Real instruments

[Harry Bissell]

Hi Roel (et al)

The only "comma" I have heard of is the "Pythagorean comma", (yeah... THAT
Pythagoras...) which refers to the difference in the Pythagorean tuning. If you
add up perfect fifths (they are sharper than equally tempered...) until you come
back around
to the tonic (several octaves up, of course) you will find that the original
note does not equal the note you end up on... therefore c is not equal to c'.

The Pythagorean comma is about 23.5 cents (100 cents to the semitone) so the "9
to a whole tone" might be just about right.

This tuning means that an instrument tuned to be "in tune" in the key of C will
be a little out in G and F, further out in D and Bb... until it is unusable for
any consonant sounds.

The issue of Piano dissonance is separate... Piano strings are more like "bars"
in that they are quite stiff (a perfect string has mass and tension but no
stiffness). This makes the upper harmonice sharper than usual. Pianos are
stretch tuned... the middle octave is right on... the upper octaves get
progressivly sharper and the lowers progressivly flatter.

The longer strings of the "Grand" piano have less stiffness than their shorter
cousins counterparts... so they are more "in tune" by comparison.

The equal tempered scale we use today (12th root of 2) is a bastard
approximation that has the advantage that the same composition played in any key
will be equally out of tune !!!

The perfect fifth (3/2) ratio is a favorite of mine since it can be digitally
(oops) synthesized from an analog VCO by dividing by three... very fatt.

BTW: string (orchestra) players actually play in "just temperment" where C# is
NOT EQUAL to Db (they do play different notes). Also why piano and violin can be
so obnoxious together unless the violinist is VERY skilled !!!

:^) Harry (who could go on for hours about this...)

Roel Das wrote:

> I'd figure to throw in my thoughts on this wildly going discussion, just to
> keep it going, really enjoying it as a classical pianoplayer (in spare time)
> that has only got a digital piano to practice on.
>
> I remember my previous teacher, a VERY good jazz pianoplayer, telling me
> about the natural harmonics of the piano, and how he was once playing a
> piece with wild arpeggios with the hold pedal, on the conservatories best
> grand piano, and how dissonant it sounded. Because of the natural overtones
> of the lower strings that sounded that much. I don't know the exact order of
> the overtones, but if you calculate the frequencies, i believe you only
> approximately get the notes that are supposed to be the natural overtones.
> (i've never calculated it, he was too much of a good player to doubt about
> this)
>
> And another point, a whole tone is divided into 9 comma's (or whatever you
> call it in English). A cross raises the tone with 5 commas, a flat lowers it
> with 5. So C# and Db differ one comma. This is never 'implemented' on any
> instrument for practical reasons. (Although I'd love to hear an instrument
> tuned this way.)
>
> This brings out the cultural aspects of tone recognition. How perfect CAN
> perfect pitch be?
> Any considerations on this?
>
> On the other side, i HATE instruments that are out of tune.
> I really like this discussion.
> All yours.
> Roel