8-note MOS of generator 11/31

Does this have a name? It seems to generate an amazing 2.3.7 MOS with
some 11 and 13 thrown in as well. It also has some fascinating
properties - the 4th scale step is either an approximate 4/3 or an
approximate 3/2.

Play a supermajor 7 tetrad and move it "diatonically" up and down the
scale - you get some ridiculously sweet "faux-diatonic" harmonies.
Then try a "subminor/supermajor7" tetrad and do the same thing. You
can hear a "hint" of diatonic harmony in there, but transposed up in
down in somewhat colorful and foreign sounding ways. The fact that
it's all subminor/supermajor though makes it sound pretty bitter, and
not quite as "clear" as regular diatonic harmony though.

Also, for future reference, is there some easy way to look up the
names of these things? I'm plowing through all of the 31-tet MOS
scales now and there are quite a few with no name within Scala.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Does this have a name?

The only name I know for it is Squares[8]. A few days ago I wrote this about squares on the xenwiki:

Squares
Squares, with wedgie <<4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (9/7) intervals, and uses it for a generator. 31edo, with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.

That's only about 7-limit squares because the 11-limit I haven't gotten to yet.

> Also, for future reference, is there some easy way to look up the
> names of these things?

Always room for more stuff on the wiki, I suppose.

How would I make a scala file out of this?

stack 8 11/31 intervals to make an octave?

Help needed in Indy.

Chris

On Thu, Jun 3, 2010 at 7:31 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> Does this have a name? It seems to generate an amazing 2.3.7 MOS with
> some 11 and 13 thrown in as well. It also has some fascinating
> properties - the 4th scale step is either an approximate 4/3 or an
> approximate 3/2.
>
> Play a supermajor 7 tetrad and move it "diatonically" up and down the
> scale - you get some ridiculously sweet "faux-diatonic" harmonies.
> Then try a "subminor/supermajor7" tetrad and do the same thing. You
> can hear a "hint" of diatonic harmony in there, but transposed up in
> down in somewhat colorful and foreign sounding ways. The fact that
> it's all subminor/supermajor though makes it sound pretty bitter, and
> not quite as "clear" as regular diatonic harmony though.
>
> Also, for future reference, is there some easy way to look up the
> names of these things? I'm plowing through all of the 31-tet MOS
> scales now and there are quite a few with no name within Scala.
>
> -Mike
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> How would I make a scala file out of this?
>
> stack 8 11/31 intervals to make an octave?
>
> Help needed in Indy.

The scale below may not be the mode you want, but these are easily generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31 15\31 22\31 24\31 31\31 would be clearer in some ways.

! squares8.scl
Squares[8] in 31et
8
!
77.419354838709677419
154.83870967741935484
425.80645161290322581
503.22580645161290323
580.64516129032258065
851.61290322580645161
929.03225806451612903
1200.0000000000000000

Thank you very much!!

I think I just found a tuning that does all Michael S. could hope for. No
note combination is worse than iffy and it is only 1.
Otherwise every chord - randomly applied to my fret board - sounds good.

It is in fractal tune smithy as selendro 7 limit p2
7/6 4/3 3/2 7/4 2/1

so - its a pentatonic?

Chris

On Thu, Jun 3, 2010 at 9:08 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@...m <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > How would I make a scala file out of this?
> >
> > stack 8 11/31 intervals to make an octave?
> >
> > Help needed in Indy.
>
> The scale below may not be the mode you want, but these are easily
> generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add
> the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31
> 15\31 22\31 24\31 31\31 would be clearer in some ways.
>
> ! squares8.scl
> Squares[8] in 31et
> 8
> !
> 77.419354838709677419
> 154.83870967741935484
> 425.80645161290322581
> 503.22580645161290323
> 580.64516129032258065
> 851.61290322580645161
> 929.03225806451612903
> 1200.0000000000000000
>
>
>

Here is an improvisation using the slendro (excuse my mis-spelling below)

