Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Troubledoor's 'ideal 72-tone Pythagorean scale'

Monz wrote:

> Troubledoor recently mentioned an 'ideal 72-tone Pythagorean scale'.
> Some of the follow-up:
>
> > [Paul Erlich]
> > http://www.egroups.com/message/tuning/11804
> >
> > I wrote,
> >
> >>> Well, it doesn't take a very complex calculation to show that,
> >>> since 12 fifths leave a residue of a Pythagorean comma, 72
> >>> fifths will leave a residue of 6 Pythagorean commas, or over
> >>> a semitone!
> >
> > Troubledoor wrote,
> >
> >> That's the actual usage I've seen in the occult books. Some of
> >> them aren't even that occult. Some are quite exoteric except
> >> that its so buried that it will never be found until I blurt it
> >> out but I won't blurt it out here because these are mystical
> >> secrets about the the Lambdoma and that's a religious artifact
> >> that should be carefully delivered lest I get shot by a religious
> >> fanatic. The whole subject is so obscured by mysticism that
> >> looney zealots are a very real scare.
> >
> > right . . .
> >
> >> Have you actually ever run the circle of fifths around and
> >> around until they made an octave?
> >
> > The "circle of fifths" never closes perfectly, but it comes close
> > after 53, closer after 665, etc . . . see Paul Hahn or Kees van
> > Prooijen's tables.
> >
>
> Troubledoor, I questioned you privately a few days ago about
> this 'ideal 71-tone Pythagorean scale', asking you why the limit
> at 72 tones, and what makes it 'ideal'.
>
> I'm willing to remain open-minded enough to consider some of
> the things about which you've posted - indeed, I often skate
> dangerously close to mysticism myself in a lot of what I write.
>
> But your answer then sounded like so much occult mumbo-jumbo
> that I wanted to wait awhile before responding; I see that
> much of the same is being used to answer publicly here.
>

I hardly used any mumbo-jumbo. I'm sorry, I'm just trying to avoid the issue and the facts.
As soon as I get to the websites that Paul Ehrlich directed me to, I can speak in a more cagey
and unspecific manner so that I seem to talk about something useful. Really though....I went
insane for 5 years and got locked up in a hospital and I go for therapy sessions weekly and I
take anti-psychotic medication because there is a great chance for error in mixing music with
mystic philosophy---which actually happened in my case. When you make mistakes in mysticism,
the price is very heavy. So you can see why I try to dance around the issue. I'll be more
useful in the coming year because the 72 tone theories are where I am headed.

>
> In addition to the sources cited by Paul, take a look at this:
>
> http://www.egroups.com/files/tuning/monz/Pythagorean-cycle.gif
>
> The number of '5th's in the cycle appears across the bottom as
> the x-axis, and the y-axis shows the 'octave'-reduced Semitone
> value (Semitones to 2 decimal places show the same thing as
> cents, with the 12-tET degree isolated before the decimal point.)
>
> You can see clearly that 12 '5ths' come fairly close to an
> 'octave' (~23 cents higher, the 'Pythagorean comma'), and that
> 53 '5ths' come a whole lot closer (only ~4 cents higher), while
> 72 is, as Paul said, more than a semitone away.
>
> The next closer values, which didn't make it onto my graph, were
> 306 '5ths' and 359 '5ths', which are ~2 cents lower and higher,
> respectively.
>
> While I agree with Paul that 72-tET is a good intonational
> resource, the only value I can see in choosing 72 as a limit
> in a Pythagorean tuning is that it makes available all the
> smaller subsets, like 36, 24, 18, and 12... IMO, this still
> doesn't make it all that valuable.
>
> No ancient who bothered to either calculate any of this math
> or listen to the result would have had any reason to deliberately
> chose a 72-tone *Pythagorean* scale. I suggest you re-evaluate
> the ideas you're developing in regard to this 'ideal scale'.
>
> PS - Where you wrote 'exoteric' you meant 'esoteric'.
>

