After a number of different Topics and some experimentation I am considering tuning pure twelfths over the entire keyboard, even across the breaks. Because of the P5-P8 test for pure twelfths, this should be practical.

Other than Mr. Stopper and Mr. Swafford I don’t know of anyone that deliberately tunes with pure twelfths. Can anyone share their experiences? Both aural and ETD responders are welcome.

I haven't in the past, but will probably try it out. Particularly after some of the news coming out of the Kansas convention where Bernhard Stopper's presentation of his aural sequence seems to have generated a lot of interest.

Let me know how it works out. This may turn me into an A-forker.

Yup, tried it many times - I think Ric Brekne posted a method years ago using tunelab.

Often stretches the middle too much for my ears in the mid-section of smaller or more regular pianos.

using only the 3:1 or 6:1 is still relying on single partial matches between two notes that may or may not have a regular partial pattern...

I much prefer to balance between the 12th, the double octave and then bring in the single octave to make sure it doesn't obviously beat.

Easy using the Verituner.

Ron Koval

Well, what prevents you from trying it and reporting the results?

From my theoretical perspective I can contribute that P12 tuning is electronically not distinguishable from a reasonable 6:3 bass smoothly to 4:1 in the treble tuning on reasonably large pianos. This is the default in tunelab and will be acceptable to customers without specific requirements. I have simulated P12 schemes on my sister in law's Wurlitzer spinet on my recent holiday, but sort of concluded that instrument can only be tuned aurally.

If you're interested I can put up some data on that piano. It actually sounded quite nice after I tuned it aurally, but what I did to get that effect is unclear. I measured everything and plan to look into it.

It's ironic that ETD's are all you need to tune concert grands close to perfection, but for those nasty neglected spinets that are tuned only every decade for a bargain price you need an aural tuner, which seems to be an endangered species. There are apparently only 2 aural tuners in my local RPT chapter.

Kees

Thanks, Ron:

I remember reading some hot and heavy volleys between Brekne and Stopper on the subject, mostly about precedence. But since I don’t use an ETD, the method itself was not of use to me.

I do know what you mean about the middle getting stretched too much sometimes. The M6s in the 4th octave can be edgy. But on the whole I think there is much in favor of pure 12ths.

Of course when there are wild partials you need to make adjustments for anything that is obnoxious. But what I now realize is that dealing with a typical jump in iH can be done coherently. With pure 12ths, the 3:2 fifth and the 2:1 octave will be consistently tempered. What more could you ask for?

I may post some results when I have some AND if there is genuine earnest interest. (Once burnt, twice shy.) Mr. Stopper’s description of how to tune pure twelfths does not work for me. I do not hear what he does. Whatever I may come up with, others may not hear what I might. This sort of thing can be fodder for those that wish to be abusive. It would be irresponsible for me to be an instrument in someone else’s misbehavior without real benefit to others.

I realize that pure twelfths are often tuned during other tuning schemes. But deliberately tuning them may be a different thing. I am thinking that it naturally requires a more exacting ET than other methods. The less tempered an interval is, the more accurate it must be to be consistent.

Sometimes I think the best way to tune the bass on a spinet is to tune it so that none of the octave partials line up. Then it is not so obvious when some can be made to line up without others being obnoxious, and some can hardly be made not to be obnoxious at all. Twelfths may fit this requirement.

If you want to put the graphs of the Wurly spinet on a new Topic you can bet I’ll enjoy studying them

This may be one of the most important and oft forgotten statements ever made on tuning... What one finds easy and intuitive, another finds baffling!

There are many paths...

That's one of the key reasons I suggest hybrid tuning or getting comfortable with modern electronic tuning devices instead of the blanket suggestion to learn aural before anything else. The longer I've been tuning, the more I find that a really musical tuning lives in the unison and how whatever temperament is spread out to the ends of the piano.

Ron Koval

Ron: I agree on the intuitive/baffling perception!

I was in Bernhard's class in KC, and he really doesn't go for 3:1's, 6:2's or 9:3's per se. He listens for beat canceling (= masking). That alone would make it quite different from a 3:1 setting on an ETD.

Then, in the outer ranges, he goes for musical justness. Very interesting to see him tune, because it was far less theoretical than I would have imagined. When I spoke with him later, he indeed explained that he went for it aurally, then established the theory later. Much like any long-lasting discovery through the years

Is Bernhard publishing his aural approach? I read somewhere on the PTG forums that Kent Swafford was (?)

So... did anyone there happen to have a ppc version of onlypure running to see if his aural approach matched the machine calculation??

Ron Koval

Thanks for posting, Pat:

I am going to try many things in my experimentation. Like octaves, I think I can tune more consistent 12ths by tuning 4ths and 5ths instead. But I also wonder about the aurally pure 12th vs. a proof tested 12th, vs. a 12th with an octave/fifth or fifth/octave included.

