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2.2. Timbre 101

In previous lessons, we've discussed this concept of "timbre," or tone color. Timbre is what allows our ears to distinguish between two instruments playing at the same pitch and loudness - it is why we can tell the difference between an oboe and a violin. Three main factors give an instrument its timbre: attack, vibrato and other stylistic variations in sound, and harmonic content.

Attack is the quality of the start of a note - this is what gives brass instruments their characteristic "ta" military sound. Remove the attack from a trombone recording and it sounds remarkably similar to a cello playing the same phrase. Wind instruments tend to have a stronger attack, while bowed instruments generally have a gentler attack, as the bow allows for sound to be more consistent. Of course, instrumentalists can use a variety of techniques to change the attack of their sound, and thus change its timbre. Violinists and fiddlers sound so different in part because of different attack styles, despite playing the same instrument.

Vibrato is a periodic pulse in the pitch of a note. Sustained notes in jazz and classical music tend to lend themselves to vibratos, which add a new richness to notes that can be difficult to notice consciously. Other stylistic techniques include tremolo, or the periodic pulse in the loudness of a note. These styles heavily affect timbre, and musicians spend years mastering them.

Harmonic content, another way of saying a note's overtones, is perhaps the single most important factor in determining a note's timbre, especially in long phrases. This is what we introduced in the previous section, and what we will focus on for the rest of the tutorial.

2.2.1. The Relationship Between Overtones and Timbre

Recall the experiment in Audacity from lesson 2.1. Here are some of the things you might have noticed:

Perhaps the most surprising of these is the last one. This is called a missing fundamental, and it happens quite often in real-life signals, much to the irritation of engineers everywhere. Our brains are able to work out the pitch we should perceive by looking at the difference between the harmonics picked up. It doesn't matter whether the fundamental is present in this calculation.

One of the predominant theories of human hearing is called "place theory," based on its claim that the ear determines pitch based on where the basilar membrane (lining the cochlea in the inner ear) is stimulated. Different pitches vibrate different little hairs on the membrane, and each overtone will vibrate a hair corresponding to its pitch (called sympathy vibration). A loud overtone at 440 Hz will vibrate one or more hairs which vibrate in sympathy at that frequency, and a softer overtone will cause less vibration. So we are able to hear overtones, work out what pitch we should perceive (even with a missing fundamental), and what timbre that pitch should have.

Coincidentally, when we hear a vowel sound, this same process goes to work to figure out which vowel it is - different vowels have different harmonic content. The 'ee' vowel sound (as in steed) has loud high overtones, giving it its nasally quality. I pose this philosophical question for you: did humans develop our love for music because our brains built up harmonic analysis structures for vowels, or did we develop language because of our structures built for the love of music?

We have reverse-engineered our brains' processes to give us voice-recognition technology and musical tuners. To learn more about how engineers, mathematicians and scientists use the same process, study Fourier analysis.

2.2.2. Using Computers to Fake Timbre

Perhaps nothing has affected music more in modern days than synthesizers. They have allowed previously never-heard sounds to become a part of our public consciousness, and have opened new levels of musical experimentation to the general public. But how do we fake sounds?

We know that is hard to nail down exactly what makes up an instrument's timbre - even if we perfectly replicate the harmonic content of a trombone, we still won't recognize that sound as "trombone," because timbre isn't just harmonic content. A critical part of that trombone brassy sound is its attack, so a synthesizer must take that into account. In addition, harmonic content of a real-life instrument isn't consistent across any single note played, much less across its entire range. In performances, small adjustments of the lip and mouth cause dramatic shifts in harmonic content in wind instruments, and irregularities in bow speed and pressure change the overtones of string instruments, with many other factors like environmental conditions weighing in.

While synthesizers today have gotten much better at replicating real instruments (particularly the incredible PianoTeq, which sounds better than many actual pianos), they often lack the power to change the harmonic content of the instruments they fake, losing that dynamic timbre that real instruments have. This leads to the flat sounds that are associated with MIDI keyboards, even as dynamic performers take the stage. Perhaps one day our synthesizers will be even better than wood-and-metal tools, but for now physics reigns supreme.

2.2.3. How Does It All Happen?

If you're like me, you're probably wondering how timbre arises in the first place. Why do instruments have overtones? What makes a brass instrument sound brassy? Much of this is at the forefront of acoustical research that is going on today, but we will be going over what we currently know in the rest of this tutorial. One thing to keep in mind: sound is extremely complicated. The study of how our brains perceive it is even more so. People make their livings studying this whole mess, and this tutorial barely scrapes the surface. I recommend Harry Olson's classic Acoustical Engineering for a more mathematical look at all the concepts given here.

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