Stretching Octaves??
Joe Pulley
octaves came up. He says that often technicians will not tune to the
octave, but will tune a little sharp. This is especially true on the
higher keys. I am no expert (not even a novice) but I have never
heard of such a thing nor do I see why it would sound better than the
straight octave would. So, all you technicians out there, what is
the story here? Is my friend confused or am I clueless?
Thanks
Joe Pulley
pul...@rouge.phys.lsu.edu
Kurt Krueger
normally used can be described as equally bad everywhere). The
idea in tuning is to minimize beats (or, with equal temperment,
to make everything beat equally). The exception is octaves ...
they can be made beatless. An ideal string will vibrate
at a fundamental frequency and also at 2x (an octave), 3x, 4x, etc.
of the fundamental. An actual string tends to vibrate slightly
higher than 2x the fundamental. Thus if you want a beatless octave,
the octave needs to be tuned a bit higher than 2x, such that it
matches the 2x harmonic of the string an octave below it.
Mark E. J. Newman
The harmonics on a piano string go sharp as you go higher up the harmonic
series, because there is a "dead" area at the end of the string which does
not vibrate, making the string effectively shorter. The effect of this dead
area is greater for higher harmonics, giving rise to distortion in their
pitch relative to the fundamental. This problem is less with long strings
(like 9 foot) than with short (as in an upright) and is one of the main
reasons (possible *the* main reason) why a longer piano sounds better.
Technicians tune the octaves on a piano to be in tune with the harmonics
of the lower strings, rather than simply to be an octave above the lower
string. This avoids an unpleasant beating in the upper harmonics when the
two notes are played at the same time. On a typical six foot piano you can
expect to tune the octaves about three beats per second sharp.
Mark.
SerkinJ
(Joe Pulley) writes:
You ask a very good question. Why should octaves differ from the
mathematically-prescribed 2:1 ratio? This question has three aspects.
1)First, an instrument tuned with mathematically perfect octaves will
sound out-of-tune: flat in the treble and sharp in the bass. This is
because a string's harmonic series, of which the octave is the first
harmonic, conforms to the mathematical model only for an imaginary string.
Physicists tell us that in the real world, the inelasticity of the string
(and the stiffness of the soundboard and other components of a piano)
skews the harmonic series to the sharp side. This phenomenon is referred
to as "inharmonicity." If, for example, you tune the A above middle-C to
440 Hz, then the octave above must be tuned slightly higher than 880, to
blend with the slightly sharp first harmonic.
2)Perfect octaves on a piano, then, are of necessity a bit wide, just
enough to compensate for inharmonicity. In fact, however, octaves can be
stretched a good deal more than that, and the piano will still sound in
tune. Although I have heard many tuners object to such stretching as
excessive, some of the finest concert tuners widen octaves to their limit,
especially for concert venues. This additional stretch puts a "smile" on
the sonority and makes it project better. How much to stretch is a matter
of taste, but there is considerable latitude.
3)Many tuners who don't believe in stretching octaves for most of the
piano's compass, will nevertheless tune the extreme treble quite a bit
sharp and the extreme bass somewhat flat. There is a kind of aural
equivalent of an optical illusion which makes this sound better. The very
top notes (more-or-less the top octave) sound more brilliant, and the
lowered bottom notes add resonance, especially in chords and arpeggios.
Interestingly, the more one widens the octaves throughout the piano, the
less one needs this exaggerated stretching of the extremes.
I realize that I'm opening a can of worms by expressing these views.
Tuners have very strong opinions about stretching octaves. My feeling is
that it is a matter of personal preference; there is no right or wrong.
If some of the fine technicians who frequent this newsgroup would like to
continue this debate, I would be happy to participate and to share my
personal preferences.
John Serkin
John Brock
Ron Torrella <torr...@ux1.cso.uiuc.edu> wrote:
>I've read, with interest, the responses of Mark (Newman), John (Serkin) and
>Kurt (Krueger). I don't think I've read a better explanation in a Piano
>Technician's Journal!
