This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment You don't really need to decide on a beat rate for the F3-A3 third. = Tune A4 and then tune A3 and A2 to get octaves and double octave that = you want. How wide you can set these octaves will vary from piano to = piano. As Bill says, aim for a compromise between a 4:2 and 6:3 octave = checking the double octave to be sure that it isn't so wide as to be = objectionable. This is a bit of an artistic judgment call and the width = of these octaves will vary from piano to piano. In general they will be = narrower on a smaller piano and wider on a larger piano. On some = spinets you may need to set the octaves a pure 4:2 or even narrower. = Then set a sequence of contiguous thirds from A2 to A4 so that their = beat rates have a relationship of 4:5. The narrower you set up your = initial double octave spread, the slower the F3-A3 third will beat. Let = the piano rather than a preconceived notion about what the F3-A3 third = should sound like guide you. Once you have laid in the sequence of = thirds it is relatively easy to fill in the rest. David Love =20 ----- Original Message -----=20 From: SidewaysWell1713@aol.com=20 To: pianotech@ptg.org=20 Sent: September 22, 2002 9:45 PM Subject: Re: Learning Aural Tuning In a message dated 9/22/02 7:14:41 PM Central Daylight Time, = mathstar@salemnet.com writes:=20 HERE THE QUESTION (Looks like several questions, but really asking = the same thing each time ...)=20 How do you really know that your A-A is ideal? That it isn't a = smidge two narrow or wide for the inharmonicity of that particular = instrument? That you have even started the temperament "correctly" for = that piano? How do you KNOW that your F33-A37 is ideal for that = particular instrument?=20 This talk about Franz Mohr, etc., highlights the point: A lot of you = folks can--in your sleep--set a really sweet temperament on any decent = piano you face, Yet the starting intervals seem arbitrarily set, to me! = "About 7 bps ..."=20 So what the heck does "about" mean? Do you have to set the whole T. = before you "know"?=20 (Is this making sense?) I'm not talking about getting just a useful = temperament, as I believe the "about" thing will do that every time. I = am talking about getting a really good temperament for each piano.=20 'Preciate some comments.=20 Alan Barnard=20 Listening in Salem=20 I'd be glad to answer your question because I do know the answer. But = I usually get some smart remark from some creep when I do. I hope I = don't because if I don't, you won't see words this list does not want me = to write.=20 The initial A3-A4 octave is best set as a compromise between a 4:2 and = 6:3 octave.=20 This has been determined by the PTG Exam Committees and Dr. Sanderson. = What you try to establish is an octave in which neither test is exactly = right. On pianos with low Inharmonicity, there might not be much = audible difference and so, if both tests seem to produce Equal Beating, = then the octave is good.=20 On high Inharmonicity pianos such as the Steinway, a clearly audible = distinction can be heard between the two tests. Tune A3 from A4 so that = the results are slightly too fast for the 4:2 octave but slightly too = slow for the 6:3 octave but placing the discrepancy right in the middle. = The kind of distinction I am talking about is very small but at the = highest level of aural tuning.=20 As for the initial F3-A3 3rd, yes, you must first *estimate* its = speed and it will vary from piano to piano. If your initial A3-A4 = octave indicates low Inharmonicity, then you would estimate a little = slower than if the indication was high Inharmonicity. A good way to = make this estimate is to have a pocket sized electronic metronome = (Schaff sells them). Set it at 120. At 6 beats per second, you will = hear 3 beats per tick. Find that point, then flatten F3 ever so = slightly to hear the beat rate increase. Listen now to hear 7 beats = against 2 ticks. This is still just in the estimate stage. There is = also a device made by Dr. Sanderson which plays the basic beat rates for = the contiguous 3rds, F3-A3-C#4-F4.=20 Now, construct an octave from F3 to F4 and use the same 4:2 and 6:3 = octave tests you did for the initial A3-A4 octave. Now, fill in the C#4 = from A3. Your F3-A3 third was 7 beats per second, your A3-C#4 will be = just a little faster. This is that hotly disputed 4:5 ratio of = contiguous 3rds. Forget about whether that is exactly the ratio or not. = What you are looking for is just a slight increase in beat speed which = will work with all the other intervals created thus far.=20 If, at this point, you cannot get this slightly faster relationship of = contiguous 3rds, F3-A3-C#4-F4-A4, then your initial F3-A3 3rd needs = adjustment. The irony of finding this essential preliminary grid is = that it is much easier to identify when the relationship is not correct = than to really be sure of when it is. So, really, it will always end up = being that it could possibly have been more perfect but having it seem = to work out will yield results which will be within the PTG's Exam = tolerance of plus or minus 1 cent.=20 Good aural tuning requires making good estimates. Once you have the = F3-A4 contiguous 3rds the best you can get them balanced, you can make = small errors on everything else and not create unintended effects. It = is the good old 4ths & 5ths through the cycle of 5ths temperament = sequence which is prone to undesirable effects as the result of = cumulative errors.=20 No one can count beats which are irrational numbers (such as 7.2, 9.4, = 12.7). All you can do is compare one pulse with another and try to = establish the proper relationship. Nothing is exactly on in ET. You = cannot have entirely pure 5ths but the amount of tempering can be = manipulated if desired. Each decision to favor has an opposite and = theoretically equal consequence but Inharmonicity can be used to a = limited degree to absorb some of the Comma, the reason why tempering is = necessary.=20 The fact that you have this question tells me you are doing quite = well, so take comfort in that.=20 Bill Bremmer RPT=20 Madison, Wisconsin=20 Click here: -=3Dw w w . b i l l b r e m m e r . c o m =3D-=20 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/f5/fd/4f/d2/attachment.htm ---------------------- multipart/alternative attachment--
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