Re: [crazy_music] Triads

> FROM: mclaren
> TO: practical microtonality group
> SUBJECT: Triads
>
> Kraig Grady wrote
>
> "A question for anyone!
> "If one generates a scale by a chain of triads, what criteria is
> [sic] useful in determining a good point to stop and or what makes a
> cyclical point?"
>
> Erv Wilson has pointed out that it's conceptually simpler in just
> intonation to stop at a point where you get a 2-interval scale rather
> than a 3-interval scale. This would theoretically favor such
> Pythagorean tunings as 5, 7, 12, 17, 29, 41, 53, 94, etc.

It is only that i have ran accross some scales that could be explained
as a chain of triads that i posed the question. True 2 interval patterns
are conceptually simpler, but so on 1 interval patterns such as your
favorites ET's.

>

> However I have composed in both 17- and 19-note Pythagorean
> tunings, both 22-note and 29-note Pythagorean tunings. Although 17-
> note Py has a 2-interval structure (23.4 cents and 90.4 cents) while
> 19-note has a 3-interval structure, my ears don't hear any difference
> in terms of the overall comprehensibility of the scales.

> This has been my response to those 3 interval scales.

>

> The same applies to 1/4-comma meantone as opposed to 12-note
> Pythagorean, or the diatonic syntonon as opposed to 19 just 5/4s in
> the 2:1, etc. Once again 1/4-comma meantone is a 3-interval system
> while 12 note Pythagorean is a 2-interval system. Likewise the
> diatonic syntonon (1/1 9/8 10/9 1/615/ 9/8 10/9 9/8 16/15 in delta
> intervals) is a 3-interval system.
> In my hands-on musical experience, all this math proves entirely
> irrelevant to the actual sound of the tunings. I have no problem
> hearing or dealing with or composing with or listening to music in 3-
> interval tunings as opposed to 2-interval tunings.
> Thus the question of 3- interval as opposed to 2-interval tunings
> must be accounted a paper tiger, a theory quibbel with no connection
> to real tunings in the real world.

I would agree that theroy has no purpose unless one has a definite
application. The three interval patterns if structured from the
superposition of a triad is useful if one felt a compositional desire to
base something on a particular triad, maybe parellel or not. Not an
unusual desire.

>
> ------
> What other issues loom when we wnat to determine where to stop in
> generating a tuning?
> Presumably Kraig is talking about JI or NJ NET tunings, since
> once you have specified the number of equal steps into which an
> octave (or other interval) is divided you automatically know where to
> stop. If you divide the octave into 23 equal parts, thenyou stop at
> 23. So Kraig's question doesn't seem to have much bearing on equal
> divisions of the octave or non-octave cyclic multiplier.

correct

>
> In JI tunings the roughness of the tuning has some bearing. As
> you cojntinue to subdivide the octave by wrapping around at the 2;1
> the roughness of the JI tuning will decrease. That is, the ratio
> twixt largest and smallest musical intervals will drop.
> However, once again roughness of a JI tuning does not seem to
> have any audible consequences. 19 just 5/4s in the 2;1 has a fairly
> high roughness, with a 181-cent interval and a a 40-cent intervals.
> With a roughness of nearly 5, you might think this JI tuning would be
> musically useless. However, until Jeff Scott purged it, I had an MP3
> clip of a piece of music using 19 just 5/4s in the 2:1 and you could
> hear for yourself that there was no problem with composing or
> listening to such JI tunings where the largest elementary interval
> was much larger than the smallest elementary interval.
> Likewise, 17-note Pythagorean sounds great, even though the
> largest elementary interfval (90 cents) was about 4 times the size of
> the smallest elementary interval (23.4 cents).
> So the roughness of a JI tunig does not seem to have any bearing
> onthe sound or function of the tuning.
> ------
> The only musically relevant constraint in my experience invovles
> the size of the smallest interval in the tuning. If the smallest
> interval drops much below about 10-15 cents, it will no longer sound
> or function like a musically distinct interval. Instead, it will
> sound like a duplicate of the higher or lower adjacent pitch.

