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Subject: Re: musical instrument tuner

Date: 05/08/03 at 11:33 PM
Posted by: Dean Huster
E-mail: dhhuster@semo.net
Message Posted:

In Reply to: Re: musical instrument tuner posted by John Dunn - Consultant on 04/08/03 at 1:45 PM:

John, on the previous thread you cited, one question remained unanswered. I thought I'd post that answer here regarding the actual frequency of the notes. The highest note on a piano keyboard (C'''') is 4186.008 Hz. The frequencies of all the notes other than "A" are irrational numbers since they are derived from oddball roots. Here's the piano's "top octave":

C = 4186.008 Hz
B = 3951.064 Hz
A# = 3729.308 Hz
A = 3520.000 Hz (exactly)
G# = 3322.436 Hz
G = 3135.964 Hz
F# = 2959.952 Hz
F = 2793.824 Hz
E = 2637.020 Hz
D# = 2489.014 Hz
D = 2349.318 Hz
C# = 2217.460 Hz

and finally back to C, an octave lower at 2093.004 Hz, which is exactly 1/2 the upper octave frequency of 4186.008 Hz.

Each note one octave lower is 1/2 the frequency. Concert pitch is A 440 or 440 Hz for the A above "middle C". An octave up from that, the A is 880 Hz. An octave below that is 220 Hz. The same is true for the octave relationship for all the notes: the next octave up is double the frequency and the next octave lower is half the frequency. This is why inexpensive electronic organs use a "top octave generator" and then twelve sets of binary dividers to derive all the notes. It's also why those same cheap organs always sounded so "flat", lacking color, depth, etc. as compared to the pipe organ they were trying to emulate. Try as they might, even a freshly tuned pipe organ won't be perfectly in tune, which is why it sounds so wonderful and magnificent.

A microphone and frequency counter is difficult to use to tune a piano because most of the piano notes (other than the lower notes) actually strike two or three strings at a time, giving the piano a richer sound. The tuner tries to make each string for a particular note in perfect tune with each other, but it will never hold. And those three notes slowly beating against each other will drive a frequency counter nuts, resulting in an erratic display. You have to dampen two of the three (or one of the two) strings and tune them individually just as a piano tuner does.

Dean

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