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

[Isaac sur Noos]

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Michiel,

I see what you mean ,I have computed all beat rates for 3 octaves and all
intervals once, and I remeber using a little metronome to learn to count
beats (just insist, and you'll know how to tune someday :>)!


As understand it you tune by fast intervals mostly. Indeed one can train to
get a good interval color for the fast beatings, and get a feel for it .One
can even consider the fast beating as if they where octaves or fiths, and
tune unissons while correcting their speed. I've done it but have find it to
be too tiring for the ears. (But I remember a Balwin spinet, the only one I
tuned I guess, and it was easier to tune without any muting, mutes gave a so
unfocused tone that it was an horror to try to hear beats, while they appear
more clearly in the full garbage ;>)

But as the 10th and 17th beat rate progression slow on most pianos in the
treble, if we follow the inharmonicity of the instrument.
If we follow beat rate progression , the treble scream a bit , (is an
advantage for some situation).

I use the 17 th's in the treble but mostly if I am lost with a high treble
note, to check my double octave.

And I use to check the progression of course, but is enough to tune by
octave (the worst interval for tuning !) to me .

Nowadays any focused tuning is musical, for instance a fourth based, even a
fiths based tuning,

Just that some tunings are more in the iH of the piano and others more in
the mood of the tuner.!

I mean that even a pure ffith tuning does not sound false to the player,
while the octaves beat as hell, but when chords are leaved sustaining, the
more the tuning respect the piano Iharmonicity, the more sustain you get,
and in Western harmony you have more immediate tone in harmony because of
the reinforcement of the partials.

Indeed Il like the lively coloration of a little untempered tuning when
large chords are sustained (leaved sounding), you have more move and partial
rubbing, that gives a "singing" quality, but the tone extinct sooner I have
seen (why ?). The tunings computed by the VT, when you hold the sustain
pedal with a large chord, the tone does not seem to want to end.
Then my I deduction is that there is a more lively tone in this situation,
while I understand it is difficult to ascertain for sure  !

BTW, my favourite first octave test (temperament) is to have the 3 major
thirds (FA - A C# - C#F) sounding together, no third may be heard more than
others, thats a neat test !

My best to you all !

Isaac OLEG





Best



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 : mardi 21 octobre 2003 01:23
  À : pianotech@ptg.org
  Objet : Fw: "The Invisible Tool"/beat rates - and where they come from


  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 -----
  From: Isaac sur Noos
  To: Pianotech
  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
  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)

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