Some chords in 19tet.

There appear to be eight 3-note chords in 19tet which might have
theoretical legitimacy. These are 0-253-632, 0-316-632, 0-379-632 and 0-
253-695, 0-316-695, 0-379-695, 0-442-695 and 0-379-758.

--- In tuning@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> There appear to be eight 3-note chords in 19tet which might
> have theoretical legitimacy.

Dare I ask what theory you're using to filter these chords?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > There appear to be eight 3-note chords in 19tet which might
> > have theoretical legitimacy.
>
> Dare I ask what theory you're using to filter these chords?
>
> -Carl
> I begin with the mathematical possibilities. Then I select those
possibilities which can be mapped onto C,F and Gmajor chords and which
form ascending heptatonic scales. I rule out any chords which overlap.
The resulting chords can at least be inputted into I-IV-V situations
however consonant or dissonant they might sound. It is just a working
model to approach any equal temperament. Rather than fiddling around
with all the math possibilities all the time I just use this method as
a preliminary plan of action. If one is going to investigate an equal
temperament then one may as well have a consistent methodology.

Dear Robert,

On May 9, 2008, at 7:06 PM, robert thomas martin wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> > >
> > > There appear to be eight 3-note chords in 19tet which might
> > > have theoretical legitimacy.
> >
> > Dare I ask what theory you're using to filter these chords?
> >
> > -Carl
> > I begin with the mathematical possibilities. Then I select those
> possibilities which can be mapped onto C,F and Gmajor chords and which
> form ascending heptatonic scales. I rule out any chords which overlap.
> The resulting chords can at least be inputted into I-IV-V situations
> however consonant or dissonant they might sound. It is just a working
> model to approach any equal temperament. Rather than fiddling around
> with all the math possibilities all the time I just use this method as
> a preliminary plan of action. If one is going to investigate an equal
> temperament then one may as well have a consistent methodology.
>

am I understanding correctly: you suggest to reduce your musical world to those chords (triads only?) by which you can express I IV V progressions? I do understand that following H. Riemann's harmonic theory (based on T S D) you can analyse very many further chords as relatives of these three fundamental harmonic functions (e.g., there is Tp, TP, Tg, etc.). Are you also including these? Also, what about modulation? More to the point, if you allow for septimal chords (as your previous lists showed), why excluding septimal root progressions (not covered by Riemann..)?

I fully understand that it can be reasonable in specific musical situations or styles to restrict yourself to I IV V, but you where talking about "theoretical legitimacy". One could possibly misunderstand your comment such as you were implying that the music of, say, Schubert (not limited to plain I IV V) has no "theoretical legitimacy" :)

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

--- In tuning@yahoogroups.com, Torsten Anders <torstenanders@...>
wrote:
>
> Dear Robert,
>
> On May 9, 2008, at 7:06 PM, robert thomas martin wrote:
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "robert thomas martin"
> > > <robertthomasmartin@> wrote:
> > > >
> > > > There appear to be eight 3-note chords in 19tet which might
> > > > have theoretical legitimacy.
> > >
> > > Dare I ask what theory you're using to filter these chords?
> > >
> > > -Carl
> > > I begin with the mathematical possibilities. Then I select those
> > possibilities which can be mapped onto C,F and Gmajor chords and
which
> > form ascending heptatonic scales. I rule out any chords which
overlap.
> > The resulting chords can at least be inputted into I-IV-V
situations
> > however consonant or dissonant they might sound. It is just a
working
> > model to approach any equal temperament. Rather than fiddling
around
> > with all the math possibilities all the time I just use this
method as
> > a preliminary plan of action. If one is going to investigate an
equal
> > temperament then one may as well have a consistent methodology.
> >
>
> am I understanding correctly: you suggest to reduce your musical
> world to those chords (triads only?) by which you can express I IV
V
> progressions? I do understand that following H. Riemann's harmonic
> theory (based on T S D) you can analyse very many further chords
as
> relatives of these three fundamental harmonic functions (e.g.,
there
> is Tp, TP, Tg, etc.). Are you also including these? Also, what
about
> modulation? More to the point, if you allow for septimal chords
(as
> your previous lists showed), why excluding septimal root
progressions
> (not covered by Riemann..)?
>
> I fully understand that it can be reasonable in specific musical
> situations or styles to restrict yourself to I IV V, but you where
> talking about "theoretical legitimacy". One could possibly
> misunderstand your comment such as you were implying that the
music
> of, say, Schubert (not limited to plain I IV V) has
no "theoretical
> legitimacy" :)
>
> Best
> Torsten
>
> --
> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586227
> Private: +44-1752-558917
> http://strasheela.sourceforge.net
> http://www.torsten-anders.de
> It is just a working method to apply to ANY equal temperament. I
used the word MIGHT have theoretical legitimacy. This method reduces
all the equal temperaments to a level playing field. This method
would also say that "there are two 3-note chords in 12tet which might
have theoretical legitimacy. These are 0-300-700 and 0-400-700."

--- In tuning@yahoogroups.com, "robert thomas martin" wrote:

> It is just a working method to apply to ANY equal temperament. I
> used the word MIGHT have theoretical legitimacy. This method reduces
> all the equal temperaments to a level playing field.

How would equal temperaments NOT be on a level playing field?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas martin" wrote:
>
> > It is just a working method to apply to ANY equal temperament. I
> > used the word MIGHT have theoretical legitimacy. This method
reduces
> > all the equal temperaments to a level playing field.
>
> How would equal temperaments NOT be on a level playing field?
>
> -Carl
>

From Robert: Equal temperaments are not on a level playing field
when everyone has their own personal favorite. My method is just an
analytical tool. It is not intended to take the place of more intense
scrutiny. A journey of a thousand miles begins with the first step
said Confucius et al. My postings Some chords in Xtet should be
regarded as only beginner's guides. They are certainly not intended
to be the first and last statement on the matter.