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'[OT] Tones on the Piano'
1999\11\03@124337 by Darrel Johansen

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Dave Johnson wrote>
>Yes, the current scale is the equal tempered scale (which just means that
>the intervals between all adjacent notes are equal). Originally the notes
>were based on the "ideal" frequencies exhibited by vibrating strings or
>columns of air - it came from physics - but the modern scale has been
>shifted around slightly to even up the intervals. In fact, it was during
>Bach's time that the changeover occurred: Bach was one of the main
>proponents of using equal temperament, but many people at the time
>thought it was an abomination. In fact, Bach wrote the Well-Tempered
>Clavier in part to demonstrate how useful equal temperament could be: you
>can play a piece in any key on the same instrument without re-tuning. In
>"true" temperament,  instruments had to be tuned to a particular key, so
>you coouldn't, for instance, change keys in the middle of a piece.

>You can find avante garde music today that uses "true" temperament, I've
>never heard it but people tell me the difference is definitely
>noticeable, and kinda strange :-).

For an excellent book on this topic see "On the Sensation of Tone" by
Herman Helmoholtz.  Equal temperament is possible on the piano, and is
exactly reproducible on a keyboard synthesizer, but most piano tuners
"fine tune" the equal temperament and end up with something a little
in-between, especially for the higher notes on the piano.  When playing
a wind instrument or singing, without piano accompaniment, often the
tuning will vary from equal temperament because the harmonies will be
much more satisfying (again, see Helmholtz).

Other temperaments are heard not just in avant garde music, but in
other cultures including native American.  Middle-Eastern music divides
the tones up even more divisions.  That allows closer harmonies to the
"ideal" physically derived ratios than equal temperament, as well as
providing nuances that are not notated (which doesn't mean they aren't
used, consciously or not) in Western music.

Darrel Johansen

1999\11\03@140425 by Harold M Hallikainen

picon face
On Wed, 3 Nov 1999 10:46:25 -0700 Darrel Johansen
<spam_OUTdarrel.johansenTakeThisOuTspamMICROCHIP.COM> writes:

>For an excellent book on this topic see "On the Sensation of Tone" by
>Herman Helmoholtz.


       By the way, Herman Von Helmholtz published what we know as
Thevenin's Theorem in  1853, while Thevenin did not publish it until
1883.  See http://www.hallikainen.com/rw/theory/theory5.html .

Harold


Harold Hallikainen
.....haroldKILLspamspam@spam@hallikainen.com
Hallikainen & Friends, Inc.
See the FCC Rules at http://hallikainen.com/FccRules and comments filed
in LPFM proceeding at http://hallikainen.com/lpfm

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