The Biosphere

Hi all,

I did some initial work on setting up a 91/90. I called the whole
thing the "biosphere," which is I think a collection of biomes. Here's
what I have so far:

http://xenharmonic.wikispaces.com/The+Biosphere

Basic ideas so far: I called the "ultrapyth" temperament "oceanfront,"
which kind of reflects what I see in my head when I hear it. There
should be an actual "ultrapyth" temperament as well, which should be
2.3.5.7.13, with maybe an 11-limit extensions as well. I'm not sure
how to set that one up yet. Oceanfront is also a decent temperament to
mix with porcupine, and I called the result "porcupinefish," which is
an actual type of fish.

I called the 91/90 and 64/63 linear temperament "tropic," because it
is both a biome and an island temperament. It's also related to
semaphore. Many temperaments that go under the archipelago will
probably also go here.

Lastly, I have a thing for "pandora" temperament down there -
something about 46-equal made me think of avatar, and I wanted to find
a suitable linear temperament to name "pandora." I ran out of time
before I could work it out. Ideally I'd set it up so that meets all of
the following features:
- decently pure harmonies (around what 46-equal offers)
- slightly sharp fifths, between those of 46-equal and 17-equal
- ideally not too complex, but I'll take what I can get.

If you want to do work on the 91/90 temperament, stumble on one that
meets the above requirements, and don't mind calling it "pandora," go
for it. If not, I'll find something at some point that works for
pandora.

Lastly, I think some of the scales Igs has posted about in the past -
like the scales that "superficially resemble porcupine" but harmonize
differently - might turn out to be biome temperaments, so watch for
those too.

That should get us started!

-Mike

Also, a note on naming - my algorithm is as follows

1) find a temperament
2) listen to it and see what it sounds like - what does it remind me
of? have fun with it
3) try to find some suitable geologic name that relates to it
4) If we're mixing temperaments with existing ones, like mixing
oceanfront with porcupine, harmonize them somehow - I went with
"porcupinefish," which is an actual species of fish

The above is just how I'm doing things, feel free to be creative and
have fun with it. Igs had a good idea as well with the list of the
standard biomes, so maybe we can work those in too as "clans" or
something.

-Mike

On Sun, Apr 24, 2011 at 9:02 PM, Mike Battaglia <battaglia01@...> wrote:
> Hi all,
>
> I did some initial work on setting up a 91/90. I called the whole
> thing the "biosphere," which is I think a collection of biomes. Here's
> what I have so far:
>
> http://xenharmonic.wikispaces.com/The+Biosphere

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Hi all,
>
> I did some initial work on setting up a 91/90. I called the whole
> thing the "biosphere," which is I think a collection of biomes. Here's
> what I have so far:

Would it ve OK to expand it to other temperaments tempering out 91/90?
Also, when I feel more inspired, to replace "I have no idea" entries with actual numbers.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Lastly, I think some of the scales Igs has posted about in the past -
> like the scales that "superficially resemble porcupine" but harmonize
> differently - might turn out to be biome temperaments, so watch for
> those too.

Hmm...the one I was referring to is in 23-EDO, and also 31-EDO: generator of a sharp 12/11 around 156 cents, equated with an 11/10 (so 121/120 is tempered out); plus two gets you 6/5, three gets you a 21/16 in the 7-limit or 17/13 if you think that's more valid, four gets you either a 10/7, five gets you 11/7, six gets you a 12/7, seven gets you...a 15/8? 32/17?; alternatively, going down from 1/1, -1 gets you 11/6, -2 gets you 5/3, -3 gets you a 32/21 (or maybe a 17/11 if you're feeling real generous), -4 gets you a 7/5, -5 gets you a 14/11 or maybe a 9/7 (in 31-EDO, at least), -6 gets you a 7/6, -7 gets you 17/16. Not really sure what a good triadic basis would be...5:6:11, maybe? There's a couple 6:7:11's but not really enough to motivate progressions.

Anyway, I don't really see anywhere for 91/90 to come into play here...the nearest 9/7 is more like a 14/11 than a 13/10. Perhaps another scale in 23 would let you get away with some 8:13:15 chords, turning the 7/6 into a 15/13 (does 91/90 do that, too?), but this porcu-like scale probably belongs on another planet.

