-----Original Message-----
From: Nathan Day 
To: Csound mailing list 
Date: Monday, April 27, 1998 6:12 AM
Subject: More on floats in Midi


>Simple 16 bit integers would allow you to divide 10 octaves into interval
>of 0.183105 cents, and a dynamic range of 130 dB into intervals 0.00198364
>dB, do we really need 32 bit floats or even floats at all.

Engineering of all sorts in general, and music engineering in particular,
has repeatedly found with pain and suffering that numbers deemed too precise
or too big to start with are nothing like big enough in the end.

Examples: 8 bit address space in calculator, not big enough for a few pages
of text.
16 bit address space in IBM PC, big enough for a chapter of a novel, but NOT
big enough for a color graphics video screen.
32 bit address space in current PCs and workstations, big enough for color
graphics, NOT big enough for a movie or for the index on a serious
database...
64 bit address space in new generation workstations, big enough for any
number of movies and entire large databases, but I suspect that in the
future, it will be found NOT big enough to hold entire libraries of entire
civilizations, or recordings of thought, or something...

8 bit sample word at 11025 KHz, big enough for cheesy game music, NOT big
enough for home hi fi.
16 bit sample word at 44100 KHz, big enough for home hi fi, but lo and
behold, NOT big enough for serious music in spite of claims to the contrary!
Music industry moves to 24 bit sample word at 96 KHz...

>Remember that
>midi is designed to represent music in a abstract musical way, not actually
>physical values like Hz and watts.

MY music is DEFINITELY represented in physical values such as Hz, location
in space by angle, phase, and loudness in dB.

>Things like tunings should be set in the
>synth not on your Midi keyboards or what every. All right dynamic tunning
>is an idea I myself find interesting but 0.183 cents should handle that.

Do not underestimate your own ears. Use Csound and synthesize sine tones 10
cents, 5 cents, 1 cent, 1/2 cent, 1/10 cent apart and SEE if you can hear
it. You have to allow not only the digits to represent that, but double the
number to allow for rounding errors in repeated computer arithmetic.

In short, it is most wise to err on the size of way too big. That means, in
practice, use the biggest size of number and most precision that the tools
allow. I guarantee you, you WILL end up hearing the difference.