Re: Digest Number 222

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> From: tuning@onelist.com [SMTP:tuning@onelist.com]
> Sent: Friday, June 18, 1999 5:12 AM
> To: tuning@onelist.com
> Subject: [tuning] Digest Number 222
>
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> There are 24 messages in this issue.
>
> Topics in today's digest:
>
> 1. Re: Digest Number 221
> From: John Starrett <jstarret@math.cudenver.edu>
> 2. Re: Chant, resonanant spaces, medieval polyphony etc.
> From: "David J. Finnamore" <dfin@bellsouth.net>
> 3. Re: list archives from last August
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> 4. More on 9-notes scales
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> 5. Re: Chant, resonanant spaces, medieval polyphony etc.
> From: "David J. Finnamore" <dfin@bellsouth.net>
> 6. Unaccompanied Singers Intonation
> From: monz@juno.com
> 7. Re: Intonational politics and 9:8, etc.
> From: "David J. Finnamore" <dfin@bellsouth.net>
> 8. Buckminster Fuller lattice designs
> From: monz@juno.com
> 9. Lattice visualization of music in real time
> From: monz@juno.com
> 10. Re: 9-limit triangular lattices
> From: Dave Keenan <d.keenan@uq.net.au>
> 11. Encapsulated PostScript for Just Intonation
> From: "Canright, David" <dcanright@monterey.nps.navy.mil>
> 12. Re: The Beethoven piece and AJI
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 13. Re: Undertones/subharmonics (?) esp. vocal
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 14. The term "Adaptive Just Intonation"
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> 15. Re: pythagorean third
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 16. Re: the "7 +/- 2" rule
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 17. Re: Query
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> 18. Re: Unaccompanied Singers Intonation
> From: rtomes@kcbbs.gen.nz (Ray Tomes)
> 19. Effects of sound on consciousness
> From: rtomes@kcbbs.gen.nz (Ray Tomes)
> 20. Re: the "7 +/- 2" rule
> From: "D. Stearns" <stearns@capecod.net>
> 21. Re: Effects of sound on consciousness
> From: Patrick Pagano <ppagano@bellsouth.net>
> 22. Re: Effects of sound on consciousness
> From: "Dale Scott" <adelscot@onr.com>
> 23. Re: Query
> From: "Dale Scott" <adelscot@onr.com>
> 24. Re: More on 9-notes scales
> From: "D. Stearns" <stearns@capecod.net>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 1
> Date: Thu, 17 Jun 1999 09:03:44 -0600 (MDT)
> From: John Starrett <jstarret@math.cudenver.edu>
> Subject: Re: Digest Number 221
>
> Ray Tomes said
> <snip>
> > Right. One reason that I have been a bit slow responding is that I was
> > taken aback when someone (sorry I forget who) said that I was wrong and
> > that chaos frequency doubling does add lower frequencies. Now that I
> > think about it the mathematical cases of chaos do in fact do that, so I
> > was wrong to say that was not so. However I will have another go at
> > putting my foot in it and say that I think that real world, continuous
> > systems do show frequency doubling and not frequency halving behaviours
> > - which is presumably why they call it frequency doubling.
> >
> I'm not sure what you are referring to, but I thought Paul E. was talking
> about period doubling behavior (therefore frequency halving). Certainly
> coutinuous chaotic systems exhibit period doubling and period halving
> depending on the way the parameter is being twiddled. I had a neat paper,
> which of course I cannot now locate, using template analysis on vocalized
> vowels to exhibit natural strange attractors in normal speech. If ordinary
> vowels are strange attractors of the vocal chords, then controlling a
> period two imbedded in the attractor would result in a true subharmonic.
> Is it possible that throat singers use this technique?
> > >I would like to make a recording of this phenomenon and send it to
> whomever on this list
> > >is interested in listening to it, analyzing, etc. I guess cassette is
> the easiest for me
> > >to make. I am really interested to get your feedback on these sounds -
> any takers?
> I would love to have such a recording. Is it possible to send me a wave
> file as an attachment?
> > Yes please. I am in New Zealand, so sending a WAV file might be
> > easiest, but if you want to use post my address is:
> > Ray Tomes, 59 Maritime Tce, Birkenhead, Auckland, New Zealand.
> <snip>
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 2
> Date: Thu, 17 Jun 1999 10:20:16 -0500
> From: "David J. Finnamore" <dfin@bellsouth.net>
> Subject: Re: Chant, resonanant spaces, medieval polyphony etc.
>
>
> Paul H. Erlich wrote:
>
> > 81/64 would probably occur with a rather large error. I wouldn't be
> > surprised if it occasionally came out as small as 5/4 or as large as 9/7
> in
> > medieval practice. Harmonic thirds were not stable sonorities so they
> went
> > by fairly quickly in the music, too quickly for much accuracy to be
> > attained.
>
> In polyphony, yes. In plain chant, "harmonic," "stable,"
> and "quickly" are less relevant concepts to the abstract
> composition, though possibly not to the performance in a
> highly resonant environment. It's not at all uncommon in
> plain chant to have a phrase like:
>
> C C D E E D E F E D E D
>
> which would cause the Es to be sung over the reverb of the
> Cs. In such as case, the simple 5-limit tetrachord
>
> 1/1 9/8 5/4 4/3
>
> would produce maximum consonance for the singers' ears, not
> Pythagorean, and certainly not a 9/7 between the C and E.
> It would surprise me less in such a case to hear a 10/9
> between the C and D (and 9/8 above) than to hear a stack of
> 9/8s. Now if you get a short enough reverb that the Cs are
> almost inaudible by the time the Es arrive, then 5-limit
> probably has as little chance as Pythagorean.
>
> Paul, you've been very helpful in clearing up
> misunderstandings and factual errors, and you've stated that
> you disagree with my conclusion, but you haven't said why.
> Or maybe I just can't read what's between your lines? I'm
> not firmly decided on the issue yet, BTW. Just exploring
> the possible validity of the supposition, and leaning
> somewhat toward it for plain chant.
>
> > In principle though, the logic of the scale was Pythagorean, so
> > the "target" for the major third would be 81/64. The implied
> fundamental, or
> > lack thereof, has absolutely nothing to do with it.
>
> I agree with that. Neither Dan nor I was trying to say that
> it does. My purpose in bringing it up was to show that it
> doesn't. Dan had seemingly compared 5/4 to 9/8, and I felt
> that was not a valid, since they represent two different
> intervals. Later he explained more thoroughly what he
> meant, and it was not what I had taken it to mean, so my
> "argument" served only to prompt a clearing up of what was
> being said, as in fact it was designed to do.
>
> David
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 3
> Date: Thu, 17 Jun 1999 10:42:40 -0500 (CDT)
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> Subject: Re: list archives from last August
>
> On Wed, 16 Jun 1999, D. Stearns wrote:
> > [Paul Hahn:]
> >> Search the list archives from last August. Look for the word
> >> "nonatonic".
