Hi John.
A few comments interspersed below:
You'll have to write Stopper to see if he is still selling
aural licenses.
This certainly extends the limits of incredulity. A license
to tune P12s???? No thanks, I'll pass. <G>
Yes, that was the general reaction when we all first heard about this
earlier (around 2003) on CAUT and Pianotech. Even if you could
realistically patent any aural approach, let alone one that has as much
prior discussion, it would be impossible to control and not worth the
effort and cost to patent to begin with.
I had to tune my mom's piano today (Steinway M redesigned and
rebuilt by Ron N). Fiddled around with how to do this. (It's not
rocket science, but would take some time to think through it well.)
I ended up just doing what I normally do. The end result is pretty
darn close to all 12ths being pure anyway. That's my preferred
style: stretch the temperament as much as I can get away with
without P4s being too busy. Tuning open unisons helps it along,
which is how I was doing it today.
Its not really hard to do. If you start off like I mentioned last time,
you have four notes of 19 done. One approach is to take those inside two
and tune P-12ths outside the temperament area to these, and then
transfer them back inside the temperament area in the form of octaves,
then continue around fudging as necessary to keep 4ths and 5ths
acceptable. It insures that the initial temperament is good whilst also
insuring that area is stretched to a 3:1 P-12th. The rest of the piano
is easy. And yes, you can get close to all 12ths being pure even using a
moderate stretch. Tho as the two graphs I supplied show things develop
differently when you hold 12ths at a constant width visa vi some other
interval. And you end up hearing this. Jim Coleman commented on this
back in 2000 when I first started posting about how I was doing this
with Tune lab 97.
Though I wouldn't claim to know all about the science behind
Stopper's methodology, I'm willing to wager that the end result is
what many of us achieve every day ... by just listening to what the
piano tells us it wants. The Stopper details seem to be scanty, so
we're left to guess a lot of what a Stopper P12 tuning sounds like.
I did hear the one he did (was it Rochester?). Sounded quite nice,
but some things were not to my liking. The treble was a bit too
stretched in the treble, and I'm one to do a stretchy tuning
myself! <G> And there were some 12ths that were not pure. However,
this may have been due to the pianos being sharp -- always so darn
cold in those hotels -- and then drifting sharp after they had been
tuned according to the ETD. Also, things change as unisons are
tuned. My mom's piano didn't have all the 12ths pure at the end of
the tuning, though they all were during it. (It happens, as we all
know. A better time to study the post-tuning intervals would be
after a piano was tuned twice.)
Your comment about the treble is one I hear nearly every time, and
indeed was exactly what Jim commented on back in 2000. Yet as I
mentioned earlier, the highest treble C8 only ends up around 35 cents
offset, which is moderate by any account. Thats because F6 resultant 3rd
partial (after tuning it's fundemental to E#4's 3rd) is what determines
C8's fundemental and this is rairly in this scheme far from 35 cents
offset.
So, those of you who have access to the OnlyPure ETD, some questions
(and we'll assume a decent piano scale of at least 5' 8" in length):
- Is A3-A4 generally between 4:2 and 6:3, and usually more of a 6:3?
- Are P5s nearly pure in a "normal" temperament region? I.e., F3-F4
- Are P4s beating a little faster than 1 bps in a "normal"
temperament
region?
- As you are tuning the middle strings of the treble, does the double
octave below beat about 1-2 bps until the other strings are tuned
to it?
Then, it decreases to just less than or equal to 1 bps? E.g.
F3-F5, and I'm
assuming tuning unisons as you go.
- Does the bass go from a tad larger than 6:3 octaves to 8:4,
then the
lowest 5-6 strings between 8:4 and 10:5? (Except on very large
pianos, which
might be 10:5 or even 12:6)
I dont have his ETD, but my A4/A3 ends up fairly in between a 6:3 and
4:2, and my D4/D3 ends up closer to a 6:3. But this again depends on
the pianos inharmonicity. Tho inharmonicity does not vary alllll that
much in this area from instrument to instrument (good instruments that
is) it does vary some. I never get much past 6:3 octaves and never
pass 8:4 in the bass. Your middle question depends on which coincident
pair you are talking about so I cant say right off. The 5ths I get are a
bit slower then usual yes.
Somewhere along the line, I think many of us end up at the same
place while arriving by different paths. I'm certainly willing to be
taught. But I'm not buying into tuning voodo. <G>
The P-12ths tuning does diverge from octave priority in a significant
way. No doubt about it. Tho it remains an equal temperament scheme. Its
differences has to do with the beginning stretch imposed on its
temperament region, and what happens the width of all other intervals
and their partials types when you hold the 3:1 12th to a constant width.
I think it was unfortunate that there has been so much use of the word
"magic" tied to the whole thing. It's got nothing to do with magic and
the association was/is I think counter productive at best.
Also, I'm thinking this out loud. I've heard that in Europe tuners
prefer to tune more narrow octaves than we do here in the States.
Is this true? If so, I've a sneaking suspicion that what Stopper
might have done is simply expand everything from what is the normal
in Europe. Any chance of this being the case? In other words,
instead of tuning 2:1 or 4:2 octaves for the temperament octave, his
octave is between 4:2 and 6:3. Granted, he would have arrived at
this by mathematical means, and I certainly applaud him for doing so!
I am not aware of any such tendency. Stretch discussions are rampant
here as well as anywhere else. In any-case Stoppers work on the
mathematics behind this and the basic concept of P-12ths as a tuning
priority has nothing to do with simply expanding on what otherwise is
normal. My own suspicion, one that is re-enforced by finding several
articles back into the very early 80s and no doubt beyond that is that
at some point some folks started to notice that the particular aural
octave test, i.e. Major 6th and double 10th could be used to achieve a
P12th. Baldersins book even declares this (and a couple other tests) as
P 12th tests. And that somewhere along the line this started to gel into
a tuning priority in itself. In 1982 an American named Gary Schulze
published an article describing in great detail and defined his own
version of the comma around P12ths and P19s. I will ask him if I can
copy excerpts from a letter he sent to me about the whole thing earlier
this year in a separate post. He cites sources for his work dateing back
to 1943 by O.H. Schuck and R.W. Young, in J. Acoust. Soc. Am. 15; 1-11
I personally think 2:1 octaves sound horrible, unless you're in the
top octave, and have properly expanded everything below it. But even
then, I like to go a bit above a 2:1. So if someone has been used
to listening to a piano tuned with primarily 2:1 octaves, there is
no doubt in my mind that a P12 tuning would sound absolutely
fabulous! And I would indeed be proud of that "discovery"! But it
doesn't have to mean than no one else has been doing it heretofore.
It is certainly fascinating, and I look forward to hearing more
...specifics.
--JF
I think everyone agrees that 2:1 octaves are only good at the very
top.... so there is no fundamental disagreement on that point. Nobody I
know here in Europe does that. There IS a good deal of talk about not
stretching the tuning... but these folks who talk about that are not
thinking in terms of coincident partials... and really don't understand
that vocabulary at all. They speak of a "natural stretch" which ends up
always equating to some resultant stretch based on some or another
standard octave priority set of aural tuning tests.
You'll note in reading Gary's note... that there are some very similar
statements to things I've underlined all along. Like how octave types
converge in the base using this priority and how in the treble octave
types get split right down the middle.
Hope this didnt get too long... but you put a lot of things on the table
for comment :)
Cheers
RicB
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