How to calculate the length of your very own vocal tract
Ever wonder just how long it was from your vocal cords to your lips? Well, holy shit, it's time to find out. No, no, I'm totally serious. THIS IS POSSIBLE. IT IS POSSIBLE WITH SCIENCE. LEAVE YOUR TAPE MEASURE AT HOME.
But no, you cry, I am a linguist, likely an amateur one! This is math and waveforms and spectrograms and fuck-all else! Well, I'd have to say you're right. It is math and waveforms and spectrograms and fuck-all else. But that's fine, that's how language works. You'll be okay.
No, seriously, stick with it. It's got some science. The good kind.
SECTION 1: THE VOCAL TRACT
fig. 1.1: the vocal tract: vocal cords on the left, lips on the right
So this is your vocal tract. A gorgeous piece of machinery, evolved by chance over millions of years into the perfect configuration for speech production. Scientists would say it is a pipe that is closed at one end and open on the other.
Wait, you say again, it is not a pipe! It is kinked in the middle! It has a tongue! A beautiful pharynx, glottis, velum, palate, and alveolar ridge! The vocal cords do not form a full closure during speech production!
WRONG. As previously stated, it is a pipe closed at one end. Tongues are irrelevant to our current discussion, as are kinks.
Regarding kinks, /msg me after this writeup. We'll have plenty to talk about.
You do have a point there, though, the vocal cords do not close during speech. They happen, however, to be the source of our acoustic energy; and so, walls shall they be, as will be shown in the following diagram:
fig. 1.2: a vocal tract with noise coming out of it
So there you have it. Proof of my assertions of the vocal tract as a pipe closed at one end. Do me a favor, pretend those blocky lines are actually a sine wave, all smooth and fluid. See how it starts, and then reaches it maximum right at your lips? That's what the first formant of a vowel looks like. Wait, formants?
SECTION 2: FORMANTS
Formants are a pretty big fucking deal. They make vowels. Yes, holy shit, they make vowels. How? Damned if I could figure it out. Luckily, science already knows, and now I will impart this knowledge to you, in greatly simplified form.
So vowels are, in layman's terms, basically chords. Like yeah, musical chords, and no, not like vocal cords. Oddly. Vowels, as far as our speech perception centers can tell, are made of three distinct frequencies sounding at the same time. (There's actually way more than three, but you can get by really well with just three.) So, based on the ratio of these sounds to one another, your brain knows what the tongue had to do to make them. From there, it decodes how high or low or front or back or rounded the vowel is.
Great. So. The vowel you'll need to make is like the "ir" in British English, as in "third", "bird", etc. If you're really at a loss for making that sound, you can settle for American English "uh" as in "uh vocal tract" or "Spartuh". Be warned, however, that this will mess up your results fairly significantly, and, upon reporting your findings to colleagues, they will think you a freak, the victim of an unmerciful god.
The reason that we are looking for this vowel is that it's the closest thing to an unconstricted vocal tract there is - there's no tongue getting in the way, altering the shape. It also makes the math easier later on - the formants are in very nearly a 1:3:5 ratio. (This is because of the influence of math upon pipes which are closed at one end. Pay it no mind.)
So go on, practice making that vowel, preferably in front of others. Their mocking smiles will only spur you on. When they inevitably ask what it is you're doing, you can honestly reply, "IT IS SCIENCE."
Section 3, the First: MISEING YOUR PLACE CORRECTLY
For this you shall need the following:
A PIPE CLOSED AT ONE END:
As stated previously, many of us come equipped with one in the form of a vocal tract, with tongues and pharynxes and things which honestly should not interfere greatly with its being a pipe closed at one end.
AN ELECTRICIZED COMPUTING MACHINE:
You are likely equipped with one of these as well, but at one point it required purchase. Make sure you have one purchased and it is prepped for use. You shall likely need a computing screen and a cyber-typewriter at the very least.
A MICROPHONE OF SOME SORT WHICH IS NOT A HAIRCOMB:
This piece of equipment is important for most pieces of science which involve pipes closed at one end, for reasons that will become apparent shortly.
IMPORTANT PIECES OF SOFTWARE:
I'll actually serious the fuck up for this one. We'll be using a program called Speech Analyzer, invented mainly by pipe-measuring specialists. It can be found at http://www.sil.org/computing/sa/index.htm , and it will be doing the important work of actually giving you a frequency to work with. It is free and all that as well. The only problem is that its recorder kind of sucks. Luckily, Sound Recorder on Windows and whatever else for whatever else should get the job done.
Section 3, the Second: OBSERVATION
OBTAIN A SAMPLE OF YOUR PIPE NOISE, PROPERLY CALIBRATED:
With your microphone activated and transcribing, produce the aforementioned "ir" vowel or your bastardized American attempt thereof. Save this somewhere convenient.
CLICK AT RANDOM:
Open up Speech Analyzer. Open your speech sample within the confines of this program. Click upon the "formants" button at the top toolbar. It is green and red and yellow, in order to show you that this is the "formants" button. Click upon the "Waveform, Spectrogram" view panel at the left. Finally, click upon a section of that stripey mess at the bottom where you are reasonably sure you produced an "ir" sound. Note at the bottom: It shall say "F1: some hertz, F2: more hertz, etc." Double check that your F2 is about three times as much as your F1. Make a note of F1.
Section 4: AN UNHOLY INTERSECTION OF MATH, SCIENCE, AND PIPES CLOSED AT ONE END
Science can tell us a lot about tubes closed at one end, provided we trade it our knowledge of the speed of sound, and the frequency of a sound made from that tube. Specifically, it can tell us the length of those tubes, and it tells us in the following terms:
F = c / 4L
Luckily for us, this was translated by pipe-measuring-specialists long ago. It means the following: The frequency of a sound made in a pipe closed at one end is equal to the speed of sound divided by four times the length of that pipe. Why four? It has to do with physics. This is all gibberish, however. How can we divide by something that we don't know what it is? This is where math comes in.
Math allows us to trade letters around willy-nilly, which would never work in, say, literature. After throwing some math at the previous equation, we end up with:
L = c / 4F
which is much easier to work with, since we can divide by something that we know what it is. Oh, also, we know the speed of sound, c. It's thirty-four-thousands-and-twenty-nine centimeters per secondum (34029 cm/s).
Pipes closed at one end:
Take that F1 that you wrote down, and insert it into the equation. Upon completion, you shall have obtained knowledge you once thought impossible: the length of your own vocal tract, complete with kinks and tongues. Here is an example: it is my own.
My ir produced an F1 of 482Hz, and an F2 of 1504Hz. Pretty close to 1:3 for someone who's not an expert in these things anyway. After throwing some math at it, I ended up with a vocal tract length of ~17.6 cm.
SECTION 5: INTERESTING FACTS CONCERNING THE LENGTHS OF PIPES CLOSED AT ONE END:
A longer vocal tract is associated with a lower voice. This is due to science. Lower voices are correlated with masculinity, larger body size, good health, and advanced age. Studies have shown that certain types of people find that attractive.
Average male vocal tract length: 17 cm.
By fucking around scientifically with perceived pitch and vocal tract length, scientists wanted to discover something about psychology. They did. They found that screwing only with vocal tract length affected listener's perception of gender, size, and age. Only by fucking with pitch could they affect perceived attractiveness and health. Fucking with pitch in the same direction as fucking with length produced the best results. Also, they think that larger women prefer longer vocal tracts and lower pitches. Also, something about deer.
Anecdotal evidence has suggested that males with a vocal tract length of ~17.6 cm look seriously dead-on killer in the right blazer.