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PhiNotPi's avatar

What size should a room be to create a major chord?

Asked by PhiNotPi (12160 points ) May 30th, 2013

At my school, there are small “practice rooms” adjacent to the main band room. These are small rooms with solid walls, so they create a lot of echo and distort the sound quality of the instruments. Anyways, a few days ago I discovered that one of the rooms seems to be able to resonate at a frequency of concert G below middle C. Whenever that note is produced, the sound of the note is amplified to be much louder than any other note. My best guess for how this occurs is that the wavelength of the note matches the length of the room.

It is well known that rooms also have width and height along with length, which means that it could resonate at many frequencies. Would it be possible to tune the room to amplify a specific major chord (like G C E G)?

What would be the required shape and size for the room?

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3 Answers

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Cupcake's avatar

This article seems related. It’s all above my head. The section “Modal Density” towards the end discusses dimensions of small practice rooms.

Related to speaker position, this is an interesting read.

gasman's avatar

For a major triad you have a root, a major third above the root, then a perfect fifth. Forget the even-tempered scale & stick to simple Pythagorean ratios of fundamental frequencies: f, (5/4)f, and (3/2)f.

In terms of wavelengths if the root tone represents one unit then the other two wavelengths are 4/5 and ⅔. Using a common denominator of 15, these lengths are in the ratio 15:12:10. In fact if measured in feet that’s a nice size room with a tall ceiling, though the fundamental (about 112 Hz) is two octaves below A-440 – might sound muddy even if perfectly tuned. By comparison the long dimension of a box tuned to a major triad built on middle C on the piano (about 523 Hz) would be 25.8 inches long – the size of a microwave.

I’m ignoring harmonics, which might be important here. The first harmonic of the root pitch, for instance, sounds an octave higher so represents a chord inversion – EGC instead of CEG. Interesting stuff. No doubt there’s a vast literature on musically tuned rectangular sound resonators…

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