Re: "raised pythagorean 'leading tone'", "flat chords"

(Subject was: Beethoven JI tuning experiment & 'lateral'
harmonies)

Dale Carr wrote:

>The description of a flat sounding chord also has me wondering.
>monz might mean that the *third of the chord* is lower than he
>expected, but not likely that there's a flat sign in front of it.
>But a *chord* might sound flat [= dull?] for some other reason than
>the tuning, so maybe he's not referring to the third at all.

I, too, have found that 5-lim JI doesn't provide very
satisfying dominant chords for music later than Baroque, at
the latest. IMO it's simply because 12:15:18 is too
consonant, too "rested," too "final" sounding, if you will,
to supply the harmonic energy its role requires. Raising
the pitch of the 15/8 somewhat (and leaving the other
pitches _alone_, thank you! ;-) gives the chord enough
"activeness" or tension to match the sense of imminent
resolution required by compositions in the Age of
Temperaments.

And I don't think it has anything to do with Pythagorean
intervals, it's just raised some to make it more active.

You know, if you raise the 12 along with the 15, you've lost
the pure 4/3 between the roots of the chords, so where has
that gotten you?! Unless you plan to shift the 1 up as
well, and then you've really got some juggling to do. It
gets worse instead of better, I think. The dissonance of a
12:15.nnn:18 helps pull off the dominant/tonic resolution in
Classical and Romantic period music, to my ears.

In fact, I'm beginning to wonder whether flattened fifths
don't actually help. But that's another story.

Renaissance compositions, even some Baroque ones, don't need
that raised LT, to my ears, because there is more of a sense
of simply hop-scotching around the lattice rather than of
building and releasing harmonic tension.

I don't personally see the point of making a Beethoven piece
5-lim JI, other than the simply educational purpose of
taking it apart and putting back together intentionally
wrongly to see what will happen. It couldn't have been
written that way, it wasn't intended to be, and it doesn't
work well, anyway. It assumes the vanishing comma, among
other things. It's analogous to what Margo said, if one
> attempted to make Bach's or Beethoven's triadic harmonies "richer" by
> adding pure 7:4's where stable triads are expected, this would be
> "ungrammatical,"

I think it best to stick to historical temperaments for
Beethoven and his musical kin about 100 years on either
side.

David J. Finnamore
Just tune it! (doh!)

[David J. Finnamore wrote:]
> I don't personally see the point of making a Beethoven piece
> 5-lim JI, other than the simply educational purpose of
> taking it apart and putting back together intentionally
> wrongly to see what will happen. It couldn't have been
> written that way, it wasn't intended to be, and it doesn't
> work well, anyway. It assumes the vanishing comma, among
> other things.

> I think it best to stick to historical temperaments for
> Beethoven and his musical kin about 100 years on either
> side.

> David J. Finnamore
> Just tune it! (doh!)

You speak of that which you do not know, because as far as I can tell,
it's not been done (or at least, done well) yet. Beethoven couldn't do
it, because the acoustic piano cannot be retuned on the fly, but WE can
do it readily, with our synthesizers and pitch bends (or tuning tables).

I reject the idea that JI and 19th-century music are somehow
incompatible. The use of JI does not force any particular musical
style!

"Intentionally wrongly"?? That's like saying it's "wrong" to play
Bach's Goldberg Variations on the piano because Bach never did. Is the
fact that it's a beautiful transcription irrelevant? Is the energy of
the work lost when it's permuted?

Actually, I'm eager to work with Brahms and some of his sweet little
piano pieces, or Schubert, more than the mad Beethoven, but I'll take
just about ANY (single-voice) MIDI file anyone has out there to be
tuned! (alas, my own keyboard and reading skills are sub-par; I depend
upon the kindness of strangers to record MIDI sequences).

JdL
I WILL Just tune it!

John A. deLaubenfels [TD209.9]
>You speak of that which you do not know, because as far as I can tell,
>it's not been done (or at least, done well) yet. Beethoven couldn't do
>it, because the acoustic piano cannot be retuned on the fly, but WE can
>do it readily, with our synthesizers and pitch bends (or tuning tables).

>I reject the idea that JI and 19th-century music are somehow
>incompatible. The use of JI does not force any particular musical
>style!

>"Intentionally wrongly"?? That's like saying it's "wrong" to play
>Bach's Goldberg Variations on the piano because Bach never did. Is the
>fact that it's a beautiful transcription irrelevant? Is the energy of
>the work lost when it's permuted?

