Yahoo Tuning Groups Ultimate Backup tuning 22 equal divisions of the octave

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Always testing my own positions, it came upon me to test my dislike of 22. It turns out I don't dislike it, in fact in some ways I find it very nice. Successive "quartertones" (enharmonic genus) are far superior to those of 24, and the crunch of the taller sonorities is much more similar to that of rationals than such chords in 12 or 24, don't you think?
>
> http://soundcloud.com/cameron-bobro/candy-for-honeycomb-keyboard

Yayyy!

Now try a porcupine scale! Or pajara decatonic, or hedgehog...

Keenan

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Always testing my own positions, it came upon me to test my dislike of 22. It turns out I don't dislike it, in fact in some ways I find it very nice. Successive "quartertones" (enharmonic genus) are far superior to those of 24, and the crunch of the taller sonorities is much more similar to that of rationals than such chords in 12 or 24, don't you think?
> >
> > http://soundcloud.com/cameron-bobro/candy-for-honeycomb-keyboard
>
> Yayyy!
>
> Now try a porcupine scale! Or pajara decatonic, or hedgehog...
>
> Keenan
>

Now that would be a challenge, as I don't think in terms of scales, and the scales of the "regular temperament paradigm" always seem to have notes where I don't need them and gaps where the fingers of my mind seek a purchase (like 12-tET does, come to think of it).

I think I could do something in "orwell", but I think orwell sounds much better tuned with the 19/84 generator than it does in 22- the 11/9 is a winner. Anyway I'll poke around and listen for something that will tickle my pickle.

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Now that would be a challenge, as I don't think in terms of scales, and the scales of the "regular temperament paradigm" always seem to have notes where I don't need them and gaps where the fingers of my mind seek a purchase (like 12-tET does, come to think of it).

What if you don't think of terms of scales, but just use a bunch of 3\22 "neutral second" steps in a row (and then break out of that pattern whenever you feel like it)?

> I think I could do something in "orwell", but I think orwell sounds much better tuned with the 19/84 generator than it does in 22- the 11/9 is a winner. Anyway I'll poke around and listen for something that will tickle my pickle.

True, orwell does have the potential for significantly better JI-approximating accuracy than in 22 (in 53 as well as in 84).

Keenan

🔗Mike Battaglia <battaglia01@...>

On Thu, Mar 29, 2012 at 4:52 PM, lobawad <lobawad@...> wrote:
>
> Now that would be a challenge, as I don't think in terms of scales, and
> the scales of the "regular temperament paradigm" always seem to have notes
> where I don't need them and gaps where the fingers of my mind seek a
> purchase (like 12-tET does, come to think of it).

I suggest thinking in terms of "fuzzy scales."

The reason I spent so much time on MODMOS is because I was trying to
take the sort of things that we do in jazz harmony and generalize them
to other tuning systems. In jazz, we definitely never stick to the
notes of one scale. In fact, it's rare that that happens: it's much
more likely that we'll switch modes every single chord to something
that's appropriate to support that chord, and chords are often chosen
for their harmonic and sonic properties than for how they fit into the
diatonic scale.

But that's not the same as thinking ascalarly: the key is to be able
to "flesh out" the chord you're playing with an appropriate scale that
supports it. The scales typically used are the diatonic, melodic
minor, and harmonic minor/major scales, as well as diminished[8] and
augmented[6], although there's no reason you couldn't experiment with
other things as well (especially if you're in 22-EDO). Doing this,
though, typically gives some kind of melodic and structural continuity
to whatever interesting foray out into novel harmonic territory you
might come up with.

And, notably, if you use a lot of meantone MODMOS's, it always gives
the sense that the landscape is split into seven parts, with each
scale containing a type of second, a type of third, a type of fourth,
etc. (The diminished scale is typically thought of as having two types
of second, although it's just as common for me to think of it as
having two types of third.)

