Ric said: > Taking the 19th root of the 3rd harmonic (or any partial for that > matter) for 19 semitones by the way... is not the same thing as spacing > those same 19 semitones the way I do with the aid of Tunelab. Nor is it > likely to result in exactly the same <<pure 12th>> unless it in turn is > based on a 12th in which the 3rd partial of the lower note is identical > to the fundamental of the higher. That said... the basic and general > spirit of basing said spacing on a perfect 3:1 12th is much the same. Yes Ric. But the differences we speak here about are ONLY caused by different ways of discretizing the inharmonicity effect. Taking the 19th root of 3rd harmonic valids surely only for the special case where the inharmonicity slope stays constant. I did not figure out more precisely at this point for not complicating the things more than necessary. Since you see this immediately, more discretizing is necessary now ;) For example in the old Mensurix Versions 1,2,3 and 4.0 the frequencies were calculated on a P12th tuning where i calculated the inharmonicity curve in that way that i took for each consecutive P12th the frequency of the 3rd harmonic and did a spline smoothing on the resulting 19th root factors. So i think what we are doing is not as far away than that what other tuners are doing by tuning octavely. (No matter what Octave ratio is used, perhaps a 6/3 may come in the case of a good inharmonicity curve most closely to P12th.) again Ric: > I find them very useful myself. Tuning, one way or the other, is not a > matter of simply taking regard to the fundamental frequencies of > strings. Nor is it a simple matter of dealing with the lowest partial > pairs in any intervals. Most of our aural octave tests are actually > dealing with differing octave types for different registers of the > piano. Being able to refer to these directly as well as referring to > aural tests allows for a degree of communication among tuners that > otherwise becomes difficult, clumsy, and less then dependable. I did not say that i tune only the fundamentals. Since i tune aurally, if i set M6th and m3rd and M3rd and double 8th+M3rd, i always keep in mind of the higher partials ( i think i must not figure out more precisely here). I only said i do not use any higher P12th ratio than the first 3/1. (you also stated to Isaac that the 12th should in no case be wider than straight) And since i built my tuning only with the help of the beat structure net, i donīt matter whether my octave is a 4/2 or a 6/3 or a 8/4 or somewhat between that. This is a straight consequence of tuning really straight P12th throughout the piano. But ok if someone remains in thinking or hearing "octavely" or for handling the discretized absolute frequencies with ETDīs it might be helpful to describe the octaves relating to a higher partials ratio. donīt letīs forget we are talking about a tuning we are both convinced of. I agree with every statement you have said about its sound impression. regards, Bernhard ----- Original Message ----- From: "Richard Brekne" <Richard.Brekne@grieg.uib.no> To: <oleg-i@noos.fr>; "Pianotech" <pianotech@ptg.org> Sent: Monday, May 31, 2004 4:18 PM Subject: Re: P12 in Tunelab Pro > Bernhard and Isaac: > > > > >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 find them very useful myself. Tuning, one way or the other, is not a > matter of simply taking regard to the fundamental frequencies of > strings. Nor is it a simple matter of dealing with the lowest partial > pairs in any intervals. Most of our aural octave tests are actually > dealing with differing octave types for different registers of the > piano. Being able to refer to these directly as well as referring to > aural tests allows for a degree of communication among tuners that > otherwise becomes difficult, clumsy, and less then dependable. > > Taking the 19th root of the 3rd harmonic (or any partial for that > matter) for 19 semitones by the way... is not the same thing as spacing > those same 19 semitones the way I do with the aid of Tunelab. Nor is it > likely to result in exactly the same <<pure 12th>> unless it in turn is > based on a 12th in which the 3rd partial of the lower note is identical > to the fundamental of the higher. That said... the basic and general > spirit of basing said spacing on a perfect 3:1 12th is much the same. > > >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. > > > > > This term <<artificial stretch>> is one I have never quite liked... in > as much as there actually are several coincident partials for any given > octave (or any other interval for that matter) combined with the fact > that there simply is no way of defining a conglomerate <<beat rate>> for > any contrived sum quantity of those coincidents in evidence for any > interval... then any decision relative to which degree of octave spacing > is arrived at is per definition <<artificial>> to begin with. There is > nothing less artificial about choosing a 2:1 octave type for A3-A4 then > there is choosing a 6:3 when it comes down to it. That most tuners > would choose something close to a 6:3... leaning on the 4:2 side is > another matter entirely. It all comes down to subjective tastes within > a rather large window of what is reasonable. > > There is no meaningful description for the net affect of the sum of all > coincidents at present. Virgil Smith claims the existence of a so called > natural beat... but this has yet to be quantified in any sense of the > word... so it usefulness remains questionable at best. > > >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) > > > > > > > This is interesting... I assume you mean that your 3:1 12th beats at > about 1/3 bps narrow. In which you will have opted for a stretch (as > artificial as any in my book) that employs pure 2:1 octaves in that > range... perhaps even resulting in narrow 2:1 octaves at the very top. > I have a friend who also likes this kind of a compressed stretch. His > background is in pipe organs btw... and he gets into straight 2:1 > octaves already at C5-C6. Personally... I find his higher treble > impossible to listen too. But he likes it. > > >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). > > > > > > Also interesting... of all the single partial schemes I've run into so > far... the P12 tuning I prescribe has the nicest Global tone. Thats > what I like best about it. Not knowing the tuning algorithm for the VT I > of course cant speak to it... but it would indeed be interesting to see > just what (in terms of coincident partials matching) it decides upon. > Especially in the light of some of the aural observations made about the > tuning. > > >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 run into certain combinations that yield some degree of increased > sustain as well... but they are not confined to just one particular > spacing.... or interval for that matter. > > >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. > > > > > I cant speak to the p5th tuning as I havent tried it yet. But the P12th > concept works great with the pianos built in inharmonicity. In fact, > I'd say it works wonderfully to the degree of taking advantage of the > instruments tonal characteristics noticeably better then octave tuning > approaches typically yield. But tastes vary to be sure. > > >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 > > > > > > > Cheers > RicB > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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