New on the integer sequences list

http://www.research.att.com/~njas/sequences/?q=Gene+Ward+Smith&sort=0&fmt=0&language=english&go=Search

http://tinyurl.com/flxtj

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> http://www.research.att.com/~njas/sequences/?
q=Gene+Ward+Smith&sort=0&fmt=0&language=english&go=Search
>
> http://tinyurl.com/flxtj

Nice. The RZH and RZF is what led me to this newsgroup.
Say, what's all the buzz about 42 that is going around,
in terms of the RZF? All I know is that it is related
to quantum theory, and has something to do with the "moment
of the RZF", what is that. Does it relate to tuning, also?

Paul Hj

> Message: 3
> Date: Thu, 30 Mar 2006 05:53:54 -0000
> From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
> Subject: New on the integer sequences list
>
> http://www.research.att.com/~njas/sequences/?q=Gene+Ward+Smith&sort=0&fmt=0&language=english&go=Search
>
> http://tinyurl.com/flxtj

Thanks Gene. I still find the zeta sequences very surprising.

Re the lists of decreasing Pepper ambiguity: these are the same sequences as decreasing maximum error penalised by (multiplying by) the edo's cardinality. I would have found this to be a simpler description.

-Jon

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul_hjelmstad@...> wrote:

> Say, what's all the buzz about 42 that is going around,
> in terms of the RZF? All I know is that it is related
> to quantum theory, and has something to do with the "moment
> of the RZF", what is that. Does it relate to tuning, also?

It's the Keating-Snaith conjecture, and it might indeed have something
to do with tuning, since the peaks of zeta on the critical line have
something to do with tuning. Certainly it's related to tuning at least
indirectly, if not directly.

Here's information on the Keating-Snaith conjecture:

http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/31/09/

www.newton.cam.ac.uk/webseminars/pg+ws/2004/rma/02/05/hughes/all.pdf

That talk is very interesting, and the business of the gaps between
the zeros mentioned in it is directly related to tuning theory, as you
can see from one of my Sloane sequences.

Here's a paper citation:

J.P. Keating, and N.C. Snaith, Random matrix theory and zeta(1/2+it).
Comm. Math. Phys. 214 (2000), no. 1, 57-89.

--- In tuning-math@yahoogroups.com, Jon Wild <wild@...> wrote:

> Re the lists of decreasing Pepper ambiguity: these are the same
sequences
> as decreasing maximum error penalised by (multiplying by) the edo's
> cardinality. I would have found this to be a simpler description.

I like the description I gave because it is unambiguous, and clearly
defines a property of the edo, not an equal temperament val. This
makes a difference; defining it your way could be taken to mean 2
should be included on the list. However, it might be worth sending in
a comment about this.

Gene wrote:

>> Re the lists of decreasing Pepper ambiguity: these are the same >> sequences as decreasing maximum error penalised by (multiplying by) the >> edo's cardinality. I would have found this to be a simpler description.
>
> I like the description I gave because it is unambiguous, and clearly > defines a property of the edo, not an equal temperament val. This makes > a difference; defining it your way could be taken to mean 2 should be > included on the list.

I guess I don't see how "decreasing maximum error penalised by cardinality" is ambiguous, or how 2 could potentially be included (in the 5-limit sequence). The maximum 5-limit error in 1-tet is 498 cents; in 2-tet it is 316 cents - penalise that by multiplying by 2 and it's worse than 1-tet, so shouldn't be on the list.

And it doesn't matter, but I don't see what you're getting at with the "property of the edo" vs "property of the equal temperament val" distinction. The universe of discourse is the set of edos, and the measure that decreases in the sequence, according to either definition, can be most simply understood as a property of the edo.

--- In tuning-math@yahoogroups.com, Jon Wild <wild@...> wrote:

> I guess I don't see how "decreasing maximum error penalised by
> cardinality" is ambiguous, or how 2 could potentially be included
(in the
> 5-limit sequence).

