Re: [tuning] Digest Number 1883

On 2/10/02 12:19 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:

> Message: 10
> Date: Sun, 10 Feb 2002 10:45:19 -0800
> From: "monz" <joemonz@yahoo.com>
> Subject: Re: Re: a few things for Joseph
>
>
> i find in teaching my piano students that the best way to
> get them to understand the key system of our mishmash hybrid
> Pythagorean/meantone-notation-and-12edo-tuning system
> is to use the "circle of 5ths" in conjunction with the
> idea of tetrachordal similarity. they learn each "major
> scale" on the piano by using four fingers of each hand,
> so the pattern is (use "expand messages" to view this
> on the Yahoo web interface):
>
> C D E F G A B C notes
> LH: 5 4 3 2 RH: 2 3 4 5 fingers
> 1 1 1/2 1 1 1 1/2 steps between
> \________/ \/ \________/
> lower tone upper
> tetrachord of tetrachord
> disjunction
>
> each hand playing an intervallically identical tetrachord,
> with the "tone of disjunction" falling between hands.
>
> then to move to the key and scale a "5th" higher,
> they simply switch the right hand with the left and
> copy the same pattern of "whole-whole-half" starting
> a "tone" higher for the new tetrachord in the right hand,
> which simply requires raising the 4th finger a "half-step".
>
> i draw the "circle of 5ths" for them as they go thru
> this procedure, and when we finish the key of C#, we
> start over again on C and go around the other way to
> do the flat keys, where the hand-switching is a bit
> different.
>
> i find that by using this method, my students get a
> very quick understanding of the whole standard system
> of keys as they are ordinarily used, and there is no
> confusion over the three pairs of keys which are
> enharmonically equivalent (Cb/B, Gb/F#, Db/C#).
> the student understands the derivation of each of those
> from both sides of the circle, so it all makes sense.
>
>
> of course, thru all of this i'm always emphasizing to
> them that i t o n l y w o r k s i n
> T H I S t u n i n g !

Actually, I find that it works most convincingly in what I have come to call
"flexible tuning."
>
> my hope is that they'll get interested enough to want
> to learn about other tunings ... but until they do show
> an interest in that, i just discreetly keep reminding
> them that the tuning on their piano is only one out of
> a huge number that could be chosen, and that in many of
> those other tunings we get flats which are different
> from sharps, and the key of Gb might not be the same
> as the key of F#.
>
Most definitely!
>
>
> -monz

I, too, Monz, was brought up focusing on the "tetrachord" of whole-step,
whole-step, half-step. What I learned from actual music, however, was that
changes in tonality--modulation, if you please--is created by modifying the
tritone. Since there is only one per major key, it is the most compelling
factor in leading the ear toward another tonality. ("by the dawn's ear-LY
light")

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. 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.
Call it "style" it you like. I call it "tonal gravity."

My response here is say that, in my opinion, the major/minor system works
best when considered in terms of flexible tuning--not 12tET tuning. If only
choral groups and orchestras were fully aware of the power of the flexible
tritone in "flinging" tonality into myriad tonal directions simply by
modifying its tuning. I stay awake nights imagining the excitement.

Gerald Eskelin

--- 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.

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.

> 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. 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.

> Call it "style" it you like. I call it "tonal gravity."
>
> My response here is say that, in my opinion, the major/minor system
works
> best when considered in terms of flexible tuning--not 12tET tuning.
If only
> choral groups and orchestras were fully aware of the power of the
flexible
> tritone in "flinging" tonality into myriad tonal directions simply
by
> modifying its tuning.

this seems to support my statement above. before modulations became
as 'flingy' as they have been since beethoven, there was really no
desire to make the augmented fourth larger than the diminshed fifth.

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

/tuning/topicId_34064.html#34108

>
> 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.
>

Monz!

I would really like to "revisit" this page again, and as I recall,
you don't have it in your "index" of pages...

Joe