In a message dated 98-01-31 11:38:51 EST, you write:
<< Dear list,
Concerning the discussions about historical temperaments, my question is not
about the relevancy of HT but about which one to use in which circumstances.
>>
Dear Michel,
I'd like to address your question about each of these composers
individually but let me tell you first in general terms, that you could use
virtually any cycle of 5th based temperament that you choose for any one or
all of them. I have known about your question before and have wanted to
respond to it but have not had the opportunity.
Although I don't have time right now, I will get back to this question and
write my opinion about which temperament might be appropriate for each of the
name you list as if each one were the only consideration.
Addressing the question as if it were a program however: Each of these is
to be a part of an evening of music. The artist says he agrees to have an HT
but doesn't know much about them. Which one?
Victorian is the mildest, your safest bet but also frankly, the least
interesting.
Valotti or Thomas Young #1 or a composite of the two will give a little
clearer, stronger definition in key color. If it is
a large hall and you have a Steinway, the Valotti will project a "razor sharp"
in-tune sound if you have good stretching in the octaves.
1/7 Comma Meantone will add particular authentic sounding harmony to the
earlier music and give you a powerful boost for the Romantics. You can't go
wrong with this. You can choose to stretch your octaves conservitavely for an
intimate setting or to the limits that the piano's inharmonicity will allow in
a large hall for good projection.
Here to explain a little more in depth about the piano's vibrato and the
effect small changes from ET has on piano harmony is some copy from a private
post I anwered:
<< Therefore, although the scale is logarithmic, the rule of thumb about 4
cents to 1 Hz. seemed quite right.>>
This is true for A4 at the fundamental, or so I know from reading.
<<Unless I am completely wrong about subtracting Hertz to get beat rates, I
still consider the changes in musical expression of 1 cent change in thirds
to be minimal. Perfect fifths might be another matter, but that would not be
the "vibrato" you were talking about. >>
Let's not "inflame" our passions by using words like "completely wrong". I am
not a scientist and I also know very little higher Math. What I say in this
regard comes from long hours of experience as an Examiner. I posted this
sentence in a previous post:
<<If you flatten or sharpen one of the notes of a major 3rd anywhere within
the F3-F4 octave, it will quite effectively change the beat speed of that
interval by "a beat or so, perhaps even a few beats per second", certainly
more than 1/4 bps.>>
In a sense, you are right, of course. If you took the Exam and you had
one error in it that was 1¢, that would be 1 point off which is then
multiplied by 2.5 and your Temperament score would be 97 1/2 (or some
Examiners round it to 98). You'd still have lots to be proud of and no one
would really think about your temperament as being anything but "equal". If
you tuned a piano out this way, the difference between the piano with or
without the error would probably not really be perceptible.
That error would have been aurally verified however. It would have
clearly been demonstrated by the Examiner that the contiguous 3rds don't work
out, there is one 5th that sounds pure and the other, contiguous to it, sounds
too tempered, the same with the 4ths and the progression of 3rds & 6ths would
have a "glitch" in it. Now, I think if the 3rds in ET as increasing in speed
by about 1/2 bps from one interval to the next. Given your example, let's
say that your F3 was sharpened by 1¢ from what would be a perfect ET. It will
depend on the actual inharmonicity the given piano has, but that will most
definitely slow it down by a perceptible amount. Indeed, some of my
Victorian tunings have F3 at 1.0 against A at 0.0. That interval, I want to
beat at 4 bps in my temperaments as opposed to 7 (in ET). Now for the higher
Math: 7-4=3. Most people would say that "a few" means "3" (or so). Most of
the time, however, I need to set that note at 2.0, 2.5 and sometimes 3.0
against A at 0.0 to get that same 4 bps. It all depends upon the individual
piano and its inharmonicity. Most of the time, F3 at 1.0 against A at 0.0
would make it beat at 5 or 6 bps.
I think that the reason only 1¢ makes an audible difference in a 3rd in
the temperament octave is because the 1¢ is not measured at the fundamental
but in one of the partials. F3 is measured on F5, the 4th partial. The
beating is heard between the 5th partial of F3 and the 4th of A3. If you
tuned a unison at F3, and measured its pitch then changed one of the strings
by 1¢, you would hear a slow beat in the unison. The RPT Exam tolerance for a
unison is also 1¢. Again, this is because it is at the threshold of where it
starts to matter. Here, at the unison level, it would not be "a few beats" it
would be closer to what you are thinking the difference would be.
There is a much different rate of change in the 3rds than there is at the
unison level. Consider that when you tune your A to the fork, you are doing
that as a unison. You try to make the unison beatless. But you check it with
a 17th, which will be much more sensitive to a very small change in pitch.
I'm sure that you don't disagree that the beating in the rapidly beating
intervals constitutes the "musical vibrato" that a piano has. This has been
taught in ET classes too. I learned it there first from George Defebaugh. It
is also taught as the piano's "resonance". Virgil Smith, who will be tuning
the ET "control piano" at the HT Recital in Providence talks about ET as
providing the piano with a "consistent resonnance" that is very beautiful. He
is not wrong about that, of course.
Only later did I learn that with Cycle of 5ths based HT's, you could
arrange that vibrato into a pattern that would actually enhance all music, not
just some or early music, all music, even modern music. I have known many HT
practitioners who have said that once they experienced this phenomenon, they
could never justify going back to ET. It just seemed wrong now. So when I
say that ET is "wrong", that is what I mean by that. The vibrato is not
right, it doesn't fit the music. Of course, when that vibrato is at random or
even worse, in opposition to the cycle of 5ths, it seems even more wrong.
This does not mean that I think that everybody else is "wrong" and I am
"right". I am only speaking in the context of discovery of tuning phenomena
as it relates to the music that we tune for. ET is thought to be the ultimate
compromise because it is "neutral" to all music. This is true, it is neutral.
There does come a time, however when a neutral position can clearly be
demonstrated as not being the best. To me, it is "wrong" to not do what I
know is best.
I realize that people may see my posts, and "zero in" on the phrase, "ET is
wrong", remember the "flame" to Conrad and hit that delete button very
quickly. But I'm not going away. I'll still be tuning HT's for as long as I
will ever tune and I will not be interested in doing an ET except for the RPT
Exam.
I think that many people must imagine me going around tuning the piano in
some wierd-sounding way and not saying anything about it as if I'm conducting
some kind of NAZI-like experiment, "just to see what it will DO to the
customer" or just to see what kind of extent I can go to and still get away
with it. This is just not what I do. I try to create a sound that is
consistent with both expectations, the modern piano's and the cycle of 5ths.
Since I have seen what other people actually do and have gotten a handle on
what kind of tolerence people in general have, I work within those tolerences
to create a Victorian Temperament.
Of course, I also do historically documented temperaments for specific
purposes. These are generally on the request of the customer and not
something I propose.
Bill Bremmer RPT
Madison, Wisconsin
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