...
>I WILL Just tune it!

Yeah! A man after my own heart.

The piece that I would love to hear in JI is Bach's Prelude No.1 from
well-tempered clavichord even though it was never intended for that.
It does however require quite a bit of work to get the JI correct as IMO
it repeats arpegios with different tuning in order to make some great
musical puns.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm

> [David J. Finnamore wrote:]
> > I don't personally see the point of making a Beethoven piece
> > 5-lim JI, other than the simply educational purpose of
> > taking it apart and putting back together intentionally
> > wrongly to see what will happen.

John A. deLaubenfels responded:

> You speak of that which you do not know, because as far as I can tell,
> it's not been done (or at least, done well) yet.

LOL! I'll have to give you that. Monz is making a valiant
effort. I seem to be having trouble playing his file
properly so far; my plug-in might not be interpreting his
pitch bends properly or something. But the musical sense of
the piece comes through wonderfully, really expressively. I
think it's going to be very nice when he's done, if you can
live with comma shifts between chord roots.

> [snip] WE can
> do it readily, with our synthesizers and pitch bends (or tuning tables).
>
> I reject the idea that JI and 19th-century music are somehow
> incompatible. The use of JI does not force any particular musical
> style!

Ah! But "you speak of that which you do not know, because
as far as I can tell," you haven't done it yet. ;-P Paul
Erlich said something extraordinarily well in TD 208.11 that
I think points up a flaw or gap in your understanding of the
situation:

> However, much music of the late Classical and Romantic periods are founded
> on 12-tET logic. Cycles of major thirds, diminished seventh chords as
> modulational pivots, and other uses of enharmonic equivalence would make
> something like deLaubenfels's proposal the closest you could get to putting
> such music in JI. There the thinking is not cylindrical but toroidal.

Because the compositions presuppose the vanishing syntonic
comma, weird little tricks have to be pulled in compensation
to force them into any low-limit JI. Go ahead, try one. As
soon as you run into a spot where you have to make an
awkward leap across the flat lattice to do something that
was done with a short step around the back side of the
toroid, you'll see what we're talking about.

> "Intentionally wrongly"?? That's like saying it's "wrong" to play
> Bach's Goldberg Variations on the piano because Bach never did.

Well, no, it's not, really. Bach may not be ideal on piano,
and 12t-ET may be too bland to reveal all of Bach's genius,
but Gould's recordings have their own charm. But forcing
modern compositions like Beethoven's into low-limit JI is
maybe more analogous to trying to explain sub-atomic
particle behavior in terms of Newtonian physics. You're
going to run into difficulties that can't be completely
surmounted. Somewhere, somehow, you're going to compromise
something, because Common Practice era compositions
presuppose the compromise.

Perhaps I overstated the case with the word "wrongly."
Believe me, nobody enjoys the sensuous buzzing of consonant
triads and tetrads more than I do. I'm a JI guy just about
to the core. I wish to goodness that a composition could
have all the benefits of both Beethoven and Montiverdi. But
they really are partially mutually exclusive. It's not
ethically "wrong," of course, I didn't mean that. I just
mean it in the sense that it's "wrong" to try to force a
rounded peg into a square hole. You can jam it in if it
makes you happy but it wasn't designed to go there, that's
all.

> Actually, I'm eager to work with Brahms and some of his sweet little
> piano pieces, or Schubert [snip]
> I WILL Just tune it!

More power to ya. There's no better way to learn.

David J. Finnamore
Just tune it! (hee, hee)

[John deLaubenfels, TD 209.9]
>
> Actually, I'm eager to work with Brahms and some of his sweet
> little piano pieces, or Schubert, more than the mad Beethoven,

Aaaahhh.......... yet another reason why I picked him!

Whose work better to mangle in the vice of an extended 5-limit
lattice?...

'the mad Beethoven' ...I love it!

-monz
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In TD 210 I wrote:

> I just
> mean it in the sense that it's "wrong" to try to force a
> rounded peg into a square hole. You can jam it in if it
> makes you happy but it wasn't designed to go there, that's
> all.

But that's not quite the best picture. Maybe this gets
closer to the mark.

7-limit JI (prime limits in this context) is like a square
peg. Non-equal meantones, even though they're formed of
only 5-limit, are like round pegs. You can jam a round peg
into a square hole if you don't mind making a few splinters.

