Re: [tuning] re: "vibe" similar to that produced by Art Tatum?

Christopher Bailey wrote,

> due to all of the play on traditional tonal language (for example,
weird-ass "substitutions" for what might have been run-of-the-mill
deceptive cadences).

Yes that's right, weird-ass "substitutions" and "modulations" that
both worked in and pushed at the traditional tonal language, and were
enabled by exploiting some pretty far-flung features or resources of
the tunings architecture -- *exactly* the sort of thing I was poking
at!

ds

At 10:44 AM 9/9/00 -0400, you wrote:
>-------
>I was thinking about Dan Stearns' [somewhat cryptic] comments on art
>Tatum's playing the other day, and yesterday I had a listening experience
>that perhaps was related: the Adagio from Mahler, Symphony 10. This
>has lots of moments/events where notes sound deliciously, poignantly
>"out-of-tune" (relative to 12Tet); I wonder if this was what Dan was
>getting at; i.e. making 12Tet sound "xenharmonic," if you will, though
>staying within its bounds.
>Probably, that wasn't what he meant at all, but at any rate, it seems like
>a fascinating piece to check out from a tuning perspective, due to all of
>the play on traditional tonal language (for example, weird-ass
>"substitutions" for what might have been run-of-the-mill deceptive
>cadences).
>
>Anyone a fan of this tune?
>Oh yah, and that's one of the reasons I like it. In fact, other examples
are the last three Beehoven piano sonatas, particularly op. 109. The first
movement does some pretty strange shifts that really suggest a more flexible
tonal system. Also, I remember hearing a portion of Gyorgy Zamfir's
recording of music from "Picnic at Hanging Rock" and some of those
modulations surprised me enough so I can't recall them at all save that they
were to-oh-tally weird-ass.
Jay
>

> [Christopher Bailey]
> http://www.egroups.com/message/tuning/12558
>
> I was thinking about Dan Stearns' [somewhat cryptic] comments on
> art Tatum's playing the other day, and yesterday I had a listening
> experience that perhaps was related: the Adagio from Mahler,
> Symphony 10. This has lots of moments/events where notes sound
> deliciously, poignantly "out-of-tune" (relative to 12Tet); I
> wonder if this was what Dan was getting at; i.e. making 12Tet
> sound "xenharmonic," if you will, though staying within its
> bounds. Probably, that wasn't what he meant at all, but at any
> rate, it seems like a fascinating piece to check out from a
> tuning perspective, due to all of the play on traditional tonal
> language (for example, weird-ass "substitutions" for what might
> have been run-of-the-mill deceptive cadences).

> [Dan Stearns]
> http://www.egroups.com/message/tuning/12560
>
> Yes that's right, weird-ass "substitutions" and "modulations"
> that both worked in and pushed at the traditional tonal language,
> and were enabled by exploiting some pretty far-flung features or
> resources of the tunings architecture -- *exactly* the sort of
> thing I was poking at!

Well, Dan, *you* know what a Mahler fan I am - if you had used
*this* example instead of Art Tatum (whom I also admire), I would
have understood your point a lot better! :)

> [Christopher]
> Anyone a fan of this tune?

YES! (With the biggest capital 'Y' you can find!!)

I'm quite certain that I'm the biggest Mahler fanatic on *this*
List, so I just *had* to answer.

(I've been making MIDI-sequences of much of Mahler's music,
and my hope is that I can live long enough to get around to
retuning some of it, in between all my other projects.)

I've been doing lots of research on the 10th ever since the score
of the Cooke performing version was published in 1977 (I was still
a kid, so I had to save up what was 'big bucks' for me then, and
ran out and bought it as soon as I could).

Mahler didn't live to finish this piece, and Cooke's version was
the first published 'completion'; my college friend Remo Mazzetti
organized the premiere of the Carpenter version, which I attended,
the Colorado Mahlerfest recently released the first recording of
the excellent Wheeler version, Mazzetti himself made the fourth
version, and a recording of a new fifth version has just been
released. Lots of info can be found in the archives of the
Mahler List:

http://listserv.uh.edu/cgi-bin/wa?A0=mahler-list&D=0&F=&H=0&O=T&S=&T=1

One of the most fascinating sonic structures Mahler ever created
(and there were many, many, many... especially from the 7th on,
and most especially in the 10th) is that big 9-note chord near
the end of the 'Adagio' (which is the first movement, for those
who don't know the 10th Symphony).

Here's a MIDI-file I made of this section (played in 12-tET):

http://www.ixpres.com/interval/monzo/mahler/10th1-ch.mid

The 12-tET degrees used are 0, 1, 2, 4, 6, 7, 8, 10 and 11,
in this order from the bass up: 0-7-10-1-4-7-10-1-4-10-1-4-8-11-2-6.
(0 = C#, the 'tonic' of the chord).

The only 12-tET notes missing from this chord are thus 3, 5, and 6
(the 'minor 3rd', 'perfect 4th', and 'major 6th'). What's
interesting is that the chord has a sort of overall 'minor' sound
(to me) *without* the 'minor 3rd'.

