Using the System Common Master Tune Parameter

Tuning-Fork Standards of History
================================

(1) International Standard as of May 1939: A=440
(2) Paris, 1859, A=435
(3) Britain, 1870's, A=452
(4) France, 18th Century, A=392 to 409
(5) Baroque Music, A=410-420
(6) Handel, A=422.5
(7) Mozart, Stein (piano maker), A=421.6
(8) Taskin (harpsichord maker), A=409
(9) Shore (trumpeter, lutenist), 1711, A=419.9

Reference: "The Oxford Companion to Musical Instruments" written
and edited by Anthony Baines, 1992, Oxford University Press,
pages 265-266 on "Pitch" and page 353 on "Tuning-fork".

All the above can be applied to the JV/XP synth family by either
accessing the SYSTEM/TUNE buttons on the TUNE page and its Master
parameter; or, via sysex messages as in the examples below for
each of the above 9 references. The default is 440.0. The range
available is (in Herz) from 427.4 to 452.6. However, if the RPN 
Master Fine Tuning parameter are used (and/or appropiate Pitch
Bend values with respect to the RPN Pitch Bend Sensitivity
parameter) the range can be extended by +/- 50 cents, which in
this case would extend the range from 415.2 to 456.9.

The Master Tune parameter of the System Common memory area uses a
range of 0-126 which starting from 427.4 increments by .2 for
each value. Therefore the formula for determining the Herz
equivalent to a given Value is Herz = 427.4 + (Value * .2).
Or to determine the Value equivalent to a given Herz tuning is
Value = (Herz - 427.4)/.2. Because of the .2 Herz increments, to
accomodate .1 "odd" increments, RPN Master Fine Tuning and/or
Pitch Bend would have to be used. The values determined below
have been "evened down" to otherwise "avoid" the problems in
(6) and (9). Because of the limited range for tuning available,
only (1) thru (3) can be converted directly. But in fact, all can
be used if their closest equal temperment pitches are transposed"
to match them. For example, in (4) if using a tuning of 392Hz is
desired, then one way to do so would be to find the nearest pitch
and "coarse" transpose the synth to still allow playing in "C" as
if it were non-transposed.

392 Hz is closest in pitch to G (391.9954), therefore transposing 
the synth/keyboard down by 2 "coarse" semitones would allow the 
appropriate playback response. The differences, in this case, 
with +/- 1 cent would be greater than that with the E.T. tuning
as is.

(1) A=440    F0 41 10 6A 12 00 00 00 06 3F 3B F7
(2) A=435    F0 41 10 6A 12 00 00 00 06 26 54 F7
(3) A=452    F0 41 10 6A 12 00 00 00 06 7B 7F F7

Problem:  Given A is the fundamental/root, determine the MIDI
Scale Tuning Cents Offset to "tune" another scale member to, such
as C.
	
Solution: C equals the minor 3rd or (within the range 0-11 
semitones) 3rd chromatic scale degree of the Root A. Therefore if
the desired tuning frequency for C is 256 Hz, the nearest A
octave below that is (for A=440) 220 Hz which in E.T. tuning
generates a C equal to 261.6256 Hz. The difference between that
and 256, in cents, a number from the 1200 roots of two, based on
the frequency difference of 5.6256 Hz, is -37 cents which can be
used by the MIDI Scale Tuning offsets for lowering the pitch of
all pitches directly without lowering the Master Tuning
frequency. Or can be used to retune the Master Tuning frequency
from 440.0 to 430.7 which will effectively do the same thing for
all C frequencies.

For your info, the frequency of the Alpha brainwave observed in
humans in deep meditative states is 12 Hz which 256 is an
"octave" multiple of. That fundamental is the basis for Prima
Sounds developed by Ralph Losey which are based on the "esoteric"
music traditions. More info can be obtained from:

  The Prima Sounds Web Page
  http://ddi.digital.net/~prima/prima.html