But once you go beyond meantone into circulating
temperaments, you've taken the ends of the round peg and
bent them around to make a donut. That donut is not going
into any hole and stay a donut. You're going to have to
tear it apart and give it an end before you can force that
end down the square hole.

The problem is that the donut shape is part and parcel with
the beauty of many Common Practice era compositions. You're
going to sacrifice something significant about the
composition for the sake of an ideal, an ideal that the
composer, or his colleagues and/or predecessors, chose to
forsake. You're going to have to break it. You need a more
compelling reason to do so, IMHO, than achieving a higher
degree of consonance.

Didn't mean to make it sound so serious but those are the
issues at hand, as I see them. As I said before, if it
makes you happy, it can't be that bad. But you should be
aware that you can't have your toroid and eat it, too.

David J. Finnamore
Just tune your own music! :-)

[I wrote:]
>> I reject the idea that JI and 19th-century music are somehow
>> incompatible. The use of JI does not force any particular musical
>> style!

[David J. Finnamore wrote:]
> Ah! But "you speak of that which you do not know, because
> as far as I can tell," you haven't done it yet. ;-P

Fair enough; certainly I haven't done it as well as I plan to, but are
you aware of my real-time adaptive JI retuning program (for Windows
95/98), available at:

http://www.idcomm.com/personal/jadl/

[Finnamore:]
> Paul Erlich said something extraordinarily well in TD 208.11 that
> I think points up a flaw or gap in your understanding of the
> situation:

[Erlich:]
>> However, much music of the late Classical and Romantic periods are
>> founded on 12-tET logic. Cycles of major thirds, diminished seventh
>> chords as modulational pivots, and other uses of enharmonic
>> equivalence would make something like deLaubenfels's proposal the
>> closest you could get to putting such music in JI. There the thinking
>> is not cylindrical but toroidal.

[Finnamore:]
> Because the compositions presuppose the vanishing syntonic
> comma, weird little tricks have to be pulled in compensation
> to force them into any low-limit JI. Go ahead, try one. As
> soon as you run into a spot where you have to make an
> awkward leap across the flat lattice to do something that
> was done with a short step around the back side of the
> toroid, you'll see what we're talking about.

Well, the "we" who have been talking about all this includes me - have
you missed all those posts? I am well aware of the challenges of the
syntonic comma, or of the Pythagorean comma, for that matter. Paul
Erlich and I have had extensive exchanges on the subject.

> Somewhere, somehow, you're going to compromise something, because
> Common Practice era compositions presuppose the compromise.

Yes. There are always tradeoffs between achieving ideal intervals on
the fly vs. the "pain" of retuning a sounding note on the fly. Another
kind of compromise involves chords which have no compelling JI tuning,
including full diminished 7ths, augmented triads, and chords with three
or more successive intervals of a fifth. I currently leave all these
tuned in 12-tET (though members of the list have suggested other
alternatives).

Also, FYI, I am into 7-limit JI; I tune my dominant 7ths 4:5:6:7 (which,
apparently, puts me in the minority of people on this list!). The
very flat 7th, which resolves downward to the 3rd degree from tonic,
compensates for the rather large step from the leading tone to tonic,
in my opinion. I hear the sharpening of the leading tone as a
seductive temptation (it DOES increase the energy in some way...) which,
once one hears the benefit of a properly tuned dominant chord (with or
without 7th), becomes unnecessary.

You are right to say that it remains to be seen how successful I, or
anyone else, will be at transcribing 19th century music to JI. And,
of course, we will always have our own opinions regarding how good a
given transcription is. I will try to provide for variation in taste,
including the option to tune dominant 7ths in ways other than 4:5:6:7.

Again I ask for MIDI sequence file(s) that you think might stump me -
we shall see!!

JdL

[me, TD 209.9:]
>> Actually, I'm eager to work with Brahms and some of his sweet
>> little piano pieces, or Schubert, more than the mad Beethoven.

[Monzo, TD 210.7:]
> Aaaahhh.......... yet another reason why I picked him!
> Whose work better to mangle in the vice of an extended 5-limit
> lattice?...
> 'the mad Beethoven' ...I love it!

Kyool! Monz, did you see my post in TD 207.7? If you responded to it,
I missed it. Since then I did successfully download your partial
sequence. It's so... SHORT, it's hard for me to tell whether the tuning
seems right or not. (please note the extreme irony in my complaining
that your sequence is too short, I who am virtually unable to play
keyboard from a score...).