> >
> > How exactly would I go about this? Where are the pre `99 digests
> archived?
>
> Y'know, that's a better question than I realized. The mills archive
> apparently doesn't go past '95 or '96, for some reason. I had thought
> that somebody else was taking up the slack and archiving them on a
> website, but I could be wrong--Joe Monzo only has a select few digests,
> and the Xenharmonikon website, where I had thought Jon Pusey was
> collecting them, doesn't seem to have them after all.
>
> In the meantime, I've appended a few relevant messages of mine.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Hey--do you think I need to lose some weight?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
> *** BEGIN APPENDIX(-AGE? 8-)> ) ***
>
> >From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
> Date: Thu, 6 Aug 1998 06:39:19 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: tuning@eartha.mills.edu
> Bcc: Rosemary Hahn <hahn@wulaw>
> Subject: RE: Scales and Numerology
>
> On Wed, 5 Aug 1998, Paul H. Erlich wrote:
> > Paul Hahn wrote,
> > >Interesting. I've lately been toying with a 9-out-of-31 scale.
> >
> > Care to let us in on it?
>
> Well, I'm still working out the details, plus I lack a means at the
> moment to tune it up and listen to how it sounds so my toying at the
> moment just means working out theoretical quirks, but the basic scale is
> 4-4-2-5-3-3-4-3-3. In the 3, 5, 7 lattice it looks like this:
>
> 6/5 --- 3/2 ---15/8
> / \ / \ /
> / \ / \ /
> / 7/5 \ / 7/4 \ / 35/32
> 8/5 --- 1/1 --- 5/3
>
>
> 28/15
>
> The pivotal pitch of the scale is pitch 28 out of 31, represented twice
> by 15/8 and 28/15 (separated by 225/224), this scale's equivalent of the
> supertonic in that it relates the "dominant" and "subdominant" harmonic
> regions to each other. There are only two complete Otonal 4:5:6:7
> tetrads, but a nice distribution of (Otonal and Utonal) 4:5:6 and 4:5:7
> triads.
>
> Eventually I plan to generalize the nonatonic framework by fixing the
> 1/1, 5/4, and 8/5 as the boundaries of three tetrachords, within which
> the other scale degrees can vary as long as they form 8/7s, 7/6s or 6/5s
> with those three "framework" pitches--but first I have to find a new
> instrument, or figure out how to get one of my existing ones to work for
> microtonality. Frankly, my theorizing has never made it to this stage
> before.
>
> Oh, John and Daniel--I know full well numerology is a bunch of hooey.
> My father is a mathematician, after all. But in this case it's kind of
> fun to speculate on what subconscious or cultural influences may have
> been at work. F'rinstance, cats have nine lives and I love cats, and as
> I mentioned before nine is significant in Norse mythology, which I have
> been interested in for a long time. Here's a quote from _The Norse
> Myths_, by Kevin Crossley-Holland:
>
> Nine worlds encompassed by the tree (which so becomes a symbol
> of universality known to mythologists as the World Tree); nine
> nights hanging on the tree; the number nine recurs again and
> again in Norse mythology. Odin learns nine magic songs from a
> giant that enable him to win the mead of poetry for the gods;
> Heimdall has nine mothers; Hermod, Odin's son, journeys for nine
> nights in his attempt to win back the god Balder from Hel; the
> great religious ceremonies at the temple of Uppsala lasted for
> nine days in every ninth year, and required the sacrifice of
> nine human beings and nine animals of every kind. Why nine was
> the most significant number in Norse mythology has not been
> satisfactorily explained, but belief in the magical properties
> of the number is not restricted to Scandinavia. In _The Golden
> Bough_, J.G. Frazer records ceremonies involving the number nine
> in countries as widely separated as Wales, Lithuania, Siam and
> the island of Nias in the Mentawai chain. Nine is, of course,
> the end of the series of single numbers, and this may be the
> reason why it symbolises death and rebirth in a number of
> mythologies; hence it also stands for the whole.
>
> No luck yet on 31 though. 8-)>
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
> >From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
> Date: Thu, 6 Aug 1998 08:54:09 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: tuning@eartha.mills.edu
> Bcc: Rosemary Hahn <hahn@wulaw>
> Subject: RE: Scales and Numerology
>
> On Thu, 6 Aug 1998, Paul Hahn wrote:
> > 6/5 --- 3/2 ---15/8
> > / \ / \ /
> > / \ / \ /
> > / 7/5 \ / 7/4 \ /35/32
> > 8/5 --- 1/1 --- 5/3
> >
> >
> > 28/15
>
> D'oh! That 5/3 should be a 5/4, of course. I guess my finger slipped.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
> >From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
> Date: Fri, 7 Aug 1998 14:42:24 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: tuning@eartha.mills.edu
> Bcc: Rosemary Hahn <hahn@wulaw>
> Subject: Re: Numbers, cont.
>
> On Thu, 6 Aug 1998, John Chalmers wrote:
> > As for 9-tone scales in 31-tet, David Rothenberg and Connie Chan studied
> > this one: 5 3 3 3 3 5 3 3 3, generated by a chain of 14 degrees of
> 31-tet.
> > This scale is an MOS, is strictly proper,
>
> Call me a heretic, but I'm beginning to wonder if these properties
> aren't as important as I'd once thought they were. Look at the success
> of the minor pentatonic in Japan, for example.
>
> > has "stability" of 1.0 and
> > "efficiency" of .7407.
>
> Shame on me, but I don't even know what these measure signify. Help,
> please.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
> >From manynote@library.wustl.edu Thu Jun 17 10:38:05 1999
> Date: Sun, 9 Aug 1998 01:34:40 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: tuning@eartha.mills.edu
> Bcc: Rosemary Hahn <hahn@wulaw>
> Subject: More nonatonic maunderings
>
> On Thu, 6 Aug 1998, Paul Hahn wrote:
> [the basic 9-out-of-31 scale is]
> > 4-4-2-5-3-3-4-3-3. [snip]
> >
> > There are only two complete Otonal 4:5:6:7
> > tetrads, but a nice distribution of (Otonal and Utonal) 4:5:6 and 4:5:7
> > triads.
>
> Hey, I just realized that if you change the first two steps to 3-5
> instead of 4-4, you just lose one 5/4 but gain a 3/2, a 7/5, and another
> (Utonal) 4:5:6:7 tetrad. Hmm . . .
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
> From manynote@library.wustl.edu Thu Jun 17 10:40:56 1999
> Date: Wed, 12 Aug 1998 09:08:56 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: John Chalmers <non12@deltanet.com>
> Subject: Re: 9-toners again
>
> On Tue, 11 Aug 1998, John Chalmers wrote:
> > I've been so
> > busy recently that I haven't been reading the tuning list very carefully
> > and must have missed your post on 3-tetrachord enneatonics. Sorry, when
> > was it?
