See Comments below, regards, Bernhard Stopper Jason Kanter wrote: > Double octave, yes. But within this, check all the twelfths -- they > should be as close to pure, beatless as possible and this will > guarantee the right amount of stretch. agree > The test for a perfect 12th is a sixth below the lower note. That is: > to test C4-G5, use Eb3 against the C4 (a sixth that beats at the > frequency of G5) and Eb against G5 - should beat the same. This will > almost always give you an octave stretch that is the sweet spot > between 4:2 and 6:3.Note - mathematically perfect ET twelfths in a > world without inharmonicity would be narrow. correct for standard ET temperament > Inharmonicity stretches them. not very correct. inharmonicity stretches *everything, still keeping the problem of the pythagorean comma.* tuning twelfths pure an ET, is the result of a *completely different* ET temperament, dividing the pythagorean comma to the octaves. See more about my work on this at http://www.stopper-scale.com > The spot of the perfect 12th turns out to be a great choice for the > stretch because the 3rd partial is usually very strong.Perfect > twelfths are also an excellent test up into the high treble. > On 8/22/07, *John Formsma* <formsma at gmail.com > <mailto:formsma at gmail.com>> wrote: > > Comments interspersed. > > On 8/21/07, Matthew Todd <toddpianoworks at yahoo.com > <mailto:toddpianoworks at yahoo.com>> wrote: > > I have been really, really studying tonight. > > Good! You will eventually get it if you keep studying the right stuff > and apply yourself. I promise. > > > Can someone please explain the system they use to tune 2:1, 4:2 > and 6:3 > > octaves. I am so close to grasping this concept, but I think I > need another > > tech to explain it to me besides Reblitz. > > Get someone else besides Reblitz. As was mentioned, Baldassin's On > Pitch, the newly revised version, and the PTG Tuning Exam Source Book > were great for helping me understand all this. > > > In the octave interval, if I were to tune a 4:2, the fourth > partial of the > > lower note theoretically has the same frequency as the 2nd > partial of the > > upper note. Do those partials normally dominate each > octave? How can I > > tell whether to tune a 4:2 or a 6:3? > > Yes, you have a dominant partial pair. Which is why you "normally" > tune certain octave sizes in certain places in the piano. The > Baldassin book has a chart that tells which octave size generally fits > best. > > However, you must get the best fit for each piano. You can't just > begin by tuning a 4:2 plus a little bit in the A3-A4 octave in every > piano, and expect it to be the best. Some pianos will require in > between a 2:1 and 4:2, and some pianos might allow for 6:3. > > To help you know what octaves will work with the piano, I find it > immensely helpful to start by working within a double octave. You > tune > A3-A4 first, then tune A2 from A3. This will help you establish the > correct octave width b/c you are using two octaves rather than one. > (Otherwise, if you begin with a A3-A4 octave that is too wide, you > will end up with bass and treble octaves that beat too much. Working > with a double octave prevents this.) > > What I do is this: Tune A4, then A3. Make it sound the best (you can > change it later). Check to make sure it's close to a 4:2 octave with > the M3-M10 test (because usually that fits most pianos well). Then > tune A2 from A3, and make it a 6:3 octave using the m3-M6 test. Then > you want to use F2 with A2, A3, and A4 to see if those octaves will > work for that piano. > > You want to first make sure that A2-A4 is not more than 1 bps. This > is *very* important. Play F2-A2, then compare it with F2-A4. (Listen > at A4.) > > Now use F2 to check A4 and A3. F2-A4 will probably be a tiny bit > faster than F2-A3. And F2-A3 will probably be a tiny bit faster than > F2-A2. If you have correctly set these octaves, the tuning will fit > that piano very well. There may be some strings in lesser pianos that > don't fit well, but they will be minimized if you get octaves right > from the first. If you do this on a well-scaled piano, you will be > astonished at how good it can sound when you're done. Octaves > complement each other, and it is just delightful. > > Clear as mud? Probably. <Grin> Get the books, do the requisite > head-scratching and pulling out. You'll get it sooner or later if you > don't give up. > > You will also find there are multiple checks for octaves. The M3-M10 > is a check for a 4:2 octave. But also another good one is the > "shared" P4/P5 test. Say you're checking A3-A4 to see if it's 4:2. If > A3-D4 beats the same as D4-A4, it's a 4:2. HOWEVER, the 4th must be > expanded, and the 5th must be contracted for this test to be valid. > So, it would go like this: Expand D4 to get a 4th beating to whatever > you can hear well. Then check D4-A4 to see if it's the same. If it's > the same, it's a 4:2. If it's faster, you have an octave smaller > than > 4:2. If it's slower, you have an octave larger than 4:2. > > I like to use this test because it's relatively easy to hear. I find > it tricky to know if the M3-M10 beats are the same because of > competing higher partials that can fool the ear. > > Wish we were able to sit down at a piano while explaining this. It > would be much more understandable. > > JF > > > > > -- > | || ||| || ||| || ||| || ||| || ||| || ||| || ||| > jason's cell 425 830 1561 -------------- next part -------------- An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/20070822/82fa46ae/attachment-0001.html
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