I think alternate tunings are a proverbially elusive carrot on a stick. If
you are going to play polyphonic music, ET (with maybe a little stretch for
inharmonicity) is the only practical solution.
Ever since ET was instituted, musicians (who are not always the most
scientific lot) have heard that it "compromises" the pure, sonorous musical
intervals. As long as that eats away in their skulls they will always seek
a way to get at those intervals. The problem is that many of them are
mathematically challenged and are convinced that there must be some way to
tweak the pitches and achieve a superior temperament. After all, if C to G
is 0.1% flat in ET, why can't you just raise it to a perfect 3:2?
But when you go tampering with ET, as everyone in this group knows, there
are two detrimental effects that take place. First of all, a note means
something different musically depending on its context. If you sharpen that
G you can get a slightly better fifth with C, but G might later be used as
the base of a G chord, or the middle note of a Db, or any other function,
even if you stay in the same key. Secondly, even an ordinary major diatonic
scale will sound different in different keys. So not only can you not
modulate within a key, none of your keys will will function alike. And this
is due to changing only a single note!
I wish I had a nickel for every person who asks me if I will be able to
produce a justly intoned piano. They just don't realize how useless that
really is. Unfortunately, as long as that carrot dangles there, they will
be convinced that there is a panacea that awaits them.
Don
----- Original Message -----
From: <A440A@aol.com>
To: <pianotech@ptg.org>
Sent: Friday, April 02, 2004 11:25 PM
Subject: Re: Non-ETs; more organic than ET?
> 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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