EBVT - the numbers

[Richard Moody]

----- 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