11/8 as generator

Recently I have been playing with the MOS paradigm and 11/8 as a generator - the 11th overtone, which is represented very accurately in 24edo. As MOS, I get a 5-note haplotonic one (0, 9, 11, 20, 22 steps in 24edo), a 7-note albitonic one (0, 7, 9, 11, 16, 18, 20, 22), a 9-note albitonic one (0, 5, 7, 9, 11, 16, 18, 20, 22) and an 11-note chromatic one (0, 3, 5, 7, 9, 11, 14, 16, 18, 20, 22).

Given the enormous anount of similar stuff that already exists, I imagine somebody else must have investigated this before - but I could not find anything about it, nor in the xenwiki nor here in the archives.

Does anybody happen to know? Temperament name os something?
--
Hans Straub

Hans wrote:

> Does anybody happen to know? Temperament name os something?

Somewhere around 2008, I was experimenting with a temperament whose generator was pretty close to 16/11 -- i.e. the 13th root of 130. It allows you to very well approximate 13-limit and 5-limit ratios without including 3 or 7. At that time, I recorded a short improv in the temperament:
http://dl.dropbox.com/u/8497979/13limitImpro.mp3

If you want to have 3/1 there as well, you get a much more complex temperament but it works anyway. So far noone seems to have named it. More here:
http://x31eq.com/cgi-bin/rt.cgi?ets=37%2C50&limit=13

Petr

>"Somewhere around 2008, I was experimenting with a temperament whose

generator was pretty close to 16/11 -- i.e. the 13th root of 130."

   Side note...I have several times messed with the idea of making a temperament with a generator that approximates both 15/11 (if that's what you meant) and 11/8 (where 15/11 and 11/8 and both very close).

    Using a generator of 546.274 cents, right in between 15/11 and 11/8, I can get something like

1/1
15/14
8/7
6/5
9/7
22/15
14/9
5/3
16/9  
15/8
2/1

The 9-note MOS is to Mavila[9] what Mavila[7] is to meantone[7] - it's 2L7s
instead of 7L2s. It also continues Agmon's series of diatonics 3L2s, 5L2s,
7L2s, etc.

-Mike

On Aug 8, 2011, at 7:03 AM, hstraub64 <straub@...> wrote:

Recently I have been playing with the MOS paradigm and 11/8 as a generator -
the 11th overtone, which is represented very accurately in 24edo. As MOS, I
get a 5-note haplotonic one (0, 9, 11, 20, 22 steps in 24edo), a 7-note
albitonic one (0, 7, 9, 11, 16, 18, 20, 22), a 9-note albitonic one (0, 5,
7, 9, 11, 16, 18, 20, 22) and an 11-note chromatic one (0, 3, 5, 7, 9, 11,
14, 16, 18, 20, 22).

Given the enormous anount of similar stuff that already exists, I imagine
somebody else must have investigated this before - but I could not find
anything about it, nor in the xenwiki nor here in the archives.

Does anybody happen to know? Temperament name os something?
--
Hans Straub

Michael wrote:

>    Side note...I have several times messed with the idea of making
> a temperament with a generator that approximates both 15/11 (if
> that's what you meant) and 11/8 (where 15/11 and 11/8 and both very
> close).
Sorry for being a bit rude this time; if you listen to the recording and find out what the actual value of 130^(1/13) is, you'll understand why I said 16/11, not 15.

Petr

>"if you listen to the recording and
find out what the actual value of 130^(1/13) is, you'll understand why I
said 16/11, not 15."

   I understand that now and never intended to judge if 16/11 was/wasn't in your recording or how you calculated it...   I am simply (still) confused about how that ties into the thread subject of "11/8 as (a) generator"...how does 16/11 (which is pretty far from 11/8) tie into that subject?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> > "if you listen to the recording and
> > find out what the actual value of 130^(1/13) is, you'll understand
> > why I said 16/11, not 15."
>
>    I understand that now and never intended to judge if 16/11
> was/wasn't in your recording or how you calculated it...   I am
> simply (still) confused about how that ties into the thread subject
> of "11/8 as (a) generator"...how does 16/11 (which is pretty far from
> 11/8) tie into that subject?
>

Well, 16/11 is the octave complement of 11/8, so I guess that ties into the subject... Petr, your piece sounds weird :-) I have not checked the sound of the scales I sketched, I am still in the math phase.

I see now that the 7-note MOS (which a wrote wrongly in my first post - is {0, 7, 9, 11, 18, 20, 22}) is of the form 2L+5s, i.e. the mavila form. So I guess the temperament would be a kind of mavila?

BTW, the xenwiki still lacks good information about mavila.
--
Hans Straub

On Tue, Aug 9, 2011 at 3:37 AM, hstraub64 <straub@...> wrote:
>
> I see now that the 7-note MOS (which a wrote wrongly in my first post - is {0, 7, 9, 11, 18, 20, 22}) is of the form 2L+5s, i.e. the mavila form. So I guess the temperament would be a kind of mavila?

That's what I was saying in my reply - you could perhaps consider it
some kind of ultra-mavila, although the generator is pretty out there
for a 3/2. Whereas meantone's fifth has to vary from 5-equal to
7-equal, and mavila has to go from 7-equal to 9-equal, this tuning has
to vary from 9-equal to 11-equal, with 20-equal providing a tuning
that generates a sort of Halberstadt-ish layout for this temperament.

-Mike

Michael wrote:

> ... I am simply (still) confused about how that ties into the thread > subject of "11/8 as (a) generator"...how does
> 16/11 (which is pretty far from 11/8) tie into that subject?

