Klarinet Archive - Posting 000659.txt from 1998/11

From: David Renaud <studiorenaud@-----.com>
Subj: Re: [kl] Re: A few "cents" worth please - was _[kl]_Concert_A_pitch,_again?
Date: Wed, 18 Nov 1998 06:11:50 -0500

Correction-
Yes, its two cents, not four between 440 &441
, thanks for the math..
I was rattling off numbers from memory,
and getting my octaves confused, sorry.

A cent is 100th of a semitone, therefore a cent
of any given octave is double the
number of Hz of the octave below it.
A440, A880, A1660, is an exponential curve.

A440,
A# 466.16, B493.84, C523.20, C#554.20,
D587.2, D#622.24, E659.2, F698.4,
F#739.84, G783.84, G# 830.56,
A880

Multiply by 1.0594631 to get the frequency of the semitone above,
Divide to get the frequency of the semitone below

John Travis has a publication, "Lets Tune Up" has extensive explanations,
charts,etc. , of the evolution and development of equal temperament

Hiroshi Nagatsuma wrote:

> My further question. I would like to have knowlegeable people's instruction.
> Octave means the frequency is doubled: if A1@-----.
> Equal temper means each interval is devided by 1/8 th root of 2, namely
> 1.0905077...(it becomes 2 by self-multiplying 8 times),then
> B1@-----. If this is true(I think so), intervals are
> devided like this by cents not equaly but somewhat logarithmically.I know an
> equal tempered interval is divided to 100 cents. But it does not seem
> equally devided.For example if A1=440Hz and B1=479Hz, 1cents does not mean
> (479-440)/100@-----. Maybe 1/100 root of 1/8 root of 2, namely 1/800 root of
> 2@-----. If this is true, a tone 4 cents higher than 440Hz is
> 1/200(@-----. By this guess 442Hz is
> 5.234...(@-----.
> ("ln" means natural logarithm).I am not sure this is right! Puzzled.?????
> Too much arithmetics???
> FYI:I read somewhere that human hearing is logarithmic not linear.
> ---
>
> >
> >
> >

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