Joe on odd limits

Here is what he has; no definition of "n-odd-limit interval" is
given, and I suggest none needs to be.

2. <odd.htm> limit: the n-limit is the set all ratios of <ratio-
of.htm> all odd numbers no greater than odd-number n, i.e., those
ratios with odd factors no larger than n.
A chord in Just Intonation where all <interval.htm>-ratios belong to
the n-limit is said to be an "n-limit" chord. A composition or style
where chords of the n-limit are considered <consonance.htm> and
chords of any higher limit are considered <dissonance.htm> is said to
be an "n-limit" composition or style.
When interpreted as a set of pitches <pitch.htm> instead of a set of
intervals, the n-limit is known as the "n-limit tonality diamond
<tondiam.htm>".

Gene, according to this definition, it seems very clear to me that "n-
odd-limit interval" would mean "any interval which is a ratio of
<ratio- of.htm> some odd number not greater than n".

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Here is what he has; no definition of "n-odd-limit interval" is
> given, and I suggest none needs to be.
>
>
> 2. <odd.htm> limit: the n-limit is the set all ratios of <ratio-
> of.htm> all odd numbers no greater than odd-number n, i.e., those
> ratios with odd factors no larger than n.
> A chord in Just Intonation where all <interval.htm>-ratios belong
to
> the n-limit is said to be an "n-limit" chord. A composition or
style
> where chords of the n-limit are considered <consonance.htm> and
> chords of any higher limit are considered <dissonance.htm> is said
to
> be an "n-limit" composition or style.
> When interpreted as a set of pitches <pitch.htm> instead of a set
of
> intervals, the n-limit is known as the "n-limit tonality diamond
> <tondiam.htm>".

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> Gene, according to this definition, it seems very clear to me
that "n-
> odd-limit interval" would mean "any interval which is a ratio of
> <ratio- of.htm> some odd number not greater than n".

Why? Clearly generic intervals are not even in question; only
consonances are being defined. The only sort of interval which seems
relevant is the two-note chord. Anyway I counsel against the usage,
which seems to be to be asking for trouble, and to be entirely
useless besides.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> > Gene, according to this definition, it seems very clear to me
> that "n-
> > odd-limit interval" would mean "any interval which is a ratio of
> > <ratio- of.htm> some odd number not greater than n".
>
> Why? Clearly generic intervals are not even in question;

Why should they be?

> only
> consonances are being defined.

Consonances are intervals too. When n happens to be prime, the
term 'n-limit consonances' has been used in the past (in my paper and
on this list before you joined; I think you must have picked it up)
to distinguish them from 'n-limit intervals' under the *prime-limit*
definition of the latter.

> The only sort of interval which seems
> relevant is the two-note chord.

That's the only kind of interval one would normally think about in
this context. Meanwhile, the odd-limit concept has led us to
interesting chordal territory such as ASSes, etc.

> Anyway I counsel against the usage,
> which seems to be to be asking for trouble,

Such as?

> and to be entirely
> useless besides.

It's only going to aid in avoiding ambiguity, as far as I can see.

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> > Anyway I counsel against the usage,
> > which seems to be to be asking for trouble,
>
> Such as?

Such as we've seen all through this thread.

> > and to be entirely
> > useless besides.
>
> It's only going to aid in avoiding ambiguity, as far as I can see.

"5-limit consonance" is not ambiguous, and "5-limit interval" is only
ambiguous if you pig-headedly insist it is going to be, by sometimes
implicitly assumuing such intervals are restricted to being
consonances, but not saying so. There's no point in deliberately
courting ambiguity in this way.

on 12/1/03 8:17 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
>>> and to be entirely
>>> useless besides.
>>
>> It's only going to aid in avoiding ambiguity, as far as I can see.
>
> "5-limit consonance" is not ambiguous, and "5-limit interval" is only
> ambiguous if you pig-headedly insist it is going to be, by sometimes
> implicitly assumuing such intervals are restricted to being
> consonances, but not saying so. There's no point in deliberately
> courting ambiguity in this way.

