On Fri, 29 Sep 2000 17:47:37 +0200, Hans-Georg Michna
<hans-georgNoEmailPlease at michna.com> wrote:
>fields at login.itd.umich.edu (Dr.Matt) wrote:
>>>There is no mathematical concept of "small". The closest thing mathematics
>>provides is "finite".
>>>>one below 20.
>>>19 works.
>>David,
>>maybe no mathematical concept, but definitely a biological and
>physical one. The steps between the tones have to be big enough
>that the human ear can very easily and clearly distinguish
>between them.
>>Given the choice between 12 and 19, we're probably not surprised
>that nature and our biology preferred 12. 19 tones would be
>unwieldy and unnecessarily complicated. I would guess that
>nature simply chose the lowest number for which the mathematics
>of hitting close to 3/2 and 4/3 happen to work.
Why don't you listen to some Karnatic music. Those people know how to
distinghuish, IIRC (and otherwise Todd will correct me) more than 90
pitches in an octave. You haven't heard intonation until you heard a
good Karnatic performance.
--
Samuel
A prelude by Johann Sebastian Bach performed by the guitarist, Lord Baden Powell
- Chr. J. van Geel