interval vector

<<
> What's an interval vector?
>
> A pitch difference expressed as a list of integers, which is much the
> same as a free albelian group.
> >>

In case this has not been clarified, the above use of the term 'interval
vector' is non-standard. According to Forte / Rahn pitch-set theory, which is
still standard in academia, an interval vector is an ordered enumerated list of
six (twelve-tone) interval classes (ic) which are present in a pitch set.

Aaron

> From: pitchcolor@aol.com [mailto:pitchcolor@aol.com]
> Sent: Wednesday, August 13, 2003 2:19 PM
> To: tuning-math@yahoogroups.com
> Subject: [tuning-math] interval vector
>
>
> > > What's an interval vector?
> >
> >
> > A pitch difference expressed as a list of
> > integers, which is much the same as a free albelian
> > group.
> >
> >
>
> In case this has not been clarified, the above use
> of the term 'interval vector' is non-standard.
> According to Forte / Rahn pitch-set theory, which
> is still standard in academia, an interval vector
> is an ordered enumerated list of six (twelve-tone)
> interval classes (ic) which are present in a pitch set.

Aaron is right about that, guys. since Gene honored
me by using my name to describe what you mean here by
"interval vector", it's best to just call it a monzo.

:)

-monz

--- In tuning-math@yahoogroups.com, pitchcolor@a... wrote:
> <<
> > What's an interval vector?
> >
> > A pitch difference expressed as a list of integers, which is much
the
> > same as a free albelian group.
> > >>
>
> In case this has not been clarified, the above use of the
term 'interval
> vector' is non-standard. According to Forte / Rahn pitch-set
theory, which is
> still standard in academia, an interval vector is an ordered
enumerated list of
> six (twelve-tone) interval classes (ic) which are present in a
pitch set.

I've taken to calling the row vector of exponents a "monzo", since I
needed a name to use when documenting my Maple programs for my own
purposes. So far as I know, academia has not taken this as
standard. :)

hi Gene,

> From: Gene Ward Smith [mailto:gwsmith@svpal.org]
> Sent: Wednesday, August 13, 2003 5:42 PM
> To: tuning-math@yahoogroups.com
> Subject: [tuning-math] Re: interval vector
>
>
> --- In tuning-math@yahoogroups.com, pitchcolor@a... wrote:
> >
> > > What's an interval vector?
> > >
> > > A pitch difference expressed as a list of integers,
> > > which is much the same as a free albelian group.
> > >
> >
> > In case this has not been clarified, the above use
> > of the term 'interval vector' is non-standard.
> > According to Forte / Rahn pitch-set theory, which
> > is still standard in academia, an interval vector
> > is an ordered enumerated list of six (twelve-tone)
> > interval classes (ic) which are present in a
> > pitch set.
>
> I've taken to calling the row vector of exponents
> a "monzo", since I needed a name to use when
> documenting my Maple programs for my own purposes.

i already responded to this, saying the same thing.

> So far as I know, academia has not taken this as
> standard. :)

i don't think other scholars would be too accepting
of *me* being the first to promote the use of my own
name for a term, so ... can *you* publish something
with it? that would be a start in gaining acceptance.

-monz

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

> > From: Gene Ward Smith [mailto:gwsmith@s...]
> > Sent: Wednesday, August 13, 2003 5:42 PM

> i don't think other scholars would be too accepting
> of *me* being the first to promote the use of my own
> name for a term, so ... can *you* publish something
> with it? that would be a start in gaining acceptance.

I've decided that this is the 21st century and paper is obsolecent.
It's up on www.xenharmony.org.

> From: Gene Ward Smith [mailto:gwsmith@svpal.org]
> Sent: Wednesday, August 13, 2003 5:52 PM
> To: tuning-math@yahoogroups.com
> Subject: [tuning-math] Re: interval vector
>
>
> --- In tuning-math@yahoogroups.com, <monz@a...> wrote:
>
> > > From: Gene Ward Smith [mailto:gwsmith@s...]
> > > Sent: Wednesday, August 13, 2003 5:42 PM
>
> > i don't think other scholars would be too accepting
> > of *me* being the first to promote the use of my own
> > name for a term, so ... can *you* publish something
> > with it? that would be a start in gaining acceptance.
>
> I've decided that this is the 21st century and paper is obsolecent.
> It's up on www.xenharmony.org.

OK ... works for me. :)

you've probably noticed by now ... almost all of my
work is published in HTML format.

-monz

pitchcolor:

>>In case this has not been clarified, the above use of the >> >>
>term 'interval > >
>>vector' is non-standard. According to Forte / Rahn pitch-set >> >>
>theory, which is > >
>>still standard in academia, an interval vector is an ordered >> >>
>enumerated list of > >
>>six (twelve-tone) interval classes (ic) which are present in a >> >>
>pitch set.
> >
Oh. Richmond Browne (1981) simply calls that a "vector", which is obviously far too general and not even correct in the general case.

