<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2600.0" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT size=2>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.</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>David Love  </FONT></DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=SidewaysWell1713@aol.com href="mailto:SidewaysWell1713@aol.com">SidewaysWell1713@aol.com</A> = </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> September 22, 2002 9:45 = PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Learning Aural = Tuning</DIV> <DIV><BR></DIV><FONT face=arial,helvetica><FONT size=2>In a = message dated 9/22/02 7:14:41 PM Central Daylight Time, <A href="mailto:mathstar@salemnet.com">mathstar@salemnet.com</A> = writes: <BR><BR><BR> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #0000ff 2px = solid; MARGIN-RIGHT: 0px" TYPE="CITE">HERE THE QUESTION (Looks like several questions, but = really asking the same thing each time ...) <BR><BR>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? <BR><BR>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 ..." <BR><BR>So = what the heck does "about" mean?  Do you have to set the whole T. before = you "know"? <BR><BR>(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. = <BR><BR>'Preciate some comments. <BR><BR>Alan Barnard <BR>Listening = in Salem <BR><BR></BLOCKQUOTE><BR><BR>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. <BR><BR>The initial A3-A4 octave is = best set as a compromise between a 4:2 and 6:3 octave. <BR>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. = <BR><BR>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. <BR><BR>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. <BR><BR>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. <BR><BR>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. = <BR><BR>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. <BR><BR>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. <BR><BR>The fact = that you have this question tells me you are doing quite well, so take comfort = in that. <BR><BR>Bill Bremmer RPT <BR>Madison, Wisconsin <BR><A href="http://www.billbremmer.com/">Click here: -=w w w . b i l l b = r e m m e r . c o m =-</A> </FONT><FONT lang=0 face=Arial color=#0f0f0f = size=2 = FAMILY="SANSSERIF"><BR><BR><BR></BLOCKQUOTE></FONT></FONT></BODY></HTML= >