I meant to say exoteric. They are popular books too. But it's all hidden. I'm pretty sure
that the 72 tone thing is for the purpose of memory. They are idealizing a way to map the
mystic trips of sound. I currently have no way to test this theory right now because I haven't
contacted the inner realms of sound for a long time. When you do yoga you literally hear a
celestial music that carries you to the planets of Pythagorus and then onward to heaven. This
was the subject of most of alchemy. It'll take me a long time to get there again because I'm
currently pursuing other matters. 72 is what fits in the RATIONAL philosophy of geometry. It
is called "sacred-geometry" officially and is based on The Golden Section and the angles of the
pentagram or starfish. I suspect the reason they insist on the Golden Section is that it
instantly invokes the pentagram and that is the easiest image to remind one of The Highest God
when the mind is in trouble with Wisdom (philo-Sophia) tripping. So from the pentagram one has
to go to the 72 tones. It's the only thing that will stick in the mind-----in the RATIONAL
mind that is. A natural musician's ear might reject all this. I won't ever know because I
don't have a gifted ear. So I use philosophy to break into the secrets of musical skills. At
least I'm not using voodoo or witchcraft to practice guitar. Although, I am not beyond that
and I've even begun to practice a Chinese form of witchcraft and with this I plan to attempt
another go at perfect pitch or absolute pitch. I basically want to play music better than the
birds. I am very envious of the neighborhood birds. Little bastards just spew out microtonal
scales all day and it makes me mad cause I have to work hard just to get a damn pentatonic
scale out.

> -monz
> http://www.ixpres.com/interval/monzo/homepage.html
>
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symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Troubledoor <troubledoor@earthlink.net>

Kraig Grady wrote:

> dear 72ers:
> http://www.anaphoria.com/viggo.html shows the sequence of Pythagorean
> Moments of Symmetry exceeding even 665 for those interested.
>

Geometric ideas shouldn't be explored without the Platonic solids (tetrahedron,
octahedron, dodecahedron, etc). He has already left the visual metaphors and is
using strict mathematics (division/ratios). So he is going to get the numbers
really big because he can't "see" when he has exceeded the visual/aesthetic
threshold. The goal as I see it is to make a visual representation that is easy
for the memory and the memory can easily store the Platonic solids so they
should never be left out. I'm sure that Paul Ehrlich's theories and Monzo's
already suffice for this purpose just that people like it when the theories have
a religious connotation because people trust that God is perfect and that
therefore He is also rational so therefore, music should be rational too. The
Chinese already had this in China many 1000s of years ago. They have 6 "wings"
or classics. The I Ching (Book of Changes) is one of them. The Book of Music
was unfortunately completely wiped out in their Imperial burning of books. My
guess is that the book was a 72 tone graphic representation of microtonal
music. So, back then, everyone already knew about it and no one thought to
write about it because everyone knew about it. Then one day, the original books
were all burned and then suddenly the Dark Ages fell upon mankind (first in
China and then in Europe) and then there was already no hope for ever finally
recording the Book of Music and so we have horrible pop music today because the
document was completely lost from collective memory. It'll slowly be
reconstructed again based on the quaternary I Ching (16 tone increments
hieroglypically represented) I rediscovered and using Schoenberg's tone row
method. It's so cheesy and simple really. Just that it is going to spark a lot
of controversy because it implies a holographic theory of universe so
self-evident that even children can understand it. And no one wants to expose
children to the dangers of mysticism so the subject will forever get buried,
again and again. A holographic theory of the universe would end history because
we would all start taking drugs all day. Mostly because people would have such
huge headaches from marvelling at how ordered the creation is. They would need
to medicate themselves constantly. No one wants headaches of that magnitude.
The universe is so ordered and rational it is haunting. The order is everywhere
and especially in music. People would hate this idea because order implies
creation and creation implies a creator and a creator implies morality and
morality is a bright light thrown back upon the self and that would suck because
many people are imperfect and imperfection is not good to dwell on because that
is the very definition of insanity. Its not a disease that visits you, its the
awareness of intrinsic imperfection that causes insanity. Insanity is a
self-revelation. Like the cartoon character that doesn't start falling until he
has looked down to realize that the ground ended many steps ago. That is very
uncomfortable for many people to know that they are born fallen and that they
must fall at some point in time. Some cartoons would just like to never look
down and just walk to ground on the other side. But then that stupid bird
always flies by and then the cartoon is suddenly aware that the ground ended.
And everyone knows that birds play microtonal music the best. I wish there were
conductor birds.