Gene:

>I've taken to calling the row vector of exponents a "monzo", since I >needed a name to use when documenting my Maple programs for my own >purposes. So far as I know, academia has not taken this as >standard. :)
> >
But that only a subset of what I called an "interval vector" because it only covers JI defined using consecutive prime numbers.

Graham

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, <monz@a...> wrote:
>
> > > From: Gene Ward Smith [mailto:gwsmith@s...]
> > > Sent: Wednesday, August 13, 2003 5:42 PM
>
> > i don't think other scholars would be too accepting
> > of *me* being the first to promote the use of my own
> > name for a term, so ... can *you* publish something
> > with it? that would be a start in gaining acceptance.
>
> I've decided that this is the 21st century and paper is obsolecent.

Hmmm, if so, then we will be phasing out the use of music stands.
And if so, then musicians must memorize their parts before coming to
rehearsals. Or are live musicians also obsolescent? ;-)

--George

--- In tuning-math@yahoogroups.com, pitchcolor@a... wrote:
> <<
> > What's an interval vector?
> >
> > A pitch difference expressed as a list of integers, which is much
the
> > same as a free albelian group.
> > >>
>
> In case this has not been clarified, the above use of the
term 'interval
> vector' is non-standard. According to Forte / Rahn pitch-set
theory, which is
> still standard in academia, an interval vector is an ordered
enumerated list of
> six (twelve-tone) interval classes (ic) which are present in a
pitch set.
>
> Aaron

That is correct. I also discovered, many years ago, that it is
possible to arrange the 35 hexachord types (reduced for the Z-
relation, when 2 hexachord types have the same interval vector)
into a nice 5 X 7 grid, based on the occurrence of intervals in
the vectors. (1 through 5 only, it excludes the tritone). If there is
any interest in this I could post my grid in the Files section...

--- In tuning-math@yahoogroups.com, "gdsecor" <gdsecor@y...> wrote:

> > I've decided that this is the 21st century and paper is
obsolecent.
>
> Hmmm, if so, then we will be phasing out the use of music stands.

You could invent an electronic music stand for us. Of course we
haven't really gotten book readers right yet, so it may be premature.

--- In tuning-math@yahoogroups.com, pitchcolor@a... wrote:

> In case this has not been clarified, the above use of the
term 'interval
> vector' is non-standard. According to Forte / Rahn pitch-set
theory, which is
> still standard in academia, an interval vector is an ordered
enumerated list of
> six (twelve-tone) interval classes (ic) which are present in a
pitch set.

Clough and Myerson use "chord" to mean a set of interval classes,
and "line" to mean an ordered tuple of interval classes. Has the
latter been taken up in academia?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "gdsecor" <gdsecor@y...> wrote:
>
> > > I've decided that this is the 21st century and paper is
> obsolecent.
> >
> > Hmmm, if so, then we will be phasing out the use of music
stands.
>
> You could invent an electronic music stand for us. Of course we
> haven't really gotten book readers right yet, so it may be
premature.

But it may be sooner than we think. Earlier this year I wrote a
piece in 19-WT using Cakewalk, and I was curious to see if I could
play the solo part on the trumpet (with a couple of slides
adjusted). Performance tempo was a bit beyond my ability, but I
found that I was able to practice it if I set the tempo slower and
set the staff view so that only a few staves displayed (with the solo
part at the top). As the file played, the measures of music
displayed so that I could easily read the part, which automatically
scrolled, so my electronic music stand even turned the pages for me.
Once I mastered the piece at a given tempo, I set it a little faster
and tried again -- something like a computer game in which you
complete each level, then move on to the next (which actually made
practicing fun).

--George

> > You could invent an electronic music stand for us

It's been done.

http://www.estand.com/products.html

Harry Connick Jr. (sp?) developed one and has toured with them for a
number of years now.

Aaron

> > You could invent an electronic music stand for us

It's been done.

http://www.estand.com/products.html

Harry Connick Jr. (sp?) developed one and has toured with them for a
number of years now.

Aaron

> Clough and Myerson use "chord" to mean a set of interval classes,
> and "line" to mean an ordered tuple of interval classes. Has the
> latter been taken up in academia?

No. Both of these terms are already too well established to be
burdened with new arbitrary definitions like these (which work well
enough in the context of a paper). However, the term 'lyne' has
become fairly standard, meaning a series of pitches in one voice of
an array. (Milton Babbitt, Andrew Mead, et al)

Aaron