# Sound & Music - Ptolemy Reduced Frequency

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1. Feb 28, 2017

### Torrie

1. The problem statement, all variables and given/known data
This is a homely. We were instructed to make a monochord and find and mark C5, G4, F4, E4, D4 & C4 by multiplying our starting length with the length rations (C5 = 1/2, G4 = 2/3, F4 = 3/4, E4 = 4/5, D4 = 8/9, C4 = 1)
Then we used "Ravenlite" the application to measure the sound frequency after holding the string at the note, and dampening the opposite side. From there, we needed to divide the frequency by the Frequency Ratio, which were the inverse of the length ratios. Then we were asked to plot the ratios.

2. Relevant equations
We were supposed to tune C4 to 300 Hz. Done.

3. The attempt at a solution
I have measured the frequency of each note.
(C4= 300Hz, D4 = 317, E4 = 348, F4 = 390, G4 = 419, C5 = 531)
But when I divide those measured frequency there seems to be no pattern at all with the frequencies. And I can hear that the the frequency gets higher, as the string gets shorter, but the reduced frequency doesn't come off that way.
(c4 = 300 Hz, D4 = 281.78, E4 = 278.4, F4 = 292.5, G4 = 279.3, C5 = 265.5)

Am I on the right track? Or doing something wrong??

2. Feb 28, 2017

### haruspex

It looks like the length of vibrating string is a bit longer than you think. E.g. if you measured it as L, but it's really L+x, then when you halve it to go up an octave you get a length of L/2+x instead of L/2+x/2. If that is the right explanation then x is approximately L/6.