Yahoo Tuning Groups Ultimate Backup tuning Augmented sixth

Hi.
I have a theory question:

In classical harmony, in C minor tonality, Ab C Eb F# is an augmented sixth chord resolving on the second inversion of Cm. But in jazz harmony when somoen have to improvise on it he will use a lydian dominant scale, the fourth degree of a Eb melodic minor scale: Ab Bb C D Eb F Gb.

What is the right way to see this? In both cases I just change a single note of the C minor scale but with two different meanings:

a) F# = an alterated subdominant chord which diatonically resolves on G
b) Gb = a VI degree of C minor with a flat seventh which chromatically resolves on the sixth

I think that an answer could come analysing in classical music literature the compresence in that chord of Gb/F# with F
or with G. This would indicate only one of these solutions as the "right one". For example:

F_F_Eb_D_C
C_C_C_B_G
Ab_Ab_G_G_Eb
F_Gb_G_G_C (an octave lower than above)

This would implicate a Ab lydian dominant. I'm not saying that this sounds "good" but better than a compresence of F# and G. Is there any example of this kind in some composition of classical music?

Lorenzo

🔗Billy Gard <billygard@comcast.net>

<<< In classical harmony, in C minor tonality, Ab C Eb F# is an augmented
sixth chord resolving on the econd inversion of Cm. But in jazz harmony when
somoen have to improvise on it he will use a lydian ominant scale, the
fourth degree of a Eb melodic minor scale: Ab Bb C D Eb F Gb. >>>

VI7->i. This is what the book "Advanced Harmony" said about how this chord
(the German Sixth) should resolve, with is a major 3rd up. I've heard on
some websites that this chord is supposed to resolve down a half-step to the
dominant. Then they suggest as an afterthought a 2nd-inversion tonic in
between them to avoid the parallel fifth.

The "lydian dominant" scale you mention here sounds just like what I have
called the "accoustic scale". It seems to clearly have its justification in
the overtone series starting at the 8th harmonic. The simple mathmatical
nature of this scale is enough to explain its mystique. The 13th chord that
corresponds to it is often used in jazz as an ending chord: 4:5:6:7:9:11:13.

Billy

🔗Lorenzo Frizzera <lorenzo.frizzera@cdmrovereto.it>

I think "VI7" goes as first choice on a second inversion of the first minor degree and than on V7 ("Mozart fifths" if I well remember).

lorenzo

----- Original Message -----
From: Billy Gard
To: tuning@yahoogroups.com
Sent: Tuesday, February 06, 2007 3:48 AM
Subject: [tuning] Re: Augmented sixth

Billy

🔗yahya_melb <yahya@melbpc.org.au>

Lorenzo Frizzera wrote:
>
> Hi.
> I have a theory question:
>
> In classical harmony, in C minor tonality, Ab C Eb F# is an
augmented sixth chord resolving on the second inversion of Cm. But in
jazz harmony when somoen have to improvise on it he will use a lydian
dominant scale, the fourth degree of a Eb melodic minor scale: Ab Bb
C D Eb F Gb.
>
> What is the right way to see this? In both cases I just change a
single note of the C minor scale but with two different meanings:
>
> a) F# = an alterated subdominant chord which diatonically resolves
on G
> b) Gb = a VI degree of C minor with a flat seventh which
chromatically resolves on the sixth
>
> I think that an answer could come analysing in classical music
literature the compresence in that chord of Gb/F# with F
> or with G. This would indicate only one of these solutions as
the "right one". For example:
>
> F_F_Eb_D_C
> C_C_C_B_G
> Ab_Ab_G_G_Eb
> F_Gb_G_G_C (an octave lower than above)
>
> This would implicate a Ab lydian dominant. I'm not saying that this
sounds "good" but better than a compresence of F# and G. Is there any
example of this kind in some composition of classical music?

Hi Lorenzo,

I think you have given the only reasonable "right"
answer - in each case! Surely the resolution chosen
fully determines the analysis? If the note in question
resolves to G, then it was an F#; if it resolves to F,
then it was a Gb. Knowing the scale notes implies the
"right" reading of the harmony.

But all is not what it seems!

