Some chords in 22tet.

Eight 3-note chords in 22tet which deserve closer study are these:
Diminished triads 0-273-655 and 0-327-655 and 0-382-655. Minor triads 0-
273-709 and 0-327-709. Major triads 0-382-709 and 0-436-709. Augmented
triad 0-382-764. For those inclined the Ars Nova program called
Counterpointer might be helpful in trying to establish some sort of
SATB voice leading principles in 22tet. Just a suggestion.

--- "robert thomas martin" wrote:

> Eight 3-note chords in 22tet which deserve closer study are these:
[snip]
> Minor triads 0-273-709 and 0-327-709.

These are 6:7:9 ("subminor triad") and 10:12:15 ("minor
triad") in just intonation.

> Major triads 0-382-709 and 0-436-709.

4:5:6 ("major triad") and 14:18:21 ("supermajor triad").

> Augmented triad 0-382-764.

This is something of what we'd call an SSS chord -- a chord
that's slightly impossible in just intonation. It's as if
5/4 + 5/4 = 14/9.

> Diminished triads 0-273-655 and 0-327-655 and 0-382-655.

Not sure what to call these. They're pretty harsh.

> For those inclined the Ars Nova
> program called Counterpointer might be helpful in trying to
> establish some sort of SATB voice leading principles in 22tet.
> Just a suggestion.

That's interesting; I wasn't familiar with counterpointer.
Does it support alternate tunings? If not, how are you
working with it?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- "robert thomas martin" wrote:
>
> > Eight 3-note chords in 22tet which deserve closer study are these:
> [snip]
> > Minor triads 0-273-709 and 0-327-709.
>
> These are 6:7:9 ("subminor triad") and 10:12:15 ("minor
> triad") in just intonation.
>
> > Major triads 0-382-709 and 0-436-709.
>
> 4:5:6 ("major triad") and 14:18:21 ("supermajor triad").
>
> > Augmented triad 0-382-764.
>
> This is something of what we'd call an SSS chord -- a chord
> that's slightly impossible in just intonation. It's as if
> 5/4 + 5/4 = 14/9.
>
> > Diminished triads 0-273-655 and 0-327-655 and 0-382-655.
>
> Not sure what to call these. They're pretty harsh.
>
> > For those inclined the Ars Nova
> > program called Counterpointer might be helpful in trying to
> > establish some sort of SATB voice leading principles in 22tet.
> > Just a suggestion.
>
> That's interesting; I wasn't familiar with counterpointer.
> Does it support alternate tunings? If not, how are you
> working with it?
>
> -Carl
> I don't have Counterpointer. I'm just presuming that it exists and
works for the Fux, Palestrina and Bach algorithms which it claims to
cater for. I also presume that it can be connected via a midi
interface to a Kurzweil which is tuned to my universal chord
algorithm. I can only suggest that you choose a microtonal chord
(anything you like) and tune a Kurzweil (or similar) and play a few
Bach chorales. Just playing a chord in isolation doesn't really do
much justice to 22tet chords. By the way I looked up your profile. It
turns out that you are 30--not such an old chap at
all.
Robert.

On May 7, 2008, at 5:50 PM, robert thomas martin wrote:
> > > For those inclined the Ars Nova
> > > program called Counterpointer might be helpful in trying to
> > > establish some sort of SATB voice leading principles in 22tet.
> > > Just a suggestion.
> >
> > That's interesting; I wasn't familiar with counterpointer.
> > Does it support alternate tunings? If not, how are you
> > working with it?
> >
> > -Carl
> > I don't have Counterpointer. I'm just presuming that it exists and
> works for the Fux, Palestrina and Bach algorithms which it claims to
> cater for. I also presume that it can be connected via a midi
> interface to a Kurzweil which is tuned to my universal chord
> algorithm. I can only suggest that you choose a microtonal chord
> (anything you like) and tune a Kurzweil (or similar) and play a few
> Bach chorales. Just playing a chord in isolation doesn't really do
> much justice to 22tet chords. By the way I looked up your profile. It
> turns out that you are 30--not such an old chap at
> all.
> Robert.
>

If you are interested, such theories could be modelled in Strasheela. I am presently working on Josquin-inspired counterpoint (less rigid than Palestrina or even Fux). I would be interested in transforming its rules for septimal intervals (possibly in 22 ET, although I would prefer a more just intonation). Any music theory wishlist / rule ideas for which you would like to have a computer program generating such music? I am always collecting ideas :)

Best
Torsten

PS: I am sorry that I still did not respond to answered I got recently from Carl, Graham, and Hans. I have a paper deadline, and the day has only 24 hours...

