HT's beyond Jorgensen

[Billbrpt@aol.com]

In a message dated 7/4/98 6:51:33 AM Central Daylight Time, rscott@wwnet.net
 writes:

<< Bill,
 
 I am preparing a library of historical temperaments to
 distribute with my TuneLab program.  I have gone through
 Jogensen and transcribed all the tables of cents offsets
 for electronic tunings.  Are there other sources of
 non-ET tunings (specified as offsets from ET in cents) 
 that you could direct me to?  There is no need to respond
 on pianotech.  You can just e-mail me directly.
 
 Robert Scott >>

There are no publications other than Jorgensen's and those listed in the SAT
 manual (which also come from Jorgensen) that I know of.  However, I just got
 the following E-mail which will give you one and from what it says, someone
 has figured out how to do the temperament I do as deviations from FAC.  I
 never do a temperament this way but it seems to be the way most people want to
 do one.  I will also list the 1/7 Comma Meantone and 2 variations of it at the
 bottom.   

There is no reason not to publish this inquiry or the response on the List.
 There may be others interested in the information.  Even if there are readers
 who will not use the information, it lets others know that there are people
 who are interested and also gives casual readers a perspective of what others
 are interested in and doing.  The time has ended for the discussion and use of
 the HT's to remain "in the closet".  Candor and free flowing discussion about
 any tuning related topic is the purpose for the existence of this List.

<<Bill,
Here are deviations for a Kellner F-A-C tuning:

 	A=0	A#=4.2	B=-0.9	C=8.1	C#=-1.7	D=2.8	D#=2.2	E=-2.8	F=6.1	F#-3.6	G=5.5	G#=0.
 3	A=0

BTW, Karen thinks she has "cracked your code" or quantified your tuning.  We
 may use her most probably ersatz numbers for comparison graphing if you don't
 mind.

Skip >>

The following are cents deviations for an FAC program that will create a 1/7
 Comma Meantone (7MT), a 1/7 Comma Modified Meantone (7MMT) and a 1/7 Comma
 Victorianized Modified Meantone (7VMMT).   The 7MT is a historically
 documented temperament from Owen Jorgensen's first publication, Tuning the
 Historical Temperaments By Ear.  It was found, by trial and error. to be a
 very useful temperament for the modern piano.  Virtually any music may be
 played on it.  The so-called "wolf" interval of Ab-Eb does not meet the
 specifications for a true "wolf" interval.  It is only about 8¢ wide.  It is a
 slight but tolerable dissonance.

In any case, if the 7MT seems to be too strong of a temperament, by using
 historical precedents, it can be mitigated to a 7MMT where the "wolf" is split
 between 2 other 5ths.  Those two  5ths will still be slightly wide but barely
 perceptively so.  The 7MMT is a further splitting of the "wolf" which
 mitigates it to the point of being only technically wide.   In a normal
 musical context, there is no dissonance but an aural or electronic test will
 prove the 5th to still be slightly wide. The FAC deviations for all three of
 these were computed by our contributor to the List, Paul Bailey, RPT.

There is also another interesting version of the 7MT which was invented by my
 Madison colleague, Timothy Farley, RPT.  Rather than an unbroken chain of -3¢
 tempered 5ths (theoretical value), he makes the EB 5th pure.  It still
 qualifies as a 7MT but has the kind of variation that was historically applied
 to such temperaments as the 1/4 & 1/5 CMT's.  It might therefore be called the
 "Farley 7MT" (F7MT).  This variation takes a bit of the harshness out of the
 bottom side of the cycle of 5ths and thus diminishes the "wolf" to about 6¢
 wide.  It too could be mitigated into a 7MMT and a 7VMMT if one so desired.

  Unfortunately, I do not have any cents deviation for FAC data for this.
 However, when I look at the table, I can insert a value that would cause this
 to happen and will publish it along side of the regular table.  Please be
 aware that I have not tried these figures, they only represent a calculation.

Here is the cents deviation table:

        7MT      7MMT      7VMMT       F7MT        F7MMT     F7VMMT           
F      4.5         4.5           4.5              4.5            4.5
 4.5    
F#    -3.3         -3.3          -3.3            -2.2           -2.2
 -2.2 
G      2.3          2.3           2.3             2.3            2.3
 2.3
G#   -5.5          0.7          -2.5             -4.4            1.8
 -1.4
A      0.0          0.0           0.0              0.0            0.0
 0.0
A#    5.6          5.6           5.6              5.6            5.6
 5.6
B     -2.2         -2.2          -2.2             -1.1            -1.1
 -1.1    
C      3.4          3.4           3.4              3.4            3.4
 3.4
C#   -4.4         -4.4           1.2             -3.3            -3.3
 2.3
D#     6.8         6.8           3.7              6.8             6.8
 3.7
E     -1.1         -1.1          -1.1             -1.1            -1.1
 -1.1


Bill Bremmer RPT
Madison, Wisconsin