I actually like Beethoven's mad spirit, except that it seems not fully
leavened with sweetness most of the time. Brahms can be every bit as
stormy as Beethoven, but he always mixes in some wonderful lyricism.

(which MAY be because Brahms had a steady stream of girlfriends, whereas
poor Beethoven was apparently celibate most or all of his life...)

Do you like the idea of a "tune-off"? Do you have any complete MIDI
(single-voice) sequences you would like to see bent?

JdL

David Finnamore wrote,

>Ah! But "you speak of that which you do not know, because
>as far as I can tell," you haven't done it yet. ;-P Paul
>Erlich said something extraordinarily well in TD 208.11 that
>I think points up a flaw or gap in your understanding of the
>situation:

>> However, much music of the late Classical and Romantic periods are
founded
>> on 12-tET logic. Cycles of major thirds, diminished seventh chords as
>> modulational pivots, and other uses of enharmonic equivalence would make
>> something like deLaubenfels's proposal the closest you could get to
putting
>> such music in JI. There the thinking is not cylindrical but toroidal.

>Because the compositions presuppose the vanishing syntonic
>comma, weird little tricks have to be pulled in compensation
>to force them into any low-limit JI. Go ahead, try one. As
>soon as you run into a spot where you have to make an
>awkward leap across the flat lattice to do something that
>was done with a short step around the back side of the
>toroid, you'll see what we're talking about.

Your point is well taken but it looks like you're a little confused about
the flat/cylindrical/toroidal distinctions. The 5-limit JI lattice is of
course an infinite flat, 2-d plane. Presupposing the vanishing syntonic
comma has been standard since the Renaissance and curls the plane onto
itself, forming a cylinder, now only infinite in one dimension, rather than
two. Finally, in the late Classical period composers began to also regularly
presuppose the vanishing of the lesser or greater diesis (or equivalently,
given the vanishing syntonic comma, they were presupposing the vanishing of
the Pythagorean comma). That curls the cylinder onto itself, forming a
toroid, finite in extent.

John A. deLaubenfels wrote:

> [are] you aware of my real-time adaptive JI retuning program (for Windows
> 95/98), available at:
>
> http://www.idcomm.com/personal/jadl/

Cool! I wasn't aware that it was available yet, I got the
idea somehow that it was just on the drawing board.

> Well, the "we" who have been talking about all this includes me - have
> you missed all those posts? I am well aware of the challenges of the
> syntonic comma, or of the Pythagorean comma, for that matter. Paul
> Erlich and I have had extensive exchanges on the subject.

Oops. Sorry, John. I did fall behind for a while and only
started catching up about 2 weeks ago. Your unabashed
enthusiasm flagged you as a newbie to me. My mistake!

> > Somewhere, somehow, you're going to compromise something, because
> > Common Practice era compositions presuppose the compromise.
>
> Yes. There are always tradeoffs between achieving ideal intervals on
> the fly vs. the "pain" of retuning a sounding note on the fly.

Well, there you have it. I was talking about fixed pitches
while you were referring to adaptive techniques. That
changes the whole picture. I agree that if you can make a
keyboard act like a string group or choir then you have
overcome most of the difficulties for all practical
purposes. The only exceptions then would be:

> chords which have no compelling JI tuning,
> including full diminished 7ths, augmented triads, and chords with three
> or more successive intervals of a fifth.

And you're leaving those in ET. [Shrugs] We had no
disagreement after all, we were just talking about different
things.

> Again I ask for MIDI sequence file(s) that you think might stump me -
> we shall see!!

If, as I thought before, you insisted on putting everything
in fixed 7-lim pitches, no problemo finding one. As it
stands, I don't think I could.

BTW, I also often prefer the 12:15:18:21 tuning for dominant
7th chords. (I'm one of the _really_ crazy tuners who even
likes double digit primes :-) But in most Romantic era
instrumental compositions it might reduce the drama too
much, especially in bombastic symphonic pieces. Juicy
vocal-based compositions like Brahm's Requiem might be
candidates for it, though, I think.

Again, my apologies for treating you like a newbie.

David J. Finnamore

[I wrote:]
>> [are] you aware of my real-time adaptive JI retuning program (for
>> Windows 95/98), available at:
>>
>> http://www.idcomm.com/personal/jadl/

[David J. Finnamore wrote:]
> Cool! I wasn't aware that it was available yet, I got the
> idea somehow that it was just on the drawing board.

