I Am by Chris Vaisvil - Blue Temperament

Chris has written a new piece using my Blue Temperament. Here's the link...

http://micro.soonlabel.com/blue-tuning/IF20110107b-I-Am.mp3

John.

Don't mean to clutter the list with shallow praise, but this is so
incredibly lovely overall, as was the last enchanting hobbit piece.

Thank you Daniel very much for your listens and comments. They are
much appreciated.

Chris

On Sat, Jan 8, 2011 at 10:45 PM, Daniel Nielsen <nielsed@...> wrote:
>
>
>
> Don't mean to clutter the list with shallow praise, but this is so incredibly lovely overall, as was the last enchanting hobbit piece.
>
>

I've been working a lot on my Dimension^2 scale...which includes a
subset/mode rather near quarter comma meantone and another rather like Ptolemy's
Homalon scales.

However, I am not blind to the fact a whole lot of people here think 7-limit
is as far as the average listener can tolerate...and Dimension^2 admittedly
contains a good few 11-limit dyads and one thirteen...so it clearly would not
work if said theory about 7-limit holds.

So I made my "own" 7-limit scale of
! E:\LIMIT of SEVEN.scl
!
Limit of Seven
6
!
15/14
8/7
5/4
10/7
12/7
2/1

I learned that the was virtually no way to get all possible dyads (minus the
semitone and seventh...the same problem so-called 5-limit scales, including
12TET often have) within 8 cents of 7-limit-or-under with a full 7 tones, so I
"settled" for a 6-tone scale..

Of course, I did due diligence and used Scala's "compare scale"
function...and it turned out my scale was simply a subset of the 21-tone
"rational Wilson Grady Blackjack scale". This seems to say that whatever
methods I'm using to find optimum scales is in-line with what Mike B and others
have been saying all along...that Blackjack is a fantastic scale system. That
said, I don't know much about Blackjack...anyone care to elaborate on it and
what it can do so far as 7-limit (or less) dyads?

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

> However, I am not blind to the fact a whole lot of people
> here think 7-limit is as far as the average listener can
> tolerate...

Making stuff up again, Michael? -Carl

On Sun, Jan 9, 2011 at 4:34 PM, Michael <djtrancendance@...> wrote:
>
>     However, I am not blind to the fact a whole lot of people here think 7-limit is as far as the average listener can tolerate...and Dimension^2 admittedly contains a good few 11-limit dyads and one thirteen...so it clearly would not work if said theory about 7-limit holds.

Uh, what? The last few days we've been discussing 2.3.7.13/10 subgroup
temperaments. What are you talking about?

-Mike

>"Making stuff up again, Michael? -Carl"

No I'm not....
I recall clearly someone on this list said that anything over 7-limit, far
as scales, would likely sound weird to most people...it serves me no purpose to
make something like that up (especially since such a statement would go AGAINST
much of the work I've done lately on my 11+ limit scales).

Also, for the record...this is obviously NOT part of your "2.3.7.13/10
subgroup temperaments discussion...that's why I started a new thread on
it...come on, that should be blatantly obvious to you.

Anyhow, it ultimately doesn't matter who said 7-limit was any sort of
listening limit, and either you are going to keep sucking up my thread making
personal accusations...or actually help me get something done.
---------------

Why not stay on topic and simply answer my question about what uses the
Blackjack temperament has far as 7-limit or less dyads and chords containing all
7-limit (or less) dyads?

On Sun, Jan 9, 2011 at 5:06 PM, Michael <djtrancendance@...> wrote:
>
> >"Making stuff up again, Michael? -Carl"
>
> No I'm not....
>     I recall clearly someone on this list said that anything over 7-limit, far as scales, would likely sound weird to most people...it serves me no purpose to make something like that up (especially since such a statement would go AGAINST much of the work I've done lately on my 11+ limit scales).

I don't ever remember someone saying that, but okay. If they said
that, then they aren't really part of the mainstream view around here.
I think Blackjack is a fantastic scale system, but it was developed
right here on this list, so...

>     Also, for the record...this is obviously NOT part of your "2.3.7.13/10 subgroup temperaments discussion...that's why I started a new thread on it...come on, that should be blatantly obvious to you.

The point was just that 13/10 is already beyond the 7-limit, and
Gene's been writing 13-limit music for ages, and Carl's also pretty
down with the 11-limit, and so I don't know who said it. Let me know
if they say it again and I will arrange for them to be flogged.

>   Anyhow, it ultimately doesn't matter who said 7-limit was any sort of listening limit, and either you are going to keep sucking up my thread making personal accusations...or actually help me get something done.

OK, sorry, but please stop making statements about how dumb everyone else is.

>     Why not stay on topic and simply answer my question about what uses the Blackjack temperament has far as 7-limit or less dyads and chords containing all 7-limit (or less) dyads?

What do you mean by what uses it has? Blackjack is a 21-note MOS of
miracle temperament, so if you're investigating it for the first time,
you might want to just look at miracle in general. It's an 11-limit
temperament that works beautifully in 72-tet. It's also supported by
31-tet and 41-tet, and I guess technically 21-tet, although that's
kind of weird.

It has some interesting properties in that there's a 10-note MOS that
works well for melody, but not for harmony. It's apparently common to
move the melody notes slightly by a tiny blackjack comma-sized step so
that concordant harmonies are formed, but the melodies are still close
enough to the original 10-note MOS to be intelligible and coherent. I
don't have a lot of experience with this but it seems like a really
cool concept.

If I were you I'd ditch the rational version and mess around with the
72-tet version of blackjack - looooots of nice 11-limit stuff to play
around in there. If you want to stick to the 7-limit for some reason
then you can as well. There's also a 13-limit extension or two, but
they're less accurate as far as I know.

-Mike

MikeB>"The point was just that 13/10 is already beyond the 7-limit, and Gene's
been writing 13-limit music for ages, and Carl's also pretty down with the
11-limit, and so I don't know who said it."

Ok look...in honesty I do specifically recall someone saying
it...specifically saying "11-limit is just weird...man"...I'm not making it up
and have/had no reason to. Anyhow I get your