student needs help : too late :..(

[Richard Moody]

The problem is finding the frequency of notes of the piano. 
	The formula is Freq.times the 12th root of 2 gives the Freq of next note
up, or in spread sheet terms, looks like       F* 2^(1/12)
	To make it simple, the first note on the piano is 27.5 Hz  (cycles per
second)  there 88 notes on the piano.  How do you find the frequency of
any note? 

Well to find the second note on the piano the formula would look like 

	27.5*2^(1/12)   = 29.135

To find two notes up up  write this  27.5*2^(2/12).  

But this is actually the Freq of the third note of the piano. We want a
formula that will give us the F of the number of the note.  So we have to
start with the freq of the note below the first note. To find that use
this formula. 

	27.5*2^-(1/12)    =    25.957
	
Notice the minus sign after the ^ sign.  Ok NOW use this to find note #1

	25.957*2^(1/12)  =  27.5


So lets test this.  We know the piano is tuned to A-440. Which means note
#49 which is A is tuned to 440 Hz.   So......

	25.957*2^(49/12)    =    440.00774   That's worth a gold star. *   Use
six decimal places to get it exact.           


	number of note = 12/LOG(2)*LOG(440/25.956544) = 49

or n# = 12/LOG(2)*LOG(F/25.956544)





----------
> From: Don <drose@dlcwest.com>
> To: pianotech@ptg.org
> Subject: student needs help any takers
> Date: Monday, March 23, 1998 9:58 AM
> 
> Hi all math types!
> 
> Can anyone out there help Andrea?
> 
> >X-POP3-Rcpt: drose@louise
> >Date: Sun, 22 Mar 1998 20:00:10 -0600
> >From: Andrea Ritchie <andrea@graceland.edu>
> >X-Mailer: Mozilla 4.04 [en] (Win95; I)
> >To: drose@dlcwest.com
> >Subject: Please help me
> >
> >I am a college student with an assignment to find an equation that
> >expresses the relationship between the frequency of a piano key and its
> >location on the keyboard. I also have to write a function that takes
the
> >frequency and returns the key location, and I have to write a function
> >that takes the key location and returns the frequency. I guess my
> >question to you is if you could possibly tell me any information about
> >piano keys and their frequencies, anything to help me with this
> >assignment. 
> >Andrea Ritchie  (andrea@graceland.edu)
> >
> >
> Regards, Don