Sound qualities of different keys on mean tone piano

The contribution to the overall sound of a piano note or chord made by st=
rings=0Awhich are excited to vibrate sympathetically with the struck note=
(s) greatly=0Aaffects the character of the overall sound and contributes =
in an essential way=0Ato the acoustic piano's unique characteristics as a=
musical instrument. While=0Afor a piano tuned to 12 TET, the harmonic r=
elationships between a string and=0Athe strings above and below it which =
will be excited to vibrate=0Asympathetically with it are nearly the same =
for all the strings in the same=0Ageneral pitch register, these relations=
hips vary greatly between keys for the=0Astrings of a piano tuned to an u=
nequal temperament, including (and especially=0Afor) quarter comma MT tem=
perament. There are strings at seventh, 14th, etc.=0Apartials for Eb and=
Bb (wolf from G# to Eb). There are strings at 5th, 10th,=0Aetc. partial=
s for Eb, Bb, F, C, G, D, A, and E. There are strings at 3d, 6th,=0A12th=
, etc. partials for all notes but G#. All notes but G# and C# have notes=
=0Aabove at 9th, 18th, etc. partials above them. E lacks a note at a 15t=
h=0Apartial above it. For lower lying notes, Eb lacks a note one octave =
and a=0Afifth below it in the Ab position. Eb, Bb, F, and C lack notes t=
wo octaves=0Aand a major third below them.

One thing which brought this realization home to me was the very differen=
t=0Acharacter of the sounds of Eb and Bb major triadic chords - and the E=
b strings=0Aalone or when Eb octaves or open fifths Eb=96Bb=96Eb are stru=
ck. These chords to=0Ame have a difficult=96to=96put=96into=96words "sol=
id" sound which makes me think of=0Avery neat rectilinearly shaped blocks=
of wood. The sounds seem low and deep=0Aand solid rather than bright or=
shrill. I believe it's the 7th and 14th etc.=0Apartials which are respo=
nsible for this effect. The key of F, which has Bb=0Aplayed in it regula=
rly, has a solid sound, but not so much as a series of Eb=0Amajor chords.=
Going the other way to the four notes which lack upper notes at=0Athe 5=
th, 10th, 20th partial positions, these notes have a very "stringy" sound=
=0Awhich can be brought out by playing minor chords on C#, F#, and B.

I notice that when Ebs are played with equal force as C#s, the Ebs sound=
=0Alouder than do the C#s. Also, the G#s do not seem to have as loud and=
=0Acarrying a sound as most of the other notes.

As a result of having the good fortune to be able to "play around" with a=
=0Apiano which my piano tuner has been able to accurately put into differ=
ent=0Atemperaments, I can get a first hand sense of a "new" field of dime=
nsions=0Aalong which that amazingly versatile (as we now know) instrument=
can be=0Acontrolled so as to produce a wide variety of sounds with diffe=
ring=0Acolorations and quality balances.=0A

On Mon, 22 Jun 1998 14:21:02 -0400, Paul H. Erlich
wrote:

>Double Equal Temperament, or 144-tET, does not provide for anything
resembling traditional "mean temperament" (presumably meaning meantone
temperament). The fifths of meantone temperament are typically around
696-698 cents, while 144-tET contains no intervals between 692 and 700
cents. 288-tET would be required to unify meantone with these other
systems of tuning.

The tuning scale steps in Double Equal Temperament available for around the 5th
are:

Name Ratio Cents
G- 2^(83/144) 691.667
G 2^(7/12) 700
G+ 2^(85/144) 708.333

In "On the Sensations of Tone" by Helmholtz, page 484, meantone temperament
"specimens of tuning" ranges for G are 697-733 cents. Likewise for Just
Intonation, on page 486, G is usually tuned to 702 cents (a ratio of 3/2). In
either case, Schillinger only claims that "the micro-units are the best
averages for
all differences between units of the 12th root of 2 and just intonation
(natural scale)". There are further comments in "Tuning" by Owen Jorgensen
concerning the tuners used by Alexander Ellis (the editor of Helmhotz' work)
which indicate their minor innacuracies but they are still within the above
cents constraints of "best averages".

-------------
Benjamin Tubb
brtubb@cybertron.com
http://home.cybertron.com/~brtubb