Yahoo Tuning Groups Ultimate Backup tuning Two more 31-tet MOS's

These two have undoubtedly been discovered before, but just to give
people some ideas:

6/31 has an MOS at 11 and 16 notes (and 21 and 26 notes), and the most
interesting of these to me is the 16 note MOS. Play a major triad (or
a major 6/9 chord) and transpose it up and down the scale. You get
alternating major and subminor chords. This one sounds especially nice
if you transpose it up and down two scale steps instead of one. This
is an approximate 8/7 interval as its generator.

9/31 has an MOS at 10 notes. This is an approximate neutral third. I
think this is the same thing as the Mohajira MOS everyone has been
talking about lately, although the wiki page for Mohajira says it has
an MOS at 9 notes, and 9 != 10. So I'm not sure if that's a mistake or
what.

Either way, what both of these have in common is that they subdivide
the fifth. Iglashion will hate this, but I love fifths. I am a sucker
for them. I am an advocate for them. I am all about the fifth. And
these scales give you nice modulation by fifths, so they're nice and
colorful. And since we're in a meantone tuning, we get thirds too with
those fifths. Play both of these as maj 6/9 chords and move them up
and down the scale and you win internets. It works really well.

I'm a bit out of the loop, so sorry if this has been discussed (I
think the recent Mohajira craze might have been about this MOS, but
there are so many Mohajira messages about so many different things I'm
not seeing it). But hopefully it will give you guys some ideas to mess
around with. (Hint: this means improvisations from Chris Vaisvil)

-Mike

🔗Carl Lumma <carl@...>

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

> 6/31 has an MOS at 11 and 16 notes (and 21 and 26 notes), and the
> most interesting of these to me is the 16 note MOS. Play a major
> triad (or a major 6/9 chord) and transpose it up and down the
> scale. You get alternating major and subminor chords. This one
> sounds especially nice if you transpose it up and down two scale
> steps instead of one. This is an approximate 8/7 interval as its
> generator.

That would be mothra, also called cynder I believe. Too, you can
extend most of those triads into 12:14:19:21 and 4:5:6:7 tetrads.

> 9/31 has an MOS at 10 notes. This is an approximate neutral third.
> I think this is the same thing as the Mohajira MOS everyone has
> been talking about lately, although the wiki page for Mohajira
> says it has an MOS at 9 notes, and 9 != 10. So I'm not sure if
> that's a mistake or what.

I believe that's beatles[10].

-Carl

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> These two have undoubtedly been discovered before, but just to give
> people some ideas:
>
> 6/31 has an MOS at 11 and 16 notes (and 21 and 26 notes), and the most
> interesting of these to me is the 16 note MOS.

Mothra! 6/31 is about perfect as a generator, though you could for instance use 88edo, which means LucyMothra. I'm starting work in a closely related temperament, rodan, which however isn't a 31 temperament. But it does have those same MOS, though the difference in step size is even more extreme in rodan.

> 9/31 has an MOS at 10 notes. This is an approximate neutral third. I
> think this is the same thing as the Mohajira MOS everyone has been
> talking about lately, although the wiki page for Mohajira says it has
> an MOS at 9 notes, and 9 != 10. So I'm not sure if that's a mistake or
> what.

Yours is the mohajira we've been talking about. I'll check the Wikipedia article and see if it is on the same topic.

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> 6/31 has an MOS at 11 and 16 notes (and 21 and 26 notes), and the most
> interesting of these to me is the 16 note MOS. Play a major triad (or
> a major 6/9 chord) and transpose it up and down the scale. You get
> alternating major and subminor chords. This one sounds especially nice
> if you transpose it up and down two scale steps instead of one. This
> is an approximate 8/7 interval as its generator.

Kind of awkward from a melodic standpoint due to the exceedingly small value of "s" (1\31), but whatever floats your boat!

It must be a mistake. Mohajira has a neutral third generator, and any tuning with a third between 3\7-EDO and 1\3-EDO will produce a 10-note MOS of the same shape as TOP Mohajia. 31's version of this scale is a little nicer than 17's and 27's, but not quite as nice as 38's.

> Either way, what both of these have in common is that they subdivide
> the fifth. Iglashion will hate this, but I love fifths. I am a sucker
> for them. I am an advocate for them. I am all about the fifth. And
> these scales give you nice modulation by fifths, so they're nice and
> colorful. And since we're in a meantone tuning, we get thirds too with
> those fifths. Play both of these as maj 6/9 chords and move them up
> and down the scale and you win internets. It works really well.

