In a message dated 3/13/99 12:20:48 AM Central Standard Time,
nossaman@SOUTHWIND.NET writes:
<< Please make an honest attempt to
reasonably define your terms so I will have even a minimal understanding of
what you are talking about. I'm asking for an understandable minimal
definition of your term. I consider the request to be reasonable enough to
warrant an honest attempt at an answer if you can generate one. I really
would like to know.
Ron >>
Well, all right but I have written it all before. I did not make up the term
"Reverse-Well, I heard it from other HT practitioners. Owen Jorgensen does
not use it in his publications but has used it in private, hand written
communications. It may be a term of recent origin to describe what seems to
be a fairly pervasive error and practice. It's not something that someone
would want to write a book or even an article about.
I guess I assume that most people know what constitutes a Well-Tempered
Tuning but maybe not and if not, it only proves my point: there is a commonly
held perception about ET that is so strong that most people in the music
business and even piano technicians have little knowledge about any other kind
of temperament possibility. If you don't know what something is, you are not
likely to want it or ask for it.
A true Well-Tempered Tuning (WT) (also called "Well-Temperament" by Owen
Jorgensen), has a characteristic alignment with the cycle of 5ths. It is the
beat speeds of the 3rds which are most important. All major 3rds of triads at
the top of the cycle of 5ths (those with 0-2 sharps or flats in the key
signature, such as C, G, F, D and Bb) will be slowly beating. They can even be
pure.
The triads with 3 or 4 sharps or flats in the key signature such as A, Eb, E
and Ab will have moderately beating 3rds (possibly similar to the speeds
associated with the 3rds of ET). The remaining triads at the bottom of the
cycle of 5ths, B, F# and Db will have very rapidly beating 3rds, faster than
in ET.
WT's always have combinations of pure 4ths and 5ths and tempered ones. What
distinguishes one WT from another is that exact combination and the exact
beating of the 3rds. Therefore in a musical context, many WT's might produce
a similar sound. Even if you are an experienced HT tuner, you probably could
not tell which temperament is on a piano just by listening to music played in
it. You might be able to tell that it is an HT but you would need to
carefully listen to the intervals to identify which temperament has been
tuned.
In a very general way of speaking, the pure 4ths and 5ths of WT's are found
among the black keys and the tempered 4ths and 5ths are found among the white
keys. The Vallotti temperament which someone on the List was recently
interested in is a perfect example of this and it is why I recommend it for ET
tuners who would like to try their first WT. It is *very* easy to remember:
All 4ths and 5ths among the black keys or those with a black and white key, B-
F# and Bb-F are pure. The rest are tempered by exactly twice the amount of ET
(theoretically 4 cents narrow but less in actual practice when adjusted for
inharmonicity).
Now here is how I believe that Reverse-Well got started: Contemporary piano
technicians tend to "favor the just 5th" as John Travis identified in his
book, "Let's Tune Up". They begin their temperament sequence with an A or C
fork and tune 4ths and 5ths around the cycle of 5ths beginning on the white
keys. Not liking to hear any tempering in a 5th, they tend to tune it either
pure or very nearly so (maybe even on the slightly wide side by mistake).
After a few 4ths and 5ths, a 3rd is produced but there is still no way to
judge whether it is too fast or too slow.
The temperament sequence continues with all or most of the 5ths a little too
pure and this sets up very rapidly beating 3rds at the *top* of the cycle of
5ths rather than at the bottom. As the sequence continues to the bottom of
the cycle of 5ths and the black keys, the technician starts running into
trouble reconciling intervals and begins to temper the 4ths and 5ths at the
bottom of the cycle of 5ths a little more than they should be for ET which
will then produce relatively slower 3rds among these triads.
Many technicians cannot distinguish the rapidly beating intervals very well
and believe that 5ths, octaves and unisons are the most important anyway. As
long as the progression of 3rds sounds "pretty even" to them, they believe
that any slight unevenness is unimportant.
This however is the big mistake. It is the beat speed of the 3rds which gives
a major triad its *primary* character (also known as "color" or tonality).
The slower beating 3rds at the top of the cycle of 5ths are almost always
associated with a tempered 5th (although there are many WT's that have F-C
pure). Such a triad in first inversion (example G3-C4-E4) will have the 3rd
(C4-E4) beat exactly the same as the 6th (G3-E4). This is known as Equal-
Beating (EB). It has a canceling out of the tempering effect to it that makes
the triad sound still and very harmonious.
