----- Original Message ----- From: Robert Scott <rscott@wwnet.net> To: <pianotech@ptg.org> Sent: Thursday, October 26, 2000 2:21 PM Subject: EBVT - the numbers > HT enthusiasts: > > Based on aural tuning directions I have calculated the following offsets > > F 3.10 > F# -1.28 > G 4.50 > G# 2.49 > A 0.00 snip > or, if you prefer offsets that are more zero-centered: > > F 1.41 > F# -2.97 > G 2.81 > G# 0.80 > A -1.69 snip > > In finding these offsets I developed a software tool called > the Temperament Designer which can hopefully help to translate > aural tuning instructions into offsets from ET for other > "historical" temperaments as well. > > One difficulty in translating aural instructions is that they > depend somewhat on inharmonicity. > > -Robert Scott > Real-Time Specialties If a aural instruction calls for 10bps for C4--E4 3rd, I don' see how the inharmonicity of the piano affects these instructions. 10 bps should occur no matter what the inharmonicity. Now these rates must first come from the theroritical partial which is harmonic.Because the piano varies in inharmonicity, the "offsets" might be different for each piano (perhaps) but still it is the offset from theoritical that is being calculated. So if a piano calls for 10bps for the C-E 3rd then the 4th partial E would have to be "off" set against the 5 partial of C by 10 cps to give 10 beats. Now if the 4th partial or the 5th partial is sharp because of inharmonicity it wouldn't matter as long as the tuner is hearing 10bps. However if you tuning the two notes by machine to give 10bps, yes the machine might need to be offset because of the individual characteristics of the piano. Offset from what? The amount that piano's string varies from theoritical partial value. So that is why I think when "cents from ET" is given for the various HT's should be the cents of the theoritical partials. Since the ear hears the beat rate no matter what the inharmonicity, it is up to the machine user to figure out the additional offsets if need be. By looking at the two sets of cents you give it they appear so different that much different beat rates would be calcualted if entered into a beat calculating spread sheet. I am assuming the one with A4 at 0.00 cents is the theoritical one. It is a simple matter to convert many of the HTs into beat rates using spread sheets if the temperamant is based on a "formula" that determines the cents width of the fifth. (Or by "offsets" from commas if you will which are translated into cents) I am trying to think of a HT that isn't. Now if the Equal Beating Victorian is only given by beat rates of 3rds and 5ths alone with no reference to narrowing of commas, yes it might be that software is needed. However it would be an interesting project to see if a spread sheet could work it out. ---ric
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