BiG DiGiTS (wasRe: hi, i'm back & a few ???)

>yes, most have lots of digits.
>
>> and they
>> wouldn't be "lower limit" primes, yes??
>
>they could all be 3-prime-limit, and there would still be an
>infinite number within any interval space.

non-octave 3 & 7 limit (cent values extremely rounded, ok? if not I'd be
typing bleedin' numbers all frikkin' night...)
{LaMonte Young, beat this, hehe...}

1/1 0
43,046,721/40,353,607 112
2,401/2,187 162
19,683/16,807 273
5,764,801/4,782,969 323
9/7 435
387,420,489/282,475,249 547
343/243 597
177,147/117,649 709
823,543/531,441 758
81/49 870
1,977,326,743/1,162,261,467 920
3,486,784,401/1,977,326,743 982
49/27 1032
1,594,323/823,543 1144
117,649/59,049 1193
729/343 1305
etc.

Of course one can just use much simpler ratios, but it might not be the
*same* when in relation to the other intervals' actual physical interactions...
AFAIK according to LaMonte Young's theory.
Also I don't think we Higher Primates have the blinkin' technology yet to
make such ultra-high ratios audibly accurate much less comprehend them with
any "detail."
I mean we barely understand infrasound and possible uses in music (besides
its more lethal military/police uses) and that's closer to our means & ends,
right?

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark"

"The wonderousness of the human mind is too great to be transferred into
music only by 7 or 12 elements of tone steps in one octave." - shakuhachi master
Masayuki Koga

"There's a rabbinical tradition that the music in heaven will be microtonal
=)" - one annotative interpretation of Talmudic writings

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"
LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

...improvisation is about change, about flux rather than stasis. ... you have
to be aware of the fact that improvisation is about a constant change. -
Steve Beresford

--- In tuning@yahoogroups.com, czhang23@a... wrote:

/tuning/topicId_43899.html#43899

>
> >yes, most have lots of digits.
> >
> >> and they
> >> wouldn't be "lower limit" primes, yes??
> >
> >they could all be 3-prime-limit, and there would still be an
> >infinite number within any interval space.
>
> non-octave 3 & 7 limit (cent values extremely rounded, ok? if
not I'd be
> typing bleedin' numbers all frikkin' night...)
> {LaMonte Young, beat this, hehe...}
>
> 1/1 0
> 43,046,721/40,353,607 112
> 2,401/2,187 162
> 19,683/16,807 273
> 5,764,801/4,782,969 323
> 9/7 435
> 387,420,489/282,475,249 547
> 343/243 597
> 177,147/117,649 709
> 823,543/531,441 758
> 81/49 870
> 1,977,326,743/1,162,261,467 920
> 3,486,784,401/1,977,326,743 982
> 49/27 1032
> 1,594,323/823,543 1144
> 117,649/59,049 1193
> 729/343 1305
> etc.
>

***Ummm. So *these* are 3-limit and 7-limit? Go figure. Actually, I
need a little help with this. Howso??

Tx!

J. Pehrson

In a message dated 2003:05:27 06:31:35 PM, jpehrson@rcn.com quotes me &
writes:

>> 1/1 0
>> 43,046,721/40,353,607 112
>> 2,401/2,187 162
>> 19,683/16,807 273
>> 5,764,801/4,782,969 323
>> 9/7 435
>> 387,420,489/282,475,249 547
>> 343/243 597
>> 177,147/117,649 709
>> 823,543/531,441 758
>> 81/49 870
>> 1,977,326,743/1,162,261,467 920
>> 3,486,784,401/1,977,326,743 982
>> 49/27 1032
>> 1,594,323/823,543 1144
>> 117,649/59,049 1193
>> 729/343 1305
>> etc.
>
>***Ummm. So *these* are 3-limit and 7-limit? Go figure. Actually, I
>need a little help with this. Howso??

All the ratios' numerators and denominators are divisible by either 3 or
7... or even both in a few cases. Having 3, 7 and/or both, these intervals
have a direct - though in many of the above cases, quite distant - relation to
the 3rd and/or the 7th harmonic(s). IIRC this relationship creates the
intervals' identities.

::to the rest of the list:: Did I explain this correctly and/or clearly
enough?

If I didn't... consult Monzo's dictionary found somewhere amongst Monzo's
pages at http://sonic-arts.org/index.html

also look at all the various JI weblinks at
http://www.math.cudenver.edu/~jstarret/microtone.html

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark"

Brett Campbell writes:
>>"After prolonged exposure to the rich, kaleidoscopic world of microtones,
>>returning to equal-tempered music was for me like going back to black and
>>white after spending a weekend immersed in color".

