May the 4ths be with you

[Richard Brekne]

Richard Moody wrote:

> > If you tune this same range such that the 6:3 are held beatless,
> > or at 0.5bps as they start out in the example above, then you'd
> hold
> > the 8:4 up a while longer... this would allow for better matching
> of
> > those triple octaves and would represent quite a stretch. Though
> the
> > 4:2's and 2:1's  would probably beat obnoxiously.
>
> Maybe try a different machine, I don't know what to say----with
> beats like that it seems there is a lot of room for improvement.

Ric, this wasnt a machine tuning. It was simply calculated frequencies
using the inharmonicity equation with measured (and published)
inharmonicity constants for a A3, A4, A5, A6. The numbers are what
they are. Unless there is something wrong with the inharmonicity
formula, I dont see how they can come out any different. Seems pretty
usuall to me tho... Tuning A3 / A4 as pure 2:1 octave types is going
to result in some movement up the ladders, especially when you try and
match A5's partial ladder to that.

The two graphs tho were from a tuning done by Dr. Sanderson for an
article he wrote way back when. Grin.. he termed the tuning a "well
tuned piano".

>
> >. We do manage to create a tuning
> > that is ET in more ways then not, and the fact that we kill all
> key color is good evidence of that.
>
> Speak for yourself on "we kill all key color".  I believe that is
> the most specious sentiment in the history of music especially
> when applied to temperament.  It is a musician's thing, if they want
> to
> talk to piano tuners about it I am all ears, but ain't holding my
> breath.

Well, I will be the first to enjoy discussion about key colour in ET.
But that being said the kind of key color found in HT is taken out of
the equation in a well executed ET. I mean thats kind of the whole
point of ET.. isnt it ??? For example... all major 3rds at 13.7 cents
apart (I think thats the right number ... Ed ?? )

I certainly like very much of the rest of your discussion on key
colour Ric, and I have enjoyed your thoughts on the matter every time
they come up. but I think personally we have to admit that there is at
least a major type of key colour found in HT's that is not in ET. But
perhaps I am wrong in this. In any case It would be interesting to see
how well tuners and musicians alike could identify these effects AFTER
having a good deal of ear training to reaquaint our ears to these
things.

I am personally not so swayed by aural comparison tests we hear talk
about today as to what conclusions we can draw from them.... that is
other then to conclude that the musical ear today is almost frightenly
ignorant of our rich and colorfull temperament past. I have conducted
a few such experiments myself and I find that those who know what they
are listening for (of which there seem to be sparse few of) know right
off what they are hearing.... and those that dont remind me much of
that first day of tuning school where that "old guy" was trying to get
me to hear the beats.

Many thanks for your interesting thoughts.

Cheers !

--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html