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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