Greetings,
Inre the comparison between 1/4C and ET, Ric writes:
>> Well.. I dont know about you folks, but I could hear almost
>immediatly that this was waaaay off from ET. I just heard the quarter
meantone
>version d it was quite obvious to my hearing.
RicM responds:
>Yes Richard, that is the color ET killed.
I must respectfully disagree. "Color" barely exists in 1/4 Comma
meantone. The usable thirds are all the same size, and the diesis (at 41
cents) isn't really musical. 1/4C's major characteristics are the sameness
between usable keys and the dissonance of the wolf. The "color" that ET
killed was more a creation of the well-tempered tunings that followed the
Werckmeister procedures of the late 1600s.
>Meantone is not usually heard on
> pianos so yes it should sound different. Meantone is the one temp
> furtherst from ET.
This is debatable. On the one hand, the diesis of MT IS far away from
anything on ET, so there is a great distance between the two on maximum
departure, however, MT and ET resemble each other in that they both have one
size of thirds, (MT actually offers dim4ths instead of thirds, so we can say
that it is "equal" in eight of its keys). I think something like a
Kirnberger is the farthest from ET, since it has thirds ranging from pure to
full syntonic commas. It is hard to get a wider (or wilder) contrast to the
equality of ET than that.
RicB writes:
>>Tho I have run BB's EBVT on a piano
at the school for almost two years now. Students pretty much dont
notice the difference.... even when I point out a few things to them.
But I hear it right off. In close keys everything is so .... well easy
going... relaxed... almost sleepy depending on the passages, where as
moving outwards things get quite a bit more lively til in the end
there are intervals and chords that are pretty much shouting at you.<<
If I remember correctly, Richard earlier wrote that his original version
of this tuning turned out to be something else, and since the mathematical
description,(via offset numbers) has been in a state of flux, so far, it is
difficult to tell exactly what is being tuned. The author has been
consistent in stating that machines can't correctly create it without direct
supervision, thus, this temperament, as tuned by anyone else, is not a known
quantity like our offset tunings with Jorgensen numbers. So, it is possible
that the temperament in use is not what was originally intended.
Even so, in terms of what Jorgensen calls "harmonic balance," the charts
and numbers of this temperament ( <A
HREF="http://www.billbremmer.com/JMKEBVT.gif">JMKEBVT.gif</A> ) don't seem to
resemble those of historical documentation. Unless I have totally overlooked
the research, I find no other temperament schemes that temper the E-G# more
than anything else, and rendering the traditional meantone "wolf" keys such
as F#, C# and Ab all alike with an ET-size third is certainly atypical. Nor
do I remember any temperament that creates a Bb-D third wider than F#-A#.
All in all, the EBVT has four M3's wider than ET and they the keys that are
found in the "middle" area of the circle of fifths. Additional consonance in
the near keys has been created by widening the middle keys, leaving the
"remote" keys such as F#, C# and Ab much like ET. A writer I know has labeled
this "sideways well."
In spite of the author's claim to have created "a new temperament which
retains the true "colors" or tonality known in the past", the EBVT, as
described, cannot do that, since, unless we accept that this form was common,
it can't be expected to support 18th or 19th century composers' intentions
with such atypical alignment of the intervals. What other temperament of the
past does this? Modulations that were conceived on a Werckmeister style
tuning would be given new directions in one such as this.
For example, a resolution, often used by Beethoven, going from a
climactic B chord to E, (stating the 2nd theme in the "Waldstein," also in
op. 109). In traditional form, the temperament assists in the move towards
resolution by furnishing a more consonant E triad. When the order of
dissonance is reversed, the move doesn't harmonically convey the resolving
sensation, even though the musical architecture indicates that is the
direction of the resolution. Ameliorating the triad via equal beating
intervals doesn't make up for the additional tension created by the more
highly tempered E-G#.
Other shortcomings of misplaced harmonic balance may be found in a
variety of music. An example sent by Paul Bailey inre use of the EBVT for
later music:
"The example I like is the Gb Impromptu of Schubert: In ET the Gb-Bb
third is so slow the piece
just sounds lethargic. In the Moore Victorian Gb-Bb is only about 16
cents, but the order of modulation
is correct, and the Impromptu sounds majestic. In a 'stronger' well
temperament, like the PBWT or the Werckmeister III or Kellner, this
Gb Impromptu expresses anxiety, and other complex and difficult
emotions; which is what I think is the correct interpretation."
