You can't translate 12-tET to Blackjack (was: Gee, did I miss a fight somewhere)

Joseph Pehrson wrote:

> How was it then, however, that the example of the quasi "pop" tune
> that Monzo put into 21 Miracle came out so well...

It didn't!

There is no way to get a diatonic out of Blackjack. It is a common mistake
to assume that a dominant 7th chord is some kind of an approximate 4:5:6:7,
or a diminished chord is some kind of approximate 5:6:7. It rarely works,
and clearly screws up in this case. They are really 4:5:6|5:6 and 5:6|5:6
respectively.

The first time usable diatonics appear in a Miracle chain is at 26 notes.
These are wafso-just diatonics with the usual comma problem. However I
think the comma will not be too noticeable in that 'Autumn Leaves'
arrangement, if we use the following tuning.

Monz,
I would be pleased if you would re-record 'Autumn Leaves' in this Canasta
subset so we can all hear it compared against 12-tET.

! Lumma_in_72.scl
!
Carl Lumma's scale in 72-EDO
12
!
116.6666667 ! Db/
200.0 ! D
266.6666667 ! D#\\
383.3333333 ! E\
500.0 ! F
583.3333333 ! F#\
700.0 ! G
816.6666667 ! Ab/
883.3333333 ! A\
966.6666667 ! A#\\
1083.333333 ! B\
2/1 ! C

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

> Monz,
> I would be pleased if you would re-record 'Autumn Leaves' in this
Canasta
> subset so we can all hear it compared against 12-tET.

Monz would have to play it in the right key, though, no? Really, you
want to transpose this suggestion so that it best accommodates the
natural and melodic minor scales on whatever tonic the key of the
song is.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
>
> > Monz,
> > I would be pleased if you would re-record 'Autumn Leaves' in this
> Canasta
> > subset so we can all hear it compared against 12-tET.
>
> Monz would have to play it in the right key, though, no?

Sure. The key he showed it in for most of his web page. E minor.
http://www.ixpres.com/interval/monzo/blackjack/autumn-leaves.htm

> Really, you
> want to transpose this suggestion so that it best accommodates the
> natural and melodic minor scales on whatever tonic the key of the
> song is.

It already does.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:.htm
>
> > Really, you
> > want to transpose this suggestion so that it best accommodates
the
> > natural and melodic minor scales on whatever tonic the key of the
> > song is.
>
> It already does.
>
You know more music theory than most musicians!

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_23495.html#23495

> Monz,
> I would be pleased if you would re-record 'Autumn Leaves'
> in this Canasta subset so we can all hear it compared against
> 12-tET.
>
> ! Lumma_in_72.scl
> !
> Carl Lumma's scale in 72-EDO
> 12
> !
> 116.6666667 ! Db/
> 200.0 ! D
> 266.6666667 ! D#\\
> 383.3333333 ! E\
> 500.0 ! F
> 583.3333333 ! F#\
> 700.0 ! G
> 816.6666667 ! Ab/
> 883.3333333 ! A\
> 966.6666667 ! A#\\
> 1083.333333 ! B\
> 2/1 ! C

Ooh, goodie... I've been waiting to use Canasta for something!

One thing before I get into it... _Autumn Leaves_ is in
G-major/E-minor, which is a very common dual-tonality jazz
thing. (My own _3 Plus 4_ does the same thing, a semitone
lower.)

Anyway, this particular Scala file is based on "C", correct?
So to make it work to fullest advantage on _Autumn Leaves_,
don't I have to transpose it to "G"?

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

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_23495.html#23496

> Monz would have to play it in the right key, though, no?
> Really, you want to transpose this suggestion so that it
> best accommodates the natural and melodic minor scales on
> whatever tonic the key of the song is.

OK, that's what I just said. Guess I should've read a
few posts ahead... too much to catch up on...