>
>Bravo!
>
>All I would add is that stretching octaves really *does* make the piano
>sing better. Sounds more cheerful.
>
>Ron Torrella
>University of Illinois
My digital piano can be set to either stretched or equal temperament.
You would think that un-stretched tuning would sound right on a digital
piano, since you no longer need to deal with the inharmonicities of
physical strings. But in fact, since in many cases we are dealing with
sampled sounds to begin with, it's possible that the problem may still
be there. Does anyone (perhaps someone with a better ear than mine)
know whether the makers of digital pianos can be counted on to do
un-stretched tuning properly?
--
John Brock
jbr...@panix.com
Ron Torrella
Kurt Krueger
|> My digital piano can be set to either stretched or equal temperament.
|> You would think that un-stretched tuning would sound right on a digital
|> piano, since you no longer need to deal with the inharmonicities of
|> physical strings.
Stretched temperment can refer to tuning keys BETWEEN the octaves a bit sharp.
When I bought my Rhodes piano some years back, the company sent me a nice
package of literature on tweaking the piano. One of the 'goodies' was
an article on stretch tuning, which I'm ASSUMING is what your digital
piano is doing when you select the stretched temperment.
I never tried to stretch tune my Rhodes, so I don't have a feeling for
the difference in sound. Presumably it will brighten the sound.
Mark E. J. Newman
>My digital piano can be set to either stretched or equal temperament.
>You would think that un-stretched tuning would sound right on a digital
>piano, since you no longer need to deal with the inharmonicities of
>physical strings. But in fact, since in many cases we are dealing with
>sampled sounds to begin with, it's possible that the problem may still
>be there. Does anyone (perhaps someone with a better ear than mine)
>know whether the makers of digital pianos can be counted on to do
>un-stretched tuning properly?
Good question! This is a really subtle one. The basic answer is that you
are quite correct - the sound of a digital piano is merely a sample, i.e.,
a recording, of an acoustic piano, so it has all the same anharmoncities that
an acoustic piano has. Presumably the people who did the sampling used a
long (nine foot) piano, which will reduce the anharmonicity, but still it
will be there to an extent. Is your digital a Kurzweil? They're the only
ones I've heard of that do both stretch and perfect tuning.
In general the stretch tuning would be the more appropriate to use, because
it will avoid the clash of upper harmonics mentioned earlier in this thread,
and it will probably also sound more "authentic" to ears used to stretch-
tuned acoustic pianos. I know I can hear the difference. My Korg M1 for
example is *not* stretch tuned, and the piano tuning sounds lifeless to my
ears for this reason, compared to my Kawai grand, which is stretched quite
a lot. Kurzweil provide non-stretch-tuned piano sounds because, although
they have harmonic clashes and sound less lively, they are good for layering
on top of other non-stretched synth sounds. If you put a stretched and a
non-stretched sound on top of each other, the ends of the keyboard will be
out of tune; not so if both are perfectly tuned.
However, there is an *additional* complication with digital pianos concerned
with *loops*. This gets a little technical. When you make a digital piano
you don't just sample each note from a real piano from beginning to end: it
would take too much memory. So you sample the beginning of the note - the
attack transient - and the middle of the note. Then when someone plays a
key on the keyboard, you play back the attack, then you play back the middle
portion of the note, and then you play it again, and again, and again, in a
"loop". Slowly you fade it off, like the note on a real piano and the result
is fairly realistic, and saves you a lot of memory space. The trouble is
that, if you Fourier analyse the resulting waveform, you find that all the
harmonics are now constrained in what tuning they can take by the loop. It
turns out they are all shifted a little be the loop process, and in fact, as
the loop is made shorter and shorter, they get closer and closer to being
perfect harmonics, even though the original sample will have those out-of-tune
harmonics. Thus the correct amount of stretch-tuning for a digital piano
depends on the lengths of the loops used. For some commercially available
piano samples, the loops are lamentably short, in order to save on memory
space, and the result is that the piano sounds lifeless, because it is not
possible to stretch the octaves very much. This is one of the reasons why
when you see piano samples for sale, a 16Mb sample will sound better than a
4Mb one. It has longer loops, so the harmonics will be closer to those of
a real piano.
