Yahoo Tuning Groups Ultimate Backup tuning 91/90 temperament names

As I was discussing with Igs in the other thread, 91/90 is a great
comma; it makes the inverse of 6:7:9 out to be 10:13:15. It can lead
to extremely pure harmonies, as pointed out by Gene in 46-equal,
although many EDOs that utilize this comma before that point don't
utilize it in that capacity. 19-equal, 24-equal, and 27-equal all
temper this comma out in different ways, which suggests some
temperaments right off the bat. Here's a few that come to mind:

A really good subfamily of this family is to also temper out 896/891,
meaning 81/64 is equated with 14/11.

Start with 2.3.7.11.13/5 - generator is 9/7, 7 of which make 6/1.
Eliminates 91/90, 896/891, and ???
http://x31eq.com/cgi-bin/rt.cgi?ets=19p_46&limit=2.3.7.11.13/5
If extended to the full 13-limit, becomes "Sensor" temperament -
http://x31eq.com/cgi-bin/rt.cgi?ets=19p_46&limit=2.3.5.7.11.13

There are probably a million ways to extend the above.

Some more obvious, but higher-error options:
From 19-EDO mixed with 24-EDO - these are all additionally Archipelago
temperaments, because the generator is still 15/13, but now it's
equated with 7/6. Higher error than the above
2.3.7.13/5 subgroup - eliminating 49/48 and 91/90:
http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.7.13&error=15.247

2.3.5.7.13 subgroup - eliminating 49/48, 91/90 and 81/80:
http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.5.7.13&error=15.247

Full 13-limit - eliminating 49/48, 91/90, 81/80, and 56/55:
http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.5.7.11.13&error=15.247

Probably a lot better ways to extend the above, possibly by merging
the whole thing with schismatic temperament instead of meantone.

This is what you get if you go the 27-equal route and eliminate 64/63
instead, giving you an "ultrapyth" temperament:

2.3.7.13/5 subgroup - eliminating 64/63 and 91/90:
http://x31eq.com/cgi-bin/rt.cgi?ets=27_32&limit=2.3.7.13/5&error=15.247

2.3.5.7.13 subgroup - eliminate 64/63, 91/90, and 245/243:
http://x31eq.com/cgi-bin/rt.cgi?ets=27_32&limit=2.3.5.7.13&error=15.247

Full 13-limit - not sure what commas this eliminates to work 11 in,
but is the 13-limit 32p and 59p temperament:
http://x31eq.com/cgi-bin/rt.cgi?ets=32p_59p&limit=2.3.5.7.11.13

Anyway, these are some initial assessments. All of this is before the
Gene temperament machine improves 1000x on the above. There's enough
stuff here to build another "archipelago"-style setup for sure, as I'm
sure I've missed some of the main points of this temperament. The
characteristic feeling of this temperament to me comes from that
6:7:9, when flipped upside down, becomes 10:13:15, which is quite
concordant and stands in stark contrast to the usual irritatingly
bright 14:18:21 supermajor triads. Since now the utonal inversion of
6:7:9 actually sounds somewhat consonant, you end up with new, very
colorful chords everywhere, which connect in various ways; as opposed
to with superpyth where supermajor triads are to be... treated with
respect.

-Mike

🔗Mike Battaglia <battaglia01@...>

Sorry, forgot the actual names. My initial impression:

I feel like all of these give off a very "nature" or "earth"-y vibe,
but not in the stereotypical sense of you being in a forest and
getting bitten by bugs. For example, when I listen to the 27-tet or
32-tet diatonic scale, I feel like I'm outside near the ocean in some
way, maybe on a reef or a dock or something. There is motion by fifth
everywhere, setting up lots of tonal structures, but all of the chords
are 6:7:9 or 10:13:15. Everything is amazingly bright, more so than
17-equal; it's as if it's become so bright that it's spilled over onto
something totally new. I am enlightened and reveling in my own
existence and near an ocean.

