I wrote:
<< These temperaments are already somewhat
> "organic",
> as opposed to the scientific and rigid ET.
>
Tom asks:
>>"Organic?" In what manner could one possibly perceive one temperament as
more "organic" than another? You lost me here! <<
Organic as in sensually defined. That is the profound difference between
non-ET and ET. The well-temperaments depended on the non-intellectual
decisions for the placement of the notes. They were done by subjective decisions
about how much faster or slower the thirds of one key will be in relation to the
others. ET demands that any given note has the same relationships
with others as closely as all the other notes do, hence, you have a built-in
comparison. You are trying to make everything the same. We can scientifically
define ET by a single ratio, 1.059....... The size of the thirds are simply a
resultant of 12 notes in one octave. A WT obeys a totally different set of
values, and these are defined by the wet-ware of the tuner. The sizes of the
thirds are decided by the amount of contrast one desires.
>>Referring to ET as rigid and scientific suggests to me the following:
When
you tune ET there are a multitude of tests and reference notes you can use to
ascertain whether you have deviated from the ideal placement of each note.
(Very scientific...) With non-ETs there are fewer ways to check your
results.
If I'm wrong about this, correct me, but perhaps one of the reasons you
feel ET is rigid and scientific is the fact that you can double check every
note
up and down the keyboard and any note that is not rigidly where it ought to
be
sticks out in the checks. The more "organic" approach might be "sounds
good, must be good/ no way to check it, so...there it is". <<
Yes, that is about correct. As Louis Armstrong said of music in
general,"If it sounds good, it is good!"
>>My final check of my bass octaves, after having tuned them to my ear and
checking them with a 3/6 or 3/10 to ascertain that they are where they should
be,
is to listen to descending M3rds, then M10ths, and finally m7ths. This
often
brings to my attention an anomaly, whereby I realize that I need to make an
adjustment. Of course, these descending parallel intervals only work in ET.
How do you to check your bass octaves? <<
I usually check them with an SAT. Since the temperaments are
deviations of the aural ET's that I programmed in for the pianos I tune, the octaves
obey the same widths. HOwever, without a machine, one can deliver very nice
bass octaves with the m3-6th tests and simply listening to the octave itself.
>>BTW, as far as the original question goes, I agree that ET tunings are more
likely to sound in tune longer than their non-ET counterparts. But that's
assuming that the pianist is playing in keys other than C and G all the time.
>>
C and G? In the Young temperament, for example, the keys of C, F, G, Bb and
D are all much smoother sounding than ET. Eb and A are almost identical. So,
the majority of keys are the same or better than ET in terms of consonance
in the thirds. Having the 5 most remote keys possessing a higher degree of
expressiveness is just a bonus! When you consider the overwhelmingly prevalent
use of the 7 "better" keys in classical music, it is hard to ignore the benefit
they offer. Is it coincidence that the frequency of key usage in
Beethoven's, Mozart's and Schubert's piano works correlates to the amount of tempering in
the tonic thirds?
For those that want to count and see, I will post most of the piano works
of Beethoven: Notice the overly fond reliance he has for Eb, which we may
either ascribe to an idiosyncrasy or the utility of using a key that is inthe
middle of the circle of fifths, but without that, it will be seen that the
number of times he uses any given major key is in near direct proportion to the
levels of dissonance in that key's thirds, assuming a Well Temperament.
Notice, in particular, how often he uses C (8), G (12), D(7), A (5), E
(4), B (1), F# (1), C# (0), Ab (4), Eb( 15!!), Bb (6), F (11). Notice the
progression? It very closely mimics the progression of dissonance in
well-temperament. Also, see how much he uses F# and B, the most dissonant keys,(once,
each), and what sort of music he places in Ab, (the Pathetique and a funeral
march...).
