EBVT tunings

[Robert Scott]

Richard Moody write:

 > Now the cents offsets you give below can be put into a spread
 > sheet and the beat rates seen.

Not easily.  To determine beat rates from a set of 12 offsets
requires that inharmonicity be taken into account, and inharmonicity
is different for each piano.  But you are almost right inthat the
beat rates you get from a theoretical calculation are going to be
fairly close to the beat rates on real pianos.

 > When you ask those to tune EBVT aurally, the beat rates should be
 > provided, otherwise how will we know if the offsets really give that
 > tuning, or if they are only close to EBVT tuning

Because 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?

 > 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.  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