Suppose some joker of a composer likes to play tricks
on you. She might decide to leave the note completely
unresolved; such ambiguity is almost a signature
technique for some music makers, who enjoy - or make
dramatic use of - the added tension.

Or another joker might play it BOTH ways, with the
melodic phrase F# Gn Gb Fn, over a held Ab Cn Eb,
thereby effecting a modulation between the two modes
and the two harmonies.

Personally, I'd rather enjoy doing both - in the same
piece! I'm always looking for inventive ways to vary
a theme or motif.

Finally, I suspect that your question would be
meaningless in any tuning that clearly distinguishes
the notes F# and Gb at the speed of the musical piece.
Only when they form an enharmonic pair, as eg in 12-EDO;
or when the tempo (or timbre) obliterates fine tuning
details, is there any real ambiguity to deal with.

HTH,
Yahya

🔗Lorenzo Frizzera <lorenzo.frizzera@cdmrovereto.it>

🔗monz <monz@tonalsoft.com>

Hi Lorenzo,

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@...> wrote:

> What are the ratios for a classical augmented sixth chord?

For orchestral music from c.1780-1930, i would feel
comfortable stating that we're on solid ground assuming
a tuning approximating 1/6-comma meantone.

Assuming this, the proportions of the Italian-6th
(i.e., the one without the 5th), to 5 decimal places, are:

4.00000 : 5.02075 : 7.06043

which, as you can see, are very nearly 4:5:7, or
extremely close to the JI chord of ratios 1/1, 5/4,
and 7/4.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Lorenzo Frizzera <lorenzo.frizzera@cdmrovereto.it>

🔗yahya_melb <yahya@melbpc.org.au>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Lorenzo,
>
>
> --- In tuning@yahoogroups.com, "Lorenzo Frizzera"
> <lorenzo.frizzera@> wrote:
>
> > What are the ratios for a classical augmented sixth chord?
>
>
> For orchestral music from c.1780-1930, i would feel
> comfortable stating that we're on solid ground assuming
> a tuning approximating 1/6-comma meantone.
>
> Assuming this, the proportions of the Italian-6th
> (i.e., the one without the 5th), to 5 decimal places, are:
>
> 4.00000 : 5.02075 : 7.06043
>
> which, as you can see, are very nearly 4:5:7, or
> extremely close to the JI chord of ratios 1/1, 5/4,
> and 7/4.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

"Sounds" right to me.

Yahya

🔗monz <monz@tonalsoft.com>

Hi Lorenzo,

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@...> wrote:
>
> Ciao Monz.
>
> > which, as you can see, are very nearly 4:5:7, or
> > extremely close to the JI chord of ratios 1/1, 5/4,
> > and 7/4.
>
> which confirm that this is NOT an augmented sixth chord
> but just a dominant chord without fifth (Italian), a
> dominant chord (German) or a dominat chord with
> #11 (French). All these possibilities are included in
> a lydian dominant scale.

No, that's not right. According to "classical" theory,
the dominant-7th chord is a dissonance which must resolve,
and in fact in 1/6-meantone tuning the minor-7th *is*
a more discordant interval than the augmented-6th.

The proportions of the analogue 3-note dominant-7th chord,
that is, the same major-3rd on the bottom but a minor-7th
on top instead of augmented-6th, in 1/6-comma meantone,
is very close to 4.00 : 5.02 : 7.14.

The 1/6-comma minor-7th is very close to the ratio 25/14,
but the major-3rd calculated from 14 is not close to an
integer ratio.

So in 1/6-comma meantone, and in fact in all meantones
other than 12-edo, this dominant-7th chord is much more
discordant than the augmented-6th chord.

It's my (and others) belief that the close resemblance
of the meantone augmented-6th chord to the JI 4:5:7 chord
was a kind of doorway into 7-limit harmony in Eurocentric
practice.

The dominant-7th chord only came to be considered a
consonant chord with the advent of the blues in the
early 1900s, where every chord is a consonant dominant-7th
-- and that was in the context of 12-EDO guitar fretting.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Lorenzo Frizzera <lorenzo.frizzera@cdmrovereto.it>

>No, that's not right. According to "classical" theory,
>the dominant-7th chord is a dissonance which must resolve,
>and in fact in 1/6-meantone tuning the minor-7th *is*
>a more discordant interval than the augmented-6th.
>
>So in 1/6-comma meantone, and in fact in all meantones
>other than 12-edo, this dominant-7th chord is much more
>discordant than the augmented-6th chord.