A Sonata #02 002 #2 a
A Sonata for Violin and Piano #09 ("Kreutzer") 047 a
A Sonata for Cello and Piano #3 069 a
A Sonata #28 101 a
A Rondo in A WoO 49 -
A flat Sonata #08 ("Pathetique") 013 2: Adagio cantabile
A flat Sonata #12 ("Funeral March") 026 a
A flat Sonata #18 031 #3 2: Scherzo
A flat Sonata #31 110 a
B Piano Concerto #5 ("Emperor"), Adagio
B flat Trio #4 011 a
B flat Piano Concerto #2 019 a
B flat Sonata #11 022 a
B flat Trio #7, "Archduke" 097 a
B flat Sonata #29, Hammerklavier 106 a
B flat Grosse Fuge for Piano Four Hands 134 -
C Sonata #03 002 #3 a
C Piano Concerto #1 015 a
C Bagatelles, Op. 033 033 5
C Rondos 051 1
C Sonata #21 ("Waldstein") 053 a
C Polonaise in C 089 -
C Sonata for Cello and Piano #4 102 #1 a
C Diabelli Variations 120 a
D Turkish March (from "Ruin of Athens") -
D Sonata #07 010 #3 a
D Sonata #15 ("Pastoral") 028 a
D Trio #5 (Ghost) 070 #1 a
D Six Variations the Turkish March from "Ruin of Athens" 076 a
D Sonata for Cello and Piano #5 102 #2 a
D flat Sonata #14 ("Moonlight") 027 #2 2
E Sonata #09 014 #1 a
E Sonata #30 109 a
E flat Trio #1 001 #1
E flat Sonata #04 007 a
E flat Sonata for Violin and Piano #03 012 #3 a
E flat Quintet in E flat for Piano and Winds 016 a
E flat Sonata #13 027 #1 a
E flat Sonata #18 031 #3 a
E flat Bagatelles, Op. 033 033 1
E flat Variations and Fugue in E flat, "Eroica" 035 a
E flat Piano Concerto #5 ("Emperor") 073 a
E flat Sonata #26, Das Lebewohl 081a a
E flat Bagatelles, Op. 126 126 3
E flat Bagatelles, Op. 126 126 6
E flat 7 Variations on "Bei Mannern, welche Liebe fuhlen" WoO 46 -
E flat Menuet in E flat WoO 82 -
E flat Ecossaises WoO 86 a
F Gavotte in F -
F Sonata for Cello and Piano #1 005 #1 a
F Sonata #06 010 #2 a
F Sonata for Cello and Piano (arr. from horn) 017 a
F Sonata for Violin and Piano #05 ("Spring") 024 a
F Six Variations on an Original Theme 034 a
F Sonata for Violin and Piano #09 ("Kreutzer") 047 2: Andante &
Variations (beginning)
F Romances 050 2
F Sonata #22 054 a
F Symphony #6, Op. 68 S. 464 a
F Andante Favori in F WoO 57 -
F# Sonata #24 078 a
G Minuet in G ? -
G Sonata #10 014 #2 a
G Sonata for Violin and Piano #08 030 #3 a
G Sonata #16 031 #1 a
G Sonata #20 049 #2 a
G Rondos 051 2
G Piano Concerto #4 058 a
G Sonata #25 079 a
G Sonata for Violin and Piano #10 096 a
G Variations on "Ich bin der Schneider Kakadu" 121a a
G Rondo a capriccio (Rage over a Lost Penny) 129 -
G Twelve Variations on Handel's "Judas Maccabeus" WoO 45 a
a Sonata for Violin and Piano #04 023 a
a Bagatelle in a, "Fur Elise" WoO 59 -
b Bagatelles, Op. 126 126 4
c Sonata #05 010 #1 a
c Sonata #08 ("Pathetique") 013 a
c Sonata for Violin and Piano #07 030 #2 a
c Piano Concerto #3 037 a
c Sonata #32 111 a
c 32 Variations in c WoO 80 a
c# Sonata #14 ("Moonlight") 027 #2 a
d Sonata #07 010 #3 2: Largo e mesto
d Sonata #17 ("Tempest") 031 #2 a
e Sonata #27 090 a
f Sonata #01 002 #1 a
f Sonata #06 010 #2 2: Allegretto
f Sonata #23 ("Appassionata") 057 a
g Sonata for Cello and Piano #2 005 #2 a
g Sonata #19 049 #1 a
g Fantasia in g 077 -
It may be of interest that when we examine Mozart, the same correlation
is found, as well as in Schubert's piano music ( to a slightly lesser
degree). As we look at composers that worked in a more ET likely area,(Ravel,
Rachmaninoff, Debussy) we see this sort of reliance on the keys change to favor a
more democratic usage. This is not surprising if we take ET as coming into
vogue in the late 1800's. (Paul Bailey does make a good case for Debussy's use of
the expressive qualities in a WT, though).
Examining the composers output in the meantone era, we see a total
avoidance of the wolf keys. Anybody see a pattern? Is it coincidence that these
composers all share the same breakdown of key choices, in the same basic
pattern, and that in each "temperament era", the levels of dissonance in the keys and
the key usage reflect each other?
I believe that the qualtites of temperament exerted a definite influence
on composition, via the choice of keys the composers made. It is also
possible to go 'inside' the classical composers' works and demonstrate that many of
their modulations create coherent progressions of increasing dissonance leading
up to resolutions if a WT is in place, and that these progressions of
dissonance do not occur in any key but the one that they chose, (but that is a
presentation that is more effective with a pianist). Enjoy!
Ed Foote RPT
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html
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