New to Tuning-Book Recommendations?

[Bernhard Stopper]

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
>
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