I think that a dominant chord is 4:5:6:7
This means that a "dominant seventh" is 7:4
In 1/6-meantone 7:4 is closer to what was called an "augmented sixth" than to a "minor seventh".
In 1/4-meantone this approximation is even better.

But a dominant chord in JI is 4:5:6:7
So the augmented sixth chord is actually a better approximation of a dominant chord.

lorenzo

🔗Daniel Wolf <djwolf@snafu.de>

Lorenzo wrote:

> I think that a dominant chord is 4:5:6:7
> This means that a "dominant seventh" is 7:4
> In 1/6-meantone 7:4 is closer to what was called an "augmented sixth" > than
> to a "minor seventh".
> In 1/4-meantone this approximation is even better.
>
> But a dominant chord in JI is 4:5:6:7
> So the augmented sixth chord is actually a better approximation of a
> dominant chord.

Lorenzo,

You might find it useful to step away, for a moment, from any possible JI ideal of either chord and simply consider the use of each chord in terms of conventional voice leading. In common practice repertoire, both the dominant seventh and the various augmented sixth chord were dissonances which had to be resolved and, functionally, each resolved via a different voice leading. The seventh of the dominant seventh chord resolved downward, and the augmented sixth, in the augmented sixth chords, resolved upward. Neither voice leading suggests a preference with regard to the tuning of the chord as a vertical sonority, whether more or less consonant, although dissonances in a given tuning environment are often the "remainders" or "margins" of that environment. However, they may well suggest a preference for the melodic intonation of the leading tone, but that depends upon whether the aesthetic is one for larger (i.e. just or meantone) or smaller (i.e. pythagorean or circulating) leading tones. The historical evidence, as found within notated repertoire, does not uniformly support a JI interpretation of either sonority; indeed, treatment of the augmented sixth chord as a sustained, and thus presumably maximally consonant, sonority, must wait until mid-19th century repertoire (e.g. Liszt, Wagner) in which a 12tet intonational environment can usually be presumed (although Wagner, to his credit AFAIC, composed no important works for keyboard instruments). With earlier, and presumably meantone, repertoire, we have the unfortunate case that the requirements shown in the notation and the more usual 12-note meantone schemes (Eb-G# or Ab to C#) rarely place the near 4:5:6:7 augmented sixth chord where one wants to have them. Locating a consistent intonational treatment of either chord type is thus impossible.

Joe Monzo is right, I believe, to identify American vernacular, especially African-American, repertoire as one in which the seventh chord is treated as a basic, and consonant, sonority, and one not constrained by a voice leading resolution to a following chord. One might also add that late 19th/early 20th century French repertoire and repertoire associated with the Skryiabinistes may well also be heard as treating the seventh chord and the augmented sixth chords as not functionally dissonant, that is, not requiring resolution. But in all of these repertoires, we are confronted with the fact, that legitimate realizations were done in a 12tet environment. I would here consider the possibility that we have a fundamental re-interpretation of the temperament, with the essential feature no longer being the tempering out of the syntonic comma, but rather the tempering out of the septimal comma. (It may be instructive that, precisely for this reason, a considerable amount of common practice music can be mapped to temperaments like 17, 19, 31, but 22, which like 12 tempers out the 64/63, might more usefully map some of this repertoire in which the seventh chords are consonant).

Daniel Wolf

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@...> wrote:

> I think that a dominant chord is 4:5:6:7

I think it's better to call that a utonal tetrad. A characteristic
feature of a dominant seventh chord is that it combines the subdominant
degree with the dominant triad; like the supertonoic triad it is a
linking chord between dominant and subdominant in functional harmony.
Hence, 36:45:54:64 I think could be termed the true JI dominant seventh
chord. In a meantone tuning, this does not become equivalent to
4:5:6:7, but it is what is actually used for a V7 in practice. Another
interesting chord is 20:25:30:36; in meantone, this
is equivalent to a dominant seventh, as the seventh of the chord is a
comma higher, and the comma is tempered out. Tempering the V7 in
meantone exhibits it as a 9-limit "magic" chord.

