This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment Hello Isaac (while being near) you said. In this I am very happy. At least the = concept even if not completely accurate, gives a working knowledge of = the system. :-) You'll notice I extracted a bit from your message and stuck it on my = reply - I'm finding out how these new fangled computer thingys work. Kindest regards Michael G (UK across the Chanel) <- ;-) ----- Original Message -----=20 From: Isaac sur Noos=20 To: Pianotech=20 Sent: Monday, October 20, 2003 10:02 PM Subject: RE: "The Invisible Tool"/beat rates - and where they come from Michael, out of any computation, the most universal admitted ratio that works in = the piano is the 4/5 ratio for 2 contigous major thirds. All these beat rates computed, does not have to do much with the beat = rates in the piano=20 On some pianos the FA major 3d is as fast as 7.3 and on others it can't = be even 6.8 bps. Regards Isaac OLEG Entretien et r=E9paration de pianos. PianoTech 17 rue de Choisy 94400 VITRY sur SEINE FRANCE tel : 033 01 47 18 06 98 fax : 033 01 47 18 06 90 cell: 06 60 42 58 77=20 -----Message d'origine----- De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la = part de Michael Gamble Envoy=E9 : lundi 20 octobre 2003 17:27 =C0 : pianotech@ptg.org Objet : "The Invisible Tool"/beat rates - and where they come from Hello list Like all of you, I imagine, I was first made aware of these beats when = listening to a piano (in my case pipe organ) being tuned. My curiosity = led me to analyse the reason and I turned to simple mathematics for the = answer. Enter my "small equation" where the fundamental (1st.Harm.) is = multiplied by the 12th. root of 2 to derive the next fundamental in the = ascending equal tempered chromatic scale. (Simply devide if you want to = go down chromatically). In every case the resultant becomes a = Fundamental Note - or 1st.Harmonic. I know this is all "old hat" but = there's probably some meat in it to be chewed over just the same. Now = taking the Fundamental and multiplying by "Two" one gets the second = harmonic. Multiplying by "Three" gets the third harmonic ad. inf. The = really interesting point now comes... Take your M10 based on A# (which = computes at 466.16376.....)The 5th. harmonic of that A# =3D = 2796.9826...... the M10 is F(which computes at 1396.9129.......) The = 2nd. harmonic of that F =3D2793.8259...... = There we have a difference of 3.1567..... Hz which is the beat you hear. = The same applies, of course, to any and all intervals in the equal = tempered scale, be they M3,M4,M5 - whatever. It is interesting to apply that "small formula" to log all the notes = of the equal tempered scale on a mathematical basis and thereby to = extract the "Beat-rate" information whole-sale. To me this information = is "an invisible tool" - and I use it - as do you. But it's nice to see = an invisible friend sometimes!=20 Of course! There are many pitfalls! Many pianos do not produce the = exact mathematical frequencies according to my table. Those times when = the first covered (wrapped) Bass string are played with their M10 - and = the beat rate does not conform to the mathematical progression of the = tables as produced in the "metals" section of the piano. Well..., That's = life :-) I find the "scientific calculator on the PC best as it = produces so many decimal places! In using such a calculator you can go = right up the scale and land up, an 8ve later with exactly twice the = number you started out with. Now that's Magic!=20 Regards Michael G (UK) ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/20/f5/14/b3/attachment.htm ---------------------- multipart/alternative attachment--
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