Vishnu and semisuper

Another comma McClain discusses is the comma of semisuper temperament,
|23 6 -14>. McClain points out this is the gap between an
approximation to sqrt(2) and its reciprocal, namely
(110592/78125)/(78125/55296). He then connects this to the yantra of
odd 5-limit integers less than the
"year of Brahma" of 8640000000 years. The largest power of 5 less than
this is 5^14, which now supposedly represents Vishnu, the "god on the
mountain"; reduced to the octave it is a semisuper comma away from the
"dragon in the deep", 729.

This may be the first time anyone has discussed this comma, and in any
case "vishnu" seems like a much cooler name than "semisuper" for both
comma and temperament.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> I checked this out, and it turns out to be a bizarre work
> of pseudo-scholarship. It does have at least one idea which
> might be interesting, the musical yantra. Given a positive
> integer n, the musical yantra for n is all integers of the
> form 3^p 5^q <= n. These he graphs in the symmetrical 5-limit
> lattice; the yantra is to be regarded as consisting of
> pitch-classes, and if we transpose and reduce to an octave,
> as a scale.

why bizarre? and why pseudo-scholarship?

i find that McClain simply presents a well-rounded picture
of ancient musical tunings, liberally sprinkled with lots
of speculation ... which is something i love to do myself,
so i certainly don't mind if others do it and present a
convincing argument.

in fact, there's lots of evidence that the ratios which
describe musical tuning "anomalies" pop up again and again
in the daily life of ancient civiliziations. diesis, comma,
etc. ... all known as small anomalies of measurement.

> Another comma McClain discusses is the comma of semisuper
> temperament, |23 6 -14>. McClain points out this is the
> gap between an approximation to sqrt(2) and its reciprocal,
> namely (110592/78125)/(78125/55296). He then connects this
> to the yantra of odd 5-limit integers less than the "year
> of Brahma" of 8640000000 years. The largest power of 5 less
> than this is 5^14, which now supposedly represents Vishnu,
> the "god on the mountain"; reduced to the octave it is a
> semisuper comma away from the "dragon in the deep", 729.
>
> This may be the first time anyone has discussed this comma,
> and in any case "vishnu" seems like a much cooler name
> than "semisuper" for both comma and temperament.

I'm with you on this, Gene!

thanks for the comments on McClain's work.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> > I checked this out, and it turns out to be a bizarre work
> > of pseudo-scholarship.

> why bizarre? and why pseudo-scholarship?
>
> i find that McClain simply presents a well-rounded picture
> of ancient musical tunings, liberally sprinkled with lots
> of speculation ... which is something i love to do myself,
> so i certainly don't mind if others do it and present a
> convincing argument.

This is hardly an accurate characterization of McClain's book. He does
sometimes label his notions speculative, but that often simply means
they are one step beyond his usual lunacy. I wouldn't call it
"speculative" to ponder the question of whether the Tetragrammaton,
YHWH, might mean 5^10 * 6^5, since the letters are the 10th, 5th, 6th
and 5th letters respectively of a Hebrew alphabet. That isn't
speculative, it is simply incompetent; no one at that time would or
even could have thought that way if they were intending to give a
secret numerical meaning to YHWH.

However, it is when he claims things as facts, rather than
speculation, that McClain is most obviously a crank. Near the
beginning of the book, after discussing how Greek mathematics at the
time of Plato was able to construct the cube root of two, which would
also mean they could discuss the twelfth
root of two, he writes this:

<<The necessity of tempering the *pure* intervals, defined by the
ratios of the integers, is one of the great themes of Plato's
Republic. In his allegorical form, "citizens" are modelled on the
tones of of the scale which must not demand "exactly what they are
owed," but must keep in mind "what is best for the city.">>

The claim that temperament is a theme of the Republic is, of course,
entirely false, yet McClain states it as a fact, which unfortunately
typifies his approach throughout the book. Not only is temperament not
to be found in the Republic, it could not have been found there, as
the Greeks did not know of it.

This isn't bad scholarship. Bad scholarship would be David Irving
trying to show that the Holocaust, as such, did not happen, and
twisting his facts in clever ways to do so. Irving is a bad scholar,
but McClain is a crank, which is different, and his book should not be
read from the point of view of expecting anything that he says about
the Rg Veda, the Bible, or Plato to make any sense. It doesn't and
won't. On the other hand, I think yantras are a nifty notion, and
"jubilee" a fine name for the 50/49 comma.

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> The claim that temperament is a theme of the Republic is,
> of course, entirely false, yet McClain states it as a fact,
> which unfortunately typifies his approach throughout the book.
> Not only is temperament not to be found in the Republic, it
> could not have been found there, as the Greeks did not know
> of it.

well, i'm inclined to argue that point with you.

one of the most ancient musical text known, CBS 10996,
a Babylonian tablet which clearly originates from Sumerian
knowledge, describes a method of tuning the lyre which
seems to involve temperament ... and in fact i belive that
it is a sort of etude for the lyre. the only way the
piece, if that's what it is, can cycle back to the same
notes it started with, is if it uses 12-tET. here is
my reconstruction of it:

http://tonalsoft.com/monzo/babylonian/cbs10996.mid

and i've argued that any Sumerian scribe familiar with
sexagesimal (base-60) math, could acheive a very close
approximation to 12-tET:

http://tonalsoft.com/monzo/sumerian/simplified-sumeriantuning.htm

if the Sumerians did it, and the Babylonians copied them
(which they did in nearly every aspect of their culture),
then it's not much of a stretch to believe that the ancient
Greeks got this knowledge from Babylon.

