A long overdue walk on the "u" side

OK, this is too kyool! I'm listening to Beethoven's Pathetique tuned
"backwards" (or should I say, "upside-down"?). I've been meaning to
turn the tuning around for years, long before I had heard of the word
"utonal". I am hearing the "minor diminished triad" 1/7:1/6:1/5 for the
first time, along with many other "backward" chords.

Paul E., you asked about the half-diminished chord: 5:6:7:9 vs.
1/7:1/6:1/5:1/4. The latter has a nice major third at the top vs. the
"car-horn" 7:9 of the first, but the latter has a much edgier sound to
my ear. It's that reversed diminished triad, 1/7:1/6:1/5: it doesn't
nestle you into a nice comfortable place like 5:6:7 does! It leaves you
buzzing around, looking for a place to land. Ah, yes: the implied
fundamentals are off by 7:10, itself a tritone; no wonder!

Anyway, for the truly fanatical tuner, I've posted be-ps-08u7.mid on
the web site, tuned exclusively upside-down (== utonal). NOTE, however,
that the major triad and its utonal counterpart, the minor triad, are
explicitly spelled differently in 12-tET, and so are tuned the same
in be-ps-08z7 and be-ps-08u7. It's only when tritones are present that
the tuning turns upside-down. A normal dominant seventh becomes the
crazy 1/9:1/7:1/6:1/5, for starters...

And, in a first attempt to include both in the SAME piece, I've posted
be-ps-08x7.mid. I reduced the desirability of just7u.tun slightly
compared to just7.tun, but I think it's going utonal more often than is
ideal.

Here's the reversed tuning file; compare to just7.tun, with
explanations, TD 330.7. For those of you who have JI Relay, this same
file saved as just7.tux (note the different extension), works with the
existing program. Go U!!

#
# just7u.tun
#
# modification history:
# 09-25-99 (jdl): weaken goodness slightly to mix w/ just7.tun...
# 09-25-99 (jdl): new from just7.tun.
#
#
#
#
# tuning:
# cols 1-8 have mbu for +/- 1 semitone voice; halve for +/- 2 (usual):
# (81.92 mbu/cent at this scale; 40.96 mbu/cent at +/- 2):
#

0 # 0; the reference, "C"
+961 # 1; 16/15 of C
+2553 # 2; 8/7 of C
+1281 # 3; 6/5 of C
-1121 # 4; 5/4 of C
-160 # 5; 4/3 of C
+801 # 6; 16/15 of 5
+160 # 7; 3/2 of C
+1121 # 8; 4/5 of C
-1281 # 9; 5/6 of C
-320 # A; 8/9 of C
0 # B; has no known place

# interval goodness:
# interval starting at:
# 0 1 2 3 4 5 6 7 8 9 10 11
# interval 0:
# +8 0 0 0 -16 0 -16 0 0 0 0 -16
+4 -4 -4 -4 -20 -4 -20 -4 -4 -4 -4 -20
# interval 1:
# +16 0 -16 -128 -16 0 -16 +8 -16 +8 -16 -16
+12 -4 -20 -132 -20 -4 -20 +4 -20 +4 -20 -20
# interval 2:
# 0 +8 -128 0 -128 +8 -8 0 0 -32 +8 -32
-4 +4 -132 -4 -132 +4 -12 -4 -4 -36 +4 -36
# interval 3:
# +8 -128 +4 -64 +8 +16 -16 -64 -32 0 +8 -64
+4 -132 0 -68 +4 +12 -20 -68 -36 -4 +4 -68
# interval 4:
# +8 +24 -128 +16 -256 +16 0 -64 +32 -128 0 -64
+4 +20 -132 +12 -260 +12 -4 -68 +28 -132 -4 -68
# interval 5:
# +16 -8 -256 0 -8 +8 -256 0 0 -256 -256 -256
+12 -12 -260 -4 -12 +4 -260 -4 -4 -260 -260 -260
# interval 6 (must repeat indentical groups of 6):
# -16 -16 +8 -32 -32 -32 -16 -16 +8 -32 -32 -32
-20 -20 +4 -36 -36 -36 -20 -20 +4 -36 -36 -36

[end of file...]

