[CAUT] Algebra follow up

[Edward Sambell]

If you would like a little brain teaser related to our line of work and perhaps 
amaze your (piano tech) friends, pose the following question:

What is the note name  of the (n)th partial of a given note. It can be caculated 
mentally. and though prime numbers can be used, generally do not bother with 
them. Ignore the pitch location. Example:

What is the note name of the 100th partial of C?
Ans. G#

or

What is the note name of the 36th partial of F#?
Ans. G#

How is this done? I am sure you can figure it out.

Ted S






________________________________
From: Susan Kline <skline at peak.org>
To: caut at ptg.org
Sent: Thu, September 23, 2010 1:18:16 AM
Subject: Re: [CAUT] Algebra follow up

 Thank you for showing your work. I nibbled around the edges, tried a     few 
sample figures to see how they worked, didn't quite get there,     went off and 
did something else, but still wondered how it should be     solved properly.

(Lazy) Susan

On 9/22/2010 1:08 PM, G Cousins wrote: 
 Correct oh (mathematically) wise one....ding ding ding ding. 
>
>Full proofing for those who care:
>
>The           check was for $31.63.
>The teller then gave him $63.31
>He spent .05, and then has $63.26, which is twice the check.
>
>Let x be the dollars of the check, and y be the cents.
>The check was for 100x + y cents
>He was given 100y + x cents
>and we are told that
>
>100y + x - 5 = 2(100x + y)
>Expanding this out and rearranging,:
>98y = 199x + 5
>
>or 199x ≡ -5 (mod 98)
>or 98*2*x + 3x ≡ -5 (mod 98)
>3x ≡ -5 ≡ 93 (mod 98)
>this leads to x = 31
>The next positive value of x which satisfies this mod equation           is x = 
>129, which would mean y = 262. But this is prohibited,           since y<100. 
>
 
>BTW 
>Been way too long since my 8th grade memories were dusted off.       Sister 
>Marie Regina would be pleased. Now if I canget this        #&$*@^   L  to work 
>with me.
>Maybe a Single Malt WOULD help  ={D . . . . . . .
>GerryC
> 
>________________________________
 To: caut at ptg.org
>From: pwilliams4 at unlnotes.unl.edu
>Date: Wed, 22 Sep 2010 14:25:57 -0500
>Subject: Re: [CAUT] Algebra follow up
>
>$31.63 is what I got.  I dont         know why my brain was all a-kimbo on 
>Monday.  Lack of malted         beverages, me thinks! 
>
>
>Paul 
>
>NOW: a piano thing! fancy that?!          Did anyone get my pic of the glue that 
>WNG sent me? Is this the         same stuff y'all have been using and is said by 
>you to be         heatable and hammer-movable?  My tests prove otherwise.  NO         
>MOVING ALLOWED.  Perhaps the moon and stars weren't aligned         properly at 
>that exact minute... 
>
>
>Paul 
>
>
>
>
>From:  G Cousins <cousins_gerry at msn.com>  
>To:  CAUT <caut at ptg.org>  
>Date:  09/21/2010 06:16 AM  
>Subject:  [CAUT] Algebra follow                 up 
>________________________________
 
>
>
>Paul,
>Hope you got the answer(s) before the School Bus arrived.  =)
>
>
>Here's a follow up question:
>
>Birch walks into a Vermont bank to cash a check from one of his         tunings. 
>
>By mistake the teller gives him his dollar amount in change, and         his 
>change amount in dollars. 
>
>On the way home he spends a nickel, yup that's right a nickel,         and now 
>notices he has 2 times the amount of his check. 
>
>How much was the check? 
>
>


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