most of my respect for McClain's work rests on my very
deep study (summer of 2000) of the great acheivements of
the Sumerians.

admittedly, i have not yet seen any "concrete" proof
that the Greeks knew of temperament ... but my own
research and speculations certainly lead me to agree
with McClain.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> > The claim that temperament is a theme of the Republic is,
> > of course, entirely false, yet McClain states it as a fact,
> > which unfortunately typifies his approach throughout the book.
> > Not only is temperament not to be found in the Republic, it
> > could not have been found there, as the Greeks did not know
> > of it.
>
>
> well, i'm inclined to argue that point with you.
>
> one of the most ancient musical text known, CBS 10996,
> a Babylonian tablet which clearly originates from Sumerian
> knowledge, describes a method of tuning the lyre which
> seems to involve temperament ... and in fact i belive that
> it is a sort of etude for the lyre.

If the Babylonians knew temperament it would not mean the Greeks did.
The closest we seem to get is in Aristoxenus, who by one
interpretation wanted to temper out the Pythagorean comma, but
Aristoxenus is against making anything precise--everything is supposed
to have a built-in fuzz factor as I understand it. In any case I've
read the Republic and I've read the Bible and they are not secret code
for 5-limit JI or temperament, either one.

> and i've argued that any Sumerian scribe familiar with
> sexagesimal (base-60) math, could acheive a very close
> approximation to 12-tET:
>
> http://tonalsoft.com/monzo/sumerian/simplified-sumeriantuning.htm

Could does not equate to did, and none of this helps to show that
Plato in the Republic and other dialogs was talking about temperament.

> most of my respect for McClain's work rests on my very
> deep study (summer of 2000) of the great acheivements of
> the Sumerians.

That is tough to do, because we know far less about the Sumerians than
we know about the Greeks.

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> If the Babylonians knew temperament it would not mean
> the Greeks did. The closest we seem to get is in
> Aristoxenus, who by one interpretation wanted to temper
> out the Pythagorean comma, but Aristoxenus is against
> making anything precise--everything is supposed to have
> a built-in fuzz factor as I understand it.

i basically agree with everything you're saying about
Aristoxenus, whose work i have also studied in great detail.

http://tonalsoft.com/monzo/aristoxenus/318tet.htm

(apologies for the sorry condition of much of this page
... i've just never gotten around to doing a proper
editing job.)

> In any case I've read the Republic and I've read the
> Bible and they are not secret code for 5-limit JI or
> temperament, either one.

i'm not so sure that either that statement or its
counter-argument could be proven ... people working
with kabbala and/or gematria may disagree with you.
i sit on the fence on this one.

> > and i've argued that any Sumerian scribe familiar with
> > sexagesimal (base-60) math, could acheive a very close
> > approximation to 12-tET:
> >
> > http://tonalsoft.com/monzo/sumerian/simplified-sumeriantuning.htm
>
> Could does not equate to did,

that's true ... and as you and i clearly place quite
different values on the question of speculation versus
proof, our discussion here is heading towards the point
where i think we just need to agree to disagree, and end it.

> and none of this helps to show that Plato in the Republic
> and other dialogs was talking about temperament.

i think that if i show that the Sumerians *could* have
developed 12-tET (and thus the possibility that they *did*),
then the fact that the Babylonians took almost the entire
Sumerian knowledge-base and culture over as their own when
they conquered Sumer (which has already been proven beyond
any doubt), and the fact that the ancient Greek knowledge-base
and mythology has *many* parallels with both Babylonian
and Sumerian (also already proven), certainly tend to
support the argument that the Greeks may have known 12-tET
from the Babylonians.

i know ... *that* is not proven ... but there's the
circumstantial evidence ...

> > most of my respect for McClain's work rests on my very
> > deep study (summer of 2000) of the great acheivements of
> > the Sumerians.
>
> That is tough to do, because we know far less about the
> Sumerians than we know about the Greeks.

i have to admit that what you say is true ... but that
statement implies that we don't know much about the Sumerians,
which is *not* true. they left behind hundreds of thousands
of clay tablets with all manner of stuff recorded upon them.
the vast majority of them have not even yet been unearthed,
let alone transcribed and translated ... but the many
thousands that have been deciphered have left us a very
clear picture of Sumerian society ... and that picture
shows that the Greeks inherited much (indirectly via the
Babylonians) from them.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> > In any case I've read the Republic and I've read the
> > Bible and they are not secret code for 5-limit JI or
> > temperament, either one.

> i'm not so sure that either that statement or its
> counter-argument could be proven ... people working
> with kabbala and/or gematria may disagree with you.
> i sit on the fence on this one.

He doesn't do gematira the way people back then would do it. Moreover
he assumes that Plato, John and the authors of the Rg Veda were very
familiar with the symmetric lattice of 5-limit tone classes, which
makes no sense at all.

> i think that if i show that the Sumerians *could* have
> developed 12-tET (and thus the possibility that they *did*),
> then the fact that the Babylonians took almost the entire
> Sumerian knowledge-base and culture over as their own when
> they conquered Sumer (which has already been proven beyond
> any doubt), and the fact that the ancient Greek knowledge-base
> and mythology has *many* parallels with both Babylonian
> and Sumerian (also already proven), certainly tend to
> support the argument that the Greeks may have known 12-tET
> from the Babylonians.

It seems to me this argument works in just the opposite way; since the
Greeks did not seem cognizant of 12-et, we might try to argue that the
Babylonians and hence the Sumerians weren't either. It strikes me as a
weak argument either way, however.