How does a tone relate to a frequency?

June 21, 2012 11:00 AM

I have been playing around with Audacity recently trying to understand a bit more about sound in general. One question I'm having trouble wrapping my head around is: How does Tone and Frequency relate? For instance, the 2600 Hz is a high-pitched tone. Does that mean that anything that produced that same tone would be at 2600 Hz? And does it mean that for the entire range of human hearing -- all of those Hz -- that one tone corresponds to a particular frequency? I am looking for some basic explanation or even tools to play with...
posted by tcv to science & nature (13 answers total)

Tone and frequency are the same thing.
posted by bensherman at 11:03 AM on June 21, 2012

Frequency is the number of times an object oscillates per second. So a 2600hz sound is produced by a speaker cone, string, reed, etc. vibrating 2600 times per second.

Tone is sort of ill-defined. A lot of people use it interchangeably with Timbre which means "what makes a particular musical sound different from another, even when they have the same pitch and loudness". You might hear someone talk about how a particular guitar has "great tone". It is subjective.

In real life, sounds contain energy in multiple frequencies. So a guitar string vibrating at 2600hz might also have a weaker "overtone" at 5200hz. Different instruments have different sets of overtones. This is why a piano and a guitar playing the same note still sound different.
posted by scose at 11:07 AM on June 21, 2012 [3 favorites]

A pure sine tone will be made up of only a single frequency (the fundamental). Other tones (square waves, etc.) will have the fundamental plus higher frequency harmonics. More explanation.
posted by exogenous at 11:11 AM on June 21, 2012 [2 favorites]

scose: "This is why a piano and a guitar playing the same note still sound different."

I thought the only reason they sound different is due to the approach to the tone? I distinctly remember a physics class where the teacher recorded a piano 'C' and a guitar 'C', then cut out the first half second or whatever and replayed them back to back and they sounded EXACTLY the same.
posted by Grither at 11:17 AM on June 21, 2012

Not just the frequency of the spectral components but the relative phase will affect the sound as well.
posted by Golden Eternity at 11:22 AM on June 21, 2012

I thought the only reason they sound different is due to the approach to the tone? I distinctly remember a physics class where the teacher recorded a piano 'C' and a guitar 'C', then cut out the first half second or whatever and replayed them back to back and they sounded EXACTLY the same.

A piano and a guitar are both using the same physical process (a vibrating string). Try comparing a piano and a trumpet: Even after you cut out the approach, they're quite different.

A sine wave generates a "pure tone", i.e., a sound with exactly one frequency. Here's a sine wave at 440 Hz, which is a standard "a" note.

One more interesting thing about frequency and perceived pitch: To get one octave higher, you double the frequency. So 880 Hz would be an "a" one octave above 440 Hz.
posted by qxntpqbbbqxl at 11:43 AM on June 21, 2012

Different instruments have different sets of overtones.

The harmonic series is fixed, so this isn't quite right. But different instruments, depending on their shape, material, etc., will have different timbres because different overtones will be emphasized, even though they are all theoretically 'there.' When you hear a 'pitch' you are hearing the 'overtone' with the highest amplitude, when you hear the quality or timbre, you are perceiving the relative amplitudes of the harmonic series above that primary note.
posted by Lutoslawski at 11:46 AM on June 21, 2012

Right. That's what I meant - the relative volume of the overtones will be different.
posted by scose at 11:48 AM on June 21, 2012

I thought the only reason they sound different is due to the approach to the tone?

Both harmonics and envelope are aspects of timbre.
posted by ludwig_van at 11:51 AM on June 21, 2012

I don't see how any of the answers so far address your question. Let me try a more simple explanation. You are asking two questions: one is about the physics of sound waves, and the other is about human perception of those waves.

WARNING: SIMPLIFICATIONS AHEAD-

Let's compare hearing to seeing. Light is an electromagnetic wave. Some light has a long wave length, some light has a short wave length (vibrating slowly/vibrating quickly). The receptors in your eyes are tuned to pick out specific lengths of waves from the whole mess of waves that is hitting your eyes. When they do, they send a little blip to your brain. It's your brain's job to make sense of that blip and to transform it from a little signal to a perception.

For example, as you read this webpage your eyes are picking up a lot of light that has a wavelength around 510 nanometers. Your brain gets the signal and decides to perceive that light as... GREEN! There is nothing inherent about electromagnetic waves with a wavelength of 510 nm that makes them green. As a human, you have an organ to sense that kind of wave and a brain that gives it the name "green."

So back to sound and hearing then:

Your ears have receptors too. Instead of rods and cones siting on a retina (as your eye uses), your ears have little hairs lined up in a tube.

When a sound wave of a certain wavelength cause a certain little hair to wiggle, that hair sends a blip to your brain. So, as with light, there is nothing special about a pressure wave vibrating through the air at 2600Hz that makes it sound "high pitched." "High pitch" is simply the perception that your brain assigns to a specific range of sound frequencies, just as "green" is what your brain assigns to a specific range of light frequencies.

For a more detailed explanation of the physics of sound and hearing, please watch this FANTASTIC video by Vi Hart: What is up with Noises? (The Science and Mathematics of Sound, Frequency, and Pitch)
posted by stephennelson at 11:55 AM on June 21, 2012 [3 favorites]

Sir James Jeans' book Science & Music - though rather elderly - is a good introduction to how sound is made and how it is perceived.
posted by scruss at 12:09 PM on June 21, 2012

Guitars are particularly good at demonstrating timbre since you can play the same note (same frequency) on different strings, just at different frets. The difference in string diameter and length of the vibrating portion of the string result in very different sounds.
posted by tommasz at 1:22 PM on June 21, 2012

You can select some sound in Audacity and then use the Plot Spectrum command in the Analyze menu to see how much energy that sound contains at each frequency level. That way you can see the overtones that scose mentioned, and you can see the different mixes of frequencies in the same note played on a string instrument versus a reed instrument versus a human voice. (You can also generate different types of tones using Audacity itself, and then analyze them.)
posted by mbrubeck at 6:23 PM on June 21, 2012