Reply to Kraig Grady

I think you're looking for Euler's "totient" function.

>I know I not being completely clear here but if we can find this word
we
>can say that it would be limit would be determined by the lowest odd
number within the context of an >uninterrupted chain of "tolent". You
would have to have this because
>if you allowed the chain to be interrupted you could say that even
though you have a 7/6 and an 7/4 in a >scale they are a 3/2 apart (this
being a partial chain) but
>sooner or later you have to examine it relation to a 5/4 or 1/1. It is
if the simplest latticing of a scale >would determine a limit.

I am very interested in what you are saying here, so if you could try to
be more clear, with a few examples, etc., I'd be delighted. I think my
response to Paul Hahn explained my view on this, but maybe there are
finer points we can get into here.

Kraig Grady wrote:

>Wilson has suggested the term "Cap"
>opposed to "limit" as being less confusing cause with limit you are
never sure whether it is inclusive or >not!

Looking at my own paper, I must admit that I used the term limit in both
the exclusive of all simpler ratios ("harmonic plane") and the inclusive
of all simpler ratios ("tonality diamond") senses. Clearly the inclusive
sense is more appropriate and Partch coined the term "ratio of N" for
the exclusive case. However, it would be nice to have a noun which
refers to a property of a ratio, that of belonging to the set of ratios
of N, to prevent the language from becoming extremely awkward (as it
would if one tried to rewrite Gary's post using the "ratio of N"
terminology). Is that where you're proposing the word "Cap"? In other
words, the odd-Cap of a ratio would be the higher of the highest odd
factor of the numerator and the highest odd factor of the denominator?
If so, then the n-limit includes all ratios whose Cap is less than or
equal to N.

I have a feeling this is not what you meant, but it would still be
useful to have such a noun. Can anyone think of a term that would convey
this meaning more simply than "belonging to the set of ratios of N"?

>> No one knows
>> what ancient Greek music sounded like, certainly not subcommatic variations
>> within the scale. There is evidence that in ancient India sruti #2 (out of
>> 22) was tempered, implying that they recognized the syntonic comma, but not
>> the diaschisma, as a pitch difference.

>In working against drones, intonation becomes even more important. I can't
>imagine how any theorist could make a mistake like that!

It's not a mistake. Since sruti #2 was expected to serve as both the 3:2
below sruti #15 (8/5) as the 4:3 below sruti #11 (45/32), but would in either
case be dissonant against the drone, a compromise was adopted on many
instruments.

Paul!
I am not familiar with ragas refers to by number only by name. Do you know
the name and/or the full set of ratios!

perlich@acadian-asset.com wrote:

> From: perlich@acadian-asset.com
>
> >> No one knows
> >> what ancient Greek music sounded like, certainly not subcommatic variations
> >> within the scale. There is evidence that in ancient India sruti #2 (out of
> >> 22) was tempered, implying that they recognized the syntonic comma, but not
> >> the diaschisma, as a pitch difference.
>
> >In working against drones, intonation becomes even more important. I can't
> >imagine how any theorist could make a mistake like that!
>
> It's not a mistake. Since sruti #2 was expected to serve as both the 3:2
> below sruti #15 (8/5) as the 4:3 below sruti #11 (45/32), but would in either
> case be dissonant against the drone, a compromise was adopted on many
> instruments.

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

>Paul!
>I am not familiar with ragas refers to by number only by name. Do you know
>the name and/or the full set of ratios!

I didn't refer to any ragas by either number or name, and I gave enough ratios
to make my point, though the full set of ratios for ma- and sa-grama, along with
the standard alterations, can be found in table 2 of my paper, table 3 illustrating
again how sruti 2 has a different JI interpretation depending on whether it is
construed as an alteration in ma-grama or in sa-grama.
(In case you do look at my paper, note that page 20 in the .pdf version is in error and should be deleted).
Clearly the entire field of Indian tuning is highly contreversial, but I wouldn't
be making these claims if I didn't feel they were supported by a good deal of
research on my part.

