4:5:6:7 again

What about a rather over discussed chord in music theory:

F B D# G# ????

F-D# is 7/4 probably
F-G# is 7/6 probably
F-B is the usual tritone 45/32

anyone else care to comment?

Mark

>F B D# G# ????

5:7:9:12 is Fokker's interpretation.

Manuel

hi Mark and Manuel,

> From: "Mark Gould" <mark.gould@argonet.co.uk>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 26, 2003 2:29 AM
> Subject: [tuning] 4:5:6:7 again
>
>
> What about a rather over discussed chord in music theory:
>
>
> F B D# G# ????
>
>
> F-D# is 7/4 probably
> F-G# is 7/6 probably
> F-B is the usual tritone 45/32
>
> anyone else care to comment?

this is really amazing. yesterday, after
i figured out those rational interpretations
of meantone "augmented 6th" chords, i started
wondering what my Excel spreadsheet would
show me for this famous "Tristan chord" in
meantone tuning!

(great minds thinking alike? ...)

> From: "Manuel Op de Coul" <manuel.op.de.coul@eon-benelux.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 26, 2003 3:22 AM
> Subject: Re: [tuning] 4:5:6:7 again
>
>
> > F B D# G# ????
>
> 5:7:9:12 is Fokker's interpretation.

that also looked like the most reasonable
interpretation to me.

... now, i wish i had saved that spreadsheet
so i could offer a few of the others. darn.

-monz

--- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:
> What about a rather over discussed chord in music theory:
>
>
> F B D# G# ????
>
>
> F-D# is 7/4 probably
> F-G# is 7/6 probably
> F-B is the usual tritone 45/32

why not 7/5?? that would make the chord a 1/(7:5:4:3) chord, the so-
called "utonal tetrad" of 7-limit harmony. a rather over discussed
chord in tuning theory. vogel is sure this is the true tristan chord.
also, if the spelling is observed and the chord is played in
meantone, the chord actually approximates 1/(7:5:4:3) *very* well.

especially if we ignore the particular spelling, other intepretations
that various authors will staunchily defend include 5:7:9:12 and, if
the chord is inverted with G# in the bass, 10:12:15:17.

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
> >F B D# G# ????
>
> 5:7:9:12 is Fokker's interpretation.
>
> Manuel

that's surprising, given fokker's interest in utonal chords and in
meantone tuning. the meantone approximation of 5:7:9:12 would be
spelled F B Eb Ab, while a meantone F B D# G# approximates 1/(7:5:4:3)
even better than that.

Martin Vogel wrote a book on the Tristanakkord. He identifies it as
subharmonic seventh down from dis (d#). I know it is a toss up whether
one really hears this akkord as subhamronic or otherwise, but my
counterpoint teacher thinks the melodies (voice-leading) help with the
subharmonic ID.

Gabor

> --- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:
> > What about a rather over discussed chord in music theory:
> >
> >
> > F B D# G# ????
> >
> >
> > F-D# is 7/4 probably
> > F-G# is 7/6 probably
> > F-B is the usual tritone 45/32
>

>why not 7/5?? that would make the chord a 1/(7:5:4:3) chord, the so-
>called "utonal tetrad" of 7-limit harmony. a rather over discussed
>chord in tuning theory. vogel is sure this is the true tristan chord.
>also, if the spelling is observed and the chord is played in
>meantone, the chord actually approximates 1/(7:5:4:3) *very* well.

>especially if we ignore the particular spelling, other intepretations
>that various authors will staunchily defend include 5:7:9:12 and, if
>the chord is inverted with G# in the bass, 10:12:15:17.

Trouble is - I can't ignore the spelling - that's the whole point of the
chord.

The 5:7:9:12 interpretation suffers from the fact that this chord has a
fundamental of C#, which given the context (A minor) is very strange unless
you consider the fact that C# major and A minor together are a 1:3 system
(in 12 equal):

C C# E E# G# A (C

Lendvai calls this a 'Complementary relation'

I like the utonal tetrad idea, reading down from D# - > B -> G# -> E#(7),
and reading the bottom note as F completes the meantone interpretation.

Mark.

>that's surprising, given fokker's interest in utonal chords and in
>meantone tuning. the meantone approximation of 5:7:9:12 would be
>spelled F B Eb Ab, while a meantone F B D# G# approximates 1/(7:5:4:3)
>even better than that.

But who wants to play Wagner in meantone and why would Fokker think
meantone has relevance to Wagner? To me 1/(7:5:4:3) sounds much too flat.

Manuel

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> But who wants to play Wagner in meantone and why would Fokker think
> meantone has relevance to Wagner?

I'd want to. The question is, would it work?

--- In tuning@yahoogroups.com, "Mark Gould" <mark.gould@a...> wrote:

> Trouble is - I can't ignore the spelling - that's the whole point
of the
> chord.
>
> I like the utonal tetrad idea, reading down from D# - > B -> G# ->
E#(7),
> and reading the bottom note as F completes the meantone
interpretation.

isn't this "ignoring the spelling"? you had F in your original post,
so i assumed it was an F and not an E#. or am i misunderstanding you?