NetNews Usenet Archive 1992 #18/NN_1992_18.iso/spool/rec/audio/11721

Internet Message Format | 1992-08-21 | 1.7 KB

Path: sparky!uunet!olivea!hal.com!decwrl!decwrl!world!DPierce
From: [e-mail] (Richard d Pierce)
Newsgroups: rec.audio
Subject: Re: Math problem - pitch control
Message-ID: <[e-mail]>
Date: 21 Aug 92 15:34:35 GMT
References: <[e-mail]> <[e-mail]>
Organization: The World Public Access UNIX, Brookline, MA
Lines: 31

In article <[e-mail]> [e-mail] (Simon Turner) writes:
>
>I believe it's just under +/- 2.  Semitone spacing (in the equal-tempered
> scale) is defined as the 13th root of two or approx. 1.054766.
>
>Two semitones are thus 1.112531 apart, or 11.25%
>

Yo, Simon, I don't know what musical scale your talking about, but the one
that sits on my keyboards and resides thoroughly entrenched in my theory
books on tuning says that there are 12 intervals (or semitones) per octave,
not thirteen, and in an equally tempered scale each semitone is thus 1/12
of an octave:

        C<->C#<->D<->Eb<->F<->F#<->G<->G#<->A<->Bb<->B<->C

suggesting very strongly that an equally tempered semitone is the 12th
root of two, or roughly 1.059463094. Two semitones span a ratio thus of
1.189207115 (I will concede that while I am VERY good at tuning a
harpsichord, I probably don't worry beyond the 4th decimal place).

An equally tempered 5th, which encompasses 7 semitones, in your scheme would
have a ratio of 1.45242, under a 12 semitone octave would have a ratio of
1.49831, which is very close to 1.5, or a ratio of 3:2. Equally tempered 5ths
are very close to pure.

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