"The Invisible Tool"/beat rates - and where they come from

[Isaac sur Noos]

This is a multi-part message in MIME format.

---------------------- multipart/alternative attachment
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 (while being near)

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 réparation 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
  -----Message d'origine-----
  De : pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]De la
part de Michael Gamble
  Envoyé : lundi 20 octobre 2003 17:27
  À : 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# = 2796.9826...... the M10 is F(which computes at
1396.9129.......) The 2nd. harmonic of that                          F
=2793.8259...... 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!
  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!
  Regards
  Michael G (UK)

---------------------- multipart/alternative attachment
An HTML attachment was scrubbed...
URL: https://www.moypiano.com/ptg/pianotech.php/attachments/db/4c/65/30/attachment.htm

---------------------- multipart/alternative attachment--