JdL

whats JIrelay, and where can i get it? -george

>From: "John A. deLaubenfels" <jadl@idcomm.com>
>
>
>OK, this is too kyool! I'm listening to Beethoven's Pathetique tuned
>"backwards" (or should I say, "upside-down"?). I've been meaning to
>turn the tuning around for years, long before I had heard of the word
>"utonal". I am hearing the "minor diminished triad" 1/7:1/6:1/5 for the
>first time, along with many other "backward" chords.
>
>Paul E., you asked about the half-diminished chord: 5:6:7:9 vs.
>1/7:1/6:1/5:1/4. The latter has a nice major third at the top vs. the
>"car-horn" 7:9 of the first, but the latter has a much edgier sound to
>my ear. It's that reversed diminished triad, 1/7:1/6:1/5: it doesn't
>nestle you into a nice comfortable place like 5:6:7 does! It leaves you
>buzzing around, looking for a place to land. Ah, yes: the implied
>fundamentals are off by 7:10, itself a tritone; no wonder!
>
>Anyway, for the truly fanatical tuner, I've posted be-ps-08u7.mid on
>the web site, tuned exclusively upside-down (== utonal). NOTE, however,
>that the major triad and its utonal counterpart, the minor triad, are
>explicitly spelled differently in 12-tET, and so are tuned the same
>in be-ps-08z7 and be-ps-08u7. It's only when tritones are present that
>the tuning turns upside-down. A normal dominant seventh becomes the
>crazy 1/9:1/7:1/6:1/5, for starters...
>
>And, in a first attempt to include both in the SAME piece, I've posted
>be-ps-08x7.mid. I reduced the desirability of just7u.tun slightly
>compared to just7.tun, but I think it's going utonal more often than is
>ideal.
>
>Here's the reversed tuning file; compare to just7.tun, with
>explanations, TD 330.7. For those of you who have JI Relay, this same
>file saved as just7.tux (note the different extension), works with the
>existing program. Go U!!
>
>#
># just7u.tun
>#
># modification history:
># 09-25-99 (jdl): weaken goodness slightly to mix w/ just7.tun...
># 09-25-99 (jdl): new from just7.tun.
>#
>#
>#
>#
># tuning:
># cols 1-8 have mbu for +/- 1 semitone voice; halve for +/- 2 (usual):
># (81.92 mbu/cent at this scale; 40.96 mbu/cent at +/- 2):
>#
>
> 0 # 0; the reference, "C"
> +961 # 1; 16/15 of C
> +2553 # 2; 8/7 of C
> +1281 # 3; 6/5 of C
> -1121 # 4; 5/4 of C
> -160 # 5; 4/3 of C
> +801 # 6; 16/15 of 5
> +160 # 7; 3/2 of C
> +1121 # 8; 4/5 of C
> -1281 # 9; 5/6 of C
> -320 # A; 8/9 of C
> 0 # B; has no known place
>
>
>
># interval goodness:
># interval starting at:
># 0 1 2 3 4 5 6 7 8 9 10 11
># interval 0:
># +8 0 0 0 -16 0 -16 0 0 0 0 -16
> +4 -4 -4 -4 -20 -4 -20 -4 -4 -4 -4 -20
># interval 1:
># +16 0 -16 -128 -16 0 -16 +8 -16 +8 -16 -16
> +12 -4 -20 -132 -20 -4 -20 +4 -20 +4 -20 -20
># interval 2:
># 0 +8 -128 0 -128 +8 -8 0 0 -32 +8 -32
> -4 +4 -132 -4 -132 +4 -12 -4 -4 -36 +4 -36
># interval 3:
># +8 -128 +4 -64 +8 +16 -16 -64 -32 0 +8 -64
> +4 -132 0 -68 +4 +12 -20 -68 -36 -4 +4 -68
># interval 4:
># +8 +24 -128 +16 -256 +16 0 -64 +32 -128 0 -64
> +4 +20 -132 +12 -260 +12 -4 -68 +28 -132 -4 -68
># interval 5:
># +16 -8 -256 0 -8 +8 -256 0 0 -256 -256 -256
> +12 -12 -260 -4 -12 +4 -260 -4 -4 -260 -260 -260
># interval 6 (must repeat indentical groups of 6):
># -16 -16 +8 -32 -32 -32 -16 -16 +8 -32 -32 -32
> -20 -20 +4 -36 -36 -36 -20 -20 +4 -36 -36 -36
>
>[end of file...]
>
>
>JdL
>
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John A. deL.: While you're at it, you might want to consider trying George
Kahrimanis' theory, where the otonal or utonal tuning for a chord is chosen
so that the progression of "1/1"s through the music is by consonant
intervals: sort of a Rameau-Riemann hybrid theory. He claims to have
verified this theory emprically through blind tests of many listeners with
progressions from the great works of classical music (including Beethoven).
I can post some of these if you're interested.