On the other hand, when I listen to 46-equal, I'm still in nature, but
now I feel like I'm in an Avatar-style rainforest, where everything is
luminescent and imbued with its own natural light, and you step on the
ground and you leave neon footprints and stuff. Everything has a very
colorful vibe to it. Neil Haverstick nailed this vibe in his piece
"Beautiful Springtime," although I doubt that he was tempering 91/90
when he played. Imagine giant mushrooms with orange caps, except the
orange caps are sort of glowing. That's about where I'm at with this
tuning. Don't read too much into the mushroom reference.

Then the semaphore-ish ones posted above evoke a different kind of
nature, this time the "island" feel, which makes sense because they're
also island temperaments. So there's a lot of overlap there.

But the characteristic is - this temperament makes supermajor chords
palatable, which for me causes the above synesthetic associations to
actually happen. For temperaments not eliminating 91/90 (like let's
say 22-ET), supermajor chords sound bright and sometimes irritating -
I'm used to them at this point, but they don't cause this serene
transcendental vibe like I wrote above. Instead, it sounds more like
you have to watch your step, because if you accidentally land on a
supermajor chord you're going to set an alarm off. It's not the same.

Any suggestions for a name for this complex, something like what we
had with the archipelago? "Nature" temperament is too cheesy and
evokes associations I don't want. Each one of these evokes different
"climates," so something like "Landscape" would be a good word,
although that's already a different temperament I think. What would
you call a selection of different landscapes?

-Mike

🔗Herman Miller <hmiller@...>

On 4/23/2011 4:59 PM, Mike Battaglia wrote:
> As I was discussing with Igs in the other thread, 91/90 is a great
> comma; it makes the inverse of 6:7:9 out to be 10:13:15. It can lead
> to extremely pure harmonies, as pointed out by Gene in 46-equal,
> although many EDOs that utilize this comma before that point don't
> utilize it in that capacity. 19-equal, 24-equal, and 27-equal all
> temper this comma out in different ways, which suggests some
> temperaments right off the bat. Here's a few that come to mind:
>
> A really good subfamily of this family is to also temper out 896/891,
> meaning 81/64 is equated with 14/11.
>
> Start with 2.3.7.11.13/5 - generator is 9/7, 7 of which make 6/1.
> Eliminates 91/90, 896/891, and ???
> http://x31eq.com/cgi-bin/rt.cgi?ets=19p_46&limit=2.3.7.11.13/5
> If extended to the full 13-limit, becomes "Sensor" temperament -
> http://x31eq.com/cgi-bin/rt.cgi?ets=19p_46&limit=2.3.5.7.11.13
>
> There are probably a million ways to extend the above.

There's a couple of other sensi temperaments with 91/90 at least.

8d&19 [<1 -1 -1 -2 2 0|, <0 7 9 13 4 10|]
46&73 [<1 -1 -1 -2 -8 0|, <0 7 9 13 31 10|]

> Some more obvious, but higher-error options:
>> From 19-EDO mixed with 24-EDO - these are all additionally Archipelago
> temperaments, because the generator is still 15/13, but now it's
> equated with 7/6. Higher error than the above
> 2.3.7.13/5 subgroup - eliminating 49/48 and 91/90:
> http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.7.13&error=15.247
>
> 2.3.5.7.13 subgroup - eliminating 49/48, 91/90 and 81/80:
> http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.5.7.13&error=15.247
>
> Full 13-limit - eliminating 49/48, 91/90, 81/80, and 56/55:
> http://x31eq.com/cgi-bin/rt.cgi?ets=24_19&limit=2.3.5.7.11.13&error=15.247

It's one of many 13-limit semaphore variants. I wonder if it's worth naming them all? You either end up with confusing names like sensor / sensis, pajarous / pajaric, etc., or on the other hand lots of unrelated names that are hard to connect to the original word (orwell / winston / julia). "19&24 semaphore" would do, but you could just as easily call it "5&19 semaphore".

