Representing timbre with a spectrogram

Presented with the sounds of a flute and a guitar playing the same pitch at the same volume, it’s easy to tell which is which; but it’s not so easy to describe the difference in any precise way. Most attempts to do so would come down to describing how each sound is produced (e.g., by blowing or twanging), which is not the same thing as describing the sound itself. Similarly, it’s not easy to notate such differences except by indicating how the sounds are made, and in most notation systems this aspect is largely limited to specifying the sound sources.

However, a given sound source doesn’t always produce the same kind of sound. The string of a violin can be bowed, plucked, or hit with the wood of the bow, and each technique results in a radically different sound. In staff notation, these playing techniques are indicated with verbal descriptions in Italian: arco, pizzicato, and col legno respectively. 

That’s generally sufficient for classical music, where there is a certain accepted ideal for the sound of (for instance) a string being bowed, and within that category the character of the sound is not supposed to vary much. The same goes for other instruments in classical music, and for classical singers.

In a lot of other music, though, variation in the character of the sounds from a single source is absolutely vital. A successful pop or rock singer not only has a unique and instantly recognisable voice, but is able to vary the tone of that voice from moment to moment to convey the emotion of a song with conviction. 

For similar aesthetic reasons, instruments that take a solo role in popular music have tended to be ones that can vary their tone widely, such as the electric guitar and the saxophone. If we want to notate such music, it might be worth trying to specify these differences of tone in a more precise and efficient way than describing them in words.

The differences we are talking about are called differences of “timbre.” Sometimes glossed as “tone quality” or “tone color,” timbre is hard to define except in a negative way: it’s whatever aspect of sound is left when we take away pitch, volume, duration, and onset timing.

The challenge in trying to notate timbre is that it can’t easily be “measured” like those other parameters of sound. The pitch of a sound is more or less high; the volume is more or less loud; the duration is more or less long; and the onset timing is more or less late. But the timbre of a sound is more or less… what? Rough? Breathy? Scrapy? Resonant? It’s hard even to agree on meaningful adjectives, let alone imagine a scale by which we could measure those qualities and determine exactly how much more “rough” (or whatever) one sound is than another.

In other words, timbre is not a one-dimensional parameter. In practice, differences in timbre tend to involve three main things:

(1) Attack: How abrupt is the onset of the sound? Does the sound begin at full volume, or is there a momentary “fade-in"? The subsequent “envelope” of intensity may also play a role, e.g., through the rate of decay (for impulsive sounds) and the “release,” i.e., how each sound ends; but the attack is usually more crucial, simply because it comes first.

(2) Overtones: A sound of definite pitch normally comprises a number of different frequencies, primarily multiples of the “fundamental” frequency that we hear as the pitch of the sound. Sounds of different timbre differ in the relative strength of these “overtones,” as do different vowel sounds in speech. Sounds of definite pitch produced by solid objects, such as bells and xylophone keys, often involve overtones that are not multiples of the fundamental frequency, and this also affects their timbre.

(3) Noise: Sound of indefinite pitch may combine with either of the above, and may do so differently for the onset of a sound and for its subsequent “steady state.” The timbre of the harpsichord is distinguished in large part by its “noisy” percussive attack, while Japanese shakuhachi flute players often intentionally mix unpitched breath sounds with flute sounds of definite pitch.

To indicate all those things in a score sounds like a lot of trouble, and even then, the information about timbre might be liable to dominate the score to a degree that overshadows other aspects of the music; so it is probably only worth doing if timbre is a special interest. Still, it can be done, and in some cases it can capture important things about the music.

To notate timbre with any real precision will require the use of sound analysis software. Other pages explain how to use this for measuring onset timing and producing a pitch-time graph. What we now want is a graph that shows the pitch, not just of the fundamental frequencies, but of the overtones as well. 

We also want the graph to show volume, or “intensity,” both overall (which will reveal the abruptness or otherwise of the attacks) and for individual overtones (since the balance of overtones partly determines timbre). 

In addition, we want it to show the intensity of any sounds of indefinite pitch (since noise is also a component of timbre). In fact, we want a graph that shows whatever sound is present throughout the spectrum of pitch - a type of graph called a “spectrogram.”

We’ll explore the use of spectrograms by comparing different performances of the same song. In a chapter of the textbook Worlds of Music, ethnomusicologist Jeff Todd Titon contrasts two renditions of the well-known hymn “Amazing Grace” in American Baptist churches, one black and one white. Each has a lead singer and a chorus, and Titon describes the vocal timbres of the two lead singers. The black leader’s timbre, he says, “alternates between buttery smooth and raspy coarse,” while the white leader’s is “unvaryingly coarse.”

Titon’s staff notation of the two performances brings out many contrasts in their handling of pitch and timing, but doesn’t capture the difference in timbre or show (for instance) when the black leader’s timbre is “buttery smooth” and when it is “raspy coarse.” Yet this “alternation” is surely not random, but related to expression. Can we shed more light on it with a spectrogram?

Here again, the simplest program to use is probably Tony. All we have to do is produce a pitch-time graph as we did before and turn on “Show Spectrogram.”