<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> See Comments below, regards, Bernhard Stopper Jason Kanter wrote: <blockquote cite="mid:c85b54f50708220940p45157e20r38d5accd56fad72b@mail.gmail.com" type="cite"> <div>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. </div> </blockquote> agree <blockquote cite="mid:c85b54f50708220940p45157e20r38d5accd56fad72b@mail.gmail.com" type="cite"> <div>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. </div> </blockquote> correct for standard ET temperament <blockquote cite="mid:c85b54f50708220940p45157e20r38d5accd56fad72b@mail.gmail.com" type="cite"> <div>Inharmonicity stretches them. </div> </blockquote> 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 <a class="moz-txt-link-freetext" href="http://www.stopper-scale.com">http://www.stopper-scale.com</a> <blockquote cite="mid:c85b54f50708220940p45157e20r38d5accd56fad72b@mail.gmail.com" type="cite"> <div>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. </div> </blockquote> <blockquote cite="mid:c85b54f50708220940p45157e20r38d5accd56fad72b@mail.gmail.com" type="cite"> <div>On 8/22/07, John Formsma <<a moz-do-not-send="true" href="mailto:formsma@gmail.com">formsma@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0px 0px 0px 0.8ex; padding-left: 1ex;">Comments interspersed. On 8/21/07, Matthew Todd <<a moz-do-not-send="true" href="mailto:toddpianoworks@yahoo.com">toddpianoworks@yahoo.com </a>> 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 </blockquote> </div> -- |  ||  |||  ||  |||  ||  |||  ||  |||  ||  |||  ||  |||  ||  |||          jason's cell 425 830 1561 </blockquote> </body> </html>