Hello, Bernhard wrote : (I also donīt find it helpful to discuss about octaves to be 2/1 4/2 or 6/3 since at that point we are leaving the beat structure net caused by the main fundamentals) In fact I described the tuning as 19th root of the 3rd harmonic and not as 19th root of a mathematical 3/1 ratio. I agree with that, expression of these octave ratio is mostly a help to get a better control on the artificial stretch used, but primarily the idea came because of the preeminence of those partials in the tone mix INCLUDING THE FUNDAMENTAL, thing than most seem to forget. When it comes to the stretch proposed by the VT, I check it again recently on a nice Erard grand with low iH strings (recent soft Firmini sings) the 12ths have around 1/3 bps in the 5-6th octave, and that gives a color I like. I understand the strength that is given with those purer intervals and the solution you came by for tempering, but I'd say it is not suited nor for any instrument, nor for any music, (while I could not really get in there saying why, very probably rounder instrument will not benefit as much from it as more incisive ones) And I have yet a few years to change my mind ;>) Best regards. Isaac OLEG Talking about EDT At this moment only a multi partial driven device can come close to what the ear listen. The most point that I did not like with partial driven methods is that there is no respect for the fundamental GLOBAL tone, then octaves for instance are often a little off (what I call artificial strech)and the kind of consistency obtained is not very natural to my ears (while giving an impression of justness indeed). Stretch as use in concert tuning, seem to me a tool to get more power at the attack of the intervals, as the tone is higher when the hammer hit the strings generally, these seem to settle down towards a lower frequency. Possibly when played together a stretched octave tend to lock the sustain to a higher pitch, for resonances reasons (is it possible ?). I know I rely too much on my musical trained hearing for tuning, this is why I can't use always the same method, and I have to listen to the result played if I want to correct a few things. Even in the most perfectly tuned piano there will be passages that will benefit of some tweaks, Using a p12 or p5 approach is of course very good, but it can apart more or less of the piano own's resonance IMO. Nowadays, I don't know if I obtained the true pure twelve tunings, I guess that yes, I like to hear more anyway. But I recognize a bit of it when I hear the Paulello piano (Stephen tunes by pure 12ths also) and I find it good but a tad strange, probably because of the ear education I have. Best Isaac
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