previous section, a carillon must work as an escapement transmission in order to produce an acceptable sound. This means adjusting the clapper so that it does not touch the bell when the key is fully depressed (or, never push the key all the way down while playing). An escaped clapper flies freely through the air, acted on by only gravity and friction. At the time of the strike, the clapper is not even directly connected to the key or the player's hand, leaving no opportunity for the carillonneur to influence the strike. The single factor he or she controls is the speed of the clapper when it escapes, which translates directly—and only—to the loudness of the resulting note.

Technically, a player could hold the clapper against the bell for a few extra milliseconds, thereby damping the lower overtones and allowing the higher ones to ring for a 'brighter' tone. The accuracy required of hand and mechanism for this is far beyond our reach. More importantly, it would require a tight clapper adjustment, fundamentally changing the way the instrument works for every note. The safeguard against deadening the bell—escapement—would be sacrificed. See the video in the previous section showing a piano without escapement.

2. Timbre analysis

Since timbre is defined by the pitch and intensity of a note's overtones, it can be roughly quantified by analyzing recorded bell sounds. The perception of tone color is more nuanced than simply measuring overtones, especially concerning the order that the overtones first sound, but the basic principle can be demonstrated.

The figure below shows the overtone content of the same bell struck using two different attacks on the key. The peaks are marked with the pitch of each overtone; the valleys are the noise floor, or background noise. The blue sample is played using a gentle, even stroke, pushing the key to the bottom. The red uses a quick flick of the wrist. The sampled audio clips are next to the figure.

Key struck with gentle wrist motion Get Flash Player to play examples! Key struck with quick wrist flick Get Flash Player to play examples!

In comparison, the figure below represents two notes played on a guitar string. Both are played with the fleshy part of the pointer finger, the blue where the sound hole meets the neck, the red near the bridge. Though the sound color changes very subtly to the ear, the overtone profiles are clearly different. A carillon bell sounding noticeably different timbres would show a similarly varied profile.

Open G guitar string played over sound hole Get Flash Player to play examples! String played near bridge Get Flash Player to play examples!

Comparison to the piano

A similar tone color control debate over the piano has been ongoing for over a century. See the references below for some very interesting papers and arguments. The similarity of the piano and carillon mechanisms, namely escapement, make for a relevant comparison. Some research has been carried out, but theorists and acoustics experts still do not fully understand the workings of the piano. Three methods for studying the touch-timbre question are used:

• Theoretically analyzing the piano mechanism and the nature of string vibrations
• Measuring and comparing the overtone spectra of recorded sounds (as I have done above)
• Blind listening tests using subject groups

Theoretical analysis still does not have an answer. Studies have shown that it is possible that vibrations in the hammer wood from different touches could introduce longitudinal waves into the string.² Askenfelt and Jansson studied pressed versus struck touches on the piano key, similar to those touches on the carillon, but did not conclude whether they were perceptible as timbre.

Measuring overtones appears reliable, but is also not definitive. According to the research I have done, it is apparently not yet known how accurate such measurements must be to represent the sensitivity of the average listener. According to the graphs above, any difference in the two bell notes above would be too subtle to hear given the guitar comparison.

Suzuki attempts to measure audability of touch differences both by measuring overtones and polling study subjects.³ Piano notes G3, G4, and G5 were sampled using the extremes of "hard" and "soft" touches. Spectral analysis showed that there was no measurable difference in G3 and G4. For G5, upper partials were slightly more intense when a hard touch was used.

Suzuki then tested non-musician subjects to see if they could hear the difference between the two touches. Testing the G5 only, the two participants were able to correctly give the touch used about 80% of the time. However, the audio clips were not normalized in volume and the hard touch clip was always louder, which may have completely accounted for the high accuracy. Suzuki writes, "Since the piano tone has a nonlinear characteristic (relative levels of higher order partials increase as the intensity of the piano tone increases), one needs to compare piano tones with different touches while keeping the peak levels constant or at least within a negligible difference"(1). He later admits that the actual levels exceeded a negligible difference (5). Further, he writes, "It seems that the level differences due to the touch are much less than pianists generally expect"(6). Unfortunately, no blind testing was done using G3 and G4, which showed no spectral changes between touch types. Further study is needed to correct for the inconsistencies in Suzuki's methods.

It is important to note that Suzuki removed the finger-key and key-keybed impact noises from the audio samples. This noise does vary with different touches at a given volume, and does change the timbre perception of the player and listener. There is, of course, no equivalent noise on the carillon for the listener on the ground. Studies by Otto Ortmann⁴ in the 1920's and Werner Goebl et al⁵ in 2004 conclude that this impact noise is the only perceptible change in varying touch.

Goebl tested 22 subjects using 50 tone-touch pairs, compared to Suzuki's 2 subjects and 3 tone pairs. Half of Goebl's tone pairs included the finger-key impact noises, while the noises were edited out of the other half. With the impact noises, "Four of the 22 participants got 80–86% correct, five 70–80%, two 60–70%, and the other 11 rated at chance level"(2). When impact noises were removed, response accuracies were at chance level. Goebl concludes, "these results confirm that the cue for differentiating the two types of touch were the touch noises before the actual tone"(3).

Moreover, Goebl speaks to the perception of loudness, "The louder a tone the more they tended to judge it a struck one....when participants were unable to identify the actual cue in this listening test (touch noise), they assigned touch by tone intensity"(3). Given that Suzuki's struck tones were all louder than the pressed tones, this calls his results into question.

Goebl also makes an interesting observation about the psychology of perception (hapto-, or haptic, refers to the sense of touch),

First, it is interesting that finger–key noises are so salient in the audio signal recorded close to the strings. And second, it is remarkable that the different touch conditions were not identified more correctly given how salient those noises were in the stimuli. This might be explained by the absence of other cues, as e.g., visual or hapto-sensorial information. We expect that especially hapto-sensorial feedback to the player influences considerably his/her aural perception of a played tone, since this feedback changes substantially with the type of touch (1).

Finally, some thoughts on the long-standing debate,

Pianists study for many years extremely intensively to advance their technique of touching the keys so that the outcoming sound satisfies their (and their teachers) high artistic demands. They establish and refine various kinds of accelerating the keys in order to obtain the finest timbral shades so that it might be hard for them to believe that piano timbre might be expressed by a single physical parameter. The physicist, on the other hand, argues that the pianist loses control over the hammer after the jack is escaped by the let-off button. Therefore, it is only the endmost velocity of the hammer that determines the intensity and thus the timbre of the piano tone (1).

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