> It also a problem of secrecy for misinformation to persist without
> correction. One misquote can persist for hundreds of years.

>
> Monz wrote:
>
>> Troubledoor recently mentioned an 'ideal 72-tone Pythagorean scale'.
>> Some of the follow-up:
>>
>
>
> -- Banaphshu
> North American Embassy of Anaphoria island
> www.anaphoria.com
> -------------------------------------------------------------------------------
>
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--
Hello,

I have recently discovered a new graphic representation for the
I Ching hexagrams that show that the I Ching was also intended to
be a hologram generator. By hologram, I mean something like the
traditional hieroglyphic style of Chinese writing except that it
has an internal sequence/logic. I accomplished this by representing
the changing lines differently. You can see the new graphic
arrangement at my webpage (it's about 2 paragraphs down):

http://home.earthlink.net/~troubledoor

You can also download the software for free. I use Norton's anti-virus with the
latest software upgrades so the download is virus free.
Please distribute it to your other I Ching friends. Thanks.

symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Monz <MONZ@JUNO.COM>

> [Troubledoor]
> http://www.egroups.com/message/tuning/11828
>
> Geometric ideas shouldn't be explored without the Platonic solids
> (tetrahedron, octahedron, dodecahedron, etc). He has already left
> the visual metaphors and is using strict mathematics
> (division/ratios). So he is going to get the numbers really big
> because he can't "see" when he has exceeded the visual/aesthetic
> threshold. The goal as I see it is to make a visual representation
> that is easy for the memory and the memory can easily store the
> Platonic solids so they should never be left out. I'm sure that
> Paul Ehrlich's theories and Monzo's already suffice for this
> purpose just that people like it when the theories have a
> religious connotation because people trust that God is perfect
> and that therefore He is also rational so therefore, music should
> be rational too.

The goal of my theory from the beginning was two-fold, and in
both cases was intended to be a simplification for the understanding
of rational musical measurement: a more accurate musical notation
that is easier to understand than 'really big number' ratios,
and lattice-diagrams to represent the relationships expressed
in the notation.

It would be 100% correct to characterize my lattice-diagrams
as 'a visual representation that is easy for the memory'. But
I never thought much about the Platonic solids - I just used
a formula that worked for my purposes.

As it turns out, 'the guy' whose work you're discussing (Erv Wilson)
has drawn hundreds (thousands?) of diagrams representing musical pitch
relationships, and many of them display connections which outline
various polyhedra. Browse around some more at www.anaphoria.com,
and try a search for 'hedron' on the Tuning List archives.

> The universe is so ordered and rational it is haunting. The order
> is everywhere and especially in music. People would hate this idea
> because order implies creation and creation implies a creator and
> a creator implies morality and morality is a bright light thrown
> back upon the self and that would suck ...<snip>

I don't agree with you that 'order implies creation', even
tho it's a commonly-held opinion.

First of all, modern physics describes the universe in which we
live as such a bizarre place that it's becoming clear (once again)
that the order we perceive is generally a function of the order
inherent in our perceptual apparatus. IOW, there's a lot of stuff
happening that's *not* rational and we just can't figure out what
it is, or we can't even see it.

Secondly, modern studies of chaos show that it is inherent in
the natural universe (at least the one we can experience).
Einstein made a famous statement about 'refusing to believe
that God plays dice', but apparently, he was wrong and that
*is* what's going on.

