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 > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives >
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