Throughout musical history from the Baroque period to the 20th Century, people
who played and wrote music *expected* any given key signature to produce a
certain tonality and chose a key to write or play in based upon that
expectation. If they wanted a smooth, quietly harmonious sound, they chose
from the top of the cycle of 5ths, if they wanted a brilliant sound for
playing fast, fleeting passages, they chose from the bottom of the cycle of
5ths and if they wanted a mildly melodious sound they chose from the middle.
The minor keys also have their own set of analogous characteristics.
Classical composers like Mozart rarely wrote at the bottom of the cycle of
5ths because the harpsichords and fortepianos of that time tuned in a typical
WT or Meantone produced harsh sounds when close harmony was played in the keys
at the bottom of the cycle of 5ths. Romantic composers beginning with
Beethoven but particularly those like Chopin and Debussy liked the singing
tone produced by wide intervals such as 10ths and 17ths in keys such as Ab and
Db. Temperaments were also becoming less contrasting in later years,
gravitating towards ET but without becoming completely equal and still bearing
mild key color distinctions. The Thomas Young temperaments and Victorian
style temperaments are good examples of this.
Now, even though ET has been the accepted norm for about 100 years, somehow,
people's sense of tonality has not really changed. This is somewhat of an
enigma but it may indicate that true ET hasn't always been practiced even
though it was believed in as a concept and was the goal. Therefore, when the
artist that Ed tuned for heard the key of G as his sense of tonality told him
it *should* sound, his longing for such a sound was finally fulfilled.
The reason why I say with such conviction that Reverse Well is an all too
common error is because that has been my observation. I am also guilty of
having done it. Before I began tuning HT's I made the same mistakes as I
outlined above. At the Convention in Providence, I was about to do the first
tuning of the Walter Grand in the EB Victorian Temperament. I listened to
what was on the piano and sure enough, it was Reverse Well. Jim Coleman was
nearby and I showed it to him saying, "You see, I'm not just making this up,
this is what really happens." During my two visits to Steinway for training,
I observed many pianos tuned in Reverse Well at Steinway Hall but there is no
way you can tell anyone there something like that. They believe what they
want to believe and that's it.
Time and time again, it has been and I am sure will continue to be my
observation. If you are an aural tuner, you should listen to your own tuning
and see if you have not been making the same error. If you play the 3rds of
an F3 to F4 temperament as you would in checking for ET and you hear F3-A3
fast, then F#3-A#3 slower, then G3-B3 fast, then Ab3-C4 slower, etc. you have
Reverse Well. I very commonly hear the 3rds B3-D#4 and Db4-F4 beating very
gently and C4-E4 beating faster than any other interval. This, my friends is
Reverse Well and it is wrong.
There are several very good tuners in the Madison Area and the Madison
Chapter. I know two really good aural tuners in my Chapter who really do
produce a fine ET and I have no problem with that. I am currently rehearsing
the Verdi Requiem with a group that uses a piano tuned in a beautifully smooth
ET and it does not bother me one bit.
However, I had to quit another group because I just could not stand to hear
music played in Reverse Well. Do you think I could have made any difference
if I told those in charge that the music sounded wrong to me because it was
tuned in Reverse Well? The same goes for the place where Jeffrey Siegel
performs. An evening of Mozart or Beethoven performed in Reverse Well would
be truly offensive to my ears but to complain about that to anyone in charge
would only reflect badly upon me and would not result in anything being
changed. That tuner harshly denounces those who use HT's and believes that
what he does is the only correct way to tune a piano.
So you see, it is not so much that I am *against* ET as I am concerned that
the typical approach to aural tuning of ET often results in an unrecognized
error that is truly harmful to all music. The modern ETD's largely prevent
this error from occurring.
Attached below is a copy of the Rules for Well-Tempered Tuning which were
copied from Owen Jorgensen's first publication, "Tuning the Historical
Temperaments by Ear", by Paul Bailey, RPT who has been a contributor to this
List and has been a faithful and undaunted practitioner of the HT's for a good
20 years. *He* certainly knows what Reverse Well is and encounters it with
the same confounding frequency that I do. The comments in parentheses were
added by me to facilitate understanding.
I hope this has been a satisfactory explanation and that by writing it, I have
done some good.