What's really so haunting is that, despite the universe being
peppered with chaotic events everywhere you turn, some of which
have an enormous impact (literally, the case of meteors!) on
evolutionary processes that are already under way, yet the
rational laws keep operating and eventually accomodate the
changes perpetrated by the random events; in some cases, the
random event proves to be powerful enough to alter the trajectory
of the evolutionary path, but still the evolutionary process
continues...

Many researchers are coming around to the idea that science
can never really describe objects, but only processes. In a sense,
on the cosmological or atomic timescales, the objects never 'really'
exist, only the laws that describe their movements. A lot of
the reason why this is so hard to grasp is because we have such an
elusive and muddy idea of what time, the fourth dimension,
really is.

And, of course, it's for this reason, based on the important
role that time plays in music, that music-theory can be so
alluring; in the same sense, music doesn't really 'exist',
it just 'happens' - that is, it can be perceived thru the
usual 3 spatial dimensions only in an abstract way, thru
analysis, whereas its 'normal' perception as directly audible
sound can only happen with temporal-based performance.

Going back to the stuff about Bode's Law: there are indeed
some interesting ratios embedded in the motions of the planets,
but they have to do not with distance but with orbital period.
There are intriguing synchronicities (meaning: ratios that are
very close to small-integer proportions) between adjacent planets:

Mercury:Venus = 9:23 (pretty close to 2:5)
Venus:Earth = 8:13 (nearly exact, close to 3:5 and 5:8)
Earth:Mars = 17:32 (close to 8:15)
Mars:Jupiter = 10:63 (pretty close to 3:19, 2:13, and 5:32)
Jupiter:Saturn = 2:5
Saturn:Uranus = 7:20 (close to 6:17 and 1:3)
Uranus:Neptune = 26:51 (pretty close to 1:2!)
Neptune:Pluto = 2:3

Perhaps there is some significance to be found in the primes
that turn up in this table - of course, they are a result of
various rounding procedures; one could find higher primes by
using more accurate ratios.

But I find it interesting that even with the rounding I've
done, the table includes 2, 3, 5, 7, 13, 17, 23, and possibly
19, but not 11; except for the omission of 11, all primes
within the 23-limit are represented. I've stated before that
I find 23 to be a kind of limit to harmonic perception in music;
is there a connection?... and why is 11 conspicuously missing?

There's also an interesting progressing in the successively-
more-accurate ratios which describe the Venus:Earth relationship:
3:5, 5:8, 8:13. The higher term in the less accurate ratio
becomes the lower term in the next more accurate one.

Pluto's orbit is highly eccentric, and many astronomers believe
that it was once an object orbiting in the Kuiper Belt, and that
it was influenced by Neptune into its current orbit; they cite
that strong 2:3 orbital-period synchronicity as evidence to
support their argument.

And the strong gravitational pull of Jupiter is obvious in
that its relationship to Saturn's period (~0.40258) is so
close to such a low-integer ratio (2:5).

Hmmm... where Bode's Law was an attempt to portray the 'grand
design' of the whole solar-system, this comparision of orbital
periods *only of adjacent planets* is similar to Paul Erlich's
comparison of *dyadic* harmonic entropy among members of a larger
set (such as a chord or scale).

I sent a private message to Paul suggesting we collaborate on
creating a piece which is an audible mapping of these planetary
relationships, to which he never responded (Paul?). And I see
in a List posting that David J. Finnamore has already done
something like this. My problem is figuring out how to map
all the different variables into sound. Any takers?

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Re: [tuning] Troubledoor's 'ideal 72-tone Pythagorean scale'

🔗Troubledoor <troubledoor@earthlink.net>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Troubledoor <troubledoor@earthlink.net>

🔗Monz <MONZ@JUNO.COM>

🔗David J. Finnamore <daeron@bellsouth.net>