Re: [tuning] Digest Number 2876

> From: "Kalle Aho" <kalleaho@mappi.helsinki.fi>
> Subject: Re: Optimal mixolydian and Dorian
>
> --- In tuning@yahoogroups.com, Bob Valentine <BVAL@I...> wrote:
>
> > Well, you realize that the basic problem is that two of the things
> you
> > are trying to optimize are at complete cross purposes. A fifth of
> 715c
> > satisfies the seventh, and 696c satisfies the third.
>
> True but that's what is so interesting in this case! And isn't
> temperament mostly about making a compromise between opposing forces?
>
> > Do your solutions to you really sound like a 4:5:6:7 chord? In my
> opinion
> > 12et C:E:G:Bb desn't sound like a 4:5:6:7 chord, and your solutions
> are
> > very close to 12et.
>
> They sounds like non-JI 4:5:6:7s and a bit more "locked" than 12-
> equal. I compared a just 4:5:6:7 chord with its best approximation in
> 12-equal and those two chords definitely have a perceptual
> similarity. The only difference is the phasing, beating and whooshing
> of the 12-equal. I used static sawtooth waveforms.
>
> Does this mean that you don't hear 12-equal mixolydian scale the way
> Paul Erlich argues it is heard? What about the dorian?

I didn't see where Paul explains how he believes it is heard, but I
will state some of how I believe that 12et mixolydian is heard.

1/1 [ 9/8 ] 5/4 4/3 3/2 [ 5/3 ] [ 16/9 ] 1/1
[ 10/9 ] [ 27/16 ] [ 9/5 ]

I have shown a few of the alternative JI pockets that we may think
we are in based on what is happenning in the melody harmony.

For instance, one spelling of a V- I7 cadence (if such a thing were
used) would probably sound like

4/3 -> 5/4
9/4 -> 2/1
9/5 -> 9/5
3/2 -> 3/2

However a bVImaj7 I7 cadence might sound like

20/9 -> 5/2
16/9 -> 16/9
5/3 -> 3/2
4/3 -> 1/1

I guess my belief system is that unless we are really sitting in a drone
based music, the immediate references are more meaningful than the tuning
to a hypothetic root. So 16/9 looks big and complex, but if the immediate
context has allowed us to resolve 4/3 of 4/3, then we aren't hearing anything
other than 3-limit. Similarly, all the intervals shown above are simple 5-limit
intervals in context to something that might have happened in the music.

I'm not a big fan of interpreting Western "sevnths" in the context of
7-limit, since missing by 30c seems to be a bit of a stretch when there
are "references" lurking nearby that are much more in tune.

This tangentially refers to another thread with the opposite phenomena, where
iit was discussed the "augmented second" being more dissonant
than the minor third despite being tuned identically in 12tet. It is becuase
any interpretation falls into a much different set of references (since
the b6 is the minor third of the 4 chord and the seventh is the major
third of the 5 chord).

But thats just how I hear things. Yes, in a very droney context mixolydian
may be heard as having a 7/4, however, if this was any of the tunings you
were suggesting then (key of C) this Bb should NOT be played with G or D
or F since then much simpler interpretations will be heard.

Wrote too much, I'll skip dorian.

Bob

--- In tuning@yahoogroups.com, Bob Valentine <BVAL@I...> wrote:

> I didn't see where Paul explains how he believes it is heard, but I
> will state some of how I believe that 12et mixolydian is heard.

On the paper Tuning, Tonality and 22-Tone Temperament.

> 1/1 [ 9/8 ] 5/4 4/3 3/2 [ 5/3 ] [ 16/9 ] 1/1
> [ 10/9 ] [ 27/16 ] [ 9/5 ]
>
> I have shown a few of the alternative JI pockets that we may think
> we are in based on what is happenning in the melody harmony.
>
> For instance, one spelling of a V- I7 cadence (if such a thing were
> used) would probably sound like
>
> 4/3 -> 5/4
> 9/4 -> 2/1
> 9/5 -> 9/5
> 3/2 -> 3/2
>
> However a bVImaj7 I7 cadence might sound like
>
> 20/9 -> 5/2
> 16/9 -> 16/9
> 5/3 -> 3/2
> 4/3 -> 1/1

Well, Paul talks about static tonality in relation to these modes in
his paper. I'm not sure what role cadences have in that kind of
thing.

> I guess my belief system is that unless we are really sitting in a
drone
> based music, the immediate references are more meaningful than the
tuning
> to a hypothetic root.

The drone stuff might be related to the concept of static tonality. I
believe mixolydian and dorian modes are well suited to jamming.

> So 16/9 looks big and complex, but if the immediate
> context has allowed us to resolve 4/3 of 4/3, then we aren't
hearing anything
> other than 3-limit. Similarly, all the intervals shown above are
simple 5-limit
> intervals in context to something that might have happened in the
music.
>
> I'm not a big fan of interpreting Western "sevnths" in the context
of
> 7-limit, since missing by 30c seems to be a bit of a stretch when
there
> are "references" lurking nearby that are much more in tune.

What I believe instead is that when the mixolydian mode is tonicized
the seventh is heard as consonant against the tonic. I think that
means it forms a (very) rough 7-limit tetrad with the tonic triad.
The tonicization (I'm not sure of the word) depends on the musical
context and maybe that would have to be droney.

> This tangentially refers to another thread with the opposite
phenomena, where
> iit was discussed the "augmented second" being more dissonant
> than the minor third despite being tuned identically in 12tet. It
is becuase
> any interpretation falls into a much different set of references
(since
> the b6 is the minor third of the 4 chord and the seventh is the
major
> third of the 5 chord).
>
> But thats just how I hear things. Yes, in a very droney context
mixolydian
> may be heard as having a 7/4, however, if this was any of the
tunings you
> were suggesting then (key of C) this Bb should NOT be played with G
or D
> or F since then much simpler interpretations will be heard.

I don't think it is necessary to avoid certain combinations. The
static tonality is possible in tonicized mixolydian because the
seventh doesn't form a dissonance against the tonic triad. It doesn't
matter if its interpretations change against other triads.

Kalle