I remember that Ptolemy thought that interval smaller the 45/44. which
is quite a bit larger. Our ears must of improved over the centuries as i
believe as a rough model, this is close. We both know that context has
some being on this.

>
> This explains why in some of Erv Wilson's larger CPS tunings very
> small intervals (less tahn 6 cents) must simply be eliminated from
> the tuning... Because they just don't sound like melodic intervals.

In the 1-3-7-9-11-15 22 tone eikosany i have two 4.5 cent intervals
which when part of a tetrad cannot be replaced by the neighboring tone.
If one were to use this tuning independent of it structure. you might
leave them out. But I have gotten use to their preseance, kinda like
someone with so gestural twitch. Such twitches gives it a character
just like Et deviations from harmonics.

>
> -------
> The other obvious criterion involves whether the triads sound
> stable with sustained harmonc series timbres. If triads in the tuning
> beat very loudly with sustained harmonic series timbres, this can
> have musical consequences. It need not necessarily become muscialy
> important -- if your style does not make use of sustained harmonic
> series timbres, or if your music uses tone clusters, or if you crank
> up the tempo of your composition to a rapid speed, or if you use
> primarily percussive inharmonic timbres, then it won't matter whether
> your tuning has extremely acoustically rough triads when played with
> sustained harmonic series timbres.
> Under other circumstances, depending on the musical style of your
> composition and the timbres and tempi you favor, however, this might
> exert some musical influence.
> So depending on your compositional style and your tikbres and
> the tmpi you favor, the question of whether your tuning has extremely
> rough triads (when played with harmonic series sustained timbres at
> slow tempo) may become an issue.

The reverse is also true. that the tuning one picks has characteristics
unique to it own and if beats occur the artist should listen to them, if
they don't like what they are doing, find one they do.

>
> -------
> Dan Stearns posted a great many numbers in his discussion of
> triads in oddball ET tunings like 9 and 11 equal.
> I don't hear or see any relevance or musical meaning of just
> intonation triads to ET triads in 9 or 11.
> 9 equal is not a JI tuning. It is an equal division of the
> octave. As a result talking about an ET tuning like 9 equal in terms
> of just ratios seems as meaningless, in my musical experience, as
> talking about the uncle of the state of Kansas, or the color of the
> number 4. JI scales are JI scales. They exist in one kind of musical
> universe. ET scales are ET scales, and they exist in another kind of
> musical universe.

Agreed. Ets can produce phenomenon unlike JI and this might as well be
exploited. I will venture to say that much happens that we can't
explain, some which might always remain explainable, yet some which
somedays we might be able to explain

>
> Trying to discuss equal divisions of the octave in terms of their
> purported approximations of this or that JI construction is in my
> musical experience as meaningless as trying to talk about a JI tuning
> in terms of its purported approximation of
> intervals like 2^[4/12].

well here we different

>
> There is just no musical connection between the two. In my
> musical experience with both 9 and 11 equal and a variety of
> different JI limits, trying to describe equal divisions of the octave
> in terms of JI constructions like "the 11:13:15 triad" represent
> nothing but confusion and a musical dead end.

in this meaning i agree.

>

>
> An equal division of the octave is not a degenerate version of
> a JI tuning. An ET is not ANY version of a JI tuning.
> Equal tunings like 9 equal and 11 equal are what they are --
> equal divisions of the octave. In order to deal with these tunings
> effetively, my musical experience has been that we must throw out
> attempts to falsely view them as warped or
> twisted or otherwise distorted JI tunings, because they aren't.