What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment in
time is always daybreak. - Lucia Dlugoszewski

The gods aren't cool enough to have invented dissonance

"The wonderousness of the human mind is too great to be transferred into
music only by 7 or 12 elements of tone steps in one octave." - shakuhachi master
Masayuki Koga

"There's a rabbinical tradition that the music in heaven will be microtonal
=)" - one annotative interpretation of Talmudic writings

"We cannot doubt that animals both love and practice music. That is evident.
But it seems their musical system differs from ours. It is another school...We
are not familiar with their didactic works. Perhaps they don't have any." -
Erik Satie

"Among the artistic hierarchy, the birds are probably the greatest musicians
to inhabit our planet." - Olivier Messiaen

"I have the feeling that the English word 'noise' has more negative
connotations than our German word 'Gerausch'. We would describe the sound of wind
blowing as Gerausch, to imply that it's a beautiful and natural sound. ...I make
noise...I like these sounds and this has nothing to do with 'anti-beauty'" -
Helmut Lachenmann

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"
LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

...improvisation is about change, about flux rather than stasis. ... you have
to be aware of the fact that improvisation is about a constant change. -
Steve Beresford

hi Hanuman and Joe,

> From: <czhang23@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, May 28, 2003 1:13 AM
> Subject: Re: [tuning] BiG DiGiTS (wasRe: hi, i'm back & a few ???)
>

>
> In a message dated 2003:05:27 06:31:35 PM, jpehrson@rcn.com quotes me &
> writes:
>
> >> 1/1 0
> >> 43,046,721/40,353,607 112
> >> 2,401/2,187 162
> >> 19,683/16,807 273
> >> 5,764,801/4,782,969 323
> >> 9/7 435
> >> 387,420,489/282,475,249 547
> >> 343/243 597
> >> 177,147/117,649 709
> >> 823,543/531,441 758
> >> 81/49 870
> >> 1,977,326,743/1,162,261,467 920
> >> 3,486,784,401/1,977,326,743 982
> >> 49/27 1032
> >> 1,594,323/823,543 1144
> >> 117,649/59,049 1193
> >> 729/343 1305
> >> etc.
> >
> >***Ummm. So *these* are 3-limit and 7-limit? Go figure. Actually, I
> >need a little help with this. Howso??
>
> All the ratios' numerators and denominators are divisible by either 3
or
> 7... or even both in a few cases. Having 3, 7 and/or both, these intervals
> have a direct - though in many of the above cases, quite distant -
relation to
> the 3rd and/or the 7th harmonic(s). IIRC this relationship creates the
> intervals' identities.

here's a prime-factorization of Hanuman's scale,
with more accurate cents-values:

3^ 7^ ~cents

[ 0 0] 0
[ 16 -9] 111.8468556
[ -7 4] 161.6186198
[ 9 -5] 273.4654754
[-14 8] 323.2372396
[ 2 -1] 435.0840953
[ 18 -10] 546.9309509
[ -5 3] 596.7027151
[ 11 -6] 708.5495707
[-12 7] 758.3213349
[ 4 -2] 870.1681905
[-19 11] 919.9399547
[ 20 -11] 982.0150461
[ -3 2] 1031.78681
[ 13 -7] 1143.633666
[-10 6] 1193.40543
[ 6 -3] 1305.252286

i wanted to try to make a lattice of it, but
it wouldn't fit in the Yahoo email window.

really, i think it's pointless to work with
the actual ratio-numbers in a case like this.
it's much easier and more comprehensible to deal
with the exponent-numbers instead.

-monz

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, czhang23@a... wrote:
>
> /tuning/topicId_43899.html#43899
>
> >
> > >yes, most have lots of digits.
> > >
> > >> and they
> > >> wouldn't be "lower limit" primes, yes??
> > >
> > >they could all be 3-prime-limit, and there would still be an
> > >infinite number within any interval space.
> >
> > non-octave 3 & 7 limit (cent values extremely rounded, ok?
if
> not I'd be
> > typing bleedin' numbers all frikkin' night...)
> > {LaMonte Young, beat this, hehe...}
> >
> > 1/1 0
> > 43,046,721/40,353,607 112
> > 2,401/2,187 162
> > 19,683/16,807 273
> > 5,764,801/4,782,969 323
> > 9/7 435
> > 387,420,489/282,475,249 547
> > 343/243 597
> > 177,147/117,649 709
> > 823,543/531,441 758
> > 81/49 870
> > 1,977,326,743/1,162,261,467 920
> > 3,486,784,401/1,977,326,743 982
> > 49/27 1032
> > 1,594,323/823,543 1144
> > 117,649/59,049 1193
> > 729/343 1305
> > etc.
> >
>
> ***Ummm. So *these* are 3-limit and 7-limit? Go figure. Actually,
I
> need a little help with this. Howso??
>
> Tx!
>
> J. Pehrson

i think what zhang meant was that these numerators and denominators
use no prime factors other than 3 and 7. so it's a "special case" of
7-prime-limit, where factors of 2 and 5 are completely absent. it's
not a particularly good illustration of the original idea, which
concerned an arbitrarily small region of interval space such as that
between 400 cents and 401 cents. but if you wanted to, you could find
an infinite number of these "all prime factors are 3 or 7" ratios
within that region, or any other finite region in interval space.