[Paul Erlich, TD 333.6:]
> While you're at it, you might want to consider trying George
> Kahrimanis' theory, where the otonal or utonal tuning for a chord is
> chosen so that the progression of "1/1"s through the music is by
> consonant intervals: sort of a Rameau-Riemann hybrid theory. He
> claims to have verified this theory emprically through blind tests of
> many listeners with progressions from the great works of classical
> music (including Beethoven). I can post some of these if you're
> interested.

I'm interested! Though I don't quite follow what you're saying... Have
you heard the Beethoven?

JdL

>Anyway, for the truly fanatical tuner, I've posted be-ps-08u7.mid on
>the web site, tuned exclusively upside-down (== utonal). NOTE, however,
>that the major triad and its utonal counterpart, the minor triad, are
>explicitly spelled differently in 12-tET, and so are tuned the same
>in be-ps-08z7 and be-ps-08u7. It's only when tritones are present that
>the tuning turns upside-down. A normal dominant seventh becomes the
>crazy 1/9:1/7:1/6:1/5, for starters...
>
>And, in a first attempt to include both in the SAME piece, I've posted
>be-ps-08x7.mid. I reduced the desirability of just7u.tun slightly
>compared to just7.tun, but I think it's going utonal more often than is
>ideal.

While all four versions are more fun to listen to than the original, there
are some important distortions in these two new versions that do not occur
in the original 5 and 7 limit ones. Is that because you haven't refined
them yet, or shall I blame it on the subharmonic series?

-C.

John A. deLaubenfels wrote,

>I'm interested! Though I don't quite follow what you're saying... Have
>you heard the Beethoven?

No, not yet . . . I need to find a time at the office when no one's around .
. .

[Carl Lumma, TD 334.6, referring to the Beethoven Pathetique:]
> While all four versions are more fun to listen to than the original,
> there are some important distortions in these two new versions that do
> not occur in the original 5 and 7 limit ones. Is that because you
> haven't refined them yet, or shall I blame it on the subharmonic
> series?-C.

Two things are going on. First, the tuning is very strange - I don't
think I'm even leaning toward using utonal much at all, though I'm
open to it. Second, the motion from otonal to utonal (as in: G,B,D ->
G,B,D,F) drags several pitches across the map in opposite directions
simultaneously, which is painful (especially since retuning is still
sudden in this program version). In the case of the 'x' tuning, with
both O and U, I think it's half-diminished chords that're causing most
of the problem; in other cases, otonal will dominate.

It's great to visit "u", but I'm not sure I want to live there!

JdL

John A. deLaubenfels wrote,

>Second, the motion from otonal to utonal (as in: G,B,D ->
>G,B,D,F) drags several pitches across the map in opposite directions
>simultaneously, which is painful (especially since retuning is still
>sudden in this program version).

That doesn't sound very clever. Perhaps the supermajor chord is called for
in this situation, and if the resolution is to a C chord, the supermajor can
be justified in terms of a sharpened leading tone. Oops, I forgot to bring
in the Kahrimanis. I'll try to remember tomorrow.