However, I think it *is* true that a dominant seventh chord carries
some sense of the 7th partial, and in a way sounds like an out of tune
utonal tetrad.

🔗djwolf_frankfurt <djwolf@snafu.de>

🔗Billy Gard <billygard@comcast.net>

<<< What are the ratios for a classical augmented sixth chord? >>>

If you are looking for an official 5-limit tuning for it, 72:90:108:125
would form a chord with a just major 3rd, just perfect 5th, and just
augmented 6th. An alternate tuning of 128:160:192:225 substitutes an "acute"
augmented 6th (a syntonic comma higher), and is a little closer to the
ear-pleasing 7:4 ratio.

But this is largely academic. The official tuning of the dominant 7th
according to the just major scale would be 36:45:54:64, but it really
doesn't sound any more pleasing to the ear than a regular piano dominant
7th.

In listening to all these "official" tunings, nothings beats the 4:5:6:7,
whether by this you are trying to depict the dominant 7th, German 7th, Swiss
6th, Tritone substitution chord, or whatever. And during the classical
period itself, I don't think anyone knew of a chord ratio for the dominant
7th, let alone of a separate one for the German 6th.

Billy

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗monz <monz@tonalsoft.com>

Hi Daniel,

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:

> Joe Monzo is right, I believe, to identify American
> vernacular, especially African-American, repertoire as
> one in which the seventh chord is treated as a basic,
> and consonant, sonority, and one not constrained by a
> voice leading resolution to a following chord. One
> might also add that late 19th/early 20th century French
> repertoire and repertoire associated with the Skryiabinistes
> may well also be heard as treating the seventh chord and
> the augmented sixth chords as not functionally dissonant,
> that is, not requiring resolution. But in all of these
> repertoires, we are confronted with the fact, that legitimate
> realizations were done in a 12tet environment. I would
> here consider the possibility that we have a fundamental
> re-interpretation of the temperament, with the essential
> feature no longer being the tempering out of the syntonic
> comma, but rather the tempering out of the septimal comma.

Yes, you are absolutely correct in pointing out
that some of the French repertoire since c.1885 also
treats the 12-edo version of the "dominant-7th" chord
as a consonance, something which i overlooked.

The earliest prominent examples of this which i know
about are Chabrier's opera _Le roi malgré lui_ (1887)
and Satie's _Trois Sarabandes_ for piano, from the
same year ... in fact the Satie pieces have strings of
unresolved dominant-9th chords.

But as you reiterate, my point remains that this
did not happen until 12-edo accepted as the context.
In the 1/6-comma meantone context which i believe
was the standard for Eurocentric orchestral playing,
the dominant-7th chord always required resolution.

What's interesting to me, considering how closely
the meantone augmented-6th chord resembles the JI
4:5:7 sonority, is the way composers as early as
Beethoven would "sit" on an unexpected augmented-6th
chord at dramatic moments in their score, before
resolving it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, "Billy Gard" <billygard@...> wrote:

> In listening to all these "official" tunings, nothings beats the
4:5:6:7,
> whether by this you are trying to depict the dominant 7th, German
7th, Swiss
> 6th, Tritone substitution chord, or whatever.

You can substitute the otonal tetrad for a V7, but then you have this
64/63 interval between 21/16 and 4/3 popping up. Some people object to
these commatic interval movements.

And during the classical
> period itself, I don't think anyone knew of a chord ratio for the
dominant
> 7th, let alone of a separate one for the German 6th.

Huyghens seems to have been aware of the septimal interpretation of
meantone and 31-et.

🔗djwolf_frankfurt <djwolf@snafu.de>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Billy Gard" <billygard@> wrote:
>
> >
> And during the classical
> > period itself, I don't think anyone knew of a chord ratio for the
> dominant
> > 7th, let alone of a separate one for the German 6th.
>
> Huyghens seems to have been aware of the septimal interpretation of
> meantone and 31-et.
>

In addition to Huyghens, one should add the name Tartini (1692-1770),
who advocated both the use of difference tones in tuning dyads and
the use of the harmonic seventh.

Inasmuch as the seventh partial was familiar from horns, trumpets,
and string instruments from the time of the tromba marina, the
exclusion of the seventh and septimal ratios from theoretical
literature has to be accounted for.

