From: lasner@watsun.cc.columbia.edu (Charles Lasner)
Subject: Re: Radio UL
Reply-To: lasner@watsun.cc.columbia.edu (Charles Lasner)
Organization: Columbia University
Date: Thu, 9 Apr 1992 06:31:23 GMT

In article <1992Apr9.005748.1609@zorch.SF-Bay.ORG> phil@zorch.SF-Bay.ORG (Phil Gustafson) writes:
>In article <1992Apr8.004651.6300@hpcvaac.cv.hp.com> billn@hpcvaac.cv.hp.com (bill nelson) writes:
>>> [some orchestras tun a bit high to get a "brighter" sound]
>>
>>And just what do they do with the fixed span instruments, such as flutes and
>>the woodwinds? The idea would work fine for the string instruments, and such
>>instruments as the trumpets which have a tuneable section. Why do you think
>>that the instrument that is often used as a tuning reference is a flute? It
>>is because the span between notes is fixed and cannot be tampered with.
>>
>
>Woodwinds have tuning slides, too.  The mouthpiece wiggles in and out a bit.
>The keys give only approximate intonation anyway, the musician knows how to
>fudge up and down a bit with twists of breath and lip.  Anyway, orchestras
>tune to the oboe, probably because its sound is so nasty nobody can ignore it,
>or because it's so cranky to play.
>
>>: 	Remember too, that most instruments that span more than a couple
>>: 	of octaves (pianos, notoriously) are not tuned equally-tempered.
>>: 	They're tuned slightly sharp at the high and low ends.  Makes
>>: 	them sound more 'in tune' and 'brighter' to those of use with
>>: 	less-than-perfect pitch.  No idea how it affects people that are
>>: 	afflicted with perfect pitch.  Sends them screaming from the room,
>>: 	I suspect.
>
>>The reason for the tempering is to make the notes sound "fuller" or
>>"broader". The notes would sound brighter if the slightly sharp and
>>flat strings were damped. 
>>
>The reason for tempered tuning is to allow the instrument to play equally
>well in all keys:  basically it makes everything a bit out of tune.  
>Fifths played on brass instruments are in tune.  On a piano, they're not

Not quite.

Electronic keyboards are tempered such that each note an octave apart is
exactly 1/2 the frequency (twice if an octave up) of the first.  Further,
the notes themselves are the twelth root of two times each other to make
the whole thing work mathematically "perfectly".

But pianos aren't tuned this way.  In fact, the lower octaves are flat of
this ideal, and the higher octaves are sharp of it.  Essentially only the
central octave of a piano can be considered evenly tempered.  

The purpose of this is to deliberately be off to create the characteristic
"chorus" effect of the beating of all the harmonic products when playing
chords that simplisticly appear to be in simple ratio to one another.

Also note that most electronic keyboards will also have all the notes
perfectly in phase with each other for any one string of octavely-related
notes, since there is only one master oscillator for them  (In some designs
there is only one master osciallator for all twelve, because they are all
derived from one master osciallator and count-down circuit) so there are
at most 12 master oscillators.  So, octaves pressed together form unison
sounds that vary only in harmonic content whereas individual oscillators
will produce phase relationships that change.  A piano will go further
because all the frequencies are "off".

So, a piano is meant to be "off" relative to the other instruments, as
this chorus beating effect will happen between instruments as well.

cjl (not part of a five man electrical band; sign sign everywhere a sign :-))