"Groovyness" as a function?

Paul,

Just so I'm on the same page, you've made a listing of either the
grooviest linnear temperments ever discovered, or a subset of same,
and you've described them with terms such as "funky" and "decent-
smelling" and similar, and ... you've been able to describe them
thusly by only looking at the numerical constructs of the scales?

I *am* right in assuming that you haven't tuned up any of these and
*listened* to them?

I just want to be on the same page on this issue.

Cheers,
Jon

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> Paul,
>
> Just so I'm on the same page, you've made a listing of either the
> grooviest linnear temperments ever discovered, or a subset of same,
> and you've described them with terms such as "funky" and "decent-
> smelling" and similar, and ... you've been able to describe them
> thusly by only looking at the numerical constructs of the scales?

By "funky", I simply meant that, since unison vectors shorter than
36/35 were being tempered out, the errors would be considerably
larger than those of 12-tET, so adaptive tuning and/or adaptive
timbring would be essential to getting a "consonant" effect -- thus
my present equipment doesn't allow me to explore them.

> I *am* right in assuming that you haven't tuned up any of these and
> *listened* to them?

Other than the funky ones, and the exceedingly complex ones that
aren't really amenable to single-keyboard playing, let's rank the
remaining ones:

(1) ~28-tET octatonic -- yes, I've played with this
(2) ~31-tET chain-of-minor thirds -- I'm going to play with this ASAP!
(3) Miracle -- yes, I've played with this
(4) Paultone -- take a wild guess
(5) ~19-tET chain-of-minor thirds -- yes, I've played with this
(6) ~Pythagorean dominant sevenths -- yes, I've played with this
(7) Negri's system -- haven't played with it yet
(8) Meantone augmented sixths -- yes, I've played with this
(9) 6+9 -- haven't played with this yet
(10) <50/49, 875/864> -- not sure
(11) Gene's 12+15=27 -- played with it a little bit

So, Jon, I've covered quite a bit of this ground experimentally, but
certainly Gene, Graham, et al have discovered some new possibilities -
- which I haven't even had _time_ to try out yet! One reason this is
interesting is that any linear temperament is no more difficult to
manage, conceptually, than conventional notation (which is based on a
chain of fifths); another is the melodically manageable MOS scales
you get -- meanwhile, having good 7-limit harmony means that most of
the "consonant" harmonies one could want will be accessible -- though
generally they'll be closer to just in the more complex systems, and
farther in the simpler systems. What is exciting is that each of
these systems is totally unique, with its own musical behavior, that
one could spend a lifetime exploring.

This work is going on at tuning-math@yahoogroups.com , and I just
thought, after 1600 messages there, this might be a good time to
report back here with an update, in case anyone was interested. Maybe
I shouldn't have done that!

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> (10) <50/49, 875/864> -- not sure

It's two chains of sharp (about 7.5 cents) subminor thirds (7/6's) a
half-octave apart. It can be done in 22-et as 5/22, and is even
closer to 11/48 in 48-et. The map to primes is:

[ 0 2]
[-4 5]
[-3 6]
[-3 7]

--- In tuning@y..., "ideaofgod" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > (10) <50/49, 875/864> -- not sure
>
> It's two chains of sharp (about 7.5 cents) subminor thirds (7/6's)
a
> half-octave apart. It can be done in 22-et as 5/22, and is even
> closer to 11/48 in 48-et. The map to primes is:
>
> [ 0 2]
> [-4 5]
> [-3 6]
> [-3 7]

So a scale like 1 4 1 4 1 1 4 1 4 1 in 22-tET -- I'll have to try
this!

Paul! (exclamation point on loan from Kraig Grady)

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> By "funky", I simply meant that...

Ah, okey-doke.

> This work is going on at tuning-math@y... , and I just
> thought, after 1600 messages there, this might be a good time to
> report back here with an update, in case anyone was interested.
> Maybe I shouldn't have done that!

Hey, Not At All! It's good that this is all happening in a clean-room
environment, and now that it is nearing FBI approval (Federal Bureau
of Intonation) it will be good to find a couple of people to start in
on some of the stuff, in addition to Joseph and Alison.

Smock on,
Jon

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_31075.html#31082

>
> So, Jon, I've covered quite a bit of this ground experimentally,
but certainly Gene, Graham, et al have discovered some new
possibilities -- which I haven't even had _time_ to try out yet! One
reason this is interesting is that any linear temperament is no more
difficult to manage, conceptually, than conventional notation (which
is based on a chain of fifths); another is the melodically manageable
MOS scales you get -- meanwhile, having good 7-limit harmony means
that most of the "consonant" harmonies one could want will be
accessible -- though generally they'll be closer to just in the more
complex systems, and farther in the simpler systems. What is exciting
is that each of these systems is totally unique, with its own musical
behavior, that one could spend a lifetime exploring.

Well, this is very exciting work... How many of these newly explored
temperaments can be notated with 72-tET?? I'm curious...(hopeful...)

>
> This work is going on at tuning-math@y... ,

Bravo!

>and I just thought, after 1600 messages there, this might be a good
>time to report back here with an update, in case anyone was
>interested. Maybe I shouldn't have done that!

But, I thought that was the original intention when Tuning Math was
set up! At that time, at least, it was *assumed* there would be a
report on the findings on the main list...

I really appreciate it, since I don't really have the background to
contribute much to Tuning Math and these updates are very valuable!

Thanks!

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Well, this is very exciting work... How many of these newly
explored
> temperaments can be notated with 72-tET?? I'm curious...
(hopeful...)

Only a few linear temperaments will be consistent with the 72-et. One
of course is Miracle, another is Ennealimmal.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_31075.html#31169

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Well, this is very exciting work... How many of these newly
> explored temperaments can be notated with 72-tET?? I'm curious...
> (hopeful...)
>
> Only a few linear temperaments will be consistent with the 72-et.
One of course is Miracle, another is Ennealimmal.

Oh! Well, go, go, Ennealimmal then! Especially since I want to
continue notating with 72-tET! I'll be anxious to actually *hear*
this scale at some point...

Maybe you can consider writing a short piece in it??

JP

Gene:
> > Only a few linear temperaments will be consistent with the 72-et.
>
> One of course is Miracle, another is Ennealimmal.

Joseph P:
> Oh! Well, go, go, Ennealimmal then! Especially since I want to
> continue notating with 72-tET! I'll be anxious to actually *hear*
> this scale at some point...

I don't know why Gene was so pessimistic there. 72-equal is consistent up to
the 11-limit. It comes up a lot in the 11-limit list, and is still
represented in the higher ones. See

<http://x31eq.com/limit11.txt>
<http://x31eq.com/limit13.txt>
<http://x31eq.com/limit15.txt>
<http://x31eq.com/limit17.txt>

I don't know if they're any good, because I haven't tried them, but there are
plenty around. One problem is that they can get quite complex, so I'll give
them a proper look when I get my ZTar.

Graham

--- In tuning@y..., Graham Breed <graham@m...> wrote:

> I don't know why Gene was so pessimistic there.

There are the n/72 generators, and more than one good one among them,
but there are lots more linear temperaments that don't work with 72.
You can find my run-down at

/tuning/topicId_29240.html#29240