New Problem: Guitar

Last year I asked (and answered) a question on why the frets of a guitar get closer together as you move down the neck.

Here are some extensions to that question:

• How can you tell the interval between two guitar strings, even if you have no musical training? (You can use a ruler if you want.)
• How can you find the half way point on a string even without the ruler?
• Why are the lower-pitched strings thicker?
• Now suppose you are standing in a hard, cement tube (like a sewer) whose ends are both closed. How can you use the guitar to measure the length of the tube?
• How could you use a metronome to measure the length of the tube?
• How could you use the guitar to find the half way point of the tube, as well as the one third point, one fourth point, etc.?
• How could you accomplish the same thing with the metronome? (Or maybe two metronomes?)
• Can you modify the techniques of the last few points to work when the tube is open on both ends, or open on one and and closed on the other?
• Why can you even tell different pitches apart when listening to them? Two different pure tones both just shake your eardrum back and forth. One might do it faster, but it’s not like your neurons are going to send 2000 messages per second to your brain for a 2000Hz tone and 3000 for a 3000Hz tone. Also, you need to be able to distinguish many frequencies at the same time in order to tell different overtones apart. How could one simple ear accomplish all that?

3 Responses to “New Problem: Guitar”

1. amzuko Says:

The last is of a different flavor than the rest.

2. Paul Murray Says:

1 – not sure about that. You need musical training to even know what an “interval” os.

2 – strike the harmonic near the middle of the string

3 – a heavier string accellerates more slowly in respose to the force resulting from the tension. So by altering the weight of the strings, you can gt diffeent pitches without great differences in tension (for a givel length).

4 – measure the length of the guitar, then find how many guitar-lengths long the tube is. Then mutiply. Also works wiioth a piano.

Or you can use frequency – the key number is that the speed of sound in air is around 300 m/s (I think).

5 – an open tube resonates like a closed tube of twice the length

6 – your inner ear has a membrane thats wide at one end and narrow at the other, wrapped up into a spiral. The neurons detect which parts of that membrane sympathetically vibrate.

… actually, I suspect that the inner ear mechanism is active: the membrane vibrates all the time, and the neurons pick up phase shifts. When this isn’t tuned properly, you have tinnitus.

3. Answer: Guitar « Arcsecond Says:

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