>
> Last Thursday. Basically, you fix 1/1, 5/4, and 8/5 as the boundaries
> of three tetrachords (pitches 1, 4, 7 of the nonatonic scale), then the
> others can vary within those bounds as long as they form a 8/7, 7/6, or
> 6/5 with one of those pitches. Nine tones is a little too few to have
> very many complete tetrads, but this technique practically guarantees
> you a reasonable number of triads. So far the interesting ones I have
> are:
>
> 4-3-3-5-3-3-4-3-3
>
> The most regular melodically. Harmonically there are only two consonant
> tetrads, one Otonal and one Utonal, both most consonant with the 1/1 of
> the scale as the root. For these reasons I think of it as being
> somewhat analogous to the major pentatonic (12TET 2-2-3-2-3). Looking
> for interesting scales I generally start with this one and then start
> varying pitches by 36/35s and 49/48s.
>
> 4-4-2-5-3-3-4-3-3
>
> The most regular harmonically, as it can be derived from three 4:6:7
> triads rooted on 1/1, 5/4, and 8/5. Possibly the best nonatonic
> equivalent of the major diatonic scale. Two Otonal tetrads on 1/1 and
> 8/5.
>
> 3-5-2-5-3-3-4-3-3
>
> The one with the most (7-limit) consonances. Also it has three tetrads
> instead of two; the same two the above scale has, plus a Utonal one.
> Sort of analogous to Mixolydian.
>
> 3-4-3-5-3-3-4-3-3
> 3-4-3-3-5-3-4-3-3
> 3-5-2-3-5-3-4-3-3
>
> Other variants with three tetrads, but the way they relate to each other
> harmonically is a little stranger. Still figuring these out.
>
> > I haven't spent much time
> looking
> > for harmonic derivations as things like 3 triads without common tones or
> > 3 tetrads with tend not to be very good scales melodically in my
> > experience.
>
> This is where Fokker's method really helps me out; it assures me of a
> relatively even distribution of pitches, as pairs of pitches separated
> by one of the "vanishing" intervals are disallowed. Surprisingly, I
> find it sort of ends up paralleling Ben Johnston's method of intervallic
> subdivision.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 4
> Date: Thu, 17 Jun 1999 10:47:14 -0500 (CDT)
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> Subject: More on 9-notes scales
>
> More from an off-list exchange I had with John Chalmers.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Hey--do you think I need to lose some weight?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
> ------------------------------------------------------------------------
>
> From manynote@library.wustl.edu Thu Jun 17 10:46:00 1999
> Date: Tue, 1 Sep 1998 11:24:31 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: John Chalmers <non12@deltanet.com>
> Subject: Re: 9-toners again
>
> Just figured out (don't know why it took me so long) that
>
> 3-3-4-3-5-3-4-3-3
>
> actually has _four_ complete tetrads using only nine pitches--in JI you
> would need at least ten pitches. This is analogous to the diatonic set
> containing six complete triads using seven pitches, when in JI you would
> need at least eight. Not only that, but it has no 2-step intervals,
> making the stepsizes more even. I think I'm going to have to work some
> more with this scale . . .
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Churchill? Can he run a hundred balls?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
> From manynote@library.wustl.edu Thu Jun 17 10:46:00 1999
> Date: Tue, 6 Oct 1998 12:37:09 -0500 (CDT)
> From: Paul Hahn <manynote@library.wustl.edu>
> To: John Chalmers <jhchalmers@UCSD.Edu>
> Subject: Re: 9-toners
>
> On Thu, 3 Sep 1998, John Chalmers wrote:
> >> 3-3-4-3-5-3-4-3-3
> >
> > I see this symmetric arrangement as two similar perfect "pentachords"
> > separated by a whole tone, an arrangement similar to the major scale in
> JI.
> > I presume this is better than the form with identical pentachords a
> fifth
> > apart.
>
> (i.e. 3-4-3-3-5-3-4-3-3)
>
> Well, better in some ways and worse in others. This one has only three
> complete tetrads instead of four, but it has 22 7-limit consonances vs.
> 21 in the first, so it's a tradeoff. It also contains the lovely
> 7-limit pentatonic scale 1/1 7/6 4/3 3/2 7/4 (2/1) as a subset. I'm
> going to have to study _this_ one some more, too.
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Foul? What the hell for?"
> -\-\-- o "Because you are chalking your cue with the 3-ball."
>
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 5
> Date: Thu, 17 Jun 1999 10:56:55 -0500
> From: "David J. Finnamore" <dfin@bellsouth.net>
> Subject: Re: Chant, resonanant spaces, medieval polyphony etc.
>
> Monz wrote:
>
> > By [Paul Erlich's] theory, 81:64 is a ratio which simply has such large
> > numbers that it's unlikely that we'll perceive it as such.
> > This is exactly what I was saying in this thread about a
> > week ago, when I suggested that other simpler ratios would
> > probably be sung for the wider-than-5:4 'major 3rd'.
>
> I think that's looking at the situation backwards. A singer
> isn't waiting to perceive an interval one way or the other.
> S/he knows when s/he is singing a third against another tone
> and will try to tune it based on:
>
> 1) a practiced tuning
> 2) ear (which is influenced by #1)
> 3) a theory about how it "should" be tuned
>
> The stronger the role played by #2, the more likely, IMHO,
> that a third will be tuned 5-limit. I said to Paul earlier
> that he was right about Pythagorean tuning for polyphonic
> song, which goes against what you said:
>
> > Note that my theories about perceiving 5-limit overtones in
> > a cathedral, which I would defend, are specifically in connection
> > with polyphonic singing.
>
> Now that I think about it again, I'm not so sure one way or
> the other. Even with the thirds being regarded as unstable,
> and seemingly going by quickly, if the environment is
> causing virtually the whole scale (plus ficta) to sound at
> once, 5-limit JI should reduce the amount of perceived
> dissonance as compared with Pythagorean tuning, making for a
> more physically sensuous experience. But were they
> concerned about making music a sensuous experience? It
> might be argued that our current obsession with experience
> results from the relatively recent widespread acceptance of
> humanism, which is antithetical to medieval philosophy.
>
> The musical form of the question is whether singers of such
> compositions would have more likely relied on their ears or
> on their knowledge of the theory to tune thirds. How
> concerned were they about maximizing consonance? Judging by
> the compositions themselves, the composers didn't lose a lot
> of sleep over it. The theorists evidently saw it in terms
> of a continuum to be traversed. But the performers? Could
> be a different story. It's seeming less likely to me now
> that we'll ever be able to make anything more than a guess.
>
> David
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 6
> Date: Thu, 17 Jun 1999 11:32:06 -0400
> From: monz@juno.com
> Subject: Unaccompanied Singers Intonation
>
> [Can Akkoc, TD 221.13]
> > I have always conjectured that legendary performers generate
> > their own impromptu adaptive tuning as they perform, depending
> > upon the 'mood' or 'mode' they are in, sometimes even when they
> > are accompanied by an ensemble playing at 12TET.
