Young's 9:7:4 and high primes, a proposed experiment

I earlier agreed that large integers were probably important for the effect of La Monte Young's 9:7:4 installation, but asked for someone to explain why they needed to be prime (or at least having few prime factors other than 2's). No-one has been forthcoming in this regard, and having examined the numbers involved I can't conceive of any reason myself.

I propose the following experiment:
Add one to all the numbers greater than 19 in La Monte's installation. This will mean that all the primes will become non-prime, and only a very few non-primes will become prime, while preserving most of the difference tones.

I don't have the resources to try this myself. Maybe some Dream House staffer can try it after-hours. One could also try *subtracting* one from all the numbers greater than 19. Or indeed from *all* the numbers.

It will of course be different, but I predict that it will be no less interesting for the loss of all those primes.

Of course, to be a serious experiment it would need a bevy of volunteer listeners, who had never heard the original installation before and were presented with the two in random order and not told which had more primes, to record their preference and the strength (or lack) thereof.

If someone's sure that this won't work. Please explain why? What's the theory?

Incidentally I still haven't got a straight answer as to what frequency the lowest first-order ('real') tone is. Nor have I been able to extract any "symmetry" from the numbers, except for a very rough mirror symmetry of the (first order) pitch distribution.

In general, I am interested in evidence anyone might know of, that primes greater than 19 have any particular significance for music (over similar sized non-primes). Or that ratios involving primes greater than 19 have any musically significant distinction from nearby ratios involving only lower primes (and their products with powers of 2).

-- Dave Keenan
http://dkeenan.com

Dave
simply put primes are the rungs of the ladder of the Harmonic spiral. The prime opens up an entire new mode revealing new identities a main example being the 7/4 or 7th harmonic. If we had stayed with the 5 limit we would never gotten this new identity. You simply must have prime #s to advance up the spiral. And I do not think anyone at Dreamhouse will be
tampering with Lamonte's Installation. 11 reveals new tones almost all new except for the 11/11 22/11 0r 11/1 of course and then 13 and 17 are similar in their New Music Resources.
I hope this helps.

Dave Keenan wrote:

> From: Dave Keenan <d.keenan@uq.net.au>
>
> I earlier agreed that large integers were probably important for the effect of La Monte Young's 9:7:4 installation, but asked for someone to explain why they needed to be prime (or at least having few prime factors other than 2's). No-one has been forthcoming in this regard, and having examined the numbers involved I can't conceive of any reason myself.
>
> I propose the following experiment:
> Add one to all the numbers greater than 19 in La Monte's installation. This will mean that all the primes will become non-prime, and only a very few non-primes will become prime, while preserving most of the difference tones.
>
> I don't have the resources to try this myself. Maybe some Dream House staffer can try it after-hours. One could also try *subtracting* one from all the numbers greater than 19. Or indeed from *all* the numbers.
>
> It will of course be different, but I predict that it will be no less interesting for the loss of all those primes.
>
> Of course, to be a serious experiment it would need a bevy of volunteer listeners, who had never heard the original installation before and were presented with the two in random order and not told which had more primes, to record their preference and the strength (or lack) thereof.
>
> If someone's sure that this won't work. Please explain why? What's the theory?
>
> Incidentally I still haven't got a straight answer as to what frequency the lowest first-order ('real') tone is. Nor have I been able to extract any "symmetry" from the numbers, except for a very rough mirror symmetry of the (first order) pitch distribution.
>
> In general, I am interested in evidence anyone might know of, that primes greater than 19 have any particular significance for music (over similar sized non-primes). Or that ratios involving primes greater than 19 have any musically significant distinction from nearby ratios involving only lower primes (and their products with powers of 2).
>
> -- Dave Keenan
> http://dkeenan.com
>
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From: Dave Keenan <d.keenan@uq.net.au>

>I don't have the resources to try this myself. Maybe
>some Dream House staffer can try it after-hours.

We just turn the sound and lights up. The synth is
located downstairs in La Monte's apt.