I've made a chart of the ratios of the 12-tET tuning of this chord,
to see what JI implications might be found in it. I present here
as much of it as I could fit:

(The first column gives the absolute 12-tET degree - i.e., the
number of semitones - from the bottom; the other columns are the
ratios of the whole chord, with values of 1/1 from 1 to 8)

Mahler 10th chord - ratios of 12-tET tuning

12-tET

54 22.6274 45.2548 67.8823 90.5097 113.137 135.765 158.392 181.02
50 17.9594 35.9188 53.8782 71.8376 89.797 107.756 125.716 143.68
47 15.1020 30.2040 45.3060 60.4080 75.510 90.612 105.714 120.82
44 12.6992 25.3984 38.0976 50.7968 63.496 76.195 88.894 101.59
40 10.0794 20.1587 30.2381 40.3175 50.397 60.476 70.556 80.63
37 8.4757 16.9514 25.4271 33.9028 42.379 50.854 59.330 67.81
34 7.1272 14.2544 21.3816 28.5088 35.636 42.763 49.890 57.02
28 5.0397 10.0794 15.1191 20.1587 25.198 30.238 35.278 40.32
25 4.2379 8.4757 12.7136 16.9514 21.189 25.427 29.665 33.90
22 3.5636 7.1272 10.6908 14.2544 17.818 21.382 24.945 28.51
19 2.9966 5.9932 8.9898 11.9865 14.983 17.980 20.976 23.97
16 2.5198 5.0397 7.5595 10.0794 12.599 15.119 17.639 20.16
13 2.1189 4.2379 6.3568 8.4757 10.595 12.714 14.832 16.95
10 1.7818 3.5636 5.3454 7.1272 8.909 10.691 12.473 14.25
7 1.4983 2.9966 4.4949 5.9932 7.492 8.990 10.488 11.99
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

But there is an extremely important point about Mahler's symphonies
that I've mentioned here before, and that is directly relevant to
the comments of both Christopher and Dan here: these pieces are
for *orchestra*, which has totally flexible intonation!

And opinions on Mahler as both composer and conductor were sharply
divided in his lifetime: he was both renowned (by many) as one of
the greatest conductors and (by a few) as one of the greatest
composers of his time, and harshly riduculed (mostly in the press)
as one of the most radical of both professions.

So there's no reason to assume that Mahler ever *intended* his
orchestral music to be tuned anywhere near 12-tET!!

I was a Mahler fan before I ever knew about Partch and non-12-tET
tunings, but ever since that discovery, I've been wondering deeply
about Mahler's conception of harmony. I've done a *lot* of
research into Mahler's life and music, and still don't have a
satisfying answer. Consult this webpage for some detailed info:

http://www.ixpres.com/interval/monzo/schoenberg/Vienna1905.htm

(Someday there will be a great JI version of Mahler's _7th_
- hopefully *I'll* get to do it!)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@y..., " Monz" <MONZ@J...> wrote:
> /tuning/topicId_12560.html#12583
> From: " Monz" <MONZ@J...>
> Date: Sun Sep 10, 2000 10:02 am
> Subject: Mahler 10th chord
> (was: "vibe" similar to that produced by Art Tatum?)
> The 12-tET degrees used are 0, 1, 2, 4, 6, 7, 8, 10 and 11,
> in this order from the bass up:
> 0-7-10-1-4-7-10-1-4-10-1-4-8-11-2-6.
> (0 = C#, the 'tonic' of the chord).
>
> The only 12-tET notes missing from this chord are thus 3, 5, and 6
> (the 'minor 3rd', 'perfect 4th', and 'major 6th'). What's
> interesting is that the chord has a sort of overall 'minor' sound
> (to me) *without* the 'minor 3rd'.

Oops, my bad. That should say "The only 12-tET notes missing
from this chord are thus 3, 5, and 9."

Also, the table I posted (which was only a small excerpt of
the much larger table I calculated) of the rational approximations
of this chord, in that post, gave the "root" as the numbers
1 thru 8.

But I have just found that the "root" low-integer giving the
best rational approximations to the 12-EDO pitches in this
chord is 10.

12-EDO
Semitones ~ratio

54 226.27417 226
50 179.5939277 180
47 151.01989 151
44 126.9920842 127
40 100.793684 101
37 84.75704755 85
34 71.27189745 71
28 50.396842 50
25 42.37852377 42
22 35.63594873 36
19 29.96614154 30
16 25.198421 25
13 21.18926189 21
10 17.81797436 18
7 14.98307077 15
0 10 10

This is interesting to me, as the trumpet holds a high "A"
thruout the duration of this passage. If the "root" C# is
taken as 10, the most likely rational interpretation for "A"
would be 8 and its "8ves" 16, 32, 64, 128, etc.

I haven't retuned this yet, mainly because there are so
many instruments that I don't have enough MIDI channels
to accomodate all the pitch-bend. The 12-EDO mp3 is at
<http://www.ixpres.com/interval/monzo/mahler/mah10th1-ch.mp3>.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_12560.html#26315

>
> I haven't retuned this yet, mainly because there are so
> many instruments that I don't have enough MIDI channels
> to accomodate all the pitch-bend. The 12-EDO mp3 is at
> <http://www.ixpres.com/interval/monzo/mahler/mah10th1-ch.mp3>.
>

This is absolutely fascinating, Monz! As I have repeatedly said, you
do TERRIFIC work, and not a moment of time you spend on it is a
waste.... You provide a valuable service to this entire community!

_________ _______ _________
Joseph Pehrson