New to Tuning-Book Recommendations?

[Isaac sur Noos]

Hi Bernhard,

I am actually getting found of the pure twelwe approach these days, I
like , on little pianos, the slower beating thirds at the break that
give us a lot of reserve when it comes to the low basses stretch, and
also how the high treble 17th stay quiet '(on the few pianos I
produced) while being yet stretched enough.

However I have no "bearing plan" (method to produce the temperament)
and I use a slightly larger octave than usual to get up to the 3:1
relation when there.
Are you using a sequence that is based on a pure twelve to begin with
? I remember you had a text on your web site, but I did not see it in
English.
If available I d like to receive it.

In "standard" tuning, we arrive at the pure twelve around octave 5-6,
but after that  I seem to recall that the twelve get shorter. In the
bass, the opposite, as we can have larger than pure twelve's (and
fifths as well).
So tempering those on a larger scale is interesting.

I tend to believe that tuning "in the spectra" of the piano focus more
on lower partials, but the result is good only with good pianos
(warmer tone).
So a lot of effort have to be made to get warmer unisons. Having a
tuning method that gives some air is then a good way to add something
to the piano.

On the other hand I find really bland the fifth based tunings, and I
also often see that more compromising than allowed by the method is
used to keep clean treble and basses.

Friendly wishes, I'm back at that tomorrow!


Isaac






> -----Message d'origine-----
> De : pianotech-bounces@ptg.org
> [mailto:pianotech-bounces@ptg.org]De la
> part de Bernhard Stopper
> Envoyé : dimanche 11 janvier 2004 10:26
> À : Pianotech
> Objet : Re: New to Tuning-Book Recommendations?
>
>
> Hi Brett,
>
> Try using the perfect duodecimo (octave + fifth) instead of
> pure fifths.
> I published this tuning in euro piano 3/88, as "Stopper
> tuning, equal
> tempereament on pure duodecimos" .
> The theory behind is to solve the well known fifth circle
> in a different
> way.
> The "normal" fifth circle can be represented mathematically as
>
> (3/2)^12 = 2^7 * pk
>
> (pk= pythagoeran comma, twelve fifths equals seven octaves
> + pythagorean
> comma)
>
> In the "normal" equal temperament, the equal fifths are
> divided by 1/12 of
> pythagorean comma, so the equation becomes the form:
>
> (3/2)^12 / pk = 2^7
>
> In my theory, the fifth term is splitted down into octaves
> and duodecimos,
>
> (3/2)^12 = 3^12 / 2^12.
>
> Substituting this term into the fifth circle, this one becomes
>
> 3^12 / 2^12 = 2^7 * pk
>
> Sorting octaves and duodecimos will result to
>
> 3^12 = 2^19 * pk
>
> This is now representing a circle of 19 octaves and 12
> dudecimos. In the
> duodecimo tuning, the 19 octaves are multiplied by a 1/19
> of the pythagorean
> comma, resulting in octaves stretched by 1/19 of
> pythagorean comma, what is
> ~ 1.2 cent per octave. (this is system inherent stretch,
> inharmonicity
> stretch has to be added to the terms when working with
> tuning machines. when
> doing aural tuning, inharmonicity stretch is included
> already by the aural
> integration when tuning aural pure intervals.)
>
> This amount of stretch is what has been found by measures
> of tunings done by
> the most good tuners.
>
> Since it has been found that mathematical pure octaves does
> not produce the
> aural feel of a pure octave, but a slightly stretched
> octave will do that,
> the philosophic importance of this tuning is that the old
> pythagorean
> tuning is transformed directly into this tuning by simply
> replacing the
> "mathematical pure" octaves by "aural pure" octaves.
>
> This is true for all the other pythagorean intervals, since
> their intervals
> can all be represented as fractions of duodecimos and octaves.
> Pythagorean fourth is 4/3 = 2^2/3, meaning two octaves divided by a
> duodecimo,
> pythagorean third is 81 /64 = 3^4/2^6, meaning four
> duodecimos divided by
> six octaves.
> etc, even for every interval found on the keyboard.
>
> So the advantages of this tuning is to get "aural pure"
> octaves AND still
> having a "beatfree" interval (duodecimos), what is
> important for a straight
> and quiet beat structure order (important for sound
> impression) AND simply
> transforming the good old pythagorean tuning by replacing
> mathematical pure
> octaves by aural pure octaves.
>
> Regards,
>
> Bernhard
>
>
>
> ----- Original Message -----
> From: <brf7@juno.com>
> To: <pianotech@ptg.org>
> Sent: Sunday, January 11, 2004 8:19 AM
> Subject: New to Tuning-Book Recommendations?
>
>
> >
> > Wow. There is an unbelievable wealth of information
> > here. I am new to piano tuning and am very much
> > interested in it. I am 21 years old, living in the
> > State of Oregon, and am going to school for land
> > surveying. Anyway, my grandfather tuned for much of
> > his life, and that is what sparked my interest. He
> > gave me a book, "The New Tuning", by Lucas Mason, in
> > which the piano is tuned using perfect fifths. This is
> > a method that he said he tried, but could never get to
> > work. I have also read the book, and have practiced
> > tuning my piano 4 or 5 times and a few other pianos
> > using this method, but always come out with distastful
> > results, mostly in that the M3rds, and the 10ths in
> > the bass, sound terrible. But, as I said, I am a
> > rookie, and so, am obviosly unskilled and doing
> > something wrong. I am aware that there are many
> > various ways to tune the temperment, so I was hoping
> > that I could get some book recommendations from anyone
> > here. I dont have time to take classes on piano tuning
> > at this point in time, but will consider doing so in
> > the future. Thanks for any responses.
> >
> > Brett Flippo
> >
> > _______________________________________________
> > pianotech list info: https://www.moypiano.com/resources/#archives
>
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