> Probably a lot better ways to extend the above, possibly by merging
> the whole thing with schismatic temperament instead of meantone.
>
>
> This is what you get if you go the 27-equal route and eliminate 64/63
> instead, giving you an "ultrapyth" temperament:
>
> 2.3.7.13/5 subgroup - eliminating 64/63 and 91/90:
> http://x31eq.com/cgi-bin/rt.cgi?ets=27_32&limit=2.3.7.13/5&error=15.247
>
> 2.3.5.7.13 subgroup - eliminate 64/63, 91/90, and 245/243:
> http://x31eq.com/cgi-bin/rt.cgi?ets=27_32&limit=2.3.5.7.13&error=15.247
>
> Full 13-limit - not sure what commas this eliminates to work 11 in,
> but is the 13-limit 32p and 59p temperament:
> http://x31eq.com/cgi-bin/rt.cgi?ets=32p_59p&limit=2.3.5.7.11.13
>
>
> Anyway, these are some initial assessments. All of this is before the
> Gene temperament machine improves 1000x on the above. There's enough
> stuff here to build another "archipelago"-style setup for sure, as I'm
> sure I've missed some of the main points of this temperament. The
> characteristic feeling of this temperament to me comes from that
> 6:7:9, when flipped upside down, becomes 10:13:15, which is quite
> concordant and stands in stark contrast to the usual irritatingly
> bright 14:18:21 supermajor triads. Since now the utonal inversion of
> 6:7:9 actually sounds somewhat consonant, you end up with new, very
> colorful chords everywhere, which connect in various ways; as opposed
> to with superpyth where supermajor triads are to be... treated with
> respect.
>
> -Mike

There's a 15&22 temperament related to porcupine
[<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]

There are simpler 13-limit porcupines, though. I call these porcupine A and porcupine B. (They don't temper out 91/90.) Which one of these, if any, gets to be called "porcupine" is something I haven't worked out; maybe Gene or someone else has some guidelines for naming higher-limit extensions of temperaments.

porcupine A (7&8) [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]
porcupine B (7&22) [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]

15&22 (which tempers out 91/90) is slightly more accurate, at the cost of much more complexity. You could name it after a particularly large species of porcupine, perhaps.

Others include a 12&15 augene variant
12&15 [<3 5 7 8 10 12|, <0 -1 0 2 2 -4|]

a 15&19 keemun variant
15&19 [<1 0 1 2 4 0|, <0 6 5 3 -2 14|]

versions of meanpop and magic
12e&19 [<1 2 4 7 -2 2|, <0 -1 -4 -10 13 4|]
19&22 [<1 0 2 -1 6 4|, <0 5 1 12 -8 -1|]

another 3-period per octave scale we don't see much, this is a version of what's called "semiaug" in the 7-limit

24&27e [<3 5 7 9 11 11|, <0 -2 0 -5 -5 1|]

and a valentine temperament, this one apparently called "dynwen"
15&46 [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 24, 2011 at 4:43 PM, Herman Miller <hmiller@...> wrote:
>
> It's one of many 13-limit semaphore variants. I wonder if it's worth
> naming them all? You either end up with confusing names like sensor /
> sensis, pajarous / pajaric, etc., or on the other hand lots of unrelated
> names that are hard to connect to the original word (orwell / winston /
> julia). "19&24 semaphore" would do, but you could just as easily call it
> "5&19 semaphore".

I'm trying to just do again what we did with the archipelago - many of
the archipelago temperaments already existed, but were then found to
"relate" to the archipelago after the fact.

My last post I think suggests a good way forward to organize this -
start with the rank-3 2.3.7.13/5 91/90 "biome" temperament as a faux
5-limit JI lattice, temper down from there, and then add in 5 and 11
and 13 as "higher primes" later.

In fact, I think it might be a good exercise to deliberately exclude 5
for now, as it'll force us to think more xenharmonically :)

> porcupine A (7&8) [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]
> porcupine B (7&22) [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]
>
> 15&22 (which tempers out 91/90) is slightly more accurate, at the cost
> of much more complexity. You could name it after a particularly large
> species of porcupine, perhaps.

So the 5-limit version of this would be a porcupine variant, but
strictly within the 2.3.7.13/5 subgroup things will be different. A
good way to name it, if we're going with the biome theme, is to work
out whatever the porcupine subgroup temperament above sounds like
synesthetically (have fun with this), and then since porcupines are
animals that live in biomes, we can just pick the name for the
specific porcupine extension based on the type of porcupine that would
live in said biome. Well, that's one option, anyway.