The EBVT offers an ET-like Gb-Bb, likewise the B and C# triads.
Modulation through these creates little harmonic change, thus a piece in Gb
is going to have many of the characteristics of ET. Pure ( EBVT )fifths
found in some of these keys are scant improvement over more traditional
temperaments.
The alignment of beating to create reinforcing triads is certainly an
interesting approach, but so much Classical, Romantic, and Baroque music goes
everywhere that it is hard to justify leaving the traditional form of
well-temperament for these "localized" benefits. This is not to say that a
composer of today could not use the EBVT to create new music, just that this
temperament seems to scramble the historical precedents. (I have tuned it
aurally and electronically, finding little difference in the resulting
harmonic balances, and the question of stretch doesn't seem to alter the
relative qualities of the keys, either.)
You(RicB) may be surprised if you were to change that temperament to
something that is more along the lines of historical record, to say, the
Broadwood tunings, or even Moore & Co.(which is mild). A more supportive
alignment values might be noticed by the students.
If one is looking for modern interpretations of the ancient tonal
palette, there are two current temperaments I can recommend. One is the Paul
Bailey WT (PBWT). Its author tells me that there have been some minor
modifications to this, but the character of the tuning is clearly evident in
the following figures. This temperament offers a progression from a C-E of
5.4 cents (which is so close to Just that it can easily masquerade as a pure
third), to the well-known syntonic comma at the F#-A#. Its progression is in
line with historical precedent and it is loaded with proportional beating
triads,(tune it up and find them, you will notice a 4:2 relationship between
the m3 and M3 of more than several triads).
C=+6.2
C#=-1.6
D=+1.4
D#=+2.3
E=-2.1
F=+6.2
F#=-3.6
G=+4.9
G#=+0.3
A=0.0
A#=+4.2
B=-0.1
The others are the Coleman temperaments: ideal examples of harmonic balance
in a variety of ascending strengths! I have used these a lot. The Coleman
11 has proven to be a great departure point for the previously ET-only ears,
and I interchange it with the Moore & Co. quite often. The Coleman 16 is
almost the strength of the Thomas Young temperament.
A # B C # D # E F # G # A
Coleman 11 0 3 -2 4 1 1 1 -2 5 -1 3 1 0
Coleman 13 0 3 -5 4 -1 -1 0 -4 5 -3 3 1 0
Coleman 14 0 4 -4 6 0 2 2 -2 6 -4 4 2 0
Coleman 15 0 4 -4 6 0 2 2 -2 6 -2 4 2 0
Coleman16 0 4 -2 6 0 2 2 -2 6 -2 4 1 0
The next time the urge to have a "tune-off" occurs, I think it would be
very instructive to compare the contemporary temperaments given above to one
another. It has been shown, at least to the PTG audience, that virtually any
"other" tuning sounds more resonant that ET, so we may have beaten that horse
to death. Appreciating the work of our modern authors may be a bit more
challenging, perhaps scintillating, no?
A more telling departure may be going to the Kirnberger tunings and
see what people sense when a Just third is compared to the 21 cent comma. I
have found at Vanderbilt, (where there are 4 practice rooms in a row, with
identical Yamaha C2's in them and the students can compare an ET, Broadwood,
Young, and Werckmeister III) the "Victorian" temperament isn't sensed as
being very different until there has been some time on the two stronger ones.
THEN the difference between the Broadwood and ET is more readily apparent.
There is much to be learned about temperament sensitivity in today's
musical world. It is a learned skill. How Keith Jarrett came to prefer the
Kirnberger tuning would be an interesting study in temperament awareness.
Why the jazzers here in Nashville sometimes ask for the Broadwood "Usual"
tuning because of its "crunchiness" instead of the Coleman 11, (which they
called "sweeter" and better for some other things), is still a matter of
curiosity to me. And why the guitar world of Steve Earle is so in love with
the Young more curious, still.
I suggest that it is a mistake to investigate non-ET with just one
temperament, regardless of origin. With musical tastes being so subjective
and temporal, easily influenced by expectation or past experience, the only
valid results come from comparing a series, looking for the common thread,
denominator, or response in listeners and musicians. By wide comparison, we
often find the most trustworthy path.
Regards,
Ed Foote RPT
(will be out for a few days hunting in the dove fields, "who needs a flame
suit when they have a shotgun"?)
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