> > <snip>
> > I would like to determine these dynamic scales for such
> > performers to uncover their 'secrets' with the hope of
> > understanding the dynamic nature of such improvised intonations.
> > This might be a crucial factor separating a 'good' performer
> > from a 'legendary' performer.
>
>
> Linus Liu has done interesting work like this. His website
> has MIDI files of _Hey Jude_ and _Hotel California_ with the
> vocal pitches tuned according to a system he's calculated
> (no details given - he has a patent), which sound quite close
> to the actual vocals by Paul McCartney and Don Henley.
>
> I don't have the URL - perhaps it's on John Starrett's site.
>
>
> Joseph L. Monzo monz@juno.com
> http://www.ixpres.com/interval/monzo/homepage.html
> |"...I had broken thru the lattice barrier..."|
> | - Erv Wilson |
> --------------------------------------------------
>
> ___________________________________________________________________
> Get the Internet just the way you want it.
> Free software, free e-mail, and free Internet access for a month!
> Try Juno Web: http://dl.www.juno.com/dynoget/tagj.
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 7
> Date: Thu, 17 Jun 1999 11:14:54 -0500
> From: "David J. Finnamore" <dfin@bellsouth.net>
> Subject: Re: Intonational politics and 9:8, etc.
>
> After reading Margo's (yet another) profoundly insightful
> post (as referenced in the subject line of this one), I
> believe that I overstepped the bounds of my knowledge of the
> subject in my previous post. My apologies.
>
> David
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 8
> Date: Thu, 17 Jun 1999 13:00:23 -0400
> From: monz@juno.com
> Subject: Buckminster Fuller lattice designs
>
> [Paul Erlich, TD 221.6]
> >
> > [me, monz]
> >> (I've always been a big fan of Buckminster Fuller's work,
> >> and I can see ways to apply his ideas to tonal lattices too.)
> >
> > [Paul]
> > Cool! Such as?
>
> Well, the reason I said that, is because Carl Lumma once posted
> the URL of a graphic that showed the interlocking of parts in
> a geodesic design by Fuller, which we would recognize as (if I
> recall correctly) a hexany and a diamond 'doing it' (Carl's words).
>
> This was part of a website devoted to Fuller's work. I saved it
> on my hard drive, but looked for it on my hard drive and in my
> 'favorites' and couldn't find it, but a search on AltaVista should
> turn it up.
>
>
> Joseph L. Monzo monz@juno.com
> http://www.ixpres.com/interval/monzo/homepage.html
> |"...I had broken thru the lattice barrier..."|
> | - Erv Wilson |
> --------------------------------------------------
>
> ___________________________________________________________________
> Get the Internet just the way you want it.
> Free software, free e-mail, and free Internet access for a month!
> Try Juno Web: http://dl.www.juno.com/dynoget/tagj.
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 9
> Date: Thu, 17 Jun 1999 12:31:13 -0400
> From: monz@juno.com
> Subject: Lattice visualization of music in real time
>
> [Paul Erlich, TD 221.8]
> >
> > [me, monz]
> >> [11 years ago] I was drawing diagrams that were altered
> >> versions of Ellis's Harmonic Cell and Harmonic Decad
> >> [Helmholtz, p 458-459], which placed Ellis's ratios in a
> >> scheme somewhat like Partch's Tonality Diamond, and then
> >> I outlined the harmonic cells in the decad, and realized
> >> that doing this in real-time with computer software would
> >> be a great way to study harmonic movement.
> >
> > [Paul]
> > So you came up with the tetrahedral-octahedral lattice around
> > this time too? I thought you went to parallelogram lattices
> > before or at the time you went beyond 5-limit.
>
> The original drawings I made of Ellis's 5-limit systems were
> tetrahedral, akin to Partch's Diamonds.
>
> At the time, I was interested in constructing a more-or-less-fixed
> 19-limit system, and the problem I was having was where to put
> the 7-, 11-, 13-, 17-, and 19-limit ratios.
>
> I could see that it was fairly easy to incorporate 7, because it
> gave a 3-dimensional layout similar to Fokker's (with which I was
> unfamiliar at the time). But including 11 and the rest was
> perplexing.
>
> It was when I independently stumbled upon the realization that
> Ellis's Duodenarium illustrated prime-factorization (of 3 and 5)
> that I began to prefer the simplicity and logic of the
> parallelogram design.
>
> I stayed with this design, using a 3x5 grid or matrix layout
> (think of it as a plane), which could be reproduced like rungs
> of a ladder for all the higher primes, until a year ago.
>
> Even tho I used it for a few years, I still wasn't entirely
> pleased with this type of design, because it was difficult to
> portray prime-factors higher than 5 which were raised to powers
> higher than +/- 1.
>
> In May of 1998, when I 'broke thru the lattice barrier', I
> realized that giving each vector a unique angle would allow me
> to incorporate any prime at any power. Of course, this design
> had been used and published, in a somewhat less complex fashion,
> by Erv Wilson and John Chalmers as long ago as the late 1960s
> (see the Wilson Archives at www.anaphoria.com), and has already
> been incorporated in software on the Mac - I believe it's
> JICalc (? - I'm a PC user) - but I wasn't aware of any of this
> until late last year, after I had thought of it independently.
>
> As I've said here before, I don't have any serious reservations
> against using tetrahedral lattices, and the reason I generally
> don't show the triangular connections on my lattices is simply
> because they clutter it up too much.
>
> The reason I prefer the parallelogram design is because I find
> it just a tad bit more logical and simple than the tetradhedral,
> altho it has its drawbacks too, as Paul has pointed out. Chief
> among them is the implications of sonance or complexity given
> by the spatial distance between certain ratio points.
>
> The beautiful thing about the JustMusic software which Ken Fasano
> and I are developing is that it will allow the user to change
> the view of a scale or system to a number of different lattice
> designs, so that the unique information provided by all the
> different designs can be viewed at once and compared.
>
> The two designs already implemented are my 'Monzo' lattice
> design, with which most of you should be familiar and which
> can be seen on my website, and my 'Planetary' graph, which
> places the 'octave'-reduced ratios around a circle representing
> the 'octave'. Thus I can see the prime-factor layout with
> the 'Monzo' lattice, as well as the logarithmic intervallic
> distance between the pitches with the 'Planetary' graph.
>
> And it can read any rational Scala file. :)
> (and eventually, the irrational ones too)
>
> And of course the most powerful aspect of it will be sequencer
> (i.e., real-time) capability.
>
>
> -monz
>
> Joseph L. Monzo monz@juno.com
> http://www.ixpres.com/interval/monzo/homepage.html
> |"...I had broken thru the lattice barrier..."|
> | - Erv Wilson |
> --------------------------------------------------
>
> ___________________________________________________________________
> Get the Internet just the way you want it.