I don't understand a thing you are say. what paper!what ratios! All ragas have names!

perlich@acadian-asset.com wrote:

> From: perlich@acadian-asset.com
>
> >Paul!
> >I am not familiar with ragas refers to by number only by name. Do you know
> >the name and/or the full set of ratios!
>
> I didn't refer to any ragas by either number or name, and I gave enough ratios
> to make my point, though the full set of ratios for ma- and sa-grama, along with
> the standard alterations, can be found in table 2 of my paper, table 3 illustrating
> again how sruti 2 has a different JI interpretation depending on whether it is
> construed as an alteration in ma-grama or in sa-grama.
> (In case you do look at my paper, note that page 20 in the .pdf version is in error and should be deleted).
> Clearly the entire field of Indian tuning is highly contreversial, but I wouldn't
> be making these claims if I didn't feel they were supported by a good deal of
> research on my part.
>
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-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

Daniel Wolf wrote,

>Although Paul Erlich probably does use the term "ancient Indian music" a
bit
>loosely, you should keep in mind that the drone appears to have been
>introduced fairly recently -- earliest in the 16th century -- so there is
an
>important change in the character of the music at that time, although the
>theoretical tradition appears so seemless.

Kraig Grady was the one who brought up the drone, as an argument to support
using just ratios. I was pointing out that sruti #2, whether tuned 16/15,
135/128, or somewhere in-between, would be dissonant against the drone and
not directly tunable to the drone by ear.

>I cannot comment about Hindustani music, but I have measured many a
>(Karnatic) vina fret, and they tend to be tuned rather than tempered, a
>finding in contradiction to Erlich's. Where one of the 12 frets has to
cover
>more than one distinct pitch, one of the two is chosen, and the other is
>reached by bending.

Daniel, at most only one fret, sruti #2, would have to be tempered. This was
in the days when sa-grama and ma-grama were both in use. Since ma-grama has
fallen out of use in modern times, it would not make sense for a modern
insturment to preserve these distinctions.

Kraig Grady wrote,

>I don't understand a thing you are say. what paper!

My paper _Tuning, Tonality, and Twenty-Two-Tone Temperament_ in
Xenharmonikon 17 or http://www-math.cudenver.edu/~jstarret/22ALL.pdf.

>what ratios!

45/32, 8/5, etc.

>All ragas have names!

Yes they do!

Kraig,

If you were asking how Fokker (or I) determined the 22 points inside the
parallelopiped, I went through a 5-limit example in my post of Fri 9/24/99
6:22 PM, entitled "Reply to Joe Monzo". I proceeded to explain to Carl Lumma
why this method works, and am still in the process of explaining matrix
multiplication to him. Let me know if anything in these discussions is
unclear to you.

-Paul

> [Paul Erlich, TD 336.8]
>
> If you were asking how Fokker (or I) determined the 22 points
> inside the parallelopiped, I went through a 5-limit example
> in my post of Fri 9/24/99 6:22 PM, entitled "Reply to Joe Monzo".
> I proceeded to explain to Carl Lumma why this method works,
> and am still in the process of explaining matrix multiplication
> to him. Let me know if anything in these discussions is
> unclear to you.

You're explaining all this to me too, Paul. :)

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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Kraig wrote,

>I find the vibes strong
>enough to overcome either the delay (on the same pitches BTW) or the
metered (mixtures of 13
>and 8) gong in the bathtub. I take it you find it too much.

I just mean you just spent the day talking about how the harmonic series is
special and yet these vibes are weak in harmonics (though the distortion
"helps") and have prominent inhamonic partials that kind of stick out.

Paul!
It is only the attack that has inharmonic tones. It seems to me, the sustained sound is
quite close to a sine (I am sure the resonators have a lot to do with this)! In large
ensembles vibes can be a big problem .In the original version of IN C all you hear is the
horrible vibe attack and nothing else. It really didn't work.

"Paul H. Erlich" wrote:

> Kraig wrote,
>
> >I find the vibes strong
> >enough to overcome either the delay (on the same pitches BTW) or the
> metered (mixtures of 13
> >and 8) gong in the bathtub. I take it you find it too much.
>
> I just mean you just spent the day talking about how the harmonic series is
> special and yet these vibes are weak in harmonics (though the distortion
> "helps") and have prominent inhamonic partials that kind of stick out.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

>It is only the attack that has inharmonic tones.

Well, they do die out rather quickly . . .

>It seems to me, the sustained sound is
>quite close to a sine

If one wanted to project the consonance of the utonal trianies, some
harmonic overtones might help.