Re: [tuning] Hello and a Question

Paul!

"Paul H. Erlich" wrote:

>
> Don't expect everyone on the list to agree with you. I don't. For example,
> how would you play a I-vi-ii-V-I progrssion in JI

Any way one wishes or is possible in JI. They are all musically useful and expressive in
different ways. I wouldn't want to give any of them up.

I would like to once again call attention to my own which like Helmholtz recognizes that
inversions are different. Formula=The sum of the pitches and the first order difference tone
but omitting any unison duplication. http://www.anaphoria.com/lullaby.html
contains the score that places all dyads though the tetrads found within the harmonic series
up to 12. This chart was put up to illustrate and serve as a model for discussion. As so often
the case with this list, the actual empirical examination by SOUND was ignored. I don't say it
is perfect as a model but is the most successful one I have found. I haven't found any use for
explanations that says G A# C D (6-7-8-9) and its inversion (from bottom to top) D A# G C are
of the same degree of Consonance.

There are several such distance measures, e.g., Euler's G.S., Barlow's

> digestibility, Wilson's harmonic complexity, and Tenney's harmonic distance.

I do not think that Wilson thinks of Harmonic Complexity as a real measure of
Consonance/disonance, just a loose guide. Somehow the question of devising a workable
measuring tool seems to have little interest to him.

> I'd be happy to discuss all this in greater depth, but there is one
> important problem with these lattice-based measures. Eventually you will
> find very distant intervals that are so close to consonant ones that one
> cannot audibly distinguish the difference. In such a scenario, what meaning
> is there to the vast difference between the "musical distances" of the two
> intervals?

This is true, but it is playing with numbers. If one was working in a tuning that contained
two such intervals, the musical context in which they would both occur at the same time is
almost non existent. One can superpose any interval up to an extreme till they equal any
interval one wants, but who is going to modulate that many places up till you get there.

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

"Paul H. Erlich" wrote:

>
>
> I wouldn't want to give up the melodic integrity of the meantone version, or
> of an adaptive version such as Vicentino's.

agreed

>
>
> >I would like to once again call attention to my own which like Helmholtz
> recognizes that inversions are different.
>
> To clarify for others, here you are referring to mirror inversions rather
> than inversions as in "first inversion, second inversion". The poster was
> asking about distances between two notes, and a two-note interval is the
> same as its mirror inversion.
>
> >Formula=The sum of the pitches and the first order difference tone but
> omitting any unison duplication.
>
> This will simply be twice the larger number in the ratio, since a + b + (a -
> b) = 2*a, unless the difference tone coincides with the lower tone, which it
> only does for the ratio 2/1, or with both tones as in 1/1. So, except for
> the unison and octave, Kraig's measure is the same as the "integer limit" of
> the ratio.

not quite. If we take my example of one of the inversions of the 6-7-8-9 and space it D=9
A#=14 G=24 C=32. in this inversion A# occurs as a 14 not a 7. Sorry if this was not clear.
Helmholtz examines triads on Pages 214-225 dover ed. In a way it might undermine the limit
idea. The difference tone of 23 occurs between the lowest and upper tones and plays a part in
this inversion sounding more harsh than simpler versions. For quite a number of years I
composed pieces based exclusively on the inversions of a chord. It is quite possible to build
up quite a bit of tension and relaxation. One of the (inversion) cataloging methods was an
adaptation of schrodingers Wave equation given to me by a quantum physicist. The formula is
now sadly lost ( I had to follow a guideline he gave me not necessarily understanding what i
was doing). although it did not produce an even consonance/disonance arrangement, I found the
results reflecting an order that was musically interesting. There seemed to be an underlying
logic to it all. maybe someone out there can reconstruct this one!!

>
>
> >>I'd be happy to discuss all this in greater depth, but there is one
> >>important problem with these lattice-based measures. Eventually you will
> >>find very distant intervals that are so close to consonant ones that one
> >>cannot audibly distinguish the difference. In such a scenario, what
> meaning
> >>is there to the vast difference between the "musical distances" of the two
>
> >>intervals?
>
> >This is true, but it is playing with numbers. If one was working in a
> tuning that contained two such intervals, the >musical context in which they
> would both occur at the same time is almost non existent. One can superpose
> any >interval up to an extreme till they equal any interval one wants, but
> who is going to modulate that many places up >till you get there.
>
> One only has to go up two 3/2s and two 5/4s to find an interval (with the
> 1/1) so close to 7/4 that the consonance of 7/4 greatly outweighs the
> largeness of the numbers in the actual interval, 225/128. That is only one
> of myriad examples.