--
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:
>
>
> On May 7, 2008, at 5:50 PM, robert thomas martin wrote:
> > > > For those inclined the Ars Nova
> > > > program called Counterpointer might be helpful in trying to
> > > > establish some sort of SATB voice leading principles in 22tet.
> > > > Just a suggestion.
> > >
> > > That's interesting; I wasn't familiar with counterpointer.
> > > Does it support alternate tunings? If not, how are you
> > > working with it?
> > >
> > > -Carl
> > > I don't have Counterpointer. I'm just presuming that it exists
and
> > works for the Fux, Palestrina and Bach algorithms which it claims
to
> > cater for. I also presume that it can be connected via a midi
> > interface to a Kurzweil which is tuned to my universal chord
> > algorithm. I can only suggest that you choose a microtonal chord
> > (anything you like) and tune a Kurzweil (or similar) and play a
few
> > Bach chorales. Just playing a chord in isolation doesn't really do
> > much justice to 22tet chords. By the way I looked up your
profile. It
> > turns out that you are 30--not such an old chap at
> > all.
> > Robert.
> >
>
> If you are interested, such theories could be modelled in
Strasheela.
> I am presently working on Josquin-inspired counterpoint (less
rigid
> than Palestrina or even Fux). I would be interested in
transforming
> its rules for septimal intervals (possibly in 22 ET, although I
would
> prefer a more just intonation). Any music theory wishlist / rule
> ideas for which you would like to have a computer program
generating
> such music? I am always collecting ideas :)
>
> Best
> Torsten
>
> PS: I am sorry that I still did not respond to answered I got
> recently from Carl, Graham, and Hans. I have a paper deadline, and
> the day has only 24 hours...
>
> --
> 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
> Perhaps you could incorporate the ideas of Knud Jeppesen into your
activities.
Robert

> > > For those inclined the Ars Nova
> > > program called Counterpointer might be helpful in trying to
> > > establish some sort of SATB voice leading principles in 22tet.
> > > Just a suggestion.
> >
> > That's interesting; I wasn't familiar with counterpointer.
> > Does it support alternate tunings? If not, how are you
> > working with it?
>
> I don't have Counterpointer. I'm just presuming that it exists and
> works for the Fux, Palestrina and Bach algorithms which it claims to
> cater for. I also presume that it can be connected via a midi
> interface to a Kurzweil which is tuned to my universal chord
> algorithm.

But counterpointer probably assumes 12 tones/octave (my
guess anyway).

> I can only suggest that you choose a microtonal chord
> (anything you like) and tune a Kurzweil (or similar) and play a
> few Bach chorales. Just playing a chord in isolation doesn't
> really do much justice to 22tet chords. By the way I looked up
> your profile. It turns out that you are 30--not such an old
> chap at all.

I just turned 31 actually. Yahoo's stupid system doesn't
update based on a birthday (it makes you update your profile
every year instead). Programmed cell death is well underway,
to be sure.

Chords in isolation doesn't do justice to any temperament.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > > For those inclined the Ars Nova
> > > > program called Counterpointer might be helpful in trying to
> > > > establish some sort of SATB voice leading principles in 22tet.
> > > > Just a suggestion.
> > >
> > > That's interesting; I wasn't familiar with counterpointer.
> > > Does it support alternate tunings? If not, how are you
> > > working with it?
> >
> > I don't have Counterpointer. I'm just presuming that it exists
and
> > works for the Fux, Palestrina and Bach algorithms which it claims
to
> > cater for. I also presume that it can be connected via a midi
> > interface to a Kurzweil which is tuned to my universal chord
> > algorithm.
>
> But counterpointer probably assumes 12 tones/octave (my
> guess anyway).
>
> > I can only suggest that you choose a microtonal chord
> > (anything you like) and tune a Kurzweil (or similar) and play a
> > few Bach chorales. Just playing a chord in isolation doesn't
> > really do much justice to 22tet chords. By the way I looked up
> > your profile. It turns out that you are 30--not such an old
> > chap at
all.
>
>
> I just turned 31 actually. Yahoo's stupid system doesn't
> update based on a birthday (it makes you update your profile
> every year instead). Programmed cell death is well underway,
> to be sure.
>
> Chords in isolation doesn't do justice to any temperament.
>
> -Carl
> If you think about the algorithms that I have supplied you should
soon realise that if you tune an external sound device then you can
use any old software program which uses 12tet, even Band in a Box. My
algorithms assume that 12tet works well however fuzzy and that the
principles which govern 12tet can be scaled to work in any other
equal temperament. In this sense there seems to be some sort of
equivalence going on. Perhaps there might be something to Stephen
Wolfram's ideas concerning cellular automata and computational
equivalence. Or perhaps not.

it seems Vincentinos book
'Ancient music adapted to modern practice'
would be a good place to look too.
seems title still applies