Does decreasing maximum error assume consistency or not? If it
doesn't, do we take the error of a val or do we compute an
inconsistent error?

The maximum 5-limit error in 1-tet is 498 cents; in
> 2-tet it is 316 cents - penalise that by multiplying by 2 and it's
worse
> than 1-tet, so shouldn't be on the list.

You are assuming we measure inconsistent error, but that will be true
only if we define it that way. If we do, then yes, it will give the
same result, but I don't think the description becomes clearer. If we
assume that we want to measure the error from assigning 3 to 2 and
also 5 to 2, ie for <1 2 2|, which seems logical enough, then the
maximum error is 884 cents, from tempering out 5/3. If instead we
measure the error for <1 2 3| then it is 814 cents from tempering out 8/5.

Certainly we don't want the extreme murkiness of Mark Rankin's
descriptions; I've written him to see if we could clean up the
language, but have had no response.

Gene:
> Does decreasing maximum error assume consistency or not? If it doesn't, > do we take the error of a val or do we compute an inconsistent error?

I would have thought a safe assumption was that not mentioning inconsistency or vals means those concepts aren't required. The definition is understandable by someone who doesn't know what consistency is, or what a val is. It's quite simply what it says it is; it measures the error, independent of whether the error is consistent or inconsistent.

It's true that it would be nice to have another sequence that disqualifies or further penalises inconsistent edos. But that's not the point here, since those edos don't get disqualified or penalised in the "Pepper ambiguity" sequence either.

In the end my point is just that "decreasing maximum error as fraction of step-size" will give the same results as "decreasing ratio of closest approx to second-closest approx" i.e. decreasing Pepper ambiguity, but with--it seemed to me!--less fuss.

--- In tuning-math@yahoogroups.com, Jon Wild <wild@...> wrote:

> I would have thought a safe assumption was that not mentioning
> inconsistency or vals means those concepts aren't required. The
definition
> is understandable by someone who doesn't know what consistency is,
or what
> a val is. It's quite simply what it says it is; it measures the error,
> independent of whether the error is consistent or inconsistent.

But it doesn't measure the error in any unambiguous way. It certainly
does not measure the error of a major triad.

>But it doesn't measure the error in any unambiguous way. It certainly
>does not measure the error of a major triad.

What if Jon clarified by saying 'dyadic error'?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >But it doesn't measure the error in any unambiguous way. It certainly
> >does not measure the error of a major triad.
>
> What if Jon clarified by saying 'dyadic error'?

Why isn't it about as clear as it possibly can be the way it is now?
Sending in an additional comment would make sense, though.

>> >But it doesn't measure the error in any unambiguous way. It certainly
>> >does not measure the error of a major triad.
>>
>> What if Jon clarified by saying 'dyadic error'?
>
>Why isn't it about as clear as it possibly can be the way it is now?
>Sending in an additional comment would make sense, though.

Jon's formulation is a lot simpler and more direct than Keenan's.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >> >But it doesn't measure the error in any unambiguous way. It
certainly
> >> >does not measure the error of a major triad.
> >>
> >> What if Jon clarified by saying 'dyadic error'?
> >
> >Why isn't it about as clear as it possibly can be the way it is now?
> >Sending in an additional comment would make sense, though.
>
> Jon's formulation is a lot simpler and more direct than Keenan's.

I don't see why; I think you need more verbiage to sort it out. You
can't just say "best" like Mark Rankin does; you need to say for each
member of the tonality diamond you choose the best tuning for that
member, *independently* of any other member. Then, you multiply the
maximum error so obtained by the number of notes in an octave.

>I don't see why; I think you need more verbiage to sort it out. You
>can't just say "best" like Mark Rankin does; you need to say for each
>member of the tonality diamond you choose the best tuning for that
>member, *independently* of any other member. Then, you multiply the
>maximum error so obtained by the number of notes in an octave.

This verbiage is a definition of dyads, which seems to be required
in a definition of Pepper ambiguity.

-Carl