Yes Terry Riley and Carl Lumma like to use this one. It all depends how long you hold the
sound. Personally i would rather use a 7/4 as a 225/128:)

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

D A# would still be interpreted as D=9 A#=14

"Paul H. Erlich" wrote:

> Those are tetrads. For dyads, which is what the poster was talking about,
> isn't the above correct?

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

"Paul H. Erlich" wrote:

> Yes, and the ratio 14/9 would still get a rating two times the higher
> number, since 14 + 9 + (14 - 9) = 28.

I love it when you play Plato!
Yes and this is the same rating as 14/11 and 14/13. These really don't sound so markedly
different to my ear. As a whole those that fall within a number or two apart, I cannot really
decide which is more consonant, but over the span of the whole material I can. This method I
came up by trial and error as i said for before. I tried as many ways of Categorizing played
though them and found this one the best . SO FAR. I expect those more cleaver than my self to
improve upon it .The problem I see with my own system (it includes most of the rest) is that
it is tied into the numbers of the harmonics in a way that might not be proportional to their
perceived dissonance. For example is 2 twice as dissonant as 1, is 13 13 times more
dissonance than 1, I don't think so. How to measure them I have not managed to do so. My
experiments with ways of scaling the initial numbered harmonics have resulted in the same
results via a different scale to get there. Any Ideas?

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Paul!
The method of examining the subject by questions , in the best cases getting the other to
come to your same conclusion. A compliment

"Paul H. Erlich" wrote:

> Kraig Grady wrote,
>
> >I love it when you play Plato!
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Kraig Grady wrote:

>
>
> "Paul H. Erlich" wrote:
>
>> Yes, and the ratio 14/9 would still get a rating two times the
>> higher
>> number, since 14 + 9 + (14 - 9) = 28.
>
> I love it when you play Plato!
> Yes and this is the same rating as 14/11 and 14/13. These really don't
> sound so markedly different to my ear. As a whole those that fall
> within a number or two apart, I cannot really decide which is more
> consonant, but over the span of the whole material I can. This method
> I came up by trial and error as i said for before. I tried as many
> ways of Categorizing played though them and found this one the best .
> SO FAR. I expect those more cleaver than my self to improve upon it
> .The problem I see with my own system (it includes most of the rest)
> is that it is tied into the numbers of the harmonics in a way that
> might not be proportional to their perceived dissonance. For example
> is 2 twice as dissonant as 1, is 13 13 times more dissonance than 1,
> I don't think so. How to measure them I have not managed to do so. My
> experiments with ways of scaling the initial numbered harmonics have
> resulted in the same results via a different scale to get there. Any
> Ideas?
>
> -- Kraig Grady
> North American Embassy of Anaphoria island
> www.anaphoria.com
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Hedy!
Yes, I confess, I wrote. somehow you didn't (Or did and something went wrong, which
happens) and i bet you had the answer to my problem:).

Hedy Sussmann wrote:

> Kraig Grady wrote:
>
> >
> >
> > "Paul H. Erlich" wrote:
> >
> >> Yes, and the ratio 14/9 would still get a rating two times the
> >> higher
> >> number, since 14 + 9 + (14 - 9) = 28.
> >
> > I love it when you play Plato!
> > Yes and this is the same rating as 14/11 and 14/13. These really don't
> > sound so markedly different to my ear. As a whole those that fall
> > within a number or two apart, I cannot really decide which is more
> > consonant, but over the span of the whole material I can. This method
> > I came up by trial and error as i said for before. I tried as many
> > ways of Categorizing played though them and found this one the best .
> > SO FAR. I expect those more cleaver than my self to improve upon it
> > .The problem I see with my own system (it includes most of the rest)
> > is that it is tied into the numbers of the harmonics in a way that
> > might not be proportional to their perceived dissonance. For example
> > is 2 twice as dissonant as 1, is 13 13 times more dissonance than 1,
> > I don't think so. How to measure them I have not managed to do so. My
> > experiments with ways of scaling the initial numbered harmonics have
> > resulted in the same results via a different scale to get there. Any
> > Ideas?
> >
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com