Billbrp writes:
> One thing Ed Foote apparently hasn't
>learned yet is that Interval Size (cents deviation from Just or "pure"
> intonation) and Beats per Second are not equivalent.
Cents deviation and bps are not equivalent, they are proportional. This
doesn't change the fact that the ebvt creates a more tempered E-G# of
17+cents than the F#-A# of 13.7. It is folly to think that going up two
semitones will somehow make the F# third seem to beat faster. It doesn't,
and the harmonic balance is poor because of it. It is this break with
tradition, (no other temperament I know of has this amount of imbalance in
the progression of its thirds), that renders the ebvt an atypical arrangement
and makes any claim of its author to its "authenticity" a pipedream. Scale
placement cannot save this poor harmonic balance.
>So, even though the Eb and E major triads are showing the largest
>sized Major 3rds, that does not mean that they have the widest, most rapidly
>beating 3rds.
>What this means is that a larger sized interval of a 3rd with 3
>or 4 accidentals in the key signature, in the middle of the scale, can still
>be slower beating than 3rds of a slightly smaller interval size and still
>having 4 or 5 accidentals in the key signature found higher in the scale.
What this displays is an appalling ignorance of psycho-acoustics. The ear
hears beating as a function of frequency, but the perception follows a
logarithmic scale, not the linear one, ie, in a given octave, an F-A
beating at 7 bps will be heard as tempered equally to the above A-C# beating
at 9 bps. If the F-A and A-C# both beat at the same speed, the A-C# will
sound more consonant in the triad, regardless of the size of fifth involved
(try it yourself). By the same measure, in a Young temperament, the C-E(4)
sounds far more consonant than the A-C# under it or above it.
If scale position determined the perceived amount of dissonance, then in
ET, F-A, tempered the same amount, would be far more dissonant than the C-E
below because it is "higher" and beats faster. That is simply not true.
According to the writings collected by Rita Steblin, Emaj was not considered
the most "expressive" key in the historical temperaments, that was reserved
for B, C#, F# and sometimes Ab, all keys that the ebvt renders in ET size.
>Ed Foote only offers you numbers copied out of a book and the insistence
>that what anybody does other than what I do must somehow be better.
I insist on nothing. What I have offered is my idea of a rational
approach to investigating ALL the temperaments. A reasonable and workable way
for comparing all the historical permutations that our instrument has been
subjected to. I have done this with two approaches: Jorgensen's "tuning to
taste" method for aural tuners, and the use of offsets for the ETD users.
Response from the field has been quite encouraging. A growing number of
professional musicians and venues are finding these approaches to be
musically superior and I expect this to continue. In his previous writings
on this list, Mr. Bremmer's offers that his own creation (the "sideways
well") is the superior way, though nobody but himself can tune that way, that
no one tunes a true ET(fraudulently selling *reverse well* in its stead), and
everybody is both out of step and in conspiracy. <sigh>
It is very simple to compare the results of Jorgensen's instructions for
aural tuning with the results of using the cent offsets for a wide variety
of temperaments. Doing so will answer the question far more clearly than the
opinions of any one individual. Ad hominum attacks are simply the
smoke-screen attempted by those on otherwise unsupportable ground.
Regards,
Ed Foote RPT
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