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

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> One thing before I get into it... _Autumn Leaves_ is in
> G-major/E-minor, which is a very common dual-tonality jazz
> thing. (My own _3 Plus 4_ does the same thing, a semitone
> lower.)
>
> Anyway, this particular Scala file is based on "C", correct?
> So to make it work to fullest advantage on _Autumn Leaves_,
> don't I have to transpose it to "G"?

No. Just use it as it is. Lumma's Scale, in this key, accomodates both
C (JI-)major and E (JI-)minor. In E minor it provides both major and
minor varieties of seventh, but only the minor sixth. But this
arrangement doesn't use the major sixth in any chords. Does it use it
in passing somewhere? If so, the Ab/ may suffice.

We also don't need all of the G major scale. If you had used an A in
the incomplete D7 chord (the second chord) we'd be in trouble. We'd
need A as well as A\. However I won't be surprised if the D-A\ wolf is
still offensive even when it is purely horizontal (between the first
two chords).

There is a vertical "wolf" minor third (actually a 12-tET minor third)
in the incomplete F#m7 chord (the 5th chord).

In terms of the note-name comments I put in the Scala file, you will
be playing it in the key of E\ minor. The chords will be A\:C:G,
D\:C:F#\, G:B\:F#\, C:B\E\, F#\:A\:E\, B\:A\:D#\\, E\:G:E\.

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> [re: retuning _Autumn Leaves_]
>
> We also don't need all of the G major scale. If you had used
> an A in the incomplete D7 chord (the second chord) we'd be
> in trouble. We'd need A as well as A\. However I won't be
> surprised if the D-A\ wolf is still offensive even when it
> is purely horizontal (between the first two chords).
>
> There is a vertical "wolf" minor third (actually a 12-tET
> minor third) in the incomplete F#m7 chord (the 5th chord).
>
> In terms of the note-name comments I put in the Scala file,
> you will be playing it in the key of E\ minor. The chords will
> be A\:C:G, D\:C:F#\, G:B\:F#\, C:B\E\, F#\:A\:E\, B\:A\:D#\\,
> E\:G:E\.
>
> Regards,
> -- Dave Keenan

Dave, you've all but done the sequencing for me! Thanks!

And Paul's right... you do know more about music-theory
than a lot of musicians.

Concerning those "incomplete chords", in case you don't know
(maybe you already do?)... The standard ways of voicing chords
in jazz often leave out the "5th", because there are frequently
many "extensions" or "extension tones" in the chord. These
are chromatically-altered notes above (i.e., higher in pitch
than) the regular chord tones, that more-or-less emulate
higher-odd-limit harmonics.

I knew that if I didn't add that "more-or-less", Paul would
get on my case about it! :) He has made the well-taken
point several times that many jazz chords are really only
possible in 12-EDO or a tuning with properties similar to it.

Anyway, my point here is that it's not just fortuitous that
some of those "difficult" notes are missing from the audio
file... Bob's tasteful (tasty?) arrangement of _Autumn Leaves_
follows well-established jazz procedures.

I think I'm gonna be too busy for the next couple of days
to get around to doing this... too bad, because there's not
much work left to do after what you've already presented!

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

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

/tuning/topicId_23495.html#23524

> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > [re: retuning _Autumn Leaves_]
> >
> > We also don't need all of the G major scale. If you had used
> > an A in the incomplete D7 chord (the second chord) we'd be
> > in trouble. We'd need A as well as A\. However I won't be
> >
> > <snip>
>
> Concerning those "incomplete chords", in case you don't know
> (maybe you already do?)... The standard ways of voicing chords
> in jazz often leave out the "5th", because there are frequently
> many "extensions" or "extension tones" in the chord. These
> are chromatically-altered notes above (i.e., higher in pitch
> than) the regular chord tones, that more-or-less emulate
> higher-odd-limit harmonics.
>
> I knew that if I didn't add that "more-or-less", Paul would
> get on my case about it! :) He has made the well-taken
> point several times that many jazz chords are really only
> possible in 12-EDO or a tuning with properties similar to it.

Sorry... I left something out of this.