> Free software, free e-mail, and free Internet access for a month!
> Try Juno Web: http://dl.www.juno.com/dynoget/tagj.
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 10
> Date: Fri, 18 Jun 1999 03:23:21 +1000
> From: Dave Keenan <d.keenan@uq.net.au>
> Subject: Re: 9-limit triangular lattices
>
> Glad you like em.
>
> 5
> ,' ^
> ,' |\
> ,' | \
> 1 -------|- 3 7-limit o-tetrad
> `. | /
> `. |/
> 7
>
> 1/7
> /| `.
> / | `.
> 1/3 ------- 1/1 7-limit u-tetrad
> ^ | ,'
> \ | ,'
> \| ,'
> 1/5
>
> 5
> ,' ^ `
> ,' |\ `
> ,' | \ ` .
> 1 =======|= 3 ========= 9 9-limit o-pentad
> `. | / , '
> `. |/, '
> 7
>
> 1/7
> , '/| `.
> , ' / | `.
> 1/9 ======= 1/3 ======= 1/1 9-limit u-pentad
> ` ^ | ,'
> ` \ | ,'
> ` .\| ,'
> 1/5
>
> I missed a few connections on the decatonics so here they are again. Note
> that F#/ = Gb\, C#/ = Db\, G#/ = Ab\, and Eb = D#\\, Bb = A#\\, F = E#\\.
>
> Erlich's symmetrical decatonic scale
>
> B/ ------- F#/ ------- C#/
> | `. /| `. /| `.
> | `. / | `. / | `.
> | A/ -------- E/ -------- B/
> | ,' ^ | ,' ^ | ,' ^
> | ,' |\ | ,' |\ | ,' |
> | ,' | \| ,' | \| ,' |
> F -------|- C -------|- G |
> | `. | /| `. | /| `. |
> | `. |/ | `. |/ | `. |
> | Eb -------- Bb -------- F
> | ,' ^ | ,' ^ | ,' ^
> | ,' |\ | ,' |\ | ,' |
> | ,' | \| ,' | \| ,' |
> B/ ------| F#/ ------| C#/ |
> `. | / `. | / `. |
> `. |/ `. |/ `. |
> A/ -------- E/ -------- B/
>
>
> Erlich's pentachordal decatonic scale
>
> B/ ------- F#/ ------- C#/ ------- G#/
> | | `. /| `. / `.
> | | `. / | `. / `.
> | | E/ -------- B/ ------- F#/
> | | ,' ^ | ,' ^ |
> | | ,' |\ | ,' | |
> | | ,' | \| ,' | |
> F --------- C -------|- G | |
> | `. /| `. | /| `. | |
> | `. / | `. |/ | `. | |
> | Eb -------- Bb -------- F --------- C
> | ,' ^ | ,' ^ | ,' ^ ,' |
> | ,' \ | ,' |\ | ,' |\ ,' |
> | ,' \| ,' | \| ,' | \ ,' |
> B/ ------- F#/ ------| C#/ ------| G#/ |
> `. | / `. | / `. |
> `. |/ `. |/ `. |
> E/ -------- B/ ------- F#/
>
> Fokker-Lumma scale
> D#--------A#
> ,'/:\`. ,'/
> F--/-:-\--C /
> /|\/ : \/| /
> / |/\ : /\|/
> A---------E---------B---------F#
> /|\ /|\`. /,'/ \`.\:/,'/
> / | \ / | \ Db-/---\--Ab /
> / D#--------A# \ | / \ | /
> /,'/:\`.\ /,'/ `.\|/ \|/
> F--/---\--C--/------G---------D
> /|\/ : \/| /
> / |/\ : /\|/
> / B---------F#
> /,' `.\:/,'
> Db--------Ab
>
> becomes
> F ========= C
> ,' ^ `. ,'/| `.
> ,' |\ `.,' / | `.
> ,' | \ ,' D# -------- A#
> Db ------|- Ab ,' ^ | ,'
> , '/| `. ,|'/|,'. \ | ,'
> , ' /,| ' `. |/,' `. \| ,'
> A ========= E ========= B ========= F#
> ,' ^ ` ,' ^ `| ,' ^ | ,'
> ,' |\ `,' |\ | `,' \ | ,'
> ,' | \ ,' ` |.\| ,' ` .\| ,'
> F =======|= C =======|= G ========= D
> ,' ^ `. |'/| `. , |'/ , '
> ,' |\ `.,'|/,| ' `. |/, '
> ,' | \ ,' D# -------- A#
> Db ------|- Ab ,' ^ | ,'
> `. | / ,'. \ | ,'
> `. |/,' `. \| ,'
> B ========= F#
>
> I don't think this is as enlightening as it is for the scales with a
> half-octave. Note that I've repeated a lot more notes here than in the
> Erlichs and the Keenan. I did it to show the whole scale in a single
> 5-limit plane
>
> D# -------- A#
> ,' ^ ,'
> ,' \ ,'
> ,' \ ,'
> A ========= E ========= B ========= F#
> ,' ^ ` ,' ^ ` ,' ^ ,'
> ,' \ `,' \ `,' \ ,'
> ,' \ ,' ` .\ ,' ` .\ ,'
> F ========= C ========= G ========= D
> ,' ^ ,'
> ,' \ ,'
> ,' \ ,'
> Db -------- Ab
>
> and to show the hexany.
>
> F ========= C
> ^ `. ,'/|
> |\ `.,' / |
> | \ ,' D# |
> | Ab ,' ^ |
> | / ,'. \ |
> |/,' `. \|
> B ========= F#
>
> Interesting that it brings the D#:Ab 8:11 closer together.
>
> Regards,
> -- Dave Keenan
> http://dkeenan.com
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 11
> Date: Thu, 17 Jun 1999 12:01:31 -0700
> From: "Canright, David" <dcanright@monterey.nps.navy.mil>
> Subject: Encapsulated PostScript for Just Intonation
>
> Dear JI Fans,
> I have just added a new section to my website:
>
> Encapsulated PostScript for Just Intonation
> http://www.mbay.net/~anne/david/eps4ji/
>
> excerpt:
> In the course of my music theoretical explorations, I have found certain
> graphical representations helpful in understanding scales and tunings in
> just intonation. And after I realized that PostScript was a general
> programming language capable of generating high-quality
> resolution-independent graphics on a wide variety of platforms, I taught
> myself enough to develop these Encapsulated PostScript graphics. Each one
> represents a particular graphical idea, and the file can be easily
> modified
> to change the scale and/or many style options (in the "USER SETUP"
> section;
> see the Variations for examples of the ease of editing). The resulting EPS
> graphic can not only be printed on any PostScript printer (or other
> printers
> using "Ghostscript"), but can also be imported (and resized if necessary)
> into many graphics, page-layout, and word-processing programs, for
> incorporation into other documents.
