tech perceptions

Greetings,
>To me the overwhelming difference between fortepianos and modern pianos is
>the fact that the former are single or double strung, whereas the latter
>are triple strung. Take that away (as Michael Harrison did), and you'll
>find that the tension, diameter, and everything else about the modern piano
>outshines the fortepiano as far as harmonicity and sensitivity to tuning.

Agreed, however, there are many that feel the imbalance of the older
pianos is an essential component of hearing the composers in their fullest. I
can't say, as I am a strong proponent of the modern pianos, just not their
modern tuning.

And then, the ganging up begins.........

>>I may also add, as a bit of music-cultural speculation, that the creation
>of >the the tuning profession probably had a net effect of densensitizing
>>players to the quality of keyboard intonation.
>
>I'll agree with that!

Ouch! That was true in the past, but the Bull has been siezed by the
horns, and many in the tuning profession are now embarked on the restoration
of the earlier intonations. This ease of production so many different
tunings will allow today's musician to hear a broader range of keyboard
intonation than his historical predecessors. This may be a component of what
B. Maclaren labels the technologically driven evolution of intonation. It
may even be the fertilizer needed to grow a new set of sounds..........(:)}}
The technian's job arose in response to a need, IMHO, it wasn't "created"
so much as called for. I suppose 12 TET offered the easiest, least
thinking, response to a problem, but according to the literature, 12 ET was
"sweetened" by the best techs, and their ability to do this without calling
attention to the keys that suffered was the hallmark of a real craftsman.
It is only in the last 100 years or so that things have really been
measured against the straight, mathematical line, and a lot of us are busily
trying to dismantle the lock. That's why I love this Tuning list, someday,
they will look back on this as the beginning of something......
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

I wrote,

>>For example, a diatonic or extended meantone scale, when scaled to
three
>>dimensions, comes out as a helix, with the chain of fifths winding
around
>>the helix so that one full turn corresponds to 3-4 fifths, putting all
the
>>notes of each consonant triad near to one another. The result is the
>>simplest and most informative diagram of the diatonic scale or
extended
>>meantone tuning that I can imagine.

Carl Lumma asked,

>You say you've done this for various scales? Do you have any pics?

Yes, and luckily they are ascii! Here is the diatonic scale, scaled down
to 3 dimensions, projected onto each of the three orthogonal planes:

2 ^
'
'
'
'
'
'
'
'
1 ^ > a
'
'
D '
i '
m ' > f > e
e '
n '
s '
i 0 ^ > d
o '
n '
'
2 ' > c > b
'
'
'
'
-1 ^ > g
'
'
'
'
'
'
'
'
-2 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1



'
'
2 ^
'
'
'
'
'
'
'
D ' > d
i 1 ^
m '
e '
n '
s '
i '
o ' > g > a
n '
'
3 0 ^
'
' > f > b
'
'
'
' > c > e
'
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
2 ^
'
'
'
'
'
'
'
D ' > d
i 1 ^
m '
e '
n '
s '
i '
o ' > g > a
n '
'
3 0 ^
'
' > b > f
'
'
'
' > c > e
'
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 2


Here is a pentachordal dectonic scale (labeled with letters p-y)

'
'
2 ^
'
'
'
'
'
'
' > y > r
D '
i 1 ^
m '
e '
n ' > u > v
s '
i '
o '
n '
'
2 0 ^
'
'
' z < > s
'
'
' > q > p
'
'
-1 ^ > w > t
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
2 ^
'
'
'
'
' > s
'
'
'
1 ^
'
' > w
D '
i ' > y
m '
e ' > v
n ' > p
s '
i 0 ^
o '
n ' > q
' > u
3 '
' > r
'
' > t
'
-1 ^
'
'
'
' > z
'
'
'
'
-2 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
2 ^
'
'
'
'
'
' > s
'
'
'
1 ^
'
'
' > w
D ' > y
i '
m '
e ' > v
n ' > p
s '
i 0 ^
o '
n ' > q
' > u
3 '
'
' > r
' > t
'
'
-1 ^
'
'
'
' > z
'
'
'
'
'
-2 ^
'
Sff^ffffffffffffffff^ffffffffffffffff^ffffffffffffffff^ff
-1 0 1 2

Dimension 2

Here is a symmetrical decatonic scale:

'
'
'
'
'
' > q
1 ^
' > w > u
'
'
D '
i '
m ' > s > y
e '
n '
s '
i 0 ^
o '
n '
'
2 ' > t > x
'
'
'
'
' > p > r
-1 ^
' > v
'
'
'
'
'
'
'
'
-2 ^
'
Sff^ffffffffffffffff^ffffffffffffffff^ff
-1 0 1

Dimension 1


'
'
'
'
'
'
1 ^ > s > y
'
' > v
'
D '
i '
m '
e '
n '
s '
i 0 ^w 2 p u 2 r
o '
n '
'
3 '
'
'
'
' > q
'
-1 ^ > t > x
'
'
'
'
'
'
'
'
'
-2 ^
'
Sff^ffffffffffffffff^ffffffffffffffff^ff
-1 0 1

Dimension 1


2 ^
'
'
'
'
'
'
'
'
1 ^ s 2 y
'
' > v
D '
i '
m '
e '
n '
s '
i 0 ^ r 2 p w 2 u
o '
n '
'
3 '
'
'
' > q
'
-1 ^ x 2 t
'
'
'
'
'
'
'
'
-2 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 2

And here is 12-tone equal temperament:

2 ^
'
'
'
'
'
'
' > c
' > f > g
1 ^
'
'
D ' > d
i ' > a#
m '
e '
n '
s ' > d#
i 0 ^
o ' > a
n '
'
2 '
' > e
' > g#
'
'
-1 ^
' > c# > b
' > f#
'
'
'
'
'
'
-2 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
1 ^
'
'
D ' > a# > f# > d
i ' c# < > f > a
m '
e '
n '
s '
i 0 ^
o '
n '
'
3 '
' > d# b < > g
' > g# > c > e
'
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
1 ^
'
'
D ' > f# a# < > d
i ' > c# > a > f
m '
e '
n '
s '
i 0 ^
o '
n '
'
3 '
' > b > d# > g
' g# < > e > c
'
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 2


Better results for 12-tET come from only scaling down to 4 dimensions,
although the result cannot really be visualized:

'
'
'
'
'
'
'
' > b > e
1 ^
' > f#
' > a
D '
i '
m ' > c#
e '
n ' > d
s '
i 0 ^
o '
n ' > g#
'
2 ' > g
'
'
' > d#
' > c
-1 ^
' > a# > f
'
'
'
'
'
'
'
-2 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
1 ^
'
' > c# > f > a
D '
i '
m '
e '
n ' > f# > a# > d
s '
i 0 ^
o '
n ' > g# > e > c
'
3 '
'
'
' > d# > b > g
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
1 ^
'
' > f# > a# > d
D '
i '
m '
e '
n ' > d# > b > g
s '
i 0 ^
o '
n ' > c# > f > a
'
4 '
'
'
' > g# > e > c
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 1


'
'
1 ^
'
' > f > c# > a
D '
i '
m '
e '
n ' > a# > d > f#
s '
i 0 ^
o '
n ' > c > g# > e
'
3 '
'
'
' > d# > g > b
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 2


'
'
1 ^
'
' > a# > d > f#
D '
i '
m '
e '
n ' > d# > g > b
s '
i 0 ^
o '
n ' > f > c# > a
'
4 '
'
'
' > c > g# > e
'
-1 ^
'

Sff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ffffffffffffff^ff
-2 -1 0 1
2

Dimension 2

'
'
1 ^
'
'
'
' f#
' d 3 a#
'
'
'
'
'
'
'
'
' g
D ' d# 3 b
i '
m '
e '
n '
s '
i 0 ^
o '
n '
'
4 '
' f
' c# 3
a
'
'
'
'
'
'
'
'
' g#
' e 3 c
'
'
'
'
-1 ^
'

S^fffffffffffffffffffffffffffffffffff^ffffffffffffffffffffffffffffffffff
f^f
-1 0
1

Dimension 3



The input distance matrices were based on the log of the odd limit of
the most likely interpretation but included a correction term to account
for the inaccuracy of 12- or 22-tET; I don't remember how I did it but
it made sense to me at the time.

I'm embarrassed to ask this, but can someone send me info on how to
unsubscribe or set nomail. (I will be away for some time) Thanks.

Joe Downing,
in Syracuse