Whether Carl is courting ambiguity I can not judge. For myself, I'm just
trying to learn the language, which involves recognizing the ambiguities.
(I *may* be approaching this learning somewhat pig-headedly at the moment.)
One person's perspective is not sufficient to establish a lack of ambiguity.
It sounds as if you don't recognize Paul's perspective as being as real as
yours in this. The bodily sense of pig-headedness is something I actually
do experience when reading your message but do not experience when reading
Paul's and so I wonder whether this might be a projection on your part.
This is of course my own projection but I offer it as a possible input in
your quest for recognition of your own propensities of character. ;)

In any case, I can not find a definition of "N-limit consonance" appearing
anywhere in the monz dictionary, except possibly implied by definition 2 on
the limit page. So I want to know what this animal is. The monz
"consonance" page refers to "interval". While it does not equate a
consonance to an interval, it defines conconance as a property of some
intervals, or as something that may emerge in the experience of some
intervals. So I have no information that distinguishes the contextual
implications of "consonance" versus "interval" in relation to "N-limit".
The only implicatory distinction I can find between "consonance" and
"interval" is that "consonance" may involve a chord (multiple intervals).

I could try to extract a definition of "N-limit consonance" from definition
2 on the limit page. From reading this:

> A chord in Just Intonation where all interval-ratios belong to the n-limit is
> said to be an "n-limit" chord. A composition or style where chords of the
> n-limit are considered consonant and chords of any higher limit are considered
> dissonant is said to be an "n-limit" composition or style.

I get an indication of a conceivable definition such as this:

N-limit consonance - A chord which is considered consonant in an N-limit
composition.

But that is no different from an N-limit chord, and if the discussion is
restricted to dyads, that is no different from an N-limit interval. Thus I
still can not distinguish an N-limit consonance from an N-limit interval.

I thought at one point that maybe "N-limit consonance" might be a way of
referring to an idealized just entity considered to be "behind" an actual
chord which is an approximation to such a consonance and which might be
heard as "referring" to such a consonance. But that's not it, is it?

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> In any case, I can not find a definition of "N-limit consonance"

As I was just saying, "N-limit consonance" is just another way of
saying "N-odd-limit interval" . . . when you want to use the word
limit but don't want to risk confusion with the 'prime' definition of
limit, and don't want to use the awkward phrase "odd-limit". Gene's
whole argument is that we should *never* use the phrase "odd-limit".
If you have an "N-limit consonance", and "N-limit diamond", or "N-
limit consistency", the odd definition of limit is automatically
implied. But, while of course agreeing with Gene that we don't want
to encourage ambiguous speech, I'm willing to accept some awkwardness
so that we can be sure we avoid any possible ambiguity in the
reader's mind.

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> > In any case, I can not find a definition of "N-limit consonance"
>
> As I was just saying, "N-limit consonance" is just another
> way of saying "N-odd-limit interval" . . . when you want to
> use the word limit but don't want to risk confusion with
> the 'prime' definition of limit, and don't want to use the
> awkward phrase "odd-limit". Gene's whole argument is that
> we should *never* use the phrase "odd-limit". If you have
> an "N-limit consonance", and "N-limit diamond", or "N-limit
> consistency", the odd definition of limit is automatically
> implied. But, while of course agreeing with Gene that we
> don't want to encourage ambiguous speech, I'm willing to
> accept some awkwardness so that we can be sure we avoid any
> possible ambiguity in the reader's mind.

i agree with you *totally*, paul.

-monz

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

Gene's
> whole argument is that we should *never* use the phrase "odd-
limit".

My argument is that we should never use the phase "odd-limit
interval" because it is confusing.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >
> > > In any case, I can not find a definition of "N-limit consonance"
> >
> > As I was just saying, "N-limit consonance" is just another
> > way of saying "N-odd-limit interval" . . . when you want to
> > use the word limit but don't want to risk confusion with
> > the 'prime' definition of limit, and don't want to use the
> > awkward phrase "odd-limit". Gene's whole argument is that
> > we should *never* use the phrase "odd-limit". If you have
> > an "N-limit consonance", and "N-limit diamond", or "N-limit
> > consistency", the odd definition of limit is automatically
> > implied. But, while of course agreeing with Gene that we
> > don't want to encourage ambiguous speech, I'm willing to
> > accept some awkwardness so that we can be sure we avoid any
> > possible ambiguity in the reader's mind.
>
>
> i agree with you *totally*, paul.
>
> -monz

Me too.

-- Dave Keenan