So my advice for anyone who's looking to go nuts in porcupine is -
DON'T limit yourself to the diatonic scale unless you want to. Do what
you want, BUT use things like the modes and MODMOS's of porcupine to
tie it all back into a porcupine-centric framework. Feel free, if you
want, to explore the generator chain as a continuous thread running
through what you're doing, and also feel free to flesh out the various
chords you want to play with whatever porcupine MODMOS modes support
them.

A quick exploration of the porcupine MODMOS's, especially in 22-EDO
should reveal that they're basically a mathematical miracle that have
a huge range of sounds within them - everything from the zarlino major
scale (Lssssss b4 #7) to a sort of otonal sounding 11-limit scale
(Lsssssss b7) to pretty much anything you want. So I'll leave you to
have fun with it.

-Mike

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Always testing my own positions, it came upon me to test my dislike
> of 22. It turns out I don't dislike it, in fact in some ways I find
> it very nice. Successive "quartertones" (enharmonic genus) are far
> superior to those of 24, and the crunch of the taller sonorities is
> much more similar to that of rationals than such chords in 12 or
> 24, don't you think?
>

Yay, definitely! I like the quartertone of 22edo, too - more than the "third-tone" of 19edo, interestingly. What I like less are 22edo's "neutral second" (or rather minor wholetone) of 3 steps and also the minor second of 6 steps - especially melodically. I find 22edo a little challenging as far as melodies are concerned - but its harmonic properties I keep finding amazing. Lately, I have been experimenting with the concept of Neo-Riemannian transformations (Richard Cohn, http://recherche.ircam.fr/equipes/repmus/mamux/Cohn%20Neo-R%20Tonnetz%20Rep.pdf ), which applies very naturally to 22edo, since its 7-limit major tetrad has the property to divide the octave into 7, 6, 5 and 4 steps (like in the above document the 12edo major triad does with 5, 4 and 3 steps), which means that starting with one interval of a given chord of this type and applying slight pitch shifts (quartertones often), there are unusually many ways that lead again to an interval of another chord of this form, offering rich possibilities for natural-sounding chord progressions, modulations and surprising harmonic turns.

Here is a 22edo composition of mine exploring these ideas (it was my contribution to the 2011 Untwelve competition):

https://share.ols.inode.at/ASJRF10WVXSCUTZF14OZ58LWJM1HS0Y33IUII4EE
--
Hans Straub

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

"In jazz, we definitely never stick to the notes of one scale. In
fact, it's rare that that happens: it's much more likely that we'll
switch modes every single chord to something that's appropriate to
support that chord..."

"But that's not the same as thinking ascalarly: the key is to be able
to "flesh out" the chord you're playing with an appropriate scale
that supports it."

"...and also feel free to flesh out the various chords you want to play
with whatever porcupine MODMOS modes support them."

Hmm...so jazz is all about chords then? Melodies just flesh out and
support chords. Is that how jazz musicians think? That seems like the
opposite of traditional classical thinking where you build the form of
the piece from motifs, phrases and themes that are pretty much melodic
entities.

Kalle

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Now that would be a challenge, as I don't think in terms of scales, and the scales of the "regular temperament paradigm" always seem to have notes where I don't need them and gaps where the fingers of my mind seek a purchase (like 12-tET does, come to think of it).
>
> What if you don't think of terms of scales, but just use a bunch of 3\22 "neutral second" steps in a row (and then break out of that pattern whenever you feel like it)?

I think that would work out to be "porcupine as a fuzzy scale", as Mike recommends in a later (non-linear time, cool) post. I'm still going to wind up with most or all of 22 on my hands, so the efficiancy aspect of the temperament has gone to waste, and if I have all of 22 at hand, I already have countless ways of my own of using it.

The reason to do as you and Mike recommend would be to use the structure itself of "porcupine". Doing so works out to an analogy of a fifths+scale skeletal structure in meantone music.

>
> > I think I could do something in "orwell", but I think orwell sounds much better tuned with the 19/84 generator than it does in 22- the 11/9 is a winner. Anyway I'll poke around and listen for something that will tickle my pickle.
>
> True, orwell does have the potential for significantly better JI-approximating accuracy than in 22 (in 53 as well as in 84).