Each tuning should be dealt with what it is empirically

>
> Each ET has its own musical properties, its own musical
> advantages and disadvantages.
> In my musical experience there is no "get rich quick scheme" that
> will magically tell us what the musical properties of equal
> divsisions of the octave are. Not MOS scales, not comparison of
> triads in the ET with some JI construct like 11:13:15, nothing.
> The *O*N*L*Y way to learn the musical properties of any given
> equal division of the octave, in my experience, is to compose with
> that ET and listening to music in that ET.
> Math is useless. JI comparison are useless.

maybe misapplied but not uselss

> Quasi-evolutionary
> theories like Yasser's are useless.

western turning did at least evolve from a 7 tone system to a 12

>
> Only composing in and listening to music in the ETs in question
> actually yields meaningless knowledge about the musical properties of
> that equal division of the octave.
> (The same applies to JI and NJ NET tunings.)
> --------
> The other big problem with trying to discuss ETs in terms of
> their purported approximation of JI constructs like "the 11:13:15
> triad" is that such JI constructs do not tell you whether you will
> get strong beats in the critical band with sustained harmonic series
> timbres. Such JI constructs also do not tell you whether you will
> get recognizable perfect fifths

> Math cannot predict whether the ET will have recognizable perfect
> fifths.

I have heard ET that sound much better than paper can predict. 34 for
one. possibly the formula for evaluating needs to be changed. i don't
think we throw out newton because it can't explain the orbit of mercury.

> Math always fails.

math always falls short of the real life experience

>
> In 9 equal, the perfect fifth does sound musically recognizable
> at 666.66 cents....but in 18-equal, with the exact same size "perfect
> fifth," the fifth does NOT sound musically recognizable.

I liove thing like this

>
> Because Dan Stearns' procedure of comparing ET tunings with JI
> constructs blots out such important musical information as whether
> the triad in question beats strongly within the critical band, and
> whether the triad in question has recognizable perfect fifths, in my
> experience the attempt to compare ET tunings with JI constructs is
> worthless.

possibly insufficient in data

>
> This, incidentally, is why John deLaubenfels' effort to
> adaptively retune compositions into 5-limit JI typically produces
> results that sound repugnant to many listeners. Delaubenfels is
> trying to use the 4:5:6 triad as a musical yardstick for major chords
> under all musical circumstances, and like Dan Stearns effort to use
> other types of JI constructs (the 11:13:15 triad, etc.) as musical
> yardsticks, this simply fails.

I sense that what John is going at is what string players do when they
play, adapt by ear to a myriad of acoustical situations expressive
goals. Where i have a problem is that I sense that do to the language
and function of different elements that make up tonal music, Certain
things like Dominants might have rules "all their own". what we want
these chords to do is not what we want others to do, i sense we intuit
different intonations for there use. Still we proceed we models that
work in some cases and others come along and finish our shortcomings.
Sometimes the question is more important than the answer and i see no
reason why such endeavors as John's might not lead to unexpected uses.
Look at Margo's work, Who would of guess that such monomaniacal (
and i do mean this lovingly and repectfully) focus on 13th century
music of not only the west but of the church in the west could lead to
where it has for her.
Sometimes the only way to make progress is to regress backward to a
previous step and start from there. Partch felt the need to go back to
the Greeks, an extreme but possibly making it easier for margo to go
back 700 years.

>
> The human ear/brain doesn't work that way. There are no small
> integer ratio detectors in our heads. In fact there are no integer
> ratio detectors in our heads at all -- period.

There is no conclusive evidence of this, against your findings i will
put for Boomliter and Creel.

> We hear in terms of
> logarithmic pitch distance, and we hear vertical intervals in terms
> of melodic and harmonic context and beats within the critical band.
> Trying to find out about ET tunings by comaring them with JI
> constructs, whether those constructs be 4:5:6 triads or 11:13:15
> triads, is in my experience musically meaningless and musically
> useless.
> So what works?
> Composing in those ETs and building upa set of rules of thumb.

Likewise there are things in JI tunings that lie outside of the math
that are just as useful.

>
> Perhaps Dan Stearns would upload 2 compositions each in 9 equal
> and 11 equal so we can hear what he's doing with those tunings
> musically. IIn my experience, the sound of a mode or triad proves
> infintiely more informative than sets of silent numbers.
> Ditto Robert Valentine, who also posted plenty of numbers.
> Perhaps Robert Valentine would upload some musical examples so we can
> hear clearly what he's discussing.

See i read it all

>
> -------------
> --mclaren

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

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