>
> Check it out! Take your favorite JI scale and make an interval matrix, or
> an
> acoustically-spaced slide rule, or a harmonic-melodic diagram, or lay out
> a
> fretboard for your ukelele...
>
> David Canright (831) 656-2782 (or -2206)
> Math. Dept., Code MA/Ca (831) 656-2355 (FAX)
> Naval Postgraduate School DCanright@NPS.Navy.mil
> Monterey, CA 93943 USA http://www.mbay.net/~anne/david/
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 12
> Date: Thu, 17 Jun 1999 15:19:13 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: The Beethoven piece and AJI
>
> Joe Monzo wrote,
>
> >>I agree that characterizing this experimental tuning as JI
> >>is *not* a good idea, at least not plain unqualified JI, for the
> >>reasons David pointed out. It's probably unfortunate that
> >>many theorists and composers, including myself, have used
> >>'just-intonation' to mean these extended types of rational
> >>systems, since JI by definition already meant the usual 5-limit
> >>tuning which provides interlocking consonant 4:5:6 triads.
> >>Perhaps 'extended JI' is a reasonable name, altho just
> >>calling it a '5-limit rational tuning' is probably best.
>
> Ray Tomes wrote,
>
> >Why not call it AJI. This is the name I came up with meaning
> >"Automatic Just Intonation" and Paul independantly (I assume) came up
> >with "Adaptive Just Intonation" for the same concept.
>
> It's about as far as you can get from the same concept! Joe Monzo is
> proposing a scheme where major triads are not necessarily tuned 4:5:6, but
> a
> reasonable number of fixed pitches are used overall. Adaptive JI tunes all
> major triads as 4:5:6, but may have a much larger variety of fixed
> pitches.
> By the way, I called it Adaptive JI after John deLaubenfels started doing
> so.
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 13
> Date: Thu, 17 Jun 1999 15:24:44 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: Undertones/subharmonics (?) esp. vocal
>
> Ray Tomes wrote,
>
> >Right. One reason that I have been a bit slow responding is that I was
> >taken aback when someone (sorry I forget who) said that I was wrong and
> >that chaos frequency doubling does add lower frequencies. Now that I
> >think about it the mathematical cases of chaos do in fact do that, so I
> >was wrong to say that was not so. However I will have another go at
> >putting my foot in it and say that I think that real world, continuous
> >systems do show frequency doubling and not frequency halving behaviours
> >- which is presumably why they call it frequency doubling.
>
> Wrong again, Ray -- it's period doubling that occurs in real world,
> continuous systems, which of course means frequency halving. The book
> _Chaos
> and Fractals_ that I mentioned before actually gives a set of experimental
> results from a non-linear acoustical system where period doubling was
> observed (you can find hundreds of other such experiments discussed in the
> literature and even in abstracts on the internet).
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 14
> Date: Thu, 17 Jun 1999 14:27:21 -0500 (CDT)
> From: Paul Hahn <Paul-Hahn@library.wustl.edu>
> Subject: The term "Adaptive Just Intonation"
>
> On Thu, 17 Jun 1999, Paul H. Erlich wrote:
> > By the way, I called it Adaptive JI after John deLaubenfels started
> doing
> > so.
>
> It took just a minute looking through my old files to find a use of the
> term "Adaptive JI" from as early as 1994. (Gary Morrison was the
> culprit.)
>
> (I think I was the one who introduced JdL to the term, BTW.)
>
> --pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
> O
> /\ "Hey--do you think I need to lose some weight?"
> -\-\-- o
> NOTE: dehyphenate node to remove spamblock. <*>
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 15
> Date: Thu, 17 Jun 1999 15:35:48 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: pythagorean third
>
> buzzy^ wrote,
>
> >i have to apologize, since i shot off my mouth before checking the
> dictionary for a definition of 'polyphony'. but, at one time i was
> >acquainted with some 17th century 'pop' music. besides being incredibly
> weird sounding to me, it didn't have more than one >melodic line.
>
> The 17th century was already the Baroque period, where modern tonality was
> established. Going back to the 16th century (the Renaissance), tonality
> had
> not yet formed, so many pieces from that period would sound far more weird
> to modern ears than Baroque pieces. Finally, going back to the period we
> were actually discussing, the period of medieval polyphony (~900-1450),
> 5-limit (triadic) harmony had not yet become part of the style, so this
> music would probably sound positively alien to you.
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 16
> Date: Thu, 17 Jun 1999 15:55:31 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: the "7 +/- 2" rule
>
> Dan Stearns wrote,
>
> >Has anyone put forth any "generalized diatonic scales" consisting of 6,
> 8,
> or 9 notes?
>
> 9 notes is the most common among these proposals. Balzano's stunningly
> beautiful (but ill-founded, IMO) proposal was a 9-out-of-20tET scale; see
> "The Group-theoretic Description of 12-fold and Microtonal Pitch Systems"
> in
> _Computer Music Journal_, Vol. 4, No. 4, Winter 1980. Both Bohlen and
> Pierce
> proposed 9-tone ones as the best "generalized diatonic scales" for their
> 13th-root-of-3 tuning (these scales repeat at the 3:1 instead of the 2:1).
> See "Harmony and New Scales" by Mathews, Pierce, and Roberts in _Harmony
> and
> Tonality_ edited by Sundberg, and Bohlen's web site. Goldsmith's
> generalized
> diatonic is 9-out-of-16-tET with inharmonic timbres; see "An
> Electronically
> Generated Complex Microtonal System of Horizontal and Vertical Harmony" by
> Goldsmith in _Journal of the Audio Engineering Society_ Vol. 19 (1971)
> no.10
> pp. 851-858. I mention all of these in the part of my paper that you
> quoted.
>
> In 12-tET we have symmetrical 6- and 8-tone scales (aka the augmented and
> diminished scales) which have as many (or more) consonant triads as the
> diatonic scale (Blackwood discusses these and gives a few examples from
> famous composers) but, due to their symmetry, are unable to project the
> sense of a "home" or tonic. Passages in the diminished scale are extremely
> common in 20th century movie scores, non-serial classical, jazz, and even
> progressive rock; the augmented scale is much less common (Blackwood
> suggests that it's because it's very hard to write a good melody without
> major seconds -- hmmm . . .)
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 17
> Date: Thu, 17 Jun 1999 16:02:00 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: Query
>
> Dale Scott wrote,
>
> >Another excellent book from a more technical perspective is Martin
> Vogel's
> >_On The Relations Of Tone_. This book contains a wealth of basic
> information
> >on such wide-ranging topics as Greek theory, Euler, JI, and ETs>12-tone,
> and
> >contains some nice, easy-to-read lattices.
>
> Yes, I would highly recommend Vogel's book as a complement to the ones I
> listed. Vogel may present certain concepts better than any of the other
> authors. The Xenharmonikon review of _On The Relations Of Tone_ found it
> racist and Germanocentric; I think these qualities are but minor blemishes
> on an otherwise fine treatise (yes, we should oppose Vogel's politics,
> just
> as we should oppose Wagner's, but that doesn't make their work less
> valuable).