Oh, hey, maybe 23's "dicot"-like scale is a good candidate: it's got lots of both otonal and utonal 8:13:15 triads. Generator of about 365 cents, a 16/13 perhaps...maybe you can work out the commas involved there?

-Igs

On Sun, Apr 24, 2011 at 11:15 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Hi all,
> >
> > I did some initial work on setting up a 91/90. I called the whole
> > thing the "biosphere," which is I think a collection of biomes. Here's
> > what I have so far:
>
> Would it ve OK to expand it to other temperaments tempering out 91/90?

If you mean existing ones, then yeah, I guess they deserve a mention.
If you mean figuring out new temperaments, then yeah, please :)

> Also, when I feel more inspired, to replace "I have no idea" entries with actual numbers.

This, on the other hand, is not okay.

-Mike

On Sun, Apr 24, 2011 at 11:22 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Hmm...the one I was referring to is in 23-EDO, and also 31-EDO: generator of a sharp 12/11 around 156 cents, equated with an 11/10 (so 121/120 is tempered out); plus two gets you 6/5, three gets you a 21/16 in the 7-limit or 17/13 if you think that's more valid, four gets you either a 10/7, five gets you 11/7, six gets you a 12/7, seven gets you...a 15/8? 32/17?; alternatively, going down from 1/1, -1 gets you 11/6, -2 gets you 5/3, -3 gets you a 32/21 (or maybe a 17/11 if you're feeling real generous), -4 gets you a 7/5, -5 gets you a 14/11 or maybe a 9/7 (in 31-EDO, at least), -6 gets you a 7/6, -7 gets you 17/16. Not really sure what a good triadic basis would be...5:6:11, maybe? There's a couple 6:7:11's but not really enough to motivate progressions.

That's apparently called "nusecond:"

http://x31eq.com/cgi-bin/rt.cgi?ets=23%2C31&limit=11

> Anyway, I don't really see anywhere for 91/90 to come into play here...the nearest 9/7 is more like a 14/11 than a 13/10. Perhaps another scale in 23 would let you get away with some 8:13:15 chords, turning the 7/6 into a 15/13 (does 91/90 do that, too?), but this porcu-like scale probably belongs on another planet.

I guess this one isn't too related to 91/90 after all.

Yeah, 91/90 turns 7/6 into 15/13. In general, it just means that the
utonal version of 6:7:9 becomes 10:13:15. So 9/7 becomes 13/10 and 7/6
becomes 15/13. I've decided it's the most useful comma of all time.

> Oh, hey, maybe 23's "dicot"-like scale is a good candidate: it's got lots of both otonal and utonal 8:13:15 triads. Generator of about 365 cents, a 16/13 perhaps...maybe you can work out the commas involved there?

It might make more sense to think of the generator as 13/8. If the
generator's 13/8, that means we're out of the 2.3.7.13/5 subgroup, as
in that subgroup there is no 13, just a 13/5. So we'd have to be in
2.3.5.7.13 then. Tempering 91/90 brings us to rank 4, and we have two
more commas to go before we get to rank 2.

Three 16/13's is equated with 15/8, meaning that 32955/32768 vanishes
- one more to go. Five generators gets you to 7/6, but that just turns
out to mean that 91/90 vanishes. One more generator gets you to 10/7,
which means 196/195 vanishes.

The result is here:

http://x31eq.com/cgi-bin/rt.cgi?ets=46_10&limit=2.3.5.7.13

Well, seems that something we did caused the period to split in two,
so this isn't quite the scale you were talking about, but it's
obviously related. The 10-note from this MOS is

129.825
259.649
364.912
494.737
600.000
729.825
859.649
964.912
1094.737
1200.000

As you can see it has 7/4 in it. As a last note, if you want to bring
the full 11-limit into it, looks like a good way to do things is
"Echidnic" temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=10_46&limit=13&key=3_-6_-1_10_1_2_2_7_6_3_7&error=9.374

Or, it could just be that this really is the temperament you were
talking about, but that each temperament just defines more than one
MOS, which is another salient point I've been meaning to address for a
while now.

-Mike