trichords unisons

[Jason Kanter]

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BEATS are based on physical cycles per second. A440 means 440 cycles per
second; if that is played along with anothert string at A439, the 440 cycles
per second and the 439 cycles per second will make a "beat" of one per
second as the two strings go in and out of phase with each other.

CENTS are an arbitrary mathematical division of a semitone's "distance" into
100 parts. Cents at A440 are based on the distance to A#, which vibrates at
466.2 cycles per second, so each cent there is about 26.2/100 or .262. So
the cents distance from 439 to 440 is just under four cents.

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jason kanter * piano tuning * piano teaching
bellevue, wa * 425 562 4127 * cell 425 831 1561
orcas island * 360 376 2799
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From: "Paul Chick \(EarthLink\)" <tune4@earthlink.net>
Reply-To: pianotech@ptg.org
Date: Wed, 5 Jun 2002 08:10:33 -0500
To: <pianotech@ptg.org>
Subject: Re: trichords unisons


Richard
Brain fog this morning is giving me trouble understanding the
difference/similarity of cents and bps (beats per second).
You stated the difference between 440 and 439 (1Hz) is almost 4 cents. This
interval beats at about one bps.  Where did I get the idea that the 1 Hz
difference between 440 & 439 was nearly 4 bps.  Being an aural tuner I can
relate to beat rates easier than cents deviations.  The math/science of
tuning is not my strong suit.  Do you know of a book that would explain
this?  My curiousity is getting to me.  Thanks for your continued input to
the list.  Many are grateful for your skills and insights.

Paul Chick
----- Original Message -----
From: "Richard Moody" <remoody@midstatesd.net>
To: "Pianotech" <pianotech@ptg.org>
Sent: Tuesday, June 04, 2002 11:51 PM
Subject: Re: trichords unisons


>
> > The difference between 440 and 439 is almost 4 cents.
> From 880 to 879 nearly 2 cents.   From 1760 to 1759 almost 1
> cent.    All of these intervals beat at one bps.
> The reason the cents get smaller is
> that the intervals of one cycle per second difference are
> smaller at higher frequencies.   Any two frequencies make an
> interval.
> An interval can be expressed as the ratio of their
> frequencies and that
> can then be expressed as cents.  The interval 440/439 is
> larger than
> 880/879.  Twice as large actually as they are an octave
> apart.   ---ric
>
>
>




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