Daniel Wolf

🔗Tom Dent <stringph@gmail.com>

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Billy Gard" <billygard@> wrote:
> >
> > >
> > And during the classical
> > > period itself, I don't think anyone knew of a chord ratio for the
> > dominant
> > > 7th, let alone of a separate one for the German 6th.
> >
> > Huyghens seems to have been aware of the septimal interpretation of
> > meantone and 31-et.
> >
>
> In addition to Huyghens, one should add the name Tartini (1692-1770),
> who advocated both the use of difference tones in tuning dyads and
> the use of the harmonic seventh.
>
> Inasmuch as the seventh partial was familiar from horns, trumpets,
> and string instruments from the time of the tromba marina, the
> exclusion of the seventh and septimal ratios from theoretical
> literature has to be accounted for.
>
> Daniel Wolf

I believe Mattheson provided a list of ratios, which amounted to all
just 5-limit intervals which he considered at all useful, in one of
his textbooks. I'd guess he used 225/128 for the aug6, which is only a
few cents shy of 7:4.

So far as I know, they (meaning 17th-18th century theorists, with very
few exceptions) didn't *exclude* the 7-limit - they just opined that,
although it existed, it was good for nothing.

Funny, when you consider what meantone does, but there you are, though
it was under their noses, it generally went unnoticed. The power of
convention...

There is one English meantone tuning instruction that asks for
Bb-Db-F-Ab and Eb-G-Bb-Db to be 'good chords' (tuned as G# and C#
resp). And I think someone English-18th-century refers to a tritone as
the most 'elegant' interval, which might have some cause in being
close to 5:7.

Also among the exceptions is also Kirnberger, a much more 'mainstream'
theorist and composer than either Huyghens or Tartini, although not
without his own fetishes. He introduced the 7th harmonic in a flute
sonata, where it played the role of E# above G, resolving to octave F#'s.

I think there is also a Baroque cantata (can't remember the composer)
where it was employed as A# above a chord of C major, resolving to G
major, on the text 'Suesser als Honig'. Hence there is an extremely
slender thread of people in 'common practice' who did recognise 7:4 as
an aug 6 and explicitly integrated it into compositions.

Details come from Vogel's book on the 'Naturseptime' - which though
wanders badly off the rails in recommending 7:4 as a dominant 7th in
Mozart... requiring a 63:64 commatic shift, or more, for every
held-over 4th degree !!

