EBVT tunings

[Richard Moody]

Sorry, none of the below makes sense unless a theoritical offset is
also given.  This will produce a theoritical beat rate.  To get a
piano to match the pattern of these beat rates is what determines if
the piano is "properly" tuned or not.  This is not only from the
tuner's point of view, but also the player's.  If the player is to
make any musical sense of a temperament sooner or later he will have
to know  the intervals are supposed to "beat".    Sure, he/she can
hear them and they should be consistant from piano to piano.  This is
where the theoritical rates come in.  They show the pattern.   Now if
inharmonicity needs to be taken into account by the machine that is
the machine's problem.  The ear of course automatically takes
inharmonicity into account to produce a major 3rd that beats at 10
bps, while the major 6th beats at 11.4 bps on any two or three or four
pianos.   Now of course the beats may nor not be exact to two places
but the pattern is true and this is what the theoritical rate
predicts.  So if it isn't too much of a problem it would really be
apprecaited if the theoritical beat rates could be given.  .

I was specifically asking for those who are already
| familiar with EBVT tuned aurally.  Such people presumably
| know how to evaluate a tuning to see if it conforms to their
| idea of EBVT.  I have already checked the offsets as well as
| I can, but what I need is independent verification on real
| pianos.  Such verification would not be independent if I
| supplied the criteria for evaluation, would it?

Well what makes my evaluation more valid than yours?  Besides without
the theoritical beat rates I have no idea of an "idea of EBVT".  What
ARE the musical objectives if any of EBVT?  Or is it only a
temperament so that the student can easily tune the harpsichord or
early piano-forte because it needs tuning so often and the player was
expected to tune, and thus gave a sound so that the music didn't sound
so awful?
|
|  > Looking at the offcets (below) for one octave if inharmonicity
|  > plays a part, the offsets should cover at least 7 octaves.
|  > Otherwise why tune A440 1.7 cents flat?
|
| Strictly speaking you are right.  To define EBVT
| exactly across the whole piano would require 88 separate offsets
| But SAT, RCT, and every other ETD I know of uses just 12 offsets
| repeated every octave to define an unequal temperament.  This is
| a simplifying approximation that is not very far off.
|
| As for why I specified A at -1.7 cents, the reason is so that the
| overall pitch change from an ET tuning is zero.  If an unequal
| temperament is specified with only positive offsets, then tuning
| that temperament amounts to a pitch-raise.

Since some notes are raised (compared to ET) and some are lowered, I
don't see how it can be considered a pitch raise.  In Meantone for
instance with a pitch center of C,  A (major 6th to C) gets lowered to
A436 aprox.  If tuning for an ensenmble and they want A440, A4 should
be at A440, and the rest of the notes adjusted according to the temp.
Easy to do with machines and spread sheets.  Tuning 12 notes
differently from ET is surely more difficult that tuning only 11 notes
from ET.  Multiply that by the number of octaves in the piano and you
have made life that much more difficult.   ---ric

Why make life more
| difficult than it has to be?  The reason we normally tie A4 to 440
| is not because we are specially interested in A4.  Rather we want
| to keep all the notes close to their optimum pitch.  This goal
| is more closely achieved by shifting all HT offsets so that their
| average is zero.
|
| -Robert Scott
|   Real-Time Specialties
|
|   A     -1.7
|   A#    -0.1
|   B     -1.2
|   C      3.6
|   C#    -0.8
|   D      0.1
|   D#     0.3
|   E     -2.6
|   F      1.4
|   F#    -3.0
|   G      2.8
|   G#     0.8
|