Re: Western world tunning?

Subject: Re: Western world tunning?
From: Kevin Austin (
Date: Fri Jun 18 2004 - 13:33:50 EDT

At 10:14 -0700 2004/06/18, Jay Smalridge wrote:
>Somebody recently asked me why the western world divides up our
>octave into twelve portions? I began to research on the web only to
>find that the majority of files basically said "Its just because it
>is" or they over estimated my vocabulary skills (mesuring the
>interval in Cents?).
>I was wondering if anyone could tell me, or point me in the right
>direction of information:
>-why it is divided into 12 semitones,

This is equal temperament. Look up the history in a good reference
(such as the articles on Intonation in Grove's).

>-why it is based on 440Hz tunning,

It isn't particularly (anymore). The reference for 'A' has continued
to drift upwards for more than 300 years. Many european orchestras
tune to 442, and higher. The higher the reference, the more tension
on the strings -- the greater the 'projection' (brilliance) of the

>-why is there no E# nor B#...

There are, but in equal temperament they have the same key on the
piano, as G# and Ab share the same key. Taken from the circle of
fifth ..

Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# G# D# A# E# B# Fx
Cx Gx Dx ....

Once again, Grove's. B# and C differ by 23.4 cents (about 1/4 semitone).

>-why do different parts of the world have more intervals in an octave..

Culture and context. Western european music used to have more (one
finds harpsichords with both D# and Eb (etc)) keys, but the
development of (extended tonality) "required" the simplification of
the intonation system to handle something which is unique to european
music -- harmony. If one doesn't play three notes together in a
'functional' fashion, then intonation differences are of reduced

To be "in tune" in both E minor and C minor, D#/ Eb has to have a
compromise where neither is "in tune" (according to the Circle of
Fifths). They are both retuned a tad. This 1/4 semitone difference is
distributed across all twelve semitones putting each about 2 cents
(1/50th of a semitone) 'out of tune'.

also Pythagorean comma



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