http://notonlymusic.com/board/download/file.php?id=379

On Thu, Jun 3, 2010 at 9:39 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> Thank you very much!!
>
> I think I just found a tuning that does all Michael S. could hope for. No
> note combination is worse than iffy and it is only 1.
> Otherwise every chord - randomly applied to my fret board - sounds good.
>
> It is in fractal tune smithy as selendro 7 limit p2
> 7/6 4/3 3/2 7/4 2/1
>
> so - its a pentatonic?
>
> Chris
>
>
> On Thu, Jun 3, 2010 at 9:08 PM, genewardsmith <genewardsmith@...
> > wrote:
>
>>
>>
>>
>>
>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
>> <chrisvaisvil@...> wrote:
>> >
>> > How would I make a scala file out of this?
>> >
>> > stack 8 11/31 intervals to make an octave?
>> >
>> > Help needed in Indy.
>>
>> The scale below may not be the mode you want, but these are easily
>> generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add
>> the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31
>> 15\31 22\31 24\31 31\31 would be clearer in some ways.
>>
>> ! squares8.scl
>> Squares[8] in 31et
>> 8
>> !
>> 77.419354838709677419
>> 154.83870967741935484
>> 425.80645161290322581
>> 503.22580645161290323
>> 580.64516129032258065
>> 851.61290322580645161
>> 929.03225806451612903
>> 1200.0000000000000000
>>
>>
>>
>
>

And here is one in squares 8

http://notonlymusic.com/board/download/file.php?id=380

I'm going to try this one more as well.

On Thu, Jun 3, 2010 at 9:08 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > How would I make a scala file out of this?
> >
> > stack 8 11/31 intervals to make an octave?
> >
> > Help needed in Indy.
>
> The scale below may not be the mode you want, but these are easily
> generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add
> the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31
> 15\31 22\31 24\31 31\31 would be clearer in some ways.
>
> ! squares8.scl
> Squares[8] in 31et
> 8
> !
> 77.419354838709677419
> 154.83870967741935484
> 425.80645161290322581
> 503.22580645161290323
> 580.64516129032258065
> 851.61290322580645161
> 929.03225806451612903
> 1200.0000000000000000
>
>
>

And the last on this tonight

Squares 8 on piano via gr-20 (as the rest of the improvisations were)

http://notonlymusic.com/board/download/file.php?id=381

On Thu, Jun 3, 2010 at 10:33 PM, Chris Vaisvil <chrisvaisvil@gmail.com>wrote:

> And here is one in squares 8
>
> http://notonlymusic.com/board/download/file.php?id=380
>
> I'm going to try this one more as well.
>
> On Thu, Jun 3, 2010 at 9:08 PM, genewardsmith <genewardsmith@sbcglobal.net
> > wrote:
>
>>
>>
>>
>>
>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
>> <chrisvaisvil@...> wrote:
>> >
>> > How would I make a scala file out of this?
>> >
>> > stack 8 11/31 intervals to make an octave?
>> >
>> > Help needed in Indy.
>>
>> The scale below may not be the mode you want, but these are easily
>> generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add
>> the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31
>> 15\31 22\31 24\31 31\31 would be clearer in some ways.
>>
>> ! squares8.scl
>> Squares[8] in 31et
>> 8
>> !
>> 77.419354838709677419
>> 154.83870967741935484
>> 425.80645161290322581
>> 503.22580645161290323
>> 580.64516129032258065
>> 851.61290322580645161
>> 929.03225806451612903
>> 1200.0000000000000000
>>
>>
>>
>
>

I know this scale! I call it "Mother", because it's the inverse MOS of Father--Mother here is ssLssLsL, Father is LLsLLsLs. Sort of like how Mavila is the inverse of the Diatonic scale--ssLsssL instead of LLsLLLs. Mother as an MOS appears in any EDO with a "supermajor" third between 1\3 (400¢) and 3\8 (450¢); it appears to reach its peak harmonic usefulness with a generator in the middle of that spectrum, around a 23/18. So it comes up with very similar properties in 17-EDO, as well as 14-EDO and (to an extent) 19-EDO and 20-EDO. I haven't worked with it very much, but (from Chris's improv) it seems worth checking out.

Not a good scale if you want a lot of fifths, though; only 4 notes out of 8 have a fifth. Of course, this doesn't bother ME, but it might bother others.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> The scale below may not be the mode you want, but these are easily generated from 11n mod 31, as n goes from 0 to 7. I wish Manuel would add the n-et notation to Scala scl format, somethinf like 2\31 4\31 11\31 13\31 15\31 22\31 24\31 31\31 would be clearer in some ways.
>
> ! squares8.scl
> Squares[8] in 31et
> 8
> !
> 77.419354838709677419
> 154.83870967741935484
> 425.80645161290322581
> 503.22580645161290323
> 580.64516129032258065
> 851.61290322580645161
> 929.03225806451612903
> 1200.0000000000000000
>

>"I think I just found a tuning that does all Michael S. could hope for. No note combination is worse than iffy and it is only 1. Otherwise every chord - randomly applied to my fret board - sounds good."
>"It is in fractal tune smithy as selendro 7 limit p2 7/6 4/3 3/2 7/4 2/1"