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
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Dave
I agree that the super-particulars are difficult to hear initially
but sustained exposure say oh well 5 hours to a continous sine environment you will definitely begin to "feel' the difference
What I was getting at is higher primes in and of themselves say 31 or 29 are needed to advance up the spiral. and in Mr. Youngs pieces some of the fundamentals are sometimes 10 octaves below the lowest note on a bosendorfer(The Well tuned piano-10octs below the low Eb) so these close relationships are more apparent. So the presence of 126hz in relation to a 128hz (The Obsidian Ocelot..) is definitely a feeling before it is an audible idetification.
I am not necessarily interested in say a 22/21 as much as just the 21 or 31 or 17 as a frequency definition. The 17,19 or 31 of any fundamental whether that be 10 or twenty octaves below something is going to have a unique, un-mapped sound. And the regular folk might not be able to tell a 16/15 from a 17/16 but hey I can and through some consistent exposure a normal listener will be able to feel then hear the diifie.And eventually the 28/27 and there we are past 19.
I really don't think there's an argument here --the harmonic spiral(dna) however you would like to define it-- just is--
"No why-just a dip" or if that is too oriental for ya "The Universe works whether we understand it or not"--FZ. And if you use A at 440 which is a waste of time anyway because we know A is around 426 of course you'll get infrapoop.
And I cannot comment on altering the Dreamhouse tuning as I am not in contact with Mr. Young but I probably would have to vote_"BLASPHEMER".

Dave Keenan wrote:

> Any chance you can pass my original question and suggested experiment on to La Monte, and report his response? Or does my suggestion amount to blasphemy?
>
> Regards,
> -- Dave Keenan
> http://dkeenan.com
>
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David,

You must have missed, or misunderstood, where I said "fizzles out somewhere around 19".

David Beardsley <xouoxno@virtulink.com> wrote:
>Read Genesis of a Music by Harry Partch. He explores
>the difference of primes.
>
>Tune a synthesizer to a five limit tuning.
>Tune a synthesizer to a seven limit tuning.
>Tune a synthesizer to a eleven limit tuning.
>Tune a synthesizer to a thirteen limit tuning.
>
>Now. Can you describe what sounds different about these tunings?
>
>Does eleven sound ugly? Do seven or five sound beautiful?
>Describe why five and seven sound different.
>
>So what do you think now?

I'm already convinced of the (successively diminishing) significance of primes up to 19.

Regards,
-- Dave Keenan
http://dkeenan.com

Dave Keenan:

Could you review for us, once, your rationale for stopping at 19?

Daniel Wolf
Frankfurt

<I'm already convinced of the (successively diminishing) significance of
primes up to 19.
<
<Regards,
<-- Dave Keenan

Daniel Wolf <DJWOLF_MATERIAL@compuserve.com> wrote:

>Dave Keenan:
>Could you review for us, once, your rationale for stopping at 19?

I will first repeat what I wrote earlier (with minor editing):
---------------------
I understand that this fizzling out [around 19] is because, for example, few people can distinguish a frequency ratio involving 23 from nearby ratios having smaller numerator and denominator. Note that for intervals smaller than a twelfth (3/1) there is always such a lower-numbered ratio within 8.4 cents of any ratio of 23. Some are as close as 2.8 cents. Apart from human discrimination, the 23rd partial of many natural timbres, if it has a significant amplitude at all, could easily differ from 23 times the frequency of the fundamental by a similar number of cents.

I agree that using sustained sine tones, and playing them at high amplitudes or passing them thru a non-linear system, will emphasise the difference tone effect, and play down the coincidence of harmonics. This may allow people to distinguish ratios near 1, such as 23/22 from 22/21. This is because the pitch change in the difference tone is (in this example) about 22 times that of the change in one of the original tones (assuming that only one tone changes). You get a kind of leverage by working near 1/1. (Note that if the tones of a 23/22 are below A(440Hz) the difference tone will below 20Hz (infrasonic) and may be perceived more as roughness). But please note that the above effect does not give any special role to primes.

