"I hate 22/15" MOS scale :-D

    John Sullivan said he hated the 22/15 diminished fifth, but put 13/9 on his top interval list.  Agreed though...13/9 isn't too bad...so I pondered the question of what would happen if I made a 7-tone scale optimized for using 13/9 as an "alternative fifth".

  Note I had to temper the perfect fifth generator slightly up and the 13/9 slightly down to get everything to fit into the octave and
get the 2 over 13/9 = 18/13 octave inverse to merge near enough to 7/5 to sound good to me.  So the generators are 628.87 cents and 708.86 cents....

   Anyhow...here's what I got

! c:\I hate twenty two over fifteen.scl
!
I hate twenty two over
15
 7
!
 137.72015
 275.45530
 493.18671
 719/500
 846.58967
 984.32065
 2/1

BTW, Chris and Igs...I'd love to see you two try to compose something with this....

   BTW, here's a second "improved" version of the scale that seems to have lots of lower-limit relations.  This time around, the generators are 628.87 cents and 693.8569 cents...with the step sizes being sLLLLLL (one small, all the rest large).

! E:\I hate twenth two over 15 LOWER LIMIT.scl
!
I hate twenty two over 15 lower limit
 7
!
 122.62535
 310.44701
 498.16101
 719/500
 816.59016
 1004.30401
 2/1

--- On Sun, 2/13/11, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@...>
Subject: [tuning] "I hate 22/15" MOS scale :-D
To: tuning@yahoogroups.com
Date: Sunday, February 13, 2011, 12:55 PM

    John Sullivan said he hated the 22/15 diminished fifth, but put 13/9 on his top interval list.  Agreed though...13/9 isn't too
bad...so I pondered the question of what would happen if I made a 7-tone scale optimized for using 13/9 as an "alternative fifth".

  Note I had to temper the perfect fifth generator slightly up and the 13/9 slightly down to get everything to fit into the octave and
get the 2 over 13/9 = 18/13 octave inverse to merge near enough to 7/5 to sound good to me.  So the generators are 628.87 cents and 708.86 cents....

   Anyhow...here's what I got

! c:\I hate twenty two over fifteen.scl
!
I hate twenty two over
15
 7
!
 137.72015
 275.45530
 493.18671
 719/500
 846.58967
 984.32065
 2/1

BTW, Chris and Igs...I'd love to see you two try to compose something with this....

Michael, this is NOT an MOS of sLLLLLL. It's sLLsLLL, aka the Locrian mode of the diatonic scale. No wonder it sounds good, the 628.87-cent interval ONLY OCCURS ONCE. You goofed.

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
>    BTW, here's a second "improved" version of the scale that seems to have lots of lower-limit relations.  This time around, the generators are 628.87 cents and 693.8569 cents...with the step sizes being sLLLLLL (one small, all the rest large).
>
> ! E:\I hate twenth two over 15 LOWER LIMIT.scl
> !
> I hate twenty two over 15 lower limit
>  7
> !
>  122.62535
>  310.44701
>  498.16101
>  719/500
>  816.59016
>  1004.30401
>  2/1
>
>
>
>
>
> --- On Sun, 2/13/11, Michael <djtrancendance@...> wrote:
>
> From: Michael <djtrancendance@...>
> Subject: [tuning] "I hate 22/15" MOS scale :-D
> To: tuning@yahoogroups.com
> Date: Sunday, February 13, 2011, 12:55 PM
>
>
>
>
>
>
>
>  
>
>
>
>
>
>
>
>
>
>     John Sullivan said he hated the 22/15 diminished fifth, but put 13/9 on his top interval list.  Agreed though...13/9 isn't too
> bad...so I pondered the question of what would happen if I made a 7-tone scale optimized for using 13/9 as an "alternative fifth".
>
>   Note I had to temper the perfect fifth generator slightly up and the 13/9 slightly down to get everything to fit into the octave and
> get the 2 over 13/9 = 18/13 octave inverse to merge near enough to 7/5 to sound good to me.  So the generators are 628.87 cents and 708.86 cents....
>
>    Anyhow...here's what I got
>
>
> ! c:\I hate twenty two over fifteen.scl
> !
> I hate twenty two over
> 15
>  7
> !
>  137.72015
>  275.45530
>  493.18671
>  719/500
>  846.58967
>  984.32065
>  2/1
>
> BTW, Chris and Igs...I'd love to see you two try to compose something with this....
>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>  137.72015
>  275.45530
>  493.18671
>  719/500
>  846.58967
>  984.32065
>  2/1
>
> BTW, Chris and Igs...I'd love to see you two try to compose something with this....