      Right, that's pentatonic.  In fact I could say almost the same (IE all combinations are fairly resolved) thing about any standard pentatonic scale under 12TET...and also hence why 5-note-per-octave chords are not at all uncommon "even" outside micro-tonality.  The cool thing is...it (Slendro) definitely has it's own sound and attitude...it doesn't sound 12TET-ish in many ways due much to the 7/6 and 7/4.
-----------------
     First type of tuning I give my child to mess with (and I'm talking age
2 or less) will most likely be a pentatonic one.  Why? Pentatonic has a high reward-per-effort ratio for those just starting music: in a good few cases even someone both completely untrained in theory and unpracticed at "playing by ear" can make intelligent and "well calculated" sounding chords with it....because of how all the dyads "wrap around each other" so well and produce almost all concordant intervals.

      The real challenge to me, is getting something with more flexibility IE with 7+ tones to have that sort of "pentatonic stability".  The scale you pointed out certainly sounds fool-proof, but composing in it just makes me feel emotionally chained far as expression due to the "missing 2 notes".

>"And the last on this tonight
Squares 8 on piano via gr-20 (as the rest of the improvisations were)
http://notonlymusic .com/board/ download/ file.php? id=381"

   Has a very odd effect...seems to hover somewhat predictably at a fair level of dissonance, never really dipping into very high dissonance, but not quite backing out to a level of resolve often either.  It's very jazzy (both the scale and the song) and has an in-between resolved tone wail to it where I sense characteristics of "two interval classes at once" in many parts.  The part of the song from 1:45-2:20 I find particularly amusing, jumping between chords that seem to fit most clearly into different tonal classes rather than feeling "in between" and have a fluttery yet chilling feel to the mood.  Sound like you are playing Jingle Bells in one part
around there, though (lol). :-D

Chris wrote :

> I think I just found a tuning that does all Michael S. could hope
> for. No
> note combination is worse than iffy and it is only 1.
> Otherwise every chord - randomly applied to my fret board - sounds
> good.
>
> It is in fractal tune smithy as selendro 7 limit p2
> 7/6 4/3 3/2 7/4 2/1
>
> so - its a pentatonic?
>
> Chris

This is what I call, in my article 7-LSM (in the TL files),
the Slendro "N" and it is the most basic slendro :
12 : 14 : 16 : 18 : 21

It belongs also to the Natte ("Natté") fractal sequence x^3 = x + 1:
7 : 9 : 12 : 16 : 18 : 21 : 28 : 37 : 49 : 65 : 86 ...

It's in the Ethno2 tunings in the Indonesian folder :

! slendro_matrix.scl
!
Ten tones for many 7-limit slendros from Lou Harrison, of the five
types N M A S J
12
!
1/1
8/7
8/7
64/49
21/16
4/3
3/2
32/21
12/7
256/147
7/4
2/1
! described in "Seven-Limit Slendro Mutations", Jacques Dudon 1/1 8:2
Jan 1994

and you find it also in the Persian folder in :

! s-n-buzurg.scl
!
Decaphonic system inspired by medieval Persian mode Buzurg (Safi al-Din)
12
!
14/13
13/12
8/7
26/21
55/42
39/28
3/2
21/13
13/8
12/7
13/7
2/1
! Estrangetes et Arabesques, Dudon 1997
! also h.13-related superposition of slendros S and N (7-limit
Slendro Mutations, Dudon 1994)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Jacques

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Does this have a name? It seems to generate an amazing 2.3.7 MOS with
> some 11 and 13 thrown in as well. It also has some fascinating
> properties - the 4th scale step is either an approximate 4/3 or an
> approximate 3/2.
>
> Play a supermajor 7 tetrad and move it "diatonically" up and down the
> scale - you get some ridiculously sweet "faux-diatonic" harmonies.
> Then try a "subminor/supermajor7" tetrad and do the same thing. You
> can hear a "hint" of diatonic harmony in there, but transposed up in
> down in somewhat colorful and foreign sounding ways. The fact that
> it's all subminor/supermajor though makes it sound pretty bitter, and
> not quite as "clear" as regular diatonic harmony though.
>
> Also, for future reference, is there some easy way to look up the
> names of these things? I'm plowing through all of the 31-tet MOS
> scales now and there are quite a few with no name within Scala.
>
> -Mike

I don't know about the 8-tone MOS, but I do know that the 11-tone MOS with 11deg31 (or 6deg17) generator is now called Sentinel, after the title of a piece Jacob Barton recorded (on blown bottles) 5 years ago using that scale, which he had just rediscovered:
/makemicromusic/topicId_9132.html#9132
and which I originally discovered in 1978, observing that it contains five 6:7:9:11 tetrads:
/makemicromusic/topicId_9132.html#9141

The as-yet unreleased article I mentioned in the second message is my 17-tone paper:
http://www.anaphoria.com/Secor17puzzle.pdf
which also describes the same 11-tone MOS scale as occurring in both the 17 and 31 divisions.

