Primes as Notes

Page 1 from the Prime Listening Guide

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Method One: We could take each note on a keyboard and assign it a letter, in fact, that is exactly what the MIDI standard does. It has 128 different notes. Middle C is 60, C# is 70, D is 71... This allows us to "play" the small primes by just playing the corresponding notes. You can hear this by clicking on the ear on the left (or use the eye to view the score).

The problem with this approach is that it only allows us to play a few primes (at most those below 128) and sound cards (as well as human ears) have difficulty with sounds at the end of their spectrums. So this will seem to start with silence.

Fortunately there is an easy way to get the sounds in our normal hearing range, but first we pause for a question break.

You should correctly answer at least one of these questions before moving on to the next page.

Questions

(Note that *=easy question, **=medium, and ***=hard.)

1. * What is the 10th key we would play? ("2" is first, "7" is fourth.)

   19, 23, 27, 29.

2. ** The MIDI standard has just 128 keys/notes, but suppose we had a very long keyboard. Could there be a keyboard large enough to play all of the primes? (It would need at least as many keys as there are primes--how many is that?)

   no, yes.

3. *** As we play primes using this method, we skip over the composite number keys. If we could play all of the primes, what percentage of the keys would we end up playing?

   0%, 31.4%, 61.8%, 100%.