Dude, that's just the ssLsLsL mode of Mohajira, in a not-so-great tuning. There's only two 13/9 "fifths" in this one.

You want to see how 13/9 works as a fifth? Use it, and the octave, as your only generators. Actually, scratch that--that makes a horrible improper scale. Uh, try using a slightly flat 6/5 as your generator, since two of those will come out to about a 13/9. 19-EDO is a good tuning, try this scale:

1/1
252.63157894736842
315.789473684210525
568.421052631578945
631.57894736842105
884.21052631578947
947.368421052631575
2/1

And then tell me how much you like the 13/9 as a fifth ;->

-Igs

>"Michael, this is NOT an MOS of sLLLLLL. It's sLLsLLL, "

   My bad, it is sLLsLLL.  I got confused thinking it only had one s because it only has one 13/9 "alternative 5th" and the rest of the 5ths are near perfect, that the should be only one "s". 

>"aka the Locrian mode"

   One major thing....since when does a mode of the diatonic scale include 13/9?

>"No wonder it sounds good, the 628.87-cent interval ONLY OCCURS ONCE.   You goofed."

   I never said the 628.87-cent interval occurs more than once in the second "low limit" version of the scale...I only said that of the first. :-S  

   In this case it DOES, of course, occur once....and even though the sLLsLLL pattern mirrors diatonic, the tempered 13/9 is not diatonic tri-tone but an undecimal diminished fifth.

  19TET, mind you, does seem to do a fair job of approximating this scale in diatonic mode...close enough where I could see why someone could argue it is close to the same thing.

>"Dude, that's just the ssLsLsL mode of Mohajira, in a not-so-great tuning. There's only two 13/9 "fifths" in this one."

    Right, in this first "high limit" anti-22/15 scale, there are only two, equally spaced apart, by design. 

    What makes the tuning I'm using a "not so great tuning"?  Well, unless you consider the usual 22/15-ish Mohajira diminished fifth a better option...   You seem to categorize scales exclusively in terms of their sLsLL...MOS patterns and, while that may be somewhat of a standard, it bears very little resemblance to what my ears tell me about the mood and stability of scales.

  For example, I hear a lot of things in different diatonic MOS arrangements that sound flat out vicious...I don't buy
"diatonic always = good" or "all diatonic MOS arrangements sound alike" or anything like that.

>"And then tell me how much you like the 13/9 as a fifth ;->"

  Well look at the spacing in the scale you gave me.  It stinks.  Call it "diatonic spacing" or whatever...but the idea of having "alternative fifths" a maximal distance apart from each other, to me, is key.  It doesn't guarantee anything, but it's a crucial step in my mind.  My "Dimension" system spaces the "bad" alternative 5ths equally apart as well.

   BTW, let's get one thing else straight.  When I say alternative fifths I do NOT mean stack them on top of each other to make a scale.  I mean take one or two of them to use in place of fifths (out of 7 fifths), maximal distance apart in the "circle of (including alternative) fifths".  You seem to be trying to pigeon-hole me in an "all or nothing scenario"...and that's
not what I'm doing or aiming for.

   My point is that, far as alternative fifths, 13/9 is one of the less painful ones and doesn't knock things "off" much when 1 to 2 of them are placed near 5+ near pure fifths.  Compare that to, say, making the similar MOS patterns using 16/11 or 40/27 or 23/15 as your fifths....and I'm pretty confident you'll hear 13/9 as one of the lesser of the "evil" non-pure fifths.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>     What makes the tuning I'm using a "not so great tuning"? 

It's a ways away from TOP Mohajira, that's all.

> Well, unless you consider the usual 22/15-ish Mohajira diminished fifth a better
> option...

What version of Mohajira has a 22/15 in it?

> You seem to categorize scales exclusively in terms of their sLsLL...MOS patterns and,
> while that may be somewhat of a standard, it bears very little resemblance to what my
> ears tell me about the mood and stability of scales.

