DAC and real musical instruments

[jhaible]

> > > Yeah, and how accurate is a piano, Hammond organ, clarinet, violin,
etc?
> >Usually, around 0.5% to 0.3%
>
> I don't think so.

I thought this was the precision of resistor dividers in keyboards, not the
answer
about acoustical instruments.

>Not in any real world situations. At  least our piano isn't that accurate
right now. And >even if we have it tuned, how long will it stay that
accurate?
> The Hammons organ uses a fixed division ratio that introduces errors. I
don't remember >the integers, I suppose somebody else can fill us in. The
exact errors should be simple to >calculate.
> The intonation of the violin and clarinet is dependent on the skill of the
player. Maybe a >really good player can achieve 0.5% to 0.3% error on a good
day? Or maybe not.
> And in any case, the entire tempered scale is a compromise. So very high
accuracy is >rather pointless. Some intervals sound less than perfect even
if they are theoretically >totally in tune. An remember that pianos are
stretch-tuned, so they deviate from the true >scale on purpose.


Now acoustical instruments can be very bad for sure, especially cheap ones,
or when played by unskilled players. The worst being "recorder ensembles" of
kindergarden children on Christmas parties. Recorders not tuned to each
other,
playing in the highest ranges, create the most horrible beat frequencies.
OTOH, some instruments' going out of tune is almoust a feature, like the
infamous
mellotron (I for one wouldn't like it to be perfectly in tune on Genesis'
"Foxtrot" album.),
or like a church organ dropping in pitch when many notes are played.

The Hammond Organ's tuning is a case of its own. You can read everywhere
that
Hammond has cut corners by using the closest pitch from an equal tempered
scale
for overtones, rather than using whole numbered ratios. I always wondered if
this really was a limitation. Sure, you'd have some beating in a single note
(mixed
from several drawbars), but as soon as you play a chord, there should be
*less*
beating than with whole numbered overtones and equal tempered keyboard. (Can
anybody confirm this ?)

Piano's stretched tuning - wasn't this invented to make the piano sound more
"harmonic" in itself, because the harmonics of the lower strings derivate
from
whole numbered relations because of the strings' physics ? So stretched
tuning
would not be an example for an error that can be tolerated in the first
place,
but for an error that was carefully corrected as good as possible. (That is,
because someone decided it should *not* be tolerated !)
I have no real piano, so I may be wrong. Can someone tell us how large,
preferably expressed not in percentage but in beat rate, how large the
deviation
of a typical streched tuning piano and a "perfect" instrument that would be
playing along, is ?

What "are real good players" doing ? Often re-tuning their guitars or
synthesizers
on the fly, often doing slight variations of their finger position on their
violins
by ear ? (To the benefit of the listener) Throwing the mellotrons out of
their rig ?
(With doubtful benefit for the listener)

JH.