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 18
> Date: Fri, 18 Jun 1999 00:03:13 GMT
> From: rtomes@kcbbs.gen.nz (Ray Tomes)
> Subject: Re: Unaccompanied Singers Intonation
>
> Can Akkoc [221.13]
>
> >I have always conjectured that legendary performers generate their own
> >impromptu adaptive tuning as they perform, depending upon the 'mood' or
> >'mode' they are in, sometimes even when they are accompanied by an
> ensemble
> >playing at 12TET.
>
> I am sure that you are right. With a piano playing a chord each section
> of a choir has a choice of which notes(s) to harmonise with. Perhaps
> that choice would vary with such factors as how far the strongest singer
> in the section is from the piano compared to other sections :)
>
> >Carl Seashore has made actual measurements on performances
> >by such virtuosos of non-keyboard or non-fretted instruments while
> >performing concertos and found this to be the case with surprising
> >deviations in tuning between the soloist and the orchestra.
>
> Can you give me any references to this. Are they likely to be in the
> local University Music School?
>
> >I would not be
> >surprised to find such variations in tuning even from one performance to
> >another on the same composition.
>
> This argues for studying many performers and many performances to get an
> adequate understanding of the possibilities and reach useful
> conclusions.
>
> >I would like to determine these dynamic scales for such performers to
> >uncover their 'secrets' with the hope of understanding the dynamic nature
>
> >of such improvised intonations. This might be a crucial factor separating
> a
> >'good' performer from a 'legendary' performer.
>
> ... and for paying particular attention to those performances which are
> considered especially fine ones! Clearly this should be added to my
> list of desirable features for pieces to analyse.
>
> -- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
> Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
> Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
> Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 19
> Date: Fri, 18 Jun 1999 00:03:18 GMT
> From: rtomes@kcbbs.gen.nz (Ray Tomes)
> Subject: Effects of sound on consciousness
>
> Paul H. Erlich [TD221.15]
>
> >Azrael wrote me off-list:
> > I am addresses the
> > effects of sound on consciousness.
>
> >If you are interested in "mystical" (what I would consider unscientific)
> >approaches, read Danielou's _Introduction to the Study of Musical Scales_
> >and Levarie and Levy's book (can't remember the name -- not listed in the
> >_Tuning & temperament bibliography_). If you are interested in scientific
> >approaches, start with Hall's _Musical Acoustics_ (there are a few
> chapters
> >on psychoacoustics and tuning) and follow the references to books and
> >journal articles from there.
>
> I know nothing about any work done by anyone else on this subject but
> have had occasion to think about and study such questions from my own
> perspective of developing the harmonics theory and how the whole
> universe works and in particular life. So the following rave is a bit
> about my theory but aimed at coming around to the question raised.
>
> IMO the universe began as a single very low frequency note, being the
> fundamental oscillation mode of the universe or something like that.
> Because the universe has a non-linear equation (this is compatible with
> GR) any such oscillation MUST develop harmonics. Because the structure
> is 3D these harmonics also form centres at which energy is concentrated.
> This concentration highlights the non-linearity at the new frequencies
> and these also develop harmonics. This leads to the development of ever
> higher frequencies so that eventually waves form which have wavelengths
> that match the distances between galaxies, stars, planets and eventually
> atoms and nucleons. There is nothing but waves.
>
> Along the way some of these waves become very stable and long-lived and
> some develop means of duplicating themselves and we call these "life".
> In the distant past the most energy was in larger waves but is now in
> the nuclear waves throughout most of the universe. So in the past any
> living things would have been much larger (the time of giants) and now
> these structures might still exist but they are composed of longer
> wavelengths and hence lower energies (according to Planck's law).
> The result is that these energies are not readily observable by science
> because they are too subtle compared to the chemical and nuclear
> energies observed on earth. Therefore they are what might be called
> spirits or Gods. These come in many shapes and sizes and may be
> galactic Gods, Solar Gods, Planetary Gods or Devas of smaller areas.
>
> The oscillations associated with these larger entities are detectable
> but have not generally been recognised for what they are. Some examples
> are the 7.5 Hz electromagnetic Schumann resonance and the 84 minutes
> gravitational oscillation of the earth (equal to the orbital period of a
> satellite at ground level). The ratio between these two periods is
> 37800 which is close to (and probably related to) my common 34560 ratio
> between levels of structure in the universe. It is also equal to the
> ratio between the electron Compton frequency and the prime mode of the
> electrons orbits as defined by the Rydberg constant. Alternatively this
> is equal to the expression 2*137.036^2 where 1/137.036 is the fine
> structure constant. Why should the Earth show this same ratio as
> present in very much faster oscillations? Answer, because the
> dimensions and mass of the earth are not random but cosmically
> determined.
>
> The period of about 84 minutes is also found in many other places in the
> solar system. The outer planets are at distances from the sun that are
> very near multiples of 82 light minutes. The sun has a 160 minute
> oscillation. The other planets (except Mars) have surface orbital
> periods of near 84, 168 or 252 minutes, all multiples of 84 minutes.
>
> The inner planets are near multiples of 3 light minutes from the Sun and
> again the sun has an oscillation of about 5.5 minutes or near double
> that (the double is because each wave has two nodes). So the periods of
> ~160, ~80, ~6 and ~3 minutes are all around us.
>
> The waves in the sea mostly have intervals of ~13 seconds in the surf
> and ~6.5 and ~3.25 seconds in harbours. Periods of 26, 51 and 102
> seconds are also found as wave groupings. Wave sizes also show clear
> variations over 3, 6 and 12 minutes and 20 and 40 minute very large
> groupings are visible from satellite photos. Surfies know that super
> waves come at 20 minute intervals.
>
> All of this is given to show that we live in a set of musically related
> waves that inundate everything. Anyone that wants to understand how
> music can touch the soul will find it useful to understand the
> environment in which the soul developed. The periods above are very
> deep in our being and we have activity cycles throughout the day and
> night (e.g. 90 minute sleep cycle) that are probably related to these
> cosmic forces.
>
> Today there are people who are scientifically studying the mystical and
> these connections are beginning to be made. The musical masters of the
> past knew that they got their music from the cosmos or God or whatever
> anyone wants to call it. They tuned in to the subtle waves that pervade
> all space and time.
>
> The ancients knew something about this too and made large structures
> which have proportions and sizes which reverberate to sounds at
> frequencies that match the cosmic energies. Celts, Egyptians, Greeks,
> Chinese and Indians.
>
> The keys such as F, C and G are the ones that contain the notes that are
> the ones that dominate the cosmic vibrations most of the time which is
> why they were chosen as the white notes. However I believe that the
> correct present frequency for A is nearer to 450 Hz rather than 440 Hz
> although it probably varies a bit with time also.