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> All the ratios' numerators and denominators are divisible by
either 3 or
> 7... or even both in a few cases. Having 3, 7 and/or both, these
intervals
> have a direct - though in many of the above cases, quite distant -
relation to
> the 3rd and/or the 7th harmonic(s). IIRC this relationship creates
the
> intervals' identities.

identities -- in what sense?

> ::to the rest of the list:: Did I explain this correctly and/or
clearly
> enough?

i don't know, but i certainly don't believe that large-number ratios
have any audible meaning except insofar as the the numerical
relations with other large-number ratios may be audible small-number
ratios.

in other words, it may be audible that many *pairs* of pitches in
zhang's scale are related by a just 9:7 ratio -- and he's certainly
justified in expressing the scale as he did if the numbers come from
successive applications of the 9:7 ratio mathematically. but take two
pitches that are related by large-digit numbers and the factorization
of those numbers ceases to have any bearing on the sound of the
interval.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, czhang23@a... wrote:
>
> > All the ratios' numerators and denominators are divisible by
> either 3 or
> > 7... or even both in a few cases. Having 3, 7 and/or both, these
> intervals
> > have a direct - though in many of the above cases, quite distant -

> relation to
> > the 3rd and/or the 7th harmonic(s). IIRC this relationship
creates
> the
> > intervals' identities.
>
> identities -- in what sense?
>
> > ::to the rest of the list:: Did I explain this correctly
and/or
> clearly
> > enough?
>
> i don't know, but i certainly don't believe that large-number
ratios
> have any audible meaning except insofar as the the numerical
> relations with other large-number ratios may be audible small-
number
> ratios.

--- In tuning@yahoogroups.com, czhang23@a... wrote:

/tuning/topicId_43899.html#43919

>
> In a message dated 2003:05:27 06:31:35 PM, jpehrson@r... quotes me
&
> writes:
>
> >> 1/1 0
> >> 43,046,721/40,353,607 112
> >> 2,401/2,187 162
> >> 19,683/16,807 273
> >> 5,764,801/4,782,969 323
> >> 9/7 435
> >> 387,420,489/282,475,249 547
> >> 343/243 597
> >> 177,147/117,649 709
> >> 823,543/531,441 758
> >> 81/49 870
> >> 1,977,326,743/1,162,261,467 920
> >> 3,486,784,401/1,977,326,743 982
> >> 49/27 1032
> >> 1,594,323/823,543 1144
> >> 117,649/59,049 1193
> >> 729/343 1305
> >> etc.
> >
> >***Ummm. So *these* are 3-limit and 7-limit? Go figure.
Actually, I
> >need a little help with this. Howso??
>
> All the ratios' numerators and denominators are divisible by
either 3 or
> 7... or even both in a few cases. Having 3, 7 and/or both, these
intervals
> have a direct - though in many of the above cases, quite distant -
relation to
> the 3rd and/or the 7th harmonic(s). IIRC this relationship creates
the
> intervals' identities.
>

***Got it. Thanks zHANg!

JP

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43899.html#43931

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, czhang23@a... wrote:
> >
> > /tuning/topicId_43899.html#43899
> >
> > >
> > > >yes, most have lots of digits.
> > > >
> > > >> and they
> > > >> wouldn't be "lower limit" primes, yes??
> > > >
> > > >they could all be 3-prime-limit, and there would still be an
> > > >infinite number within any interval space.
> > >
> > > non-octave 3 & 7 limit (cent values extremely rounded, ok?
> if
> > not I'd be
> > > typing bleedin' numbers all frikkin' night...)
> > > {LaMonte Young, beat this, hehe...}
> > >
> > > 1/1 0
> > > 43,046,721/40,353,607 112
> > > 2,401/2,187 162
> > > 19,683/16,807 273
> > > 5,764,801/4,782,969 323
> > > 9/7 435
> > > 387,420,489/282,475,249 547
> > > 343/243 597
> > > 177,147/117,649 709
> > > 823,543/531,441 758
> > > 81/49 870
> > > 1,977,326,743/1,162,261,467 920
> > > 3,486,784,401/1,977,326,743 982
> > > 49/27 1032
> > > 1,594,323/823,543 1144
> > > 117,649/59,049 1193
> > > 729/343 1305
> > > etc.
> > >
> >
> > ***Ummm. So *these* are 3-limit and 7-limit? Go figure.
Actually,
> I
> > need a little help with this. Howso??
> >
> > Tx!
> >
> > J. Pehrson
>
> i think what zhang meant was that these numerators and denominators
> use no prime factors other than 3 and 7. so it's a "special case"
of
> 7-prime-limit, where factors of 2 and 5 are completely absent. it's
> not a particularly good illustration of the original idea, which
> concerned an arbitrarily small region of interval space such as
that
> between 400 cents and 401 cents. but if you wanted to, you could
find
> an infinite number of these "all prime factors are 3 or 7" ratios
> within that region, or any other finite region in interval space.

***Oh... finally this is sinking in. In other words, there is an
infinite number of fractions that could appear between, let's say, a
difference in value of one cent, or between *anything* since the
number line extends infinitely, apparently...

JP