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## RE: [Nature Recordists] RE: Marty's Magic Number

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• Think I can figure out your question (but realize that my students drug me to the bar after class ended tonight and I am not really responsible for being
Message 1 of 7 , Nov 1, 2001
Think I can figure out your question (but realize that my students drug me
to the bar after class ended tonight and I am not really responsible for
being logical and old grannies are not supposed to be bothering their
fragile brains with logs and exponents and such but......)

Marty's Magic number we will call A (could have been X but I liked A
tonight)

You know that to get from Note 1 to a note a half tone higher you multiply
the frequency by A. We will use F1 to stand for the initial frequency.

to raise it an octave you must raise it 12 half tones or

F1*A*A*A*A*A*A*A*A*A*A*A In old FORTRAN notation A**12 indicating A to the
power 12... sorry I work in plain text and do not have exponents.

We know that the frequency of a note an octave higher is twice that of the
original note SO.... 2*F1 is equal to the note one octave higher

OR....

F1*A**12 = 2F1 (or F1 multiplied by A 12 times is equal to twice the
original frequency)

Dividing both sides of the equation by F1 you get rid of them and are left
with

A**12 = 2

To get Martys magic number, A, we have to handle that messy exponent and
that calls for the magic of logs.

Take the logarithm of each side..

ln(A**12) = ln(2)

12*lnA = ln(2)

ln(A) = ln(2)/12

taking the exponential of each side of the equation

exp(lnA) = exp(ln(2)/12)

But the left side of the equation is merely A

So you get A = exp(ln(2)/12) or
A = 1.059463094 or at least that is what I got when I typed
=exp(ln(2)/12) into an excel worksheet (couldn't find my slide rule)

Is that close enough to your number?

Note it does not matter what base you are working, base2, natural logs or
base10 etc just as long as your base is consistent throughout

Happy Halloween - I am headed for another chocolate bar then to get some
sleep - a three hour class of bird and butterfly identification has done me
in. Hope I managed to explain this clearly

Barb

-----Original Message-----
From: Marty Michener [mailto:marty@...]
Sent: October 31, 2001 1:18 PM
To: naturerecordists@yahoogroups.com
Subject: Re: [Nature Recordists] RE: Log base 2 and Halloween Sounds

>HI Barb: I love discussions of sound and music and numbers, esp.
>logs. All the sensory systems seem to do log input tricks.

Here is a question that is seldom asked or even wondered,
that I asked myself in high school:

What is the numerical music interval, the number by
which you multiply any music note by to get the
next (halftone) above it. Hint twelve of this operation
makes exactly an octave.

I use this number off the top of my head to at least
get music teachers attention and wonder some about math.

Ans: ca. 1.0595 - But how do you get it? - it is almost as
handy to know as pi, since you can always figure out the pitch
of any note starting with A=440 and then multiplying a lot. ;^)

my very best,

Marty Michener
MIST Software Associates
75 Hannah Drive, Hollis, NH 03049

coming soon : EnjoyBirds bird identification software.

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• Barb & recordists: Barb is exactly correct. In my own words, any number A that you use as the geometric series constant, must, when raised to the twelfth
Message 2 of 7 , Nov 1, 2001
Barb & recordists:

Barb is exactly correct. In my own words, any number
"A" that you use as the geometric series constant, must,
when raised to the twelfth power, be exactly 2.00.

Or: A = 12th root of 2.00, and of course I rounded to 1.0595.

I also have a son who is both mathemagical and musical,
now taking Honors Music Compositon, 11th grade. His
favorite subject. He is way over my head in both subjects.
If A=440, then B is 440 x A^2, C is 440 x A^3, etc.

best to all,

Marty Michener
MIST Software Associates
75 Hannah Drive, Hollis, NH 03049

coming soon : EnjoyBirds bird identification software.
• Barb how nice to have such a clear and logical explanation. A rare thing these days. I bet your students all get high marks! Best wishes from down under.
Message 3 of 7 , Nov 1, 2001
Barb how nice to have such a clear and logical explanation. A rare thing
these days. I bet your students all get high marks!

Best wishes from down under.

Stuart Fairbairn
fbairn@...
Sydney Australia
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