Hello Isaac, here a receipt for the 12th temperament (aural tuning). 1. F21 to Tuning Fork (440Hz) ~4,2 beats (absoulute beatrate is not important at this moment) so take ~ 4 2. Match beatrate A49 to F21 to the same beatrate as heard in the 1. step 3. F21 to D30 (sixth) with the same beatrate. This will result the 3. harmonic of this D30 to the same pitch as the A49 = 440 Hz, the 12th is set now. 4. Tune a minor 3rd D30 -F33 beatrate 7,8 (absolute beatrate not important at this moment) 5. Tune a Fifth D30 - A37, with the control of major 3rd F33 - A37 at beatrate 7,1 (since the exact beatrates of the minor/major 3rd cannot be counted exactly (and of course they are slightly different on different instruments due to inharmonicity), tune the major third slightly less faster than the minor 3rd, this will make sure that the Octave A37-A49 is set by this procedure in the room of a perfect 3/1 12th with the desired stretch of about 1,2 cent and the fifth ~ 1,2 cent smaller. Continue your octave partition as you are used to do. (minor 3rds, major 3rds, major 6ths progressing, 5ths controlling by minor 3rd-major 3rd where the major is always slightly less faster than the minor 3rd) For tuning down the bass i use control of minor 3rd / major 6th with the minor 3rd about 10 % less beatrate than the major 6th. (for example minor 3rd D30-F33 beatrate 7,8 with major 6th D30-B39 beatrate 7,0) Since the tuning is straight linear to the 3/1 ratio, i am used to hear the minor 3rd down until to the last note, there are no regions where intervals change their relations. For tuning up the treble is take the usual 4ths/5ths and check with the match of major 6th - (double octave + maj. 3rd) as used to set the 12th at the beginning. For the last octave i use a 12th gripping device because beatrates are too fast to hear with the sixths and double-octave-3rd. As said, i tune the whole piano straight with pure 12ths, and with the use of major/minor 3rds and 6ths it is much more easier for me to produce an exact temperament, so I never check the octaves.... Since most tuners are using a slightly strectched octave, this tuning is not so far from what everybody is doing right now. It just helps to set the stretch sytematically und to reproduce a straight ratio through the whole piano. If you want to set the base 12th with a tuning device, tune A49 with the device, and at second step tune the 3rd harmonic of D30 to the same pitch as your A49. Proceed with machine or aurally. Hope this is helpful Best regards Bernhard Stopper www.piano-stopper.de/homepe.htm ----- Original Message ----- From: "Isaac sur Noos" <oleg-i@noos.fr> To: "Pianotech" <pianotech@ptg.org> Sent: Sunday, January 25, 2004 11:54 PM Subject: RE: New to Tuning-Book Recommendations? > 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 > > > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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