Hi Brett, I've find the pure fifths tuning not adapted at every piano, and nowadays a little too static despite the fast rolling of thirds and aggressive tenths. The basic trick to realize if you follow the probably same method developed by Serge Cordier, is to use not pure 3:2 fifths but pure 6:4. That mean the test for purity is not the equal beating of the Major sixth and the tenth based on the same bass note, but the equal beating of the contiguous minor third and the major third within the fifth. (that makes a slight difference, may be not very perceptible but the interval "locks "well at this level. Then when the minor chord (for inst C-E-G, having those two intervals beating the same , have a particular tone easy to be used to check. Nowadays in this system, the treble tend to get aggressive too much to my ears, and most of the "pure fifth" tuners are obliged to recon ciliate it, tuning short octaves and breaking the tenth progression in the 6-7 octave (for what I've seen). The method described to expand the temperament is based on a smooth progression of 17 ths, it is difficult to do for a beginner. As others have said try to learn a more basic way before (while I've seen beginners learning pure fifth tuning with acceptable results also, as the tuning is done "in the tone" and not trying to meet a theory when it comes to beats. The 12th tuning method seem to give a good tone projection in concert halls, many concert tuners stretches as hell, the importance being to be consistent any good method for that is good. I believe that what is aimed is a permanent state of tension in the whole tuning, the ear get exited by the stretch, and it carry better also. Nowadays in passages where the piano may sing strong stretch is not always welcome, particularly in the treble. Most pianists can't really express their preferences in term of stretch or temperament. Among the 80' concert tuners there in Paris where little differences in temperament and stretch, all only due to their hearing and as a result of the method employed. these differences where only noticeable for a tuner indeed. The Cordier tuning (or Mason for your part of the world) have its adepts among musicians In the end, the ability of the tuner to hear the sound returned by the hall and to install a justness that is also allowing the piano to be in tune with itself is what counts IMO (in terms of stretch). Coherence in the temperament system employed is also what counts, as well some tuners have really uneven "equal temperaments" because they stretch more than usual, but end with a pleasing tuning as well. What bothers me a little with stretches that are higher than what the piano can accept is that they tend to break the spectra continuity above some point. Then I don't know what happens to the hearing of the audience, but I believe that the instrument is less in value than with a more holistic tuning. What we are after is not justness anyway, only the impression of it ! Being 48 I have yet some time to change my mind ! Greetings to all , have a nice Sunday. Isaac OLEG > -----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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