> Others include a 12&15 augene variant
> 12&15 [<3 5 7 8 10 12|, <0 -1 0 2 2 -4|]
>
> a 15&19 keemun variant
> 15&19 [<1 0 1 2 4 0|, <0 6 5 3 -2 14|]
>
> versions of meanpop and magic
> 12e&19 [<1 2 4 7 -2 2|, <0 -1 -4 -10 13 4|]
> 19&22 [<1 0 2 -1 6 4|, <0 5 1 12 -8 -1|]
>
> another 3-period per octave scale we don't see much, this is a version
> of what's called "semiaug" in the 7-limit
>
> 24&27e [<3 5 7 9 11 11|, <0 -2 0 -5 -5 1|]
>
> and a valentine temperament, this one apparently called "dynwen"
> 15&46 [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]

Nice! I'll set up a 91/90 page on the xenharmonic wiki and start adding these.

-Mike

🔗Graham Breed <gbreed@...>

On 25 April 2011 00:43, Herman Miller <hmiller@...> wrote:

> There's a couple of other sensi temperaments with 91/90 at least.

> 8d&19 [<1 -1 -1 -2 2 0|, <0 7 9 13 4 10|]
> 46&73 [<1 -1 -1 -2 -8 0|, <0 7 9 13 31 10|]

8d&19p is in my database as "sensisept". You may say that's
confusing, because "sensisept" should only be used in the 7-limit, and
be synonymous with "sensi". In response, I say that in that case
there was no point in defining the name "sensisept" in the first
place. Which, indeed, we may agree on, but that's the current state
of the database.

I make 73 ambiguous, and what you've given there doesn't fit the
better mapping of it. It is, however, recorded as "sensus":

http://x31eq.com/cgi-bin/rt.cgi?ets=46+73&limit=13

A "p" disambiguates it:

http://x31eq.com/cgi-bin/rt.cgi?ets=46+73p&limit=13

> It's one of many 13-limit semaphore variants. I wonder if it's worth
> naming them all? You either end up with confusing names like sensor /
> sensis, pajarous / pajaric, etc., or on the other hand lots of unrelated
> names that are hard to connect to the original word (orwell / winston /
> julia). "19&24 semaphore" would do, but you could just as easily call it
> "5&19 semaphore".

It's worth naming them all, but not worth taking the names too
seriously. Even if it's "19&24" semaphore, it won't always come up as
19&24, and if it does you can give that derivation anyway (which is
generally a good idea). Semaphore-like names could be morse and
telegraph.

Julia isn't in my database, but I assume it's connected to Winston
because Julia was Winston's girlfriend. Not hard to connect at all.
What could be a problem is a liberal use of common names. It's
similar to the ". . .if you should happen to hire Jose" problem here:

http://www.ietf.org/rfc/rfc1178.txt

We could still do with some more names for orwell variants. I was
thinking of napoleon and squealer.

> 15&22 (which tempers out 91/90) is slightly more accurate, at the cost
> of much more complexity. You could name it after a particularly large
> species of porcupine, perhaps.

What happened to opossum? That's the first porcupine-like thing I see:

http://x31eq.com/cgi-bin/rt.cgi?ets=15+8d&limit=13

> a 15&19 keemun variant
> 15&19 [<1 0 1 2 4 0|, <0 6 5 3 -2 14|]

That isn't the keemun variant I came up with. What I see is
specifically a darjeeling variant:

http://x31eq.com/cgi-bin/rt.cgi?ets=15_19e&limit=13

> versions of meanpop and magic
> 12e&19 [<1 2 4 7 -2 2|, <0 -1 -4 -10 13 4|]
> 19&22 [<1 0 2 -1 6 4|, <0 5 1 12 -8 -1|]

I actually named a load of magic variants last night. That one's
"sorcery". Not live yet. (Note that I count 19 and 22 as both
ambiguous in the 13-limit.)