There is, for me, a very big discrepancy between 19/84 orwell and orwell tuned to 22: the 11/9 is tempered beyond audibility in 22. This is a deal-killer for me. But I use another temperament specifically for 7:9:11 things I like in orwell, more on that in another post.

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Always testing my own positions, it came upon me to test my dislike
> > of 22. It turns out I don't dislike it, in fact in some ways I find
> > it very nice. Successive "quartertones" (enharmonic genus) are far
> > superior to those of 24, and the crunch of the taller sonorities is
> > much more similar to that of rationals than such chords in 12 or
> > 24, don't you think?
> >
>
> Yay, definitely! I like the quartertone of 22edo, too - more than the "third-tone" of 19edo, interestingly. What I like less are 22edo's "neutral second" (or rather minor wholetone) of 3 steps and also the minor second of 6 steps - especially melodically. I find 22edo a little challenging as far as melodies are concerned - but its harmonic properties I keep finding amazing. Lately, I have been experimenting with the concept of Neo-Riemannian transformations (Richard Cohn, http://recherche.ircam.fr/equipes/repmus/mamux/Cohn%20Neo-R%20Tonnetz%20Rep.pdf ), which applies very naturally to 22edo, since its 7-limit major tetrad has the property to divide the octave into 7, 6, 5 and 4 steps (like in the above document the 12edo major triad does with 5, 4 and 3 steps), which means that starting with one interval of a given chord of this type and applying slight pitch shifts (quartertones often), there are unusually many ways that lead again to an interval of another chord of this form, offering rich possibilities for natural-sounding chord progressions, modulations and surprising harmonic turns.
>
> Here is a 22edo composition of mine exploring these ideas (it was my contribution to the 2011 Untwelve competition):
>
> https://share.ols.inode.at/ASJRF10WVXSCUTZF14OZ58LWJM1HS0Y33IUII4EE
> --
> Hans Straub
>

These stepwise transformations are like the stepwise transformations in 41-edo I have mentioned, and likewise tend to break the symmetry of an MOS. 22 has the advantage of being small enough to use the whole thing, whereas reckoning a subset of 41 can be a pain, not because it is difficult, but because in mid-work your ear might lead you somewhere you hadn't anticipated. I think your piece clearly demonstrates how suited 22 is for the tetrad transformations you are doing.

🔗lobawad <lobawad@...>

See my reply to Keenan. With the full complement of 22, I can jam til the cows come home in many different ways, so doing as you suggest here would only make sense if I wanted to express structures particular to "porcupine". But your approach certainly would work for that. I have another idea for invoking "porcupine" specifically, without having to think about diatonic scales other than as byproducts of the process. Hopefully I'll get some time soon to try it out, and thanks for taking the time to write such a detailed post.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 29, 2012 at 4:52 PM, lobawad <lobawad@...> wrote:
> >
> > Now that would be a challenge, as I don't think in terms of scales, and
> > the scales of the "regular temperament paradigm" always seem to have notes
> > where I don't need them and gaps where the fingers of my mind seek a
> > purchase (like 12-tET does, come to think of it).
>
> I suggest thinking in terms of "fuzzy scales."
>
> The reason I spent so much time on MODMOS is because I was trying to
> take the sort of things that we do in jazz harmony and generalize them
> to other tuning systems. In jazz, we definitely never stick to the
> notes of one scale. In fact, it's rare that that happens: it's much
> more likely that we'll switch modes every single chord to something
> that's appropriate to support that chord, and chords are often chosen
> for their harmonic and sonic properties than for how they fit into the
> diatonic scale.
>
> But that's not the same as thinking ascalarly: the key is to be able
> to "flesh out" the chord you're playing with an appropriate scale that
> supports it. The scales typically used are the diatonic, melodic
> minor, and harmonic minor/major scales, as well as diminished[8] and
> augmented[6], although there's no reason you couldn't experiment with
> other things as well (especially if you're in 22-EDO). Doing this,
> though, typically gives some kind of melodic and structural continuity
> to whatever interesting foray out into novel harmonic territory you
> might come up with.
>
> And, notably, if you use a lot of meantone MODMOS's, it always gives
> the sense that the landscape is split into seven parts, with each
> scale containing a type of second, a type of third, a type of fourth,
> etc. (The diminished scale is typically thought of as having two types
> of second, although it's just as common for me to think of it as
> having two types of third.)
>
> So my advice for anyone who's looking to go nuts in porcupine is -
> DON'T limit yourself to the diatonic scale unless you want to. Do what
> you want, BUT use things like the modes and MODMOS's of porcupine to
> tie it all back into a porcupine-centric framework. Feel free, if you
> want, to explore the generator chain as a continuous thread running
> through what you're doing, and also feel free to flesh out the various
> chords you want to play with whatever porcupine MODMOS modes support
> them.
>
> A quick exploration of the porcupine MODMOS's, especially in 22-EDO
> should reveal that they're basically a mathematical miracle that have
> a huge range of sounds within them - everything from the zarlino major
> scale (Lssssss b4 #7) to a sort of otonal sounding 11-limit scale
> (Lsssssss b7) to pretty much anything you want. So I'll leave you to
> have fun with it.
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

