In a message dated 6/26/99 8:02:12 AM Central Daylight Time, you write:
<< This type of scaling regime (used by so many manufacturers)
results in pianos which exhibit inferior tuning stability, while at the
same time the tuner is left with the impossible task of blending the
tenths and seventeenths with the fourths and fifths. Nothing fits as it
should!
Why do piano designers keep producing pianos with such inappropriate
scales? Why should tuners have to battle with pianos which have such poor
scale design? >>
About 10 years ago, I found the answer to this problem. The whole idea that
one *must* make ones 4ths, 5ths, 3rds, 6ths & 10ths perfectly even for the
piano to sound its *best* is simply not true. There is no music that
requires it and as the writer has pointed out, the very way that so many
pianos have been designed, whether on purpose or by default, resists it.
These days, you see people talk in terms of Equal Temperament but then
readily admit to the near impossibility of it. Then, a "little" unevenness
is said to be acceptable giving the "no artist ever complained about a few
uneven 3rds" line of thinking.
History tells us that all the way up to the 20th Century and well into it,
people thought of any kind of temperament arrangement that left all 24 major
& minor keys *accessible* (meaning musically acceptable and playable) as
"equal" temperament. This began with J.S. Bach and continued into the
Romantic era with composers like Chopin, Liszt, Debussy, etc.
Today, however, people try and try again to completely equalize the scale,
hoping that the closer they can come to that perfect state of equality in
temperament, the better the music will sound. This only makes all keys (all
major and minor triads) sound analogous to each other. The only distinction
is the pitch and the fact that as you ascend or descend the scale
chromatically, the speed of the rapidly beating intervals (3rds, 6ths, &
10ths) changes by a mere 1/2 beat per second. It makes the choice of key to
write or play in ambiguous, the only difference being how high or low on the
keyboard you will be.
Still, there are some who swear that they can hear a distinction among these
keys. This can only be because the temperament they tune or have had tuned
for them really is not equal and therefore really does have tonal
distinctions or it is because of the *memory* of the distinctions that the
different tonalities *should* have is firmly implanted in the mind. The
person perceives color much as a person who views a black & white image can
imagine the colors that would be there if the image were in true color.
The answer to the dilemma of not being able to perfectly equalize a scale is
to learn what the Rules for Well-Tempered Tuning that Andreas Werkmeister
(see post script) wrote are and to tailor or shape a modern piano's
temperament so that it fits these rules but also does not deviate so much
from theoretical ET that it offends the contemporary ear. This will give
your piano a superior sound that will have a different texture and character
for each key that you play in. It will suit all music the way that only ET
is thought of today as being able to do.
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.
5.No fourth or fifth should be altered or tempered from just intonation by
more than one half syntonic comma.
6.No octave should be altered at all from just 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
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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