<div dir="ltr"><div>I don't understand why anyone would assume that the mathematical model for 19 tone to the P12 equal temperament would be followed any more closely in practice than that of the 12 tone to the octave equal temperament.</div> <div> </div> <div>When we tune 12 tone to the octave ET we modify the tuning for aesthetic reasons and to deal with the change in inharmonicity across the scale and to tune the treble as sharp as we like to hear.</div> <div> </div> <div>Same thing with the P12th ET.</div> <div> </div> <div>Stopper's tuning appears to deal with inharmonicity in an appropriate and consistent manner. In the bass, some pianos are tuned wider than that to which I am accustomed and some are more narrow, but the effect is the same -- a coherent sound to the overall tuning. As for the treble, I strongly suspect that Stopper picked a deviation for C8 that is similar for all pianos. Other techs do the same thing; one approach to getting two pianos tuned together has been to pick a deviation for C8 and do the stretch necessary to make that chosen deviation happen at C8. The curve leading up to C8 will be different on the two pianos, but the approach is valid.</div> <div> </div> <div>For what it's worth, Stopper has realeased tuning programs for guitar, violin, and cello through Apple's AppStore for iPhone and iPod Touch. Anyone with an iPhone or a 2nd gen iPod Touch can get a free taste of Stopper's tuning program by downloading the free version of Stopper's guitar-tuning program.</div> <div> </div> <div> </div> <div>Kent Swafford</div> <div> </div> <div>PS -- I don't know if the piano tuning program will or will not be released for the iPhone.</div> <div> </div> <div>KES<br><br></div> <div class="gmail_quote">On Mon, Oct 13, 2008 at 5:49 AM, Richard Brekne <span dir="ltr"><<a href="mailto:ricb@pianostemmer.no">ricb@pianostemmer.no</a>></span> wrote:<br> <blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">  Fred writes<br>  I frankly don't think dividing a 12th evenly into 19 is<br>  significantly different from dividing an octave evenly into 12<br> <br><br>Actually it is... tho the distinction in the temperament area is a bit subtle. If you require that D3 and A4 have a pure 3:1 relationship... then require that A4 and A3 have a pure 6:3 relationship then your 3:2 D3 and A3 is not necessarily going to work out quite like you want it... and you may be forced to fudge.  Course that kind of thing develops around the temperament octave as you go. <br> But more then this, and evenly divided 12ths temperament extended into the treble so that all notes above this area are tuned to pure 3:1 to their respective 12ths below then the treble curve around the F5 - F6 area is significantly different then in an Octave type based curve. Jim Coleman commented on this when my own P 12ths for Tune Lab was released back around the turn of the century. Indeed, it was a characteristic he liked quite abit.<br> <br>Stoppers approach, if it indeed does use the Perfect 12th the whole way will do exactly what Fred states... by definition all 12ths are tuned pure and some middle area 12th interval must be used as a temperament basis.  I have not heard it...but if his device works well.. then it simply must stretch the bass as described briefly in my last or as Fred mentions, (and Jim Coleman confirmed years ago) the bass will simply be too narrow to sound good.  I suspect Stopper knows this and uses 12th types in some fashion or another consciously or otherwise  to provide an appropriate stretch.<br> <br>Fred is also correct in saying that the very top will be a conservative stretch.  Whether or not one thinks any particular stretch anywhere is pleasing or not in the end falls into the realm of personal preference.... subjectivity.  That said... I think most folks if viewed statistically would find a strict P-12th relationship in the low bass in bigger pianos to be a bit to....tense.<br> <br>Cheers<br>RicB<br><br><br></blockquote></div><br></div>