On Fri, Mar 30, 2012 at 4:11 AM, Kalle Aho <kalleaho@...>
wrote:
>
> Hmm...so jazz is all about chords then? Melodies just flesh out and
> support chords. Is that how jazz musicians think? That seems like the
> opposite of traditional classical thinking where you build the form of
> the piece from motifs, phrases and themes that are pretty much melodic
> entities.

Yeah, sort of. Earlier bebop stuff is basically like I said - the
basic thing is the chord, of which the third and seventh are the most
important parts. Then, you can flesh that out with different
extensions, which are typically left open to the musician to decide in
the moment. And then, for every extension, there's a set of modes that
"support" that, which you can pick for melody. It's not always thought
of in that order - sometimes people play the melody first and then
choose chords and modes to support that and so on, but that's the
basic idea.

As jazz evolved, particularly when you start getting into the post bop
era, it's more common to think of modes instead of just chords - like
modes themselves are just thought of as generalized 7-note chords or
something, each with their own sound and flavor, so that chord
progressions almost turn into "mode progressions." (I really like this
style.)

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Mar 30, 2012 at 12:57 PM, lobawad <lobawad@...> wrote:
>
> I think that would work out to be "porcupine as a fuzzy scale", as Mike
> recommends in a later (non-linear time, cool) post. I'm still going to wind
> up with most or all of 22 on my hands, so the efficiancy aspect of the
> temperament has gone to waste, and if I have all of 22 at hand, I already
> have countless ways of my own of using it.

It's not just that - it's also for melodic reasons. What you're saying
is like, why should I use three different minor scales when I can just
think, freeform, in "minor?" And the answer is - of course, you can,
but using different 7-note scales ends up giving some melodic
continuity to the whole thing. Same with porcupine: do whatever you
want, but know it'll always be there for melodic purposes, among other
reasons.

-Mike

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 30, 2012 at 12:57 PM, lobawad <lobawad@...> wrote:
> >
> > I think that would work out to be "porcupine as a fuzzy scale", as Mike
> > recommends in a later (non-linear time, cool) post. I'm still going to wind
> > up with most or all of 22 on my hands, so the efficiancy aspect of the
> > temperament has gone to waste, and if I have all of 22 at hand, I already
> > have countless ways of my own of using it.
>
> It's not just that - it's also for melodic reasons. What you're saying
> is like, why should I use three different minor scales when I can just
> think, freeform, in "minor?" And the answer is - of course, you can,
> but using different 7-note scales ends up giving some melodic
> continuity to the whole thing. Same with porcupine: do whatever you
> want, but know it'll always be there for melodic purposes, among other
> reasons.