Once we are depending on difference tones rather than coincidence of harmonics for our musical distinctions, primeness, (and beyond 19, even integer-ness), becomes irrelevant. I expect that, to most people, the difference between 23/22 and 22/21 is much the same as the difference between 22/21 and 21/20 or 22/21 and 21.04348/20.04545, if they have the same difference tone.

As I understand it, the reason low primes are important in ordinary music with ordinary timbres is that, for example, when the 2nd harmonic of one note coincides with the 3rd harmonic of the other you also get the 4th harmonic coinciding with the 6th, the 6th with the 9th, the 8th with the 12th, the 10th with the 15th. You get all these others for free. This removes *many* pairs of harmonics from contributing to dissonance via critical band roughness.

When the 23rd harmonic of one tone coincides with some other harmonic of the other tone, we also get the 46th harmonic (if it exists) coinciding for free. Big deal! (Note that the 46th harmonic of A(440Hz) is ultrasonic).
---------------------

I admit that the above is based more on received authority than personal experience. My personal experience would have put the cuttoff (not that there is any definite one) at 13 rather than 19 but I now accept that barbershop chords include ratios of 17 and 19.

I don't believe that any significant music exists where any part of its significance *depends* on a ratio involving primes greater than 19. Which is why I proposed the experiment which will remove the large primes from La Monte Young's 9:7:4 in a way that I expect will not diminish its significance. (namely by adding one to every multiplier).

I just searched the index to Manuel Op de Coul's marvelous scale library http://www.tiac.net/users/xen/scala/scales.html and found ony one scale (out of more than 2000) described as a higher-than-19-limit scale. It is:
JI_22C.SCL 31-limit rational interpretation of 22-tET, Marion McCoskey

Regards,
-- Dave Keenan
http://dkeenan.com

>From: Dave Keenan <d.keenan@uq.net.au>

>I don't believe that any significant music exists where any part of its
>significance *depends* on a >ratio involving primes greater than 19. Which
>is why I proposed the experiment which will remove the >large primes from
>La Monte Young's 9:7:4 in a way that I expect will not diminish its
>significance. >(namely by adding one to every multiplier).
>

I went to the installation a couple of weeks ago. It was very interesting,
particularly for the way even slight head movements change the sound. There
are two main areas of sound, a mass of sine tones in a low frequency
region, and another at a high frequency region. The low frequency sounds
reminded me of what I got when I had Csound generate some of the suns
spherical harmonic frequencies, and that got me to wondering if particular
sets of frequencies will have a particular sound, or if it is not a general
effect of massed sine tones that are beating with one another that would
sound pretty simillar no matter what particular frequencies were used. That
is: is there anything special about the frequencies chosen, or would other
sets of frequencies of similar density produce similar (although not
identical) effects. I tend to think a sound sculpture like this is painted
in rather broad strokes and being overly concerned with details might just
be intellectual masturbation.

The large cabinets in the four corners of the room (with what seem to be
two-foot woofers) face the walls with about six inches of clearance. If you
go there, be sure to stick your head into the space between the speaker and
the wall. You won't be disappointed!

dante

One instance I know of use of the 23 is in the dominant chord where you
have the 9- 23- 32. Difference tones are not an effect, they are an
inescapable phenomenon!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

It's been my experience in comparing
different tunings of static chords (which
is what La Monte Young's "Dreamhouse" is)
that even when the difference in tuning
is less than 1 cent - i.e., below the threshold
of audible perception - I still detect an
unusual difference in the sound.

In a complex chord, with complex timbres,
(note that Young uses sine waves)
there is a kind of swirling sound resulting
from not just the harmonies themselves, but
also from the audible summation tones,
and it is decidedly different with even
very minute changes in pitch.

If your sound card or MIDI sythn is good
enough, you may be able to hear this in the
excerpt from my "Hendrix Chord" piece on
my website. The chord starts as 12-equal,
then pitch-bends up to a just chord, which
gets higher in pitch each time it bends.
(The just chords which are really close in
pitch are actually the first few which are
not on the web excerpt, but you may still
hear the effect.)