I don't categorize scales in terms of mood and stability because those are not traits that scales tend to share, unless you're grouping scales that are only minutely different from each other. I categorize scales in terms of things they have in common with one another, because that (to a large extent) tells me generally what kinds of melodies they can render and what kinds of chords and progressions are available. If that doesn't work for you, then don't use it.

>   For example, I hear a lot of things in different diatonic MOS arrangements that sound
> flat out vicious...I don't buy "diatonic always = good" or "all diatonic MOS arrangements > sound alike" or anything like that.

Michael, you are the king of putting words in peoples' mouths.

>   Well look at the spacing in the scale you gave me.  It stinks.  Call it "diatonic spacing"
> or whatever...but the idea of having "alternative fifths" a maximal distance apart from
> each other, to me, is key.  It doesn't guarantee anything, but it's a crucial step in my
> mind.  My "Dimension" system spaces the "bad" alternative 5ths equally apart as well.

I don't see anything wrong with the spacing of that scale. It may be a little melodically weird but you can still make perfectly reasonable chord progressions. If you think 13/9 is a good alternative fifth, then what's wrong with using a scale where it takes the place of the 3/2's?

>    BTW, let's get one thing else straight.  When I say alternative fifths I do NOT mean
> stack them on top of each other to make a scale.  I mean take one or two of them to use > in place of fifths (out of 7 fifths), maximal distance apart in the "circle of (including
> alternative) fifths". 

But you're not using them "in place" of any 3/2's. In both of the scales you posted, you substituted 13/9 for intervals that would normally be diminished fifths, i.e. 45/32's or 40/27's or 10/7's or 16/11's or whatever. So what makes them "alternative fifths" if you aren't using them as alternatives to normal 3/2 fifths? You should just call them "alternative diminished fifths", since that's apparently how you use them. That seems a lot more plausible, anyway. I mean, no one's going to be fooled into thinking that 13/9 or 10/7 or 22/15 are 3/2's.

-Igs

Me>   For example, I hear a lot of things in different diatonic MOS arrangements that sound

> flat out vicious...I don't buy "diatonic always = good" or "all
diatonic MOS arrangements > sound alike" or anything like that.

Igs>Michael, you are the king of putting words in peoples' mouths.

    Well, you brought up the scale I found as "it's just a diatonic scale, no wonder it sounds good!" and I assumed you meant "diatonic scales sound good"...is it really that big a jump of an assumption on my part?

>"But you're not using them "in place" of any 3/2's. In both of the
scales you posted, you substituted 13/9 for intervals that would
normally be diminished fifths, i.e. 45/32's or 40/27's or 10/7's or
16/11's or whatever."

  Well...a diminished fifth is a fifth...hence my terminology of use of a diminished fifth as an "alternative fifth".  If I were not substituting for a fifth, I would be trying to, say, substitute for a tri-tone.  10/7, for the record, is of course a tri-tone, not a diminished fifth...while 13/9 is a diminished fifth.

>"So what makes them "alternative fifths" if you aren't using them as
alternatives to normal 3/2 fifths? You should just call them
"alternative diminished fifths", since that's apparently how you use
them."

    Ugh......ok.   My point was if I made a 9:12:13 chord, for example, it would be significantly different sounding and a lot more "fifth-ish sounding" than a 1/1 4/3 7/5 chord that uses a tri-tone.
  You're right though...if you mean to say a 9:12:13 chord is not a substitute for a 1/1 4/3 3/2 chord, for example.  When you said "diatonic" I assume you meant the standard diatonic where there are two tri-tones.

>"That seems a lot more plausible, anyway. I mean, no one's going to be
fooled into thinking that 13/9 or 10/7 or 22/15 are 3/2's."

  And yet in your first song of "map of an internal landscape" you used some sort of funky wolf fifths (40/27 or 16/11 I believe)...and, honestly, in context, it did fool me.  Plus, apparently, John was fooled in thinking I "can't have used a 13/9" in my melodic example when, in reality, I certainly did!  Perhaps we all have "bad ears"....

    And again, 10/7 is not even in the ballpark...it's not even a fifth (diminished or not), it's a tritone!   And I'm swapping types of fifths (including diminished and augmented), but not tritones, minor sixths, etc!

   When I say alternative fifth I mean any type of fifth, diminished types included!  Anyhow, fine...I'll call them "diminished fifths swapped into the circle of fifths" or "augmented fifths swapped into the circle of fifths" (can I possibly be more specific)?