Moving forward with 91/90 - starting with a rank-3 "faux-5-limit JI lattice"

Hi everyone,

Since the Gene Temperament machine isn't feeling very keen, I guess
I'll just have to try to keep momentum going myself for now.

It occurred to me that when we find 5-limit temperaments, we start
with the 5-limit JI lattice, which is rank 3, and temper downward from
there. An analogous starting point can be constructed as a basis point
for figuring out 91/90.

The core concept with 91/90 is that it merges 6:7:9 into 10:13:15, and
thus makes supermajor chords a lot more pleasant. So if we start with
the 2.3.7.13/15 subgroup, and just temper out 91/90, we end up with a
rank 3 system analogous to the 5-limit JI lattice, except instead of
dealing with 4:5:6 and its utonal inversion 10:12:15, we're dealing
with 6:7:9 and its utonal inversion 10:13:15. The three dimensions of
the system can be thought of as 2/1 vs 1/2, 3/2 vs 4/3, and 7/6
(15/13) vs 9/7 (13/10). You can also think of it as 2/1, 3/1, and 7/1,
I guess, but it's probably more intuitive to think of it the other way
so that you can see the parallels with 5-limit JI.

So if we start with this planar temperament and just ignore 5 and 11
for the moment, we will probably get some awesome rank-2 temperaments
right away. I think many variants of common 5-limit temperaments will
emerge - e.g. we'll see one that's similar to porcupine, except maybe
four generators will land you at 13/10 instead of 4/3 - and we'll see
one that's similar to meantone and superpyth, except with really wide
fifths. Then we can also look at extending this lattice into "higher"
primes, except in this case "higher" means things like 5, 11, and 13.

As for names: the temperament equating 81/80 with 13/10 reminds me of
being outside on a white-sanded beach near a dock, whatever 46-equal
is doing reminds me of being outside on Pandora from Avatar in the
neon jungle, and the semaphore-ish ones remind me of being outside on
an island, which is great because they're also island temperaments.

I suggest the name "biome" for the 91/90 2.3.7.13/15 rank-3
temperament, as the word biome describes everything I've described
above: a climate and its underlying biosphere. It's more elegant than
"ecosystem." Then the ultrapyth temperament in that subgroup that
eliminates 91/90 and 64/63 can be named after a certain biome ("dock"
temperament?), whatever 46-equal is doing can be called "pandora"
temperament, the semaphore-ish ones are already "island" temperament,
and so on. We're right now calling 91/90 the "xentonic" comma as a
working title, but if anyone comes up with something really elegant
for it let's change it.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> I suggest the name "biome" for the 91/90 2.3.7.13/15 rank-3
> temperament, as the word biome describes everything I've described
> above: a climate and its underlying biosphere. It's more elegant than
> "ecosystem."

http://en.wikipedia.org/wiki/Biome#Walter_System

A good list of biome names, if that's the scheme we're going with for this..."clan"?

> Then the ultrapyth temperament in that subgroup that
> eliminates 91/90 and 64/63 can be named after a certain biome ("dock"
> temperament?)

Ugh. I don't like it. How about "mediterranean", obliquely and very indirectly referencing Greece, and thus giving the subtlest of nods to Pythagoras and the "ultrapythagorean" feel of that temperament?

> whatever 46-equal is doing can be called "pandora"

If this is the biome clan, shouldn't we use names of biomes? "Subtropical" maybe, or "rainforest"?

> We're right now calling 91/90 the "xentonic" comma as a
> working title, but if anyone comes up with something really elegant
> for it let's change it.

The "biome" comma comes to mind as an obvious choice.

-Igs

On Sun, Apr 24, 2011 at 5:40 PM, cityoftheasleep
<igliashon@...> wrote:
>
> http://en.wikipedia.org/wiki/Biome#Walter_System
>
> A good list of biome names, if that's the scheme we're going with for this..."clan"?

Who knows what it is. It's another archipelago type thing. I don't
think we have to stick primarily to those names though, especially as
this is an entire unexplored world of musical territory, although we
can use many of them.

> > Then the ultrapyth temperament in that subgroup that
> > eliminates 91/90 and 64/63 can be named after a certain biome ("dock"
> > temperament?)
>
> Ugh. I don't like it. How about "mediterranean", obliquely and very indirectly referencing Greece, and thus giving the subtlest of nods to Pythagoras and the "ultrapythagorean" feel of that temperament?

It doesn't really sound mediterranean to me though... It sounds like
I'm on a desert island, with white sand, and there's all coral in the
water and stuff, which is bright blue, and everything is extremely
bright. Really bright. The sun is too bright - however, it's actually
become so bright that it's spilled over into 10:13:15 territory, where
you discover that the blinding brightness doesn't hurt your eyes
anymore, once you yield to it and learn to accept it, because the
supermajor triads are consonant! How profound.

In the sky, you can of course see the earth mother, who is a really
attractive brunette, encouraging you to accept the blinding brightness
and realize that it doesn't hurt your eyes. That's my actual
impression, to hell with the dock thing. Not really mediterranean,
maybe "tropical," but not really that either. This is like mavila's
happier cousin or something, in that the fifths are sharp instead of
flat, but since they form 10:13:15 triads instead of 14:18:21 it's not
so bad.

Anyway, the real takehome point for me is that since this whole
concept is completely xenharmonic, we're probably going to get lots of
associations that don't sound like boring old natural regular earth,
so the list of biome names might be too limiting - these are brand new
biomes we're discovering, after all.

> > whatever 46-equal is doing can be called "pandora"
>
> If this is the biome clan, shouldn't we use names of biomes? "Subtropical" maybe, or "rainforest"?

Biomes all across the universe, yes.

> > We're right now calling 91/90 the "xentonic" comma as a
> > working title, but if anyone comes up with something really elegant
> > for it let's change it.
>
> The "biome" comma comes to mind as an obvious choice.

I was thinking that since the theme here seems to be the discovery of
new musical biomes, many of which are tripping me right the hell out,
some kind of name like "new world" comma would be nice, or something
that has to do with explorers, or like you've stumbled on a whole new
world of... biomes... or something.

-Mike