Did it seem to you that the temperament was exceptionally equal? I wonder if that is part of the purity that people hear.

Instead of the graphs just a result: no matter how you tune the whole piano with SBI's (which can be P4 P5 P8 P12 P15), there is always a large jump in M3 beatrate across the break. It varies from a 2 bps jump (up when going down if IH drops below the break) for the Wurlitzer, to 1 bps for a large Heintzman upright. (Those are the only two pianos I have IH data for all notes.)

Conversely, if you tune the lower midrange paying attention to contiguous M3's there will be unprogressive SBI's across the break.

I don't know what your customers prefer but mine prefer the M3's to behave well (which is also unequal so probably not comparable).

Kees

Not sure what you mean by the "burnt" stuff. I think you refer to a couple of folks who argued that what you posted was unimportant because they did not understand it.

For my part I have genuine interest in your posts about tuning fundamentals and you have opened my eyes to many issues which I was not aware of and are not covered in any tuning literature. I have and am still learning a lot from your contributions.

Thank you Jeff!

Now that I'm in the acknowledgements mode; to get to the level of understanding Jeff I studied the materials on Bill Bremmer's website which was all I needed to understand piano tuning. Thank you Bill!

Kees

Doel:

You are welcome and I very much appreciate your mathematical confirmation of what I understand intuitively and experience in practice. There is no one else.

My customers like how I tune, otherwise they would not continue to be my customers! Your 2 bps jump in the M3’s on the Wurlitzer spinet is a bit more than what I experience. But I am thinking that I let the RBIs influence me too much sometimes.

Do you remember how the least overall jumps in beatrates (I think I may start calling it what it really is: jumps in tempering) across a break in the graphs that you produced for another Topic were for pure twelfths? I am now trying to figure out the best way for me to tune pure twelfths. I think it will probably be by playing a stacked P5 and P8 simultaneously. Whether tuning either the upper or lower note, the interval being tuned will be ... tempered as much as the other one when the twelfth is pure. This can be determined by the experience of “beat cancelling” that occurs when the P5 (3:2) and P8 (2:1) are beating at the same rate.

But tuning the temperament itself is another challenge since this cannot be done with twelfths alone. The basic sequence is up a fifth, up a fifth, down an octave. The octave is problematic for me and I think the answer will be to create the octave by tuning down a fourth from the second note in the basic sequence. Then the tempering of the second fifth can be checked by testing the 2:1 octave, unless the fourth is influenced by a break. Then the fourth may need to be altered instead. The RBI checks are created the same as any 4th and 5th sequence, but with even more available. In particular there are many more M6s which makes the listening to m3s completely unnecessary and, just as important, more inside/outside tests. Of course there will be jumps in … tempering across scaling breaks except for the fifths and octaves.

Another interesting thing is the choice of the first twelfth. D3-A4 seems a natural for how the first RBIs fall when going two steps CCW in the circle before starting back at A and gong CW. The first RBI will be G3-E4. I can live with that. G3 is rarely wound. As I said before, this may make me into an A-forker!

If you feel like it, you might want to try 8:4 octaves to see what the M3's do then. I expect they will be much smoother because the test for the 8:4 octave is the m6-M3 test.

Jim: Bernhard is, as far as I understood, reluctant to posting them in a public forum. He will, however, give them to anyone who PM:s him.



Ron: No, i don't think anybody ran the OnlyPure software side-by-side. Bernhard himself, though, says he gets the same result aurally and by his ETD, and I have no reason to believe otherwise.


Hi Jeff,

Yes, the temperament seemed very equal indeed - this with a tuning sequence that didn't use any RBI's at all. That was actually one of the most impressing things about Bernhard's tuning!

Indeed a little less, but still a large effect on the spinet.
Somewhat irrelevant I think as 8:4 octaves in the midrange are not an option I think.

Kees

Debugging today I found I made an error. With 8:4 octaves the M3's are progressive across the break even on the Wurly, exactly as you predicted. The P5's however jump from 1/2 bps narrow below to 1.5 bps wide after the break.

Using a 6:3 in the bass to 4:1 in the treble scheme the M3 bps jumps from G3 to G#3 from 8 to 7 (more like what you observed I think), the P5 from 1 bps narrow to 0.3 bps narrow (anti-progressive).

Using a P12 scheme M3 jumps from 9 to 6 (very bad) and P5 from 0.3 to 0.8 (progressive).

Kees
PS (added in edit): A scheme that produces nice tuning curves and strictly progressive P5's is tuning by equal beating P4/P5's from the lower common note. Not sure how you could set such a temperament aurally. This seems to produce nice P12's too in the midrange at least (under 0.3 bps).
PPS (added in edit 2): On larger pianos the P4/P5 scheme produces too narrow octaves. Adjusting the scheme to have P4 beat twice as fast at P5's from a common lower note works well in that case.