Sincerely,
Bill Bremmer RPT
Madison, Wisconsin
Rules for Well-Tempered Tuning
by Andreas Werkmeister from the publication:
Tuning The Historical Temperaments By Ear
OWEN JORGENSEN
pages 246-7-7
1.Each tonality or key center should sound differently and should have its
own
distinct color characteristics or "Affekt." This is in direct opposition to
the ideals of equal temperament in which all tonalities have the same
identical neutral color
except for increasing or decreasing beat speeds. The purpose of well
temperament is to allow harmonic color-change through modulation.
2.The same as in equal temperament, one must be able to modulate freely in
all possible keys without experiencing any unacceptable out-of-tune wolf
sounds. Thus, all twelve tones may be used enharmonically which is
impossible in the class of restricted temperaments including just
temperaments or meantone temperaments.
3. During modulation through a series of fourths or fifths, the color
changes of the
"Affekts" must be consistent and even.
From a detailed study and evaluation of the beat speeds and
qualities of all the most prominent documented historical temperaments, the
following rules for well temperament are evident:
RULES
1. THE TWELVE SEMITONES OF THE OCTAVE MUST NOT all be of the same size.
2.No fifth , minor sixth, or minor third should be wider than just.
3.No fourth, major sixth, or major third should be narrower than just.
4.No major or minor third and no major or minor sixth should be altered or
tempered from just intonation by more than one syntonic comma. (22 cents)
5.No fourth or fifth should be altered or tempered from just intonation by
more than one half syntonic comma. (11 cents)
6.No octave should be altered at all from just intonation. (In actual
practice on a modern piano, the octave may be widened very slightly from just
((pure)) intonation).
7.No major third should be smaller or closer to just intonation than C E.
8. F A must be the same size or larger than C E.
9. Bb D must be the same size or larger than F A. Also, Bb D just be
larger than
C E.
10. Eb G must be the same size or larger than Bb D.
11. Ab C must be the same size or larger than Eb G.
12. Db F must be the same size or larger than Ab C. Also, Db F must be the
same size or larger than B D#. (Db F may be the same size, smaller or
larger than Gb Bb. No other major thirds may be larger than Db F and Gb
Bb.)
13. Gb Bb must be the same size or larger than Ab C.
14. B D# must be the same size or smaller than F# A#.
15. E G# must be the same size or smaller than B D#.
16. A C# must be the same size or smaller than E G#.
17. D F# must be the same size or smaller than A C#. Also, D F# must be
larger than C E.
18. G B must be the same size or smaller than D F#.
19. C E must be the same size or smaller than G B.
20. No minor third should be larger or closer to just intonation than E G
or A C.
There are necessary exceptions, but it is definitely preferable that A
C not be larger or closer to just intonation than E G. To have E G larger
than A C is
considered a fine accomplishment.
21. D F must be the same size or smaller than A C. Also, D F must be
smaller than
E G.
22. G Bb must be the same size or smaller than D F.
23. C Eb must be the same size or smaller than D F.
24. F Ab must be the same size or smaller than C Eb. Also, F Ab must be
the same size or smaller than Eb Gb. (F Ab may be the same size, smaller,
or larger than Bb Db. No other minor thirds may be smaller than F Ab or
Bb Db.)
25. Bb Db must be the same size or smaller than C Eb.
26. Bb Db must be the same size or smaller than C Eb.
27. G# B must be the same size or larger than D# F#.
28. C# E must be the same size or larger than G# B.
29. F# A must be the same size or larger than C# E.
30. B D must be the same size or larger than F# A.
31. E G must be the same size or larger than B D.
32. The following tonalities are found to be more brilliant or richer than
the same tonalities in equal temperament:
F minor Ab major
Bb minor Db major
Eb minor Gb or F# major
G# minor B major
33. The following tonalities are found to be less brilliant or plainer than
the same tonalities in equal temperament:
E minor G major (the one that Ed's customer
liked)
A minor C major
D minor F major
34. The following tonalities are sometimes found to be quite similar to the
same tonalities in equal temperament:
C# minor E major
F# minor A major
B minor D major
G minor Bb major
C minor Eb major
35.Breaking any of the above 34 rules ruins the evenness of chord-color
progression or the basic tonality of C major. Also, unnecessary extra
beatings or wolf sounds could be introduced.
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Paul Bailey RPT
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