Here's your local engineer and amateur physicist jumping into deep water
again. It's been a long time since I have read my piano tuning guidelines
but I remember setting the temperance octave [A below middle C to A above
middle C] spot on equal and then tuning the next octave up and then the next
octave down [A to A] pulling/stretching the upper octaves sharp 1.5 to 2.0
cents and the lower descending octave 1.5 to 2 cents flat. Repeating this
octave step tuning was done in alternate succession until all strings above
and below were pulled up to pitch. This stretching is done to avoid
sympathetic excitation of harmonically related strings which would produce
second order distortion and a muddy response. I did not know this back in
the day and the first piano I tuned came out sounding like any old lounge
lizard's studio piano at a sing along bar. It was later on that I discovered
the different flavors of tempering and stretching. Way back in the day
[Mozart et al], aside from adding color to octaves it was noted that various
forms of tempering; Pythagorean, Just Intonation, Quarter Meantone etc. had
an effect on the tonal quality of the instrument as the closer you come to
Equal Temperament the more pronounced the distortion. If I remember
correctly A0 on a concert grand would end up about 15 cents flat from A3 and
conversely A7 would be about 15 cents sharp. This stretch curve is about
doubled for upright pianos. When done skillfully the upper register octaves
have a nice "ring" to them. I tune my wife's autoharp stretching the same as
I would for a concert grand piano.
Aside from my little handheld KORG tuner I have a program called AP Tuner in
my laptop computer. It has "stretch" tables built in that can be selected
and I highly recommend it for piano, autoharp, and hammered dulcimer tuning.
Now I've said all that in order to set the stage for the following three
questions; First, for three octave diatonics is +/- 1 cent stretch either
side of the octave from hole 4 to 7 sufficient? Has anyone ever tried to
excite reeds with high volume audio to verify harmonic excitation? Is there
really a problem with second order distortion that is seen in stringed
instruments and do harp manufacturers do anything about it when tuned at the
factory?
For more detail I would suggest "Music, Physics, and Engineering"
(9780486217697)by Harry F. Olson... it's in paperback from Cambridge
Press... Amazon has it and you can even find PDF downloads for free on the
Web. It is a great book and you don't need to be a physicist or engineer
[though it might help to understand the math] to understand how all the
different instruments discussed work.
Joel B. Chappell
21 Billings Street
Milford, NH 03055
-----Original Message-----
Subject: Re: [Harp-L] Stretching Exercises
Great info. I haven't got to the tuning stages yet, so I saved this email
in my Harp Tweaking folder.
The human ear might not be able to tell 3c in a blind experiment, but you
sure can hear if a note is not zero-beat with another. It's one way I get
precise tuning on my guitars by listening to the beats and harmonics and
zeroing them. It sounds better farther up the neck that way. If I use the
chromatic tuner and tune those notes right on pitch, they have to be tweaked
again to get them to sound spot on.
Thanks again for real info I can use.
When life asks you to jump in...
Splash!
----- Original Message -----
From: "Richard Sleigh"<rharp@xxxxxxxxxx><snip>
They may be textbook perfect formula wise and sound like crap. Reeds are
ornery critters and since they mess with
you, you gotta mess with them till they behave.
We all end up finding something that works for us by trusting our ears and
being stubborn enough to keep tuning till we get the hang of it.
Richard Sleigh