Anyway, if you search the message archives for 'Handel' you'll find a
lot of discussion on this just a couple of months ago.

~~~T~~~

🔗Kraig Grady <kraiggrady@anaphoria.com>

On the basis of difference tones.
Erv Wilson has proposed one interpretation of the dominant 7 used in cadences as stemming from the subdominant.
with 9- 23 27 -32 with the difference tone between 32/23 being also 9 reinforcing the root.
The whole issue of different intonational practices at different structural points in a Phrase is unfortunately little examined as a possibility.
It seems that it would make sense that the intonation of a passage could change according to its use and , i believe such processes happen all the time , even in traditional music when players are allowed o do small shifts.
It is one reason i believe any single proposed tuning for much music, fails in its inability to take this into account.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> The earliest prominent examples of this which i know
> about are Chabrier's opera _Le roi malgré lui_ (1887)
> and Satie's _Trois Sarabandes_ for piano, from the
> same year ... in fact the Satie pieces have strings of
> unresolved dominant-9th chords.

I should also have mentioned that another landmark
in the Satie _Sarabandes_ is his use of unresolved
major-7th chords, mixed in with the dominant-9ths.

In fact the first Sarabande begins on an Ab major-7th
chord, progressing from there to a Db dominant-9th
then a Gb dominant-9th. A sheet-music sample of the
opening can be seen here:

http://www.everynote.com/piano.show/1945.music

Of the course the very famous _Gymnopedie No. 1_ (1888)
begins with alternating G major-7th and D major-7th chords,
which i think is the first time in musical history
that was ever done ... after its adoption in jazz in
the 1950s, it eventually became ubiquitous in 1970s
pop music.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> I believe Mattheson provided a list of ratios, which
> amounted to all just 5-limit intervals which he considered
> at all useful, in one of his textbooks. I'd guess he used
> 225/128 for the aug6, which is only a few cents shy of 7:4.

This was exactly the pair of intervals used by Fokker in
his book _Just Intonation_ (1949), to train singers to
find a doorway into 7-limit harmony by means of familiar
5-limit intervals.

I wrote about this book here long ago, i believe in 1999.
It should still be in the archives.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> I believe Mattheson provided a list of ratios, which amounted to all
> just 5-limit intervals which he considered at all useful, in one of
> his textbooks. I'd guess he used 225/128 for the aug6, which is
only a
> few cents shy of 7:4.

This is, of course, 7/4 raised by the septimal kleisma of 225/224.
It's identical to 7/4 in meantone, but also in miracle or any other
marvel-type tuning, and is I think the first 5-limit interval which
can be used without retuning to give an acceptable 7/4. Of course, if
you don't think it is good enough then 2187/1250 surely ought to be.

Can anyone confirm this? I presume this is Johann Mattheson; but
where?

> Funny, when you consider what meantone does, but there you are,
though
> it was under their noses, it generally went unnoticed. The power of
> convention...

That's for sure--tune up meantone, especially of the flatter variety
such as 1/4-comma, and you get septimal intervals for free.

> I think there is also a Baroque cantata (can't remember the
composer)
> where it was employed as A# above a chord of C major, resolving to G
> major, on the text 'Suesser als Honig'. Hence there is an extremely
> slender thread of people in 'common practice' who did recognise 7:4
as
> an aug 6 and explicitly integrated it into compositions.

That's very interesting, it would be nice to know more.

🔗Tom Dent <stringph@gmail.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
>
> > I believe Mattheson provided a list of ratios, which amounted to all
> > just 5-limit intervals which he considered at all useful, in one of
> > his textbooks. I'd guess he used 225/128 for the aug6, which is
> only a
> > few cents shy of 7:4.
>
> This is, of course, 7/4 raised by the septimal kleisma of 225/224.
> It's identical to 7/4 in meantone, but also in miracle or any other
> marvel-type tuning, and is I think the first 5-limit interval which
> can be used without retuning to give an acceptable 7/4. (...)
>
> Can anyone confirm this? I presume this is Johann Mattheson; but
> where?

The name is correct, the place I can't be sure of: first guess is the
Vollkommene Capellmeister, which I once looked all the way through to
see if there was anything useful about temperament (short answer: no).
If it was there, it is one of the early chapters.

> > I think there is also a Baroque cantata (can't remember the
> composer)
> > where it was employed as A# above a chord of C major, resolving to G
> > major, on the text 'Suesser als Honig'. Hence there is an extremely
> > slender thread of people in 'common practice' who did recognise 7:4
> as
> > an aug 6 and explicitly integrated it into compositions.
>
> That's very interesting, it would be nice to know more.

Details are in the book (1991) by the indefatigable Martin Vogel, 510
pages on the 'natural seventh'. All in German, naturlich.

~~~T~~~

🔗djwolf_frankfurt <djwolf@snafu.de>

🔗love_love8812 <love_love8812@yahoo.com>

--- In tuning@yahoogroups.com, "Billy Gard" <billygard@...> wrote:
>
> <<< In classical harmony, in C minor tonality, Ab C Eb F# is an
augmented
> sixth chord resolving on the econd inversion of Cm. But in jazz
harmony when
> somoen have to improvise on it he will use a lydian ominant scale,
the
> fourth degree of a Eb melodic minor scale: Ab Bb C D Eb F Gb. >>>
>
> VI7->i. This is what the book "Advanced Harmony" said about how
this chord
> (the German Sixth) should resolve, with is a major 3rd up. I've
heard on
> some websites that this chord is supposed to resolve down a half-
step to the
> dominant. Then they suggest as an afterthought a 2nd-inversion
tonic in
> between them to avoid the parallel fifth.
>
> The "lydian dominant" scale you mention here sounds just like what
I have
> called the "accoustic scale". It seems to clearly have its
justification in
> the overtone series starting at the 8th harmonic. The simple
mathmatical
> nature of this scale is enough to explain its mystique. The 13th
chord that
> corresponds to it is often used in jazz as an ending chord:
4:5:6:7:9:11:13.
>
> Billy
>