Mark.
Ron Torrella
>My digital piano can be set to either stretched or equal temperament.
>You would think that un-stretched tuning would sound right on a digital
>piano, since you no longer need to deal with the inharmonicities of
>physical strings. But in fact, since in many cases we are dealing with
>sampled sounds to begin with, it's possible that the problem may still
>be there. Does anyone (perhaps someone with a better ear than mine)
>know whether the makers of digital pianos can be counted on to do
>un-stretched tuning properly?
>--
John -
Which digital piano has settings for stretched or equal temperament tunings?
Seems to me that there wouldn't be much difference (read "gimmick?")
between them. Unless you're referring to a sample of "just tuning" or some
other type of "historical" tuning.
What I find surprising is that anyone can discern *any* kind of tuning on
digital pianos. I'm currently practicing on a Yamaha P-100 at home for an
upcoming recital and I'm doing all I can to avoid paying much attention
to the tuning. It's pretty gross!
So, whaddya got there, John?
Ron Torrella
School of Music
University of Illinois
Mark E. J. Newman
>Which digital piano has settings for stretched or equal temperament tunings?
The newer Kurzweils have them.
>What I find surprising is that anyone can discern *any* kind of tuning on
>digital pianos. I'm currently practicing on a Yamaha P-100 at home for an
>upcoming recital and I'm doing all I can to avoid paying much attention
>to the tuning. It's pretty gross!
Surprising. Sounds like there may be something wrong with your digital
piano. I play a Yamaha PF-85, which is predecessor to the PF-P100 and the
tuning of the fundamentals of the notes is utterly impeccable. I imagine
it's crystal controlled so it's probably accurate to parts in a million -
much better than you'll ever be able to hear with your ears. I've played
a P100 in the store, and it sounded just as good to me. If yours sounds
audibly out of tune then there's some very gross electronic problem with
it and you should have someone take a look at it.
Mark.
John Brock
I have a Technics PX103 (which I'm quite happy with). I'm pretty sure
the other digital pianos I looked at (Yamaha and Kawai mainly) also
could be set for stretched or un-stretched tuning. In addition, some
of the Kawai pianos at least could be set to different temperaments
(mean-tone, just, etc.), which my Technics won't do. My ear is not
particularly sensitive to subtle variations in intonation, and I don't
hear much difference between stretched and un-stretched tuning on my
piano. The un-stretched sounds just a touch duller perhaps. I'm kind
of sorry I can't use my piano to play Bach with the temperament Bach
would have used, but I probably wouldn't hear the difference anyway.
My question was purely out of curiosity.
--
John Brock
jbr...@panix.com
Ron Torrella
Actually, I suspect that since you can hear a difference between stretched
and unstretched tunings, you'd quickly hear the difference between equal
temperament and "just temperament" tunings. Give them a listen sometime.
It'll give you a new perspective on Bach and Mozart and Beethoven!
Israel Stein
>jbr...@panix.com (John Brock) writes:
Sorry, but neither Bach nor Mozart used "just intonation" tunings - Bach
was thought to use a temperament involving 4 tempered fifths and 8 pure
ones (such as the Kirnberger) and by Mozart's time it was up to 6 of each
kind. They are called Well Temperaments or Circulating Baroque Temperaments.
Just intonation was a tuning system used in the early Renaissance and was
soon replaced by Meantone.
Israel Stein
Israel Stein
I suspect that you would hear the difference very clearly - assuming that
the equal temperament is really equal (or at least close). My experience
has been that most musicians - including amateurs - hear the difference
between an equal and a 1/4 comma baroque temperament quite easily.
Israel Stein