The point I was making was the the "5th" is often omitted
because:

a) there are not enough voices in the ensemble to include
both the "5th" and the "extensions",

and/or

b) including the "5th" would muddy the texture too much, with
all those exotic chromatic "extensions" already in there.

Studying jazz harmony really opened my eyes to a world of
possibilities I had never known existed, even with my thorough
traditional-Eurocentric musical background.

It really is a whole other animal. Forget about trying to
apply most of what you learn in a regular theory book, and
find some good studies by knowledgeable jazz theorists.

If any two writings did it for me, they were:

_Jazz Improvisation 1: Tonal and Rhythmic Principles_,
by John Mehegan
1959, revised edition 1984, Watson-Guptill Publications / New York,
LOC # 84-50368

and an essay in a serious jazz journal that I unfortunately
don't have handy and may have lost, so I can't cite it.

The main feature of the latter was the total revamping of jazz
harmonic analysis, by replacing the diatonic Roman numerals of
traditional analysis (I ii iii IV V vi vii) with a concept of
chord root-movement grounded in a closed "circle of 5ths".

The "target" or tonic of a piece would be called "N", and
each step of the chord-root in a subdominant direction (= 3^-1)
would be labeled "N-1", while the less common (in jazz) movement
in the dominant direction (= 3^1) would be labeled "N+1".

(Note than "N+1"-type movement was the *more* common type
in "classical" music.)

This theory agreed totally with the audible experiences I'd
had with manifold and myriad jazz styles throughout my life.
It was a revelation.

To bring this post more on-topic, I'll note that Margo may
find some very odd bedfellows here, between jazz and Gothic,
since this type of jazz chord-root movement is entirely
Pythagorean in concept, if not in actual tuning.

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

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

> The "target" or tonic of a piece would be called "N", and
> each step of the chord-root in a subdominant direction (= 3^-1)
> would be labeled "N-1", while the less common (in jazz) movement
> in the dominant direction (= 3^1) would be labeled "N+1".
>
> (Note than "N+1"-type movement was the *more* common type
> in "classical" music.)

Really? I thought classical music typically went dominant-to-tonic,
and not the other way around. Yes it does. Both jazz and classical
progressions typically travel in the same direction along the chain
of fifths.

> To bring this post more on-topic, I'll note that Margo may
> find some very odd bedfellows here, between jazz and Gothic,
> since this type of jazz chord-root movement is entirely
> Pythagorean in concept, if not in actual tuning.

Well, there's much more to jazz chord-root movement than a chain of
fifths. Though that is what you're supposed to practice first, and
for a long period of time.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_23495.html#23558

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > The "target" or tonic of a piece would be called "N", and
> > each step of the chord-root in a subdominant direction (= 3^-1)
> > would be labeled "N-1", while the less common (in jazz) movement
> > in the dominant direction (= 3^1) would be labeled "N+1".
> >
> > (Note than "N+1"-type movement was the *more* common type
> > in "classical" music.)
>
> Really? I thought classical music typically went
> dominant-to-tonic, and not the other way around. Yes it does.
> Both jazz and classical progressions typically travel in
> the same direction along the chain of fifths.

Perhaps I was a little too terse here. Yes, Paul,
you're correct that classical *progressions* generally
go dominant-to-tonic. But modulations, which is what
I was thinking of, generally go the other way.

Now that sounds like I'm comparing apples and oranges.
But the was jazz composers and performers generally think,
each chord progression is a sort of tiny V-I modulation.
That's probably the main thing I got out of the two sources
I cited. And the V-I is usually extended to a ii-V-I.

I know that may sound very weird to a classically-trained
musician, but it's true. When a soloist improvises over any
typical jazz progression, the scales upon which his improvisation
are based come from the *key* that's specified by these
pseudo ii-V-I progressions.

I say "pseudo-" because the piece hasn't *really* modulated...
it's only a very local type of ocurrence. So in a way, jazz
musicians also think Monophonically (in the Partchian sense)
or monotonally (in the Schoenbergian sense).

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