tritone (was: Digest Number 1891)

> From: Gerald Eskelin <stg3music@earthlink.net>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, February 12, 2002 5:55 PM
> Subject: Re: [tuning] Digest Number 1891
>
>
> On 2/12/02 4:05 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:
>
> > Message: 4
> > Date: Tue, 12 Feb 2002 20:38:50 -0000
> > From: "paulerlich" <paul@stretch-music.com>
> > Subject: Re: Digest Number 1883
> >
> > --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> >
> > > In my opinion, the dynamic tritone (considering the 4:7
> > > "lowered" tuning of the dominant seventh pitch combined
> > > with the conventional "raising"of the leading tone propels
> > > a shift in tonality like a magnet.
> >
> > hi gerry.
> >
> > this is a nice theory.
>
> Glad you like it. ;-)
> >
> > however, as i recall monz put together some midi dominant seventh to
> > tonic resolutions, and the one where the seventh of the dominant
> > seventh was a 7:4 over its tonic, and the third of the dominant
> > seventh was a 'high third' over its tonic, sounded ugly and
> > unconvincing to everyone. perhaps its time to dig up those web pages
> > again.
>
> Even to me??? Whoa! It's hard to believe we're talking about the same
thing.
> (Do we have to go back there? Clearly I wasn't convinced then. On the
other
> hand, that might be a good place to start our 'experiments.')

> >
> >
> >> The diminished fifth
> >> sucks like a vacuum toward a major or minor third resolution and an
> >> augmented fourth pushes like an explosion toward a major or minor
> > sixth.
> >
> > i agree that this is a defining feature of tonal music as it
> > developed in the western world. i disagree that the augmented fourth
> > has to be larger than the diminished fifth for it to work. that
> > tendency is only about half as old as tonality.
>
> Yes. And what a discovery. While the clerics of the middle ages forbade
the
> tritone, and the devil-may-care Renaissance composers bent the rules, it
was
> the early Baroque that discovered the full value of the "tritone." Some of
> those slow introductions to their concertos were mind blowing. No wonder
the
> harpsichordist tried to add extra digitals on his 'axe.'
>
> > perhaps it became
> > important once (a) the system was fully 'closed' at 12 pitches; and
> > (b) modulations were so common and so great in span (on the chain of
> > fifths) that a given tritone could easily resolve to two different
> > tonal centers.
>
> That's my point, dear heart. It's the ambiguous *keyboard* "tritone"
> that prompted its "three whole steps" nickname.

no it's not, Gerry.

we've been thru this before, and my responses then were addressed
directly to you.

the "tritone" is so named because in P y t h a g o r e a n
tuning and theory it's 3 "tones", (9/8)^3 = 729/512 =
~611.7300052 cents = "augmented 4th".

the "diminished 5th" in Pythagorean tuning is a different
ratio from this, and is clearly audible as such.

now of course i must acknowledge that the word "tritone"
is used generically to mean *both* the "augmented 4th"
*and* the "diminished 5th" -- and T H I S is probably
more likely the result of keyboard-based thinking.

but the original name "tritone" has a clear basis in
Pythagorean tuning. see my Dictionary entry, which
gives measurements for more different kinds of "tritones"
than anyone will probably ever care about:
http://www.ixpres.com/interval/dict/tritone.htm

-monz

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On 2/12/02 10:13 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:

>
> Message: 15
> Date: Tue, 12 Feb 2002 19:36:38 -0800
> From: "monz" <joemonz@yahoo.com>
> Subject: tritone (was: Digest Number 1891)
>

Me:

> It's the ambiguous *keyboard* "tritone"
> that prompted its "three whole steps" nickname.
>
Monz:
>
> no it's not, Gerry.
>
> we've been thru this before, and my responses then were addressed
> directly to you.

That doesn't mean the info stuck, Monz. Had I remembered I would have added
appropriate qualifiers.
>
> the "tritone" is so named because in P y t h a g o r e a n
> tuning and theory it's 3 "tones", (9/8)^3 = 729/512 =
> ~611.7300052 cents = "augmented 4th".
>
> the "diminished 5th" in Pythagorean tuning is a different
> ratio from this, and is clearly audible as such.

Yes. This agrees with my point that they are different from "keyboard"
tuning.
>
> now of course i must acknowledge that the word "tritone"
> is used generically to mean *both* the "augmented 4th"
> *and* the "diminished 5th" -- and T H I S is probably
> more likely the result of keyboard-based thinking.

You got it! *That's* the one I was talking about. The term is handy when
referring to either (or both) "inversions" as they function (usually as
dominant in common practice) in musical contexts .
>
> but the original name "tritone" has a clear basis in
> Pythagorean tuning. see my Dictionary entry, which
> gives measurements for more different kinds of "tritones"
> than anyone will probably ever care about:
> http://www.ixpres.com/interval/dict/tritone.htm

Always good to know derivations. Let's see if it *sticks* this time.
(Something tells me it will.)

Gerald Eskelin