Hi John. Yes, tune the entire tenor and treble outside of my temperment area to P 12ths. I start with D3 - A4 as a P 12th, fit A3 appropriately inbetween and temper that whole section with those three as anchors. From then, D#3-A#4 and upwards everything is tuned to perfect 12ths. Kinda eliminates the need for any generated tuning curve in the first place as you can direct reference the 3rd partial of the lower note all the way and insure an exactomundo match when tuning the fundemental of the 12th above. Actually... this way of tuning is not all that new. I know of at least 3 who have offered some information about this from 15 - 20 years ago, and it wouldnt suprise me at all to discover much earlier musings on the subject matter. The most thorough mathamatical treatise on the subject I am aware of is from Bernhard Stopper from around 15 years back. Interestingly... most of these and indeed my own <<discovery>> of the P12ths tuning seem to have come about rather independent of one another. Probably because of the overall dominance of the octave tuneing perspective, and because of the fact that when first attempted the P 12ths tuning is suprisingly... for not to say amazingly... effective and easy to accomplish. A great aural test is to play the major 6th below the lowest note of the 12th and compare that with that same 6th against the upper note. Of course the beat rates should be the same... but its one of the easiest tests to hear clearly and quickly. Cheers RicB Bec and John wrote: > >> And I'll go a step further... the cleaner the 12ths are the better >> the overall stretch of the whole tenor treble area > > > Interesting. I'll have to try that out sometime. Just to clarify, > after you set the temperament octave you use the 12ths as the primary > means to tune (at least within the tenor treble area)? > > - John >
This PTG archive page provided courtesy of Moy Piano Service, LLC