--George

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:

> I don't know about the 8-tone MOS, but I do know that the 11-tone MOS with 11deg31 (or 6deg17) generator is now called Sentinel, after the title of a piece Jacob Barton recorded (on blown bottles) 5 years ago using that scale, which he had just rediscovered:

The 7-limit 17&31 temperament, using the patent val for 17, has wedgie <<4 -15 9 -33 3 63|| whereas squares has wedgie <<4 16 9 16 3 -24||. If you use them in 31, or as a no-fives temperament, they become the same. Should sentinal be the name of the 17&31 temperament?
There doesn't seem to be a lot of point to the mapping for 5, and you are using it for a no-fives system, so it would just be no-fives squares. Going to the 11-limit gives <<4 16 9 10 16 3 2 -24 -32 -3|| for the squares wedgie, where the -15 mapping fits even less well.

Squares in the 11-limit version tempers out 81/80, 99/98, 121/120, 243/242, 441/440, 540/539 and 2401/2400, and is a pretty interesting temperament.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Squares in the 11-limit version tempers out 81/80, 99/98, 121/120, 243/242, 441/440, 540/539 and 2401/2400, and is a pretty interesting temperament.
>

George won't like it, I suppose, but you can explore the wonders of 17 notes to the octave in various ways, one being the Squares[17] MOS. For this you have ssLsssssLsssssLss, with the small steps being 1/31 and the large steps 2/31. If that's too much for you, Squares [11] goes
sLsssLsssLs with s being 2/31 and L being 5/31, whereas Squares[14] is
ssssLssssLsssL, with s=2/31 and L=3/31.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> George won't like it, I suppose, but you can explore the wonders of 17 notes to the octave in various ways, one being the Squares[17] MOS. For this you have ssLsssssLsssssLss, with the small steps being 1/31 and the large steps 2/31.

Here's an old posting where the way tetrads mutate as you go around the circle of generators in both Beatles[17] and Squares[17] is explored. Beatles[17] goes LLsLsLLsLsLLsLsLs, in the 19/64 tuning L is 5/64 and s is 2/64.

/tuning-math/message/6067

Is it possible to combine two pentatonics?

I'd imagine there are a few ways to do this

where 3 notes are shared
01234
    56789
where 2 notes are shares
01234
     56789
where 1 note is shared
01234
        56789
and of course 2 pentatonics head on

0123456789

Now, interesting technique by Jacques Dundon - the tunings he has in
ethno 2 don't always go in the same direction. Sometimes a note will
go down a 4th or jump up out of the regular order (ascending by the
generator). This makes for some wild chord fingering but it actually
makes musical sense - I think in this way he packs more variety into a
12 note system. You may want to look into the technique.

Chris

On Fri, Jun 4, 2010 at 12:11 AM, Michael <djtrancendance@...> wrote:

      The real challenge to me, is getting something with more
flexibility IE with 7+ tones to have that sort of "pentatonic
stability".  The scale you pointed out certainly sounds fool-proof,
but composing in it just makes me feel emotionally chained far as
expression due to the "missing 2 notes".

Ok Jacques - thanks for the information.

I missed a whole bunch of messages here on this topic - it is as if I
didn't receive them until today.

Chris

On Fri, Jun 4, 2010 at 6:15 AM, Jacques Dudon <fotosonix@...> wrote:
>
>
>
> Chris wrote :
>
> I think I just found a tuning that does all Michael S. could hope for. No
> note combination is worse than iffy and it is only 1.
> Otherwise every chord - randomly applied to my fret board - sounds good.
> It is in fractal tune smithy as selendro 7 limit p2
> 7/6 4/3 3/2 7/4 2/1
> so - its a pentatonic?
> Chris
>
> This is what I call, in my article 7-LSM (in the TL files),
> the Slendro "N" and it is the most basic slendro :
> 12 : 14 : 16 : 18 : 21
> It belongs also to the Natte ("Natté") fractal sequence x^3 = x + 1:
> 7 : 9 : 12 : 16 : 18 : 21 : 28 : 37 : 49 : 65 : 86 ...
> It's in the Ethno2 tunings in the Indonesian folder :
>
> ! slendro_matrix.scl
> !
> Ten tones for many 7-limit slendros from Lou Harrison, of the five types N M A S J
>  12
> !
>  1/1
>  8/7