As Hans said, I could possibly use a quasi-11/8 generator for my temperament but then the mapping would be octave-inverted and the approximated ratios would all use negative generator counts.

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Aug 9, 2011 at 3:37 AM, hstraub64 <straub@...> wrote:
> >
> > I see now that the 7-note MOS (which a wrote wrongly in my first
> > post - is {0, 7, 9, 11, 18, 20, 22}) is of the form 2L+5s, i.e.
> > the mavila form. So I guess the temperament would be a kind of
> > mavila?
>
> That's what I was saying in my reply - you could perhaps consider it
> some kind of ultra-mavila, although the generator is pretty out
> there for a 3/2. Whereas meantone's fifth has to vary from 5-equal
> to 7-equal, and mavila has to go from 7-equal to 9-equal, this
> tuning has to vary from 9-equal to 11-equal, with 20-equal
> providing a tuning that generates a sort of Halberstadt-ish layout
> for this temperament.
>

Stacking four of the flat fifths, I land on a major second, not a minor third, which, as I understand, would be the case of mavila. So "ultra-mavila" might be indeed be a name for it.

Stacking three sharp fourths (the mentioned 11/8), however, I land on a very sharp major (or augmented) third, which would again match mavila.

But as you mention 20edo, I see there is indeed a name defined for scales based on generator 11/8: "Score" (http://xenharmonic.wikispaces.com/Chromatic+pairs#Score) - with the MOS scales with 5, 7, 9 and 11 notes as the ones found. So I am currently thinking that "Score" is the name...

Moreover, on the 20edo pagge in the xenwiki, I see some other names for scales of this type: "Balzano" (for the 9-tone and the 11-tone one), "Rothenberg generalized diatonic" (for the 9-tone one), and "Agmon diatonic DS4" (for the 11-tone one).

Now I am wondering how these different names suit together...
--
Hans Straub

On Tue, Aug 9, 2011 at 7:31 AM, hstraub64 <straub@...> wrote:
> >
> > That's what I was saying in my reply - you could perhaps consider it
> > some kind of ultra-mavila, although the generator is pretty out
> > there for a 3/2. Whereas meantone's fifth has to vary from 5-equal
> > to 7-equal, and mavila has to go from 7-equal to 9-equal, this
> > tuning has to vary from 9-equal to 11-equal, with 20-equal
> > providing a tuning that generates a sort of Halberstadt-ish layout
> > for this temperament.
> >
>
> Stacking four of the flat fifths, I land on a major second, not a minor third, which, as I understand, would be the case of mavila. So "ultra-mavila" might be indeed be a name for it.
>
> Stacking three sharp fourths (the mentioned 11/8), however, I land on a very sharp major (or augmented) third, which would again match mavila.
>
> But as you mention 20edo, I see there is indeed a name defined for scales based on generator 11/8: "Score" (http://xenharmonic.wikispaces.com/Chromatic+pairs#Score) - with the MOS scales with 5, 7, 9 and 11 notes as the ones found. So I am currently thinking that "Score" is the name...

I think that Score is a subgroup of some other more fundametnal
temperament. Perhaps Gene can weigh in?

> Moreover, on the 20edo pagge in the xenwiki, I see some other names for scales of this type: "Balzano" (for the 9-tone and the 11-tone one), "Rothenberg generalized diatonic" (for the 9-tone one), and "Agmon diatonic DS4" (for the 11-tone one).

I dunno much about Balzano or Rothenberg, but Agmon's diatonic series
is 3L2s (father[5]), 5L2s (meantone[7]), 7L2s (mavila[9]), 9L2s (this
one). What's interesting about this one is that the 600 cent tritone
in the LLLLsLLLLLs scale in 20-equal expands out into a 720-cent
fifth. Hm.

-Mike

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

> I think that Score is a subgroup of some other more fundametnal
> temperament. Perhaps Gene can weigh in?

You can put it inside the 13-limit 11&20 temperament, for which 31 provides a decent tuning.

On Tue, Aug 9, 2011 at 8:46 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I think that Score is a subgroup of some other more fundametnal
> > temperament. Perhaps Gene can weigh in?
>
> You can put it inside the 13-limit 11&20 temperament, for which 31 provides a decent tuning.

There's a ton of 11&20's - http://x31eq.com/cgi-bin/rt.cgi?ets=11%2C20&limit=13

Are you talking about the one at the top, 11cdeef & 20cdef? What are
we going to call it, Hanstone?

-Mike

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

> There's a ton of 11&20's - http://x31eq.com/cgi-bin/rt.cgi?ets=11%2C20&limit=13

When I say 11&20, it means what Graham calls 11p&20p. Hence, there's only one 11&20, and a bunch with vals with letters dangling from them. And I'm sticking with that system.

>"Well, 16/11 is the octave complement of 11/8, so I guess that ties into
the subject..."
Doh...I missed the obvious...that 2 / (11/8) = 16/11...so of course it makes sense now how this all ties together.  :-P

   As a side note...I'm still amazed/disappointed no one has commented on my scale that uses 546.2743 cents (right in between 15/11 and 11/8) as a generator.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>    As a side note...I'm still amazed/disappointed no one has commented on my scale that uses 546.2743 cents (right in between 15/11 and 11/8) as a generator.

I don't recall it. If you want a comment, it could be related to the 57&68 temperament, tempering out 385/384, 6250/6237 and 2420/2401.