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html
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Kraig Grady <kraiggrady@anaphoria.com> wrote:
>One instance I know of use of the 23 is in the dominant chord where you
>have the 9- 23- 32.

I'm not sure what you are saying here Kraig. Are you saying that the dominant seventh chord (in 12-tET?) relies for its effect on its proximity to 18:23:27:32? I note that 23/18 is 24 cents wider than the 12-tET major third, so maybe you're saying that barbershop quartets sing these ratios?

I note that 18:23:27:32 has a prime-limit of 23 and an odd-limit of 27. It has difference tones of 4, 5, 9 and 14. Only the 4 and the 9 are octave-equivalent to tones of the chord (the m7th and root respectively).

Why not 20:25:30:36 which has a prime-limit of 5 and an odd-limit of 25?
It has difference tones: 5, 6, 10, 11, 16. The 5 and 10 are octave-equivalent to the root.

Or 36:45:54:64. Differences 9, 10, 18, 19, 28. 9 and 18 = root.

Ok, I guess I'll have to listen to them to see if I can distinguish them from each other and everything else in between.

I guess I'd better throw in 14:18:21:25 and 16:20:24:29 as well. How about 7:9:11:13, probably a bit extreme? I suspect we have to keep the fifth as 3/2, keep the M3rd between 5/4 and 9/7 and the m7th between 7/4 and 29/16. We already know 4:5:6:7 is quite distinct, so we can leave it out.

Are there any other candidates for dominant 7th chord? Anyone want to vote for any of those above?

Just looking at the numbers it is difficult to see why anyone would prefer one over another, unless it were due to mental saturation by 12-tET or a specific musical context. (I think 36:45:54:64 is closest to 12-tET and most likely to be required by context).

>Difference tones are not an effect, they are an
>inescapable phenomenon!

Yes. Perhaps I made an unfortunate choice of words. I said in an earlier post that they were "real". Can't one still refer to the "effect" that a physical phenomenon has on the mind?

Regards,

-- Dave Keenan
http://dkeenan.com

>From: Dave Keenan <d.keenan@uq.net.au>

>I don't believe that any significant music exists where any part of its
>significance *depends* on a >ratio involving primes greater than 19. Which
>is why I proposed the experiment which will remove the >large primes from
>La Monte Young's 9:7:4 in a way that I expect will not diminish its
>significance. >(namely by adding one to every multiplier).
><

In my experience, these kinds chords turn out to be extremely sensitive. I
did a series of installation in Kiel, Germany and Zug, Switzerland that
involved similar structures to La Monte Young's. Moving the pitches up or
down a place in the series as I tested for room resonances really deadened
the shimmering effect these things have. I also had great difficulties
making DAT or CD recordings of the pieces. I actually ended up transposing
them into the 'key' of the DAT sampling rate and going into a big studio
where a Tonmeister was able to synch the Rayna to the DAT.

>From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
>In my experience, these kinds chords turn out to be extremely sensitive. I
>did a series of installation in Kiel, Germany and Zug, Switzerland that
>involved similar structures to La Monte Young's. Moving the pitches up or
>down a place in the series as I tested for room resonances really deadened
>the shimmering effect these things have.

Are you saying that you avoided or exploited the resonant frequencies? I
look forward to hearing your CD.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Daniel Wolf <DJWOLF_MATERIAL@compuserve.com> wrote:

>In my experience, these kinds chords turn out to be extremely sensitive. I
>did a series of installation in Kiel, Germany and Zug, Switzerland that
>involved similar structures to La Monte Young's. Moving the pitches up or
>down a place in the series as I tested for room resonances really deadened
>the shimmering effect these things have. I also had great difficulties
>making DAT or CD recordings of the pieces. I actually ended up transposing
>them into the 'key' of the DAT sampling rate and going into a big studio
>where a Tonmeister was able to synch the Rayna to the DAT.

But do the numbers that work for any given room, always favor primes, no matter how large?