As an undocumented feature, you can get a link for families defined by
unison vectors. Here's what we're talking about:

http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90

The intersection with 225:224:

http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90+225/224

And 385:384, giving the intersection with 11-limit marvel, which
brings up some more things:

http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90+225/224+385/384

For simpler mappings, you go to a higher page:

http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90&page=5

(Not intuitive -- I had to check the page source.)

Graham

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 25, 2011 at 1:02 AM, Graham Breed <gbreed@...> wrote:
>
> On 25 April 2011 00:43, Herman Miller <hmiller@...> wrote:
>
> > There's a couple of other sensi temperaments with 91/90 at least.
>
> > 8d&19 [<1 -1 -1 -2 2 0|, <0 7 9 13 4 10|]
> > 46&73 [<1 -1 -1 -2 -8 0|, <0 7 9 13 31 10|]
>
> 8d&19p is in my database as "sensisept". You may say that's
> confusing, because "sensisept" should only be used in the 7-limit, and
> be synonymous with "sensi". In response, I say that in that case
> there was no point in defining the name "sensisept" in the first
> place. Which, indeed, we may agree on, but that's the current state
> of the database.

So wait, is sensi the same thing as semisixths?

> As an undocumented feature, you can get a link for families defined by
> unison vectors. Here's what we're talking about:
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90

I'm confused, how is this different than just putting in 91/90 in the
uv page? That's what it looks like.

Is there a way to do the above for subgroups? The following has caused
destruction:

http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90&limit=2.3.7.13/5

It would be really useful in sorting through this 91/90 stuff,
especially if the approach is to start with the 2.3.7.13/5 91/90
planar temperament as some kind of faux 5-limit JI lattice and work
from there.

-Mike

🔗Graham Breed <gbreed@...>

🔗Mike Battaglia <battaglia01@...>

🔗Graham Breed <gbreed@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Herman Miller <hmiller@...>

On 4/25/2011 1:02 AM, Graham Breed wrote:

> What happened to opossum? That's the first porcupine-like thing I see:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=15+8d&limit=13
>
>> a 15&19 keemun variant
>> 15&19 [<1 0 1 2 4 0|,<0 6 5 3 -2 14|]
>
> That isn't the keemun variant I came up with. What I see is
> specifically a darjeeling variant:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=15_19e&limit=13

I have it as 15&19e [<1 0 1 2 0 0|, <0 6 5 3 13 14|]. Yes, that's on the list, and opossum, triforce, beatles, various versions of negri, progression, zinith, and others. It's hard to know where to start.

opossum (7d&15):
[<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|]

triforce (9&15):
[<3 4 7 8 10 10|, <0 2 0 1 1 3|]

beatles (7c&10):
[<1 1 5 4 2 4|, <0 2 -9 -4 5 -1|]

Some negri variations that support 91/90:

[<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]
[<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
[<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]
[<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]

Various pajara temperaments:

[<2 3 5 6 7 7|, <0 1 -2 -2 -1 2|]
[<2 3 5 6 7 7|, <0 1 -2 -2 0 2|]
[<2 3 5 6 8 7|, <0 1 -2 -2 -6 2|]
[<2 3 5 6 6 7|, <0 1 -2 -2 5 2|]

Leapday (29&46) is on the list.

[<1 2 11 9 8 7|, <0 -1 -21 -15 -11 -8|]

>> versions of meanpop and magic
>> 12e&19 [<1 2 4 7 -2 2|,<0 -1 -4 -10 13 4|]
>> 19&22 [<1 0 2 -1 6 4|,<0 5 1 12 -8 -1|]
>
> I actually named a load of magic variants last night. That one's
> "sorcery". Not live yet. (Note that I count 19 and 22 as both
> ambiguous in the 13-limit.)
>
> As an undocumented feature, you can get a link for families defined by
> unison vectors. Here's what we're talking about:
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90

That's a useful feature.

> The intersection with 225:224:
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90+225/224
>
> And 385:384, giving the intersection with 11-limit marvel, which
> brings up some more things:
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90+225/224+385/384
>
> For simpler mappings, you go to a higher page:
>
> http://x31eq.com/cgi-bin/uv.cgi?uvs=91/90&page=5
>
> (Not intuitive -- I had to check the page source.)
>