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Torsten Anders wrote:
>
>
> On May 7, 2008, at 5:50 PM, robert thomas martin wrote:
> > > > For those inclined the Ars Nova
> > > > program called Counterpointer might be helpful in trying to
> > > > establish some sort of SATB voice leading principles in 22tet.
> > > > Just a suggestion.
> > >
> > > That's interesting; I wasn't familiar with counterpointer.
> > > Does it support alternate tunings? If not, how are you
> > > working with it?
> > >
> > > -Carl
> > > I don't have Counterpointer. I'm just presuming that it exists and
> > works for the Fux, Palestrina and Bach algorithms which it claims to
> > cater for. I also presume that it can be connected via a midi
> > interface to a Kurzweil which is tuned to my universal chord
> > algorithm. I can only suggest that you choose a microtonal chord
> > (anything you like) and tune a Kurzweil (or similar) and play a few
> > Bach chorales. Just playing a chord in isolation doesn't really do
> > much justice to 22tet chords. By the way I looked up your profile. It
> > turns out that you are 30--not such an old chap at
> > all.
> > Robert.
> >
>
> If you are interested, such theories could be modelled in Strasheela.
> I am presently working on Josquin-inspired counterpoint (less rigid
> than Palestrina or even Fux). I would be interested in transforming
> its rules for septimal intervals (possibly in 22 ET, although I would
> prefer a more just intonation). Any music theory wishlist / rule
> ideas for which you would like to have a computer program generating
> such music? I am always collecting ideas :)
>
> Best
> Torsten
>
> PS: I am sorry that I still did not respond to answered I got
> recently from Carl, Graham, and Hans. I have a paper deadline, and
> the day has only 24 hours...
>
> --
> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586227
> Private: +44-1752-558917
> http://strasheela.sourceforge.net <http://strasheela.sourceforge.net>
> http://www.torsten-anders.de <http://www.torsten-anders.de>
>
>

Carl Lumma wrote:

>> Augmented triad 0-382-764.
> > This is something of what we'd call an SSS chord -- a chord
> that's slightly impossible in just intonation. It's as if
> 5/4 + 5/4 = 14/9.

I still call them augmented triads. They're the obvious generalization of stacking thirds when you temper out 225:224.

Graham

Dear Kraig,

thank you very much for this pointer, I wasn't aware of this title.

Best
Torsten

On May 8, 2008, at 12:10 AM, Kraig Grady wrote:
> it seems Vincentinos book
> 'Ancient music adapted to modern practice'
> would be a good place to look too.
> seems title still applies
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://> anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Torsten Anders wrote:
> >
> >
> > On May 7, 2008, at 5:50 PM, robert thomas martin wrote:
> > > > > For those inclined the Ars Nova
> > > > > program called Counterpointer might be helpful in trying to
> > > > > establish some sort of SATB voice leading principles in 22tet.
> > > > > Just a suggestion.
> > > >
> > > > That's interesting; I wasn't familiar with counterpointer.
> > > > Does it support alternate tunings? If not, how are you
> > > > working with it?
> > > >
> > > > -Carl
> > > > I don't have Counterpointer. I'm just presuming that it > exists and
> > > works for the Fux, Palestrina and Bach algorithms which it > claims to
> > > cater for. I also presume that it can be connected via a midi
> > > interface to a Kurzweil which is tuned to my universal chord
> > > algorithm. I can only suggest that you choose a microtonal chord
> > > (anything you like) and tune a Kurzweil (or similar) and play a > few
> > > Bach chorales. Just playing a chord in isolation doesn't really do
> > > much justice to 22tet chords. By the way I looked up your > profile. It
> > > turns out that you are 30--not such an old chap at
> > > all.
> > > Robert.
> > >
> >
> > If you are interested, such theories could be modelled in > Strasheela.
> > I am presently working on Josquin-inspired counterpoint (less rigid
> > than Palestrina or even Fux). I would be interested in transforming
> > its rules for septimal intervals (possibly in 22 ET, although I > would
> > prefer a more just intonation). Any music theory wishlist / rule
> > ideas for which you would like to have a computer program generating
> > such music? I am always collecting ideas :)
> >
> > Best
> > Torsten
> >
> > PS: I am sorry that I still did not respond to answered I got
> > recently from Carl, Graham, and Hans. I have a paper deadline, and
> > the day has only 24 hours...
> >
> > --
> > Torsten Anders
> > Interdisciplinary Centre for Computer Music Research
> > University of Plymouth
> > Office: +44-1752-586227
> > Private: +44-1752-558917
> > http://strasheela.sourceforge.net <http://> strasheela.sourceforge.net>
> > http://www.torsten-anders.de <http://www.torsten-anders.de>
> >
> >
>
>
--
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