Why should you expect them to be recordable. I'd expect problems that have nothing to do with sample-rates. Surely these things *depend* on the room and the ability of the listener to walk around the space and experience the changes.

Regards,
-- Dave Keenan
http://dkeenan.com

Message text written by INTERNET:tuning@onelist.com
>But do the numbers that work for any given room, always favor primes, no
matter how large?

Why should you expect them to be recordable. I'd expect problems that have
nothing to do with sample-rates. Surely these things *depend* on the room
and the ability of the listener to walk around the space and experience the
changes.

Regards,
-- Dave Keenan
http://dkeenan.com
<

In general, I tried to find a very low frequency in the room to serve as a
'missing' fundamental, and above this pitch, tried to avoid coincidences
between the room resonances and the sine wave freqencies. This is almost
impossible with the kinds of clusters I like, but this can be nuanced a bit
by attenuating the sine waves in question .

My initial rationale for avoiding the room resonances was that I was
interested in using the the standing waves to create an alternative,
audible architecture within the gallery space, and wanted this to be as
distinct from the bricks and mortar construction as possible. As I worked
more with these materials, I found that they projected best when the room
resonances were avoided.

My impression -- and I claim nothing more than a subjective impression --
remains that using prime or relatively prime relationships make the
individual pitches more distinct. Move things up or down the series by an
integer and it starts to get muddy. You really have to try it yourself.

Daniel Wolf wrote,

>My impression -- and I claim nothing more than a subjective impression
--
>remains that using prime or relatively prime relationships make the
>individual pitches more distinct. Move things up or down the series by
an
>integer and it starts to get muddy. You really have to try it
yourself.

I would be willing to believe that _relatively_ prime relationships
(i.e., lowest terms) matter here. If you move things up or down the
series by an integer, you will make a lot of the relationships fail to
be in lowest terms, so they will imply a fundamental at multiples (i.e.,
harmonics) of the system fundamental. If all these fundamentals are
actually heard (which is possible through the virtual-pitch phenomenon),
then there will be more pitches, and thus a muddier texture, than if all
relationships are in lowest terms (in which case they all imply the same
fundamental).

Dave Keenan wrote:

>
>
> I'm not sure what you are saying here Kraig. Are you saying that the dominant seventh chord (in 12-tET?) relies for its effect on its proximity to 18:23:27:32? I note that 23/18 is 24 cents wider than the 12-tET major third, so maybe you're saying that barbershop quartets sing these ratios?
>
>

Erv wilson pointed this one out to me as what string players do when they raise the leading tone!
I mention it merely to point out how a higher harmonics might be all round us already in paying all those european artifacts! BTW I just heard from the ghost of Harry Partch the other night, He said,
"Offer them freedom and all they want is to be Enslaved!"
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Kraig Grady <kraiggrady@anaphoria.com> wrote:

>Dave Keenan wrote:
>
>> I'm not sure what you are saying here Kraig. Are you saying
>>that the dominant seventh chord (in 12-tET?) relies for its
>>effect on its proximity to 18:23:27:32? I note that 23/18 is
>>24 cents wider than the 12-tET major third, so maybe you're
>>saying that barbershop quartets sing these ratios?

>Erv wilson pointed this one out to me as what string
>players do when they raise the leading tone!
>I mention it merely to point out how a higher harmonics
>might be all round us already in paying all those european
>artifacts! BTW I just heard from the ghost of Harry Partch
>the other night, He said,
>"Offer them freedom and all they want is to be Enslaved!"

You're a riot Kraig - and I agree! We have this infinite array
of tuning resources available to us and there's always
someone who has to limit that array and give some reason why
composers and musicans can't use those upper limit primes.
In this day of micro-tunable synthesizers, give me a solid
reason why we can't advance up the harmonic series?

It's there
for you to use folks! The sky isn't even the limit! There is
no limit - the possibilities are infinite!
Why stop at the 19th harmonic? Or even 2001?

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* J u x t a p o s i t i o n E z i n e
* M E L A v i r t u a l d r e a m house monitor
*
* http://www.virtulink.com/immp/lookhere.htm