But I don't think in minor or major. Melody and melodic continuity doesn't have to be bound to a scale at all- a percieved scale or scales can arise from melodic figures. Or tetrachords (abstracted, "ajnas", really) can interlock. They're the structure, the scales percieved later are kind of "byproducts". See Kalle's post- and what he says doesn't just apply to "classical" music.

🔗Jake Freivald <jdfreivald@...>

🔗Keenan Pepper <keenanpepper@...>

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> These stepwise transformations are like the stepwise transformations
> in 41-edo I have mentioned, and likewise tend to break the symmetry
> of an MOS. 22 has the advantage of being small enough to use the
> whole thing, whereas reckoning a subset of 41 can be a pain, not
> because it is difficult, but because in mid-work your ear might lead
> you somewhere you hadn't anticipated. I think your piece clearly
> demonstrates how suited 22 is for the tetrad transformations you are
> doing.
>

Thanks for the comment!
Your remark about transformations in 41edo sounds interesting, but apparently I missed that post. Could you give me a link to it?
--
Hans Straub

🔗lobawad <lobawad@...>

My thoughts on the subject are scattered about, so I'll have to write a digest when I get the chance. In the meantime, here:

http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro

you can hear the equation of 25/24 and 36/35 to a single step being used to smoothly move between 5 and 7 limit intervals, an example of the "only a step away" idea.

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > These stepwise transformations are like the stepwise transformations
> > in 41-edo I have mentioned, and likewise tend to break the symmetry
> > of an MOS. 22 has the advantage of being small enough to use the
> > whole thing, whereas reckoning a subset of 41 can be a pain, not
> > because it is difficult, but because in mid-work your ear might lead
> > you somewhere you hadn't anticipated. I think your piece clearly
> > demonstrates how suited 22 is for the tetrad transformations you are
> > doing.
> >
>
> Thanks for the comment!
> Your remark about transformations in 41edo sounds interesting, but apparently I missed that post. Could you give me a link to it?
> --
> Hans Straub
>

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "hstraub64" <straub@> wrote:
> > Yay, definitely! I like the quartertone of 22edo, too - more than
> > the "third-tone" of 19edo, interestingly. What I like less are
> > 22edo's "neutral second" (or rather minor wholetone) of 3 steps and
> > also the minor second of 6 steps - especially melodically.
>
> Aww, but these are some of the best parts! 6/5 being divided into two
> equal parts (strongly associated with tempering out 121/120) is
> awesome. It's an awesome munit.
>

Don't get me wrong - both intervals are definitely important ones, and, yes, maybe they can be seen as typical for the character of 22edo. The presence of two kinds of wholetones, connected with the non-meantonenesss, has some fascination, and the 6/5 is an undispensable part of both the major and the minor tetrad anyway. They just sound somehow dissonant to me, both have a kind of tension in them - maybe that's part of what makes them interesting.
--
Hans Straub

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> My thoughts on the subject are scattered about, so I'll have to
> write a digest when I get the chance. In the meantime, here:
>
> http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro
>
> you can hear the equation of 25/24 and 36/35 to a single step being
> used to smoothly move between 5 and 7 limit intervals, an example
> of the "only a step away" idea.
>

At first sight, I did not hear so much there. Gotta give it a closer listen.
But indeed, I remember that in 41edo there are a number of pairs of important intervals separated by one step. Yeah, this might be an idea to track closer in 41edo.
And, yes, these chromatic pitch shifts tend to break out of any scale. Indeed I tend to use all or most of the pitch classes I have available. Might indeed become a problem when the number of notes grows big...
--
Hans Straub

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "hstraub64" <straub@> wrote:
>
> > Here is a 22edo composition of mine exploring these ideas (it was
> > my contribution to the 2011 Untwelve competition):
> >
> > https://share.ols.inode.at/ASJRF10WVXSCUTZF14OZ58LWJM1HS0Y33IUII4EE
>
> Speaking of which, when the hell are we going to get composer's
> discussions of their works, with tuning information and etc?
>

Just saw that the details about the composers and the pieces including tuning informations are now on the Untwelve site. Gotta have a closer listen, there, too...
--
Hans Straub