Doel:

Thanks for crunching the numbers!

Yes, tuning 8:4 octaves is “off the table” due to the tempering of other intervals. And since that is what is needed for progressive M3s, for such a piano if tuned "coherently", then progressive M3s are “off the table” along with strict CM3s. This is the true value of this sort of investigation. To find out what cannot be done.

The 6:3 bass 4:1 treble is Dr. White’s prescription (take a fifth in the morning and another at night…). But his reasoning was for useful tests rather than dealing with iH. I wonder if there has been a general study of things that have been done right, but for the wrong reason.

And I don’t see where tuning equal beating 4ths and 5ths with a common bottom note would be that difficult. Maybe that is what often happens, anyway. The fifth is a very complex sound, especially on spinets.

And thanks for the heads up on what is expected to happen to M3s on a Wurly spinet tuned to pure 12ths. But I am not sure that a 3 bps jump would be that bad. I guess I’ll have to find out someday. Interesting that you came up with a 2 bps jump when tuning aurally.

Thanks for the reply. Could you clarify a bit, though? When you say that the sequence didn't use any RBIs at all, do you mean just that no RBIs were tuned, or that no RBIs were even listened to as checks? And were there RBI checks after the temperament was set to prove that it was ET, or did it just seem to be very equal? There was an ugly discussion about this sort of thing not long ago.

I must have been unclear, that's not what happened. I set the temperament octave using my ETD to a specific unequal temperament and the result was completely messed up M3 rates, which are what's important for this temperament. I tried to set ET too with the ETD with the same result; about a 2 bps jump in M3 beatrate in the wrong direction.

Then I tuned the whole thing aurally in unequal temperament getting the M3's right and it sounded fine. Of course now the P5 and P4's were not according to spec anymore but they are more or less random in most UT's anyways.

Kees

I'm not Pat, but I attended the first class Bernhard taught, (a second one was added at the convention), and Bernhard did not use any RBI checks as he tuned. He only listened to the three note combinations described in class, unisons as he went.

When he was done, he played all the major thirds chromatically. They seemed a little rough from where I was sitting, and I simply blamed that on the cold air blowing on the tenor break of the piano, but when I actually got to sit down at the piano, acoustics as they were, the RBI did indeed sound quite smooth and equal. Nothing jumped out at me when I played chromatic octaves, 12ths, and double octaves across the scale. I then went to quickly grab the temperament worksheet he handed out, but someone was at the piano before I could get back, and most people were interested simply in playing on the piano, which is very important, but I can't tell anything about a tuning except for unisons when I listen to playing, so that was as far as I got in analyzing the tuning.

After that I was thoroughly impressed with his work.

Does that answer some questions?

Regards,

No RBI's used for tuning whatsoever. For verifying, Bernhard ran a few chromatic M3's. They sounded smooth.

I now understand, that I don't understand. I am in the dark when it comes to UTs. It's OK.

Thanks, Thomas and Pat:

So there was a temperament worksheet handout! If it is not copyrighted, could it be posted here? Or do you think it best for me to contact Mr. Stopper directly?

Jeff,

Although I'm neither Thomas nor Pat, I would suggest that you do the latter. Having done so myself, I think that you, in particular, may find his hand-out interesting. I am currently trying to wrap my mind (and hopefully, in the near future, my ears too) around it, because it intrigues me.

Jeff and all,

I wrote my last post in a rush, but found it to be true even as I read it today Bernhard didn't use any RBI's for tuning, but ran them for confirmation. They sounded good, and proved his method.

Jeff: Bernhard hesitates posting his sequence in this forum, but would without doubt provide it if you contacted him personally. As you don't use PM's at pianoworld, you'd have to get in touch with him using his official email, info@piano-stopper.de.

I don't think it's OK. In my opinion you can't understand equal temperament if you don't understand unequal temperaments which it evolved from, and is a particular instance of. The historical temperaments all try to balance the badness of the M3, as this is musically most significant. When music reached the stage where all M3's are equally used it started making sense to make the all "the same". The 5ths were never an issue, except for nonsense tunings like Kirnberger I.

Just my personal opinion, not intended to start any kind of argument. I am aware that your position is also defensible.

Kees

Doel:

I think we can continue to have discussions and not arguments.

I have no idea what to think when I read about the “badness of M3s” when I also read that M3s weren’t used for tuning until modern times. I would have to study the subject much more than I have the interest for it to really understand UTs.

But could you elaborate on: ”In my opinion you can't understand equal temperament if you don't understand unequal temperaments which it evolved from, and is a particular instance of.” Maybe you mean in a musical rather than in a theoretical sense.