>
> Again, rhythms should match keys in being related musically (when the
> BPM is considered as a low frequency note) and both should be related to
> the size of the dimensions of cathedrals etc which should be (and
> probably were) related to the natural frequencies for sound and
> dimensions in nature. In my experience structures from neolithic sites
> all over Europe show common units which are close to the modern imperial
> units.
>
> The human body is also a cathedral. Its oscillation modes have
> eigenstates which lead to certain energy centres and conduits which are
> called chakras, ki, and other names by eastern people who understood
> these things once long ago. These frequencies are related to the
> Schumann resonance and the other natural oscillations. If you want to
> reach the consciousness then playing the human instruments emotional
> centres will reach as deep as is possible to go. The large scale
> structure of music including shape and repeats will reach deeper into
> the soul if it matches the longer periods that I have mentioned.
>
> The main periods may be considered to be musically / harmonically
> related as follows:
>
> 162 81 40.5 20.3 minutes outer planets
> > ratio 7
> 23.1 11.6 5.8 2.9 minutes inner planets
>
> 20.3 minutes / 12 = 101.5 seconds
>
> 102 51 25.5 12.8 6.4 3.2 seconds waves in ocean / sea
> 8.5
>
> probable connection 2.9 minutes / 12 / 12 / 9 = 0.134 seconds => 7.45 Hz
>
> ratio 24 27 30 32 36 40 45 48
> freq. 179 201 224 238 268 298 335 358 Hz earth oscillation
> note F G A Bb C D E F
>
> so that the scale of F is strongly related to the earth resonance.
>
> -- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
> Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
> Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
> Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 20
> Date: Thu, 17 Jun 1999 21:30:41 -0400
> From: "D. Stearns" <stearns@capecod.net>
> Subject: Re: the "7 +/- 2" rule
>
> [Paul Erlich:]
> >Balzano's stunningly beautiful (but ill-founded, IMO) proposal was a
> 9-out-of-20tET scale;
>
> Thanks for the references Paul. I do remember this one from your paper...
> If you don't mind could you perhaps tell me a bit more about it? I don't
> quite understand how the 'minor third times the size of the major third
> equals the size of the entire set' of a 7-out-of-12 (in 12-tET) leads to a
>
> 9-out-of-20 in 20-tET.
>
>
> >In 12-tET we have symmetrical 6- and 8-tone scales
>
> Yes, but how about any non-12, 6 or 8 note "generalized diatonic scale"
> proposals along the lines of the others you cited?
>
> Dan
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 21
> Date: Thu, 17 Jun 1999 22:07:51 -0400
> From: Patrick Pagano <ppagano@bellsouth.net>
> Subject: Re: Effects of sound on consciousness
>
> Testify Brother
>
>
>
>
>
> __________________________________________________________________________
> _____
> __________________________________________________________________________
> _____
>
> Message: 22
> Date: Thu, 17 Jun 99 21:24:54 PDT
> From: "Dale Scott" <adelscot@onr.com>
> Subject: Re: Effects of sound on consciousness
>
> Ray,
>
> Wow, this is most fascinating. How long have you been thinking about
> stuff like this?
> The practice of arithmetical/musical cosmology goes back to ancient times,
> of course.
> One author who treats this subject from an anthropological perspective is
> Ernest G.
> McClain; I'd highly recommend his books _The Myth of Invariance_ and _The
> Pythagorean
> Plato_. Until you find those, check out a netization of his article
> "Music Theory and Ancient
> Cosmology" at
> http://members.aol.com/markalex9/Reviews/mcclain.html
>
> For anyone wanting more of a general (although fairly non-technical)
> introduction to the topic,
> take a look at _Harmonies of Heaven and Earth_ by Joscelyn Godwin. It
> includes info on
> thinkers including, but not limited to, Plato, Ptolemy, Werckmeister,
> Robert Fludd, Marius
> Schneider, Gurdjieff, and, most notably, Kepler. Although the information
> given is sometimes
> pretty sketchy, the bibliography refers the reader to some good primary
> and secondary sources.
>
> Dale Scott
> ----------
> > From: rtomes@kcbbs.gen.nz (Ray Tomes)
> >
> > Paul H. Erlich [TD221.15]
> >
> > >Azrael wrote me off-list:
> > > I am addresses the
> > > effects of sound on consciousness.
> >
> > >If you are interested in "mystical" (what I would consider
> unscientific)
> > >approaches, read Danielou's _Introduction to the Study of Musical
> Scales_
> > >and Levarie and Levy's book (can't remember the name -- not listed in
> the
> > >_Tuning & temperament bibliography_). If you are interested in
> scientific
> > >approaches, start with Hall's _Musical Acoustics_ (there are a few
> chapters
> > >on psychoacoustics and tuning) and follow the references to books and
> > >journal articles from there.
> >
> > I know nothing about any work done by anyone else on this subject but
> > have had occasion to think about and study such questions from my own
> > perspective of developing the harmonics theory and how the whole
> > universe works and in particular life. So the following rave is a bit
> > about my theory but aimed at coming around to the question raised.
> >
> > IMO the universe began as a single very low frequency note, being the
> > fundamental oscillation mode of the universe or something like that.
> > Because the universe has a non-linear equation (this is compatible with
> > GR) any such oscillation MUST develop harmonics. Because the structure
> > is 3D these harmonics also form centres at which energy is concentrated.
> > This concentration highlights the non-linearity at the new frequencies
> > and these also develop harmonics. This leads to the development of ever
> > higher frequencies so that eventually waves form which have wavelengths
> > that match the distances between galaxies, stars, planets and eventually
> > atoms and nucleons. There is nothing but waves.
> >
> > Along the way some of these waves become very stable and long-lived and
> > some develop means of duplicating themselves and we call these "life".
> > In the distant past the most energy was in larger waves but is now in
> > the nuclear waves throughout most of the universe. So in the past any
> > living things would have been much larger (the time of giants) and now
> > these structures might still exist but they are composed of longer
> > wavelengths and hence lower energies (according to Planck's law).
> > The result is that these energies are not readily observable by science
> > because they are too subtle compared to the chemical and nuclear
> > energies observed on earth. Therefore they are what might be called
> > spirits or Gods. These come in many shapes and sizes and may be
> > galactic Gods, Solar Gods, Planetary Gods or Devas of smaller areas.
> >
> > The oscillations associated with these larger entities are detectable
> > but have not generally been recognised for what they are. Some examples
> > are the 7.5 Hz electromagnetic Schumann resonance and the 84 minutes
> > gravitational oscillation of the earth (equal to the orbital period of a
> > satellite at ground level). The ratio between these two periods is
> > 37800 which is close to (and probably related to) my common 34560 ratio
> > between levels of structure in the universe. It is also equal to the
> > ratio between the electron Compton frequency and the prime mode of the
> > electrons
(Message over 64 KB, truncated)