1/7 Comma Meantone Data

[Billbrpt@AOL.COM]

For those who expressed interest in tuning the 1/7 Comma Meantone Temperament,
I have two different ways to program an SAT.  The first is a set of deviations
for an FAC program.  I have no experience using this method but it is easier,
perhaps than the way I do it.  I cannot vouch for the results, however.

!/7 Comma Meantone using an FAC program:  Add or subtract the following
figures for each note of the program.

F:     4.5
F#:   -3.3
G:     2.3
G# : -5.5
A:     0.0
A#:   5.6
B:    -2.2
C:     3.4
C#:  -4.4
D      1.2
D#:    6.8
E:    -1.1


The next way uses the SAT to create true 1/7 Syntonic Comma 5ths adjusted for
inharmonicity by the Direct Interval method.  THESE ARE ***NOT*** DEVIATIONS
OF AN FAC PROGRAM!!!   All values are read on octave 5.  Therefore, you must
reset the SAT at C4 to read on C5 when you get to it while storing the figures
(otherwise it will read on C6 and produce incorrect results).  You must also
create you own octaves, however you prefer to do that.

You must first determine how your piano fits into one of three broad
categories of inharmonicity:  High, Medium or Low.  To do this, you take a
sampling the way it used to be done for the old Stretch Factor calculation.
(See the Manual).  In the TUNE mode, read the note F4 on F5, stop the lights,
press SHIFT and RESET to "zero out" the reading, then press OCTAVE up so that
you are now reading on F6.  Measure and stop the lights again.

Any figure of 4.8 or below will be a Low Inharmonicity scale.

Any figure between 4.9 and 5.8 will be a Medium Inharmonicity scale.

Any figure of 5.9 or above will be a High inharmonicity scale.

These determinations are meant to be for the selection of which set of figures
you will use to tune this temperament and are not meant to be used or
interpreted in any other application.

F3-F4 1/7 Comma Meantone Temperament for a LOW Inharmonicity piano:

F3:    3.6
F#3: -2.7
G3:   1.8
G#3: -4.5
A3:    0.0
A#3:  4.5
B3:   -1.8
C4:    2.7
C#4:  -3.6
D4:    0.9
D#4:  5.4
E4:    -0.9
F4:    3.9


F3-F4 1/7 Comma Meantone Temperament for a MEDIUM Inharmonicity piano:

F3:   3.2
F#3:  -2.4
G3:   1.6
G#3:  -4.0
A3:    0.0
A#3:  -4.8
B3:   -1.6
C4:    2.4
C#4:  -3.2
D4:    0.8
D#4:  4.6
E4:    -0.8
F4:    3.7


F3-F4 1/7 Comma Meantone Temperament for a HIGH Inharmonicity piano:

F3:   2.8
F#3: -2.1
G3:   1.4
G#3:  -3.5
A3:    0.0
A#3:  3.5
B3:    -1.4
C4:    2.1
C#4:  -2.8
D4:    0.7
D#4:   4.2
E4:    -0.7
F4:    3.6

The 1/7 Comma Meantone is the mildest of all Meantone Temperaments.  Much of
its harmony sounds like a typical Well-Temperament, even perhaps like the
Victorian style yet it still has a trace of the "Wolf" interval that occurs
between Ab-Eb.  Each 5th of the scale is tempered exactly the same amount,
that is, 1/7 of 1 Syntonic Comma but adjusted for Inharmonicity except the 5th
Ab-Eb which is several cents wide.  This gives the key of Ab a truly
remarkable sound and is especially powerful while playing Romantic literature.

Generally, the Meantone Temperaments are thought of as "restrictive" and "non-
circulating" meaning that not all of the keys are useful.  A true "wolf" key
is very harsh and considered a dischord and not useful for music except
perhaps for its "shock" value.  In the 1/7 Comma Meantone Temperament however,
the Ab-Eb 5th is wide and slightly dissonant but does not qualify as a true
"wolf" and when used in a musical context, it becomes an asset, not a
liability.

I learned about this temperament from my colleague Timothy Farley RPT of the
Madison Chapter.  He was looking for the mildest possible Meantone Temperament
and was advised by Owen Jorgensen of its existence.  The aural tuning
instructions for it can be found in  Owen's first publication, "Tuning the
Historical Temperaments by Ear".

It has 11 examples of Equal Beating 2nd inversion Major triads which give the
piano a very smooth, "in tune with itself" sound.  The remaining Ab triad has
an uncannily powerful, almost "electrified" sound.  You hear great contrasts
of tonality in no matter which music is played.  It is useful for all periods
of music, even and perhaps especially contemporary styles such as New Age and
Jazz.

It is not for everyone, however.  It is just too much for some people.  Mr.
Farley found a way to mitigate it somewhat by making the 4th that occurs
between B3 and E4 pure in the F3-F4 temperament sequence.  If there is an
interest in the mitigated version, I will publish it at a later date.

This temperament is much stronger in character than the Equal Beating
Victorian that I often talk about and usually tune.  I only tune it for people
who I know like it and want it.

Good luck with your temperament adventure!

Bill Bremmer RPT
Madison, Wisconsin