There's a lot that still IS on the drawing board! This program DOES
respond on the fly to the set of notes playing, but, because it has no
knowledge of how long the current set will last, it can't engage many of
the maximizing algorithms that a "leisure retuning" program can (leisure
meaning, able to look forward in time, having the whole sequence at
hand). Luckily, the program gets behind me a lot of the boring
bookkeeping that sucks a lot of time out of the writer, so I'm set to go
for the next phase.

[me:]
>> Well, the "we" who have been talking about all this includes me -
>> have you missed all those posts? I am well aware of the challenges
>> of the syntonic comma, or of the Pythagorean comma, for that matter.
>> Paul Erlich and I have had extensive exchanges on the subject.

[DJF:]
> Oops. Sorry, John. I did fall behind for a while and only
> started catching up about 2 weeks ago. Your unabashed
> enthusiasm flagged you as a newbie to me. My mistake!

No problem! I like being enthusiastic, and in many ways I AM a
"newbie". Six months ago I didn't know of the term "5-limit", because
I was off in my own world doing adaptive JI (since about 1993) on a
NeXT computer, using my own words for things.

>>> Somewhere, somehow, you're going to compromise something, because
>>> Common Practice era compositions presuppose the compromise.
>>
>> Yes. There are always tradeoffs between achieving ideal intervals on
>> the fly vs. the "pain" of retuning a sounding note on the fly.

> Well, there you have it. I was talking about fixed pitches
> while you were referring to adaptive techniques. That
> changes the whole picture. I agree that if you can make a
> keyboard act like a string group or choir then you have
> overcome most of the difficulties for all practical
> purposes. The only exceptions then would be:

>> chords which have no compelling JI tuning,
>> including full diminished 7ths, augmented triads, and chords with
>> three or more successive intervals of a fifth.

> And you're leaving those in ET. [Shrugs] We had no
> disagreement after all, we were just talking about different
> things.

OK. Glad we're clearer to each other now! I'm almost (perversely?)
disappointed if we have no disagreement now: does that leave me
nothing to prove? (just kidding: I still have to prove it out to my
own taste, at least!!).

>> Again I ask for MIDI sequence file(s) that you think might stump me -
>> we shall see!!

> If, as I thought before, you insisted on putting everything
> in fixed 7-lim pitches, no problemo finding one. As it
> stands, I don't think I could.

But... all I need is any 12-tET MIDI sequence. I'll split the notes out
into different channels as necessary, and bend them to taste.

> BTW, I also often prefer the 12:15:18:21 tuning for dominant
> 7th chords. (I'm one of the _really_ crazy tuners who even
> likes double digit primes :-) But in most Romantic era
> instrumental compositions it might reduce the drama too
> much, especially in bombastic symphonic pieces. Juicy
> vocal-based compositions like Brahms' Requiem might be
> candidates for it, though, I think.

I seem to stand alone in my assessment that 12:15:18:21 dom 7ths are
not overly stable ("reduce the drama too much"). They ARE wonderfully
tuned, with six lovely JI intervals, yet they are also SO plaintive, so
begging for resolution, to my ear. I think Ray Tomes may be the only
other list member who has agreed! In any case, I am resigned to
writing software that does not lock in this tuning (even the current
program, JI Relay, requires only a change to the tuning file).

Double-digit primes definitely have possibilities, I agree. I've
played a bit with 11 and 13, which fill in all the integers of the
higher octave (8 to 16). The chords are surprising (of course!) and
rich. I haven't tried 17, which some advocate using (for a Neopolitan
2nd? I can't recall).

JdL

John A. deLaubenfels wrote:
>
> I seem to stand alone in my assessment that 12:15:18:21 dom 7ths are
> not overly stable ("reduce the drama too much"). They ARE wonderfully
> tuned, with six lovely JI intervals, yet they are also SO plaintive, so
> begging for resolution, to my ear.

I'll sign on as a 12:15:18:21 enthusiast. I love *good* barbership
singing. I think the "begging for resolution" comes about because of
the small 21:20 downward "leading" semitone to the perfectly concordant
3rd in the 8:12:16:20 resolution chord. It makes up for the
less-than-urgent quality of the larger 15:16 upward leading tone.

- Fred