For the record, I don't "hate" the fifth. I just think that insisting on its purity rules out a wide variety of exciting and novel musical structures, like Blackwood, Father, and Mavila.

> I'm a bit out of the loop, so sorry if this has been discussed (I
> think the recent Mohajira craze might have been about this MOS, but
> there are so many Mohajira messages about so many different things I'm
> not seeing it). But hopefully it will give you guys some ideas to mess
> around with. (Hint: this means improvisations from Chris Vaisvil)

The 10-note Mohajira scale hasn't gotten much press. I used it in two songs on "Map of an Internal Landscape": "Midnight in the Garden of Missed Connections" and "A Blur of Faces Beneath the Green Light".

-Igs

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 4, 2010 at 3:31 AM, genewardsmith
<genewardsmith@...> wrote:
>
> There appears to be no such article to check.

It's the xenharmonic wiki, under the page for "Meantone":

http://xenharmonic.wikispaces.com/Meantone+family

"It has a 7-note MOS with three larger steps and four smaller ones,
going sLsLsLs."

These are lies.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 4, 2010 at 2:55 AM, Carl Lumma <carl@...> wrote:
>
> I believe that's beatles[10].
>
> -Carl

I just screwed around with it using the 19/64 generator, which seems
to be the 7-limit version of the one I posted. The thirds are replaced
with supermajor 450 cent thirds, and the fifths are wider. Does this
mean that beatles and mohajira are related in a way? Is beatles like
the 7-limit version of mohajira or something?

They sound perceptually very similar. If I play the chord progression
from the OP in the beatles version, it sounds very similar, but more
floaty and exotic and 7-limit ish.

-Mike

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 4, 2010 at 1:16 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I just screwed around with it using the 19/64 generator, which seems
> > to be the 7-limit version of the one I posted. The thirds are replaced
> > with supermajor 450 cent thirds,
>
> What? 19\64 = 356.25¢...where does 450¢ come from?
>
> -Igs

I meant the major thirds. In 31-tet, the generator bisects a fifth,
and 4 fifths is a near-perfect 5/4. In 64, the generator bisects a
very sharp fifth of 713 cents, and 4 of them are 450 cents.

-Mike

🔗cityoftheasleep <igliashon@...>

🔗Michael <djtrancendance@...>

I discovered this 7-tone scale by allowing more dyads to be considered legal as good/legal dyads in the "Infinity" scale series:

1/1
11/10
6/5
33/25 (about 4/3)
10/7
11/7
9/5
2/1

The only really lousy interval I see here is the 29/20 (1.54-ish), a weird tri-tone-ish sounding alternative 5th between 10/7 and then 11/10.

Have any of you seen this scale before? If this turns out to be yet another mode or form of Mohajira...wow.

-Michael

🔗Michael <djtrancendance@...>

🔗cityoftheasleep <igliashon@...>

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

> I'll say this again...I really enjoyed "Midnight in the Garden of Missed Connections". I've made a bunch of independently designed programs that have lead me to Mohajira scales under 31TET. I'm beginning to like both systems...a lot.
>

I made an error: in "Midnight", I technically use "Beatles" temperament, since it's 27-EDO. Same MOS scale, different temperament family. I think the Beatles generator is closer to 16/13, and Mohajira closer to 11/9.

🔗cityoftheasleep <igliashon@...>

It's definitely not a Mohajira. I'm trying to think of any MOS scales that can approximate it...I could *almost* see it as 0-4-8-12-16-20-26-31 out of 31-EDO, but that's not an MOS because of the last two steps. Everything up to the 9/5 can be approximated by a series of neutral seconds somewhere between 11/10 and 12/11, but after that.... So I'm coming up empty. I guess you COULD go up to 62-EDO, and use 0-8-16-24-32-40-51-62, which would flatten the approximate 9/5 to something closer to a 16/9, but then it would be sssssLL, a permutation of the Mavila scale.

Gene?

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> I discovered this 7-tone scale by allowing more dyads to be considered legal as good/legal dyads in the "Infinity" scale series:
>
> 1/1
> 11/10
> 6/5
> 33/25 (about 4/3)
> 10/7
> 11/7
> 9/5
> 2/1
>
> The only really lousy interval I see here is the 29/20 (1.54-ish), a weird tri-tone-ish sounding alternative 5th between 10/7 and then 11/10.
>
>
> Have any of you seen this scale before? If this turns out to be yet another mode or form of Mohajira...wow.
>
> -Michael
>

🔗martinsj013 <martinsj@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jun 4, 2010 at 3:31 AM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > There appears to be no such article to check.
>
> It's the xenharmonic wiki, under the page for "Meantone":
>
> http://xenharmonic.wikispaces.com/Meantone+family
>
> "It has a 7-note MOS with three larger steps and four smaller ones,
> going sLsLsLs."
>
> These are lies.

It's talking about Mohajira[7]. Hence, truth.

🔗genewardsmith <genewardsmith@...>

It's not familiar to me. Scala tells us it has all those good strictly proper-constant structure-epimorphic properties. It's also got quite a collection of thirds in its cirle of thirds.

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 4, 2010 at 4:20 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > "It has a 7-note MOS with three larger steps and four smaller ones,
> > going sLsLsLs."
> >
> > These are lies.
>
> It's talking about Mohajira[7]. Hence, truth.

Gene,

Oh. That'll be the last time I write to the tuning list past my
bedtime. I also accidentally sent Carl the same exact message twice
offlist too. I'll have to be careful to make sure that doesn't happen
again.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 4, 2010 at 4:19 PM, martinsj013 <martinsj@...> wrote:
>
> Mike,
> I think it's correct, another version of the one discussed earlier with 11/9 or 2^(11/38) generator. NB it says 7-note, not 9-note which you mentioned before ("9 != 10")
>
> Steve M.

Steve,

-Mike

🔗Herman Miller <hmiller@...>

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >> 6/31 has an MOS at 11 and 16 notes (and 21 and 26 notes), and the
>> most interesting of these to me is the 16 note MOS. Play a major
>> triad (or a major 6/9 chord) and transpose it up and down the
>> scale. You get alternating major and subminor chords. This one
>> sounds especially nice if you transpose it up and down two scale
>> steps instead of one. This is an approximate 8/7 interval as its
>> generator.
> > That would be mothra, also called cynder I believe. Too, you can
> extend most of those triads into 12:14:19:21 and 4:5:6:7 tetrads.
> >> 9/31 has an MOS at 10 notes. This is an approximate neutral third.
>> I think this is the same thing as the Mohajira MOS everyone has
>> been talking about lately, although the wiki page for Mohajira
>> says it has an MOS at 9 notes, and 9 != 10. So I'm not sure if
>> that's a mistake or what.
> > I believe that's beatles[10].
> > -Carl

Beatles is <0, 2, -9, -4], but 9/31 makes more sense as <0, 2, 8, -11] which is semififths / mohajira. Beatles more typically has a 27-note MOS, not usually 31. (There may be another tuning called "mohajira" but this is the one we've been calling "semififths" until recently).

In summary:

1/31 slender
2/31 valentine
3/31 miracle
4/31 nusecond
5/31 luna
6/31 cynder / mothra
7/31 orwell
8/31 myna
9/31 semififths / mohajira
10/31 wï¿½rschmidt
11/31 squares
12/31 semisept
13/31 meantone
14/31 ?
15/31 tritonic

There's a 31&73 temperament [<1, -7, -4, 1], <0, 19, 14, 4]> that could fit with the 14/31 generator, but I don't know if it has a name.

🔗Herman Miller <hmiller@...>

Mike Battaglia wrote:
> On Fri, Jun 4, 2010 at 2:55 AM, Carl Lumma <carl@...> wrote:
>> I believe that's beatles[10].
>>
>> -Carl
> > I just screwed around with it using the 19/64 generator, which seems
> to be the 7-limit version of the one I posted. The thirds are replaced
> with supermajor 450 cent thirds, and the fifths are wider. Does this
> mean that beatles and mohajira are related in a way? Is beatles like
> the 7-limit version of mohajira or something?
> > They sound perceptually very similar. If I play the chord progression
> from the OP in the beatles version, it sounds very similar, but more
> floaty and exotic and 7-limit ish.
> > -Mike

They're related in that they have the same mapping of 3: the generator mapping of beatles is <0, 2, -9, -4] and mohajira is <0, 2, 8, -11] so they have the <0, 2] in common.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> There's a 31&73 temperament [<1, -7, -4, 1], <0, 19, 14, 4]> that could
> fit with the 14/31 generator, but I don't know if it has a name.
>

It's using what passes for an 11/8 in 31et, so it really only makes sense to think of it as an 11-limit temperament. As such, the
wedgie becomes <<19 14 4 1 -22 -47 -64 -30 -46 -11|| and it can be called 31&42, with the 31 predominating. Tempers out 126/125, 2420/2401, 3993/3920, and 589824/588245.

Anyway, the rest of them have names, so, dammit, this has to have one too. I say it's herman temperament. If herman isn't comfortable with that, it's munster temperament.

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Beatles is <0, 2, -9, -4], but 9/31 makes more sense as
> <0, 2, 8, -11] which is semififths / mohajira. Beatles more
> typically has a 27-note MOS, not usually 31. (There may be
> another tuning called "mohajira" but this is the one we've been
> calling "semififths" until recently).
>
> In summary:
>
> 1/31 slender
> 2/31 valentine
> 3/31 miracle
> 4/31 nusecond
> 5/31 luna
> 6/31 cynder / mothra
> 7/31 orwell
> 8/31 myna
> 9/31 semififths / mohajira
> 10/31 würschmidt
> 11/31 squares
> 12/31 semisept
> 13/31 meantone
> 14/31 ?
> 15/31 tritonic

Thanks Herman!

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Jun 5, 2010 at 12:09 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> > There's a 31&73 temperament [<1, -7, -4, 1], <0, 19, 14, 4]> that could
> > fit with the 14/31 generator, but I don't know if it has a name.
> >
>
> It's using what passes for an 11/8 in 31et, so it really only makes sense to think of it as an 11-limit temperament. As such, the
> wedgie becomes <<19 14 4 1 -22 -47 -64 -30 -46 -11|| and it can be called 31&42, with the 31 predominating. Tempers out 126/125, 2420/2401, 3993/3920, and 589824/588245.
>
> Anyway, the rest of them have names, so, dammit, this has to have one too. I say it's herman temperament. If herman isn't comfortable with that, it's munster temperament.

I was thinking Herman temperament as well. I second this motion.

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

A question :

Then these all represent scale degrees of 31 edo?

Thanks,

Chris

> >
> > In summary:
> >
> > 1/31 slender
> > 2/31 valentine
> > 3/31 miracle
> > 4/31 nusecond
> > 5/31 luna
> > 6/31 cynder / mothra
> > 7/31 orwell
> > 8/31 myna
> > 9/31 semififths / mohajira
> > 10/31 würschmidt
> > 11/31 squares
> > 12/31 semisept
> > 13/31 meantone
> > 14/31 ?
> > 15/31 tritonic
>
> Thanks Herman!
>

🔗Herman Miller <hmiller@...>

genewardsmith wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> >> There's a 31&73 temperament [<1, -7, -4, 1], <0, 19, 14, 4]> that
>> could fit with the 14/31 generator, but I don't know if it has a
>> name.
>> > > It's using what passes for an 11/8 in 31et, so it really only makes
> sense to think of it as an 11-limit temperament. As such, the wedgie
> becomes <<19 14 4 1 -22 -47 -64 -30 -46 -11|| and it can be called
> 31&42, with the 31 predominating. Tempers out 126/125, 2420/2401,
> 3993/3920, and 589824/588245.
> > Anyway, the rest of them have names, so, dammit, this has to have one
> too. I say it's herman temperament. If herman isn't comfortable with
> that, it's munster temperament.

19/42 generator. Casablanca temperament.

🔗Herman Miller <hmiller@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> 19/42 generator. Casablanca temperament.

Fine, if you are sure you really want to promote the 42 tuning.
This is actually not a bad temperament, and if you stick to the 7-limit, far more accurate than using 42 would suggest it is. Check out the 7-limit tunings of this: <135 214 314 379 466|. Everything's cooking but the 11, which makes <135 214 314 379 467| seem like the right choice. That leads to more complexity though, with wedgie
<<19 14 4 32 -22 -47 -15 -30 26 76||. In 31et, these are still the same, but this one would offically have a generator of 15/11~48/35.

Anyway, this one is 31&73, not 31&42, so it isn't casablanca. As a non-fives system, it's a microtemperament, which might interest somebody. It also supports zeus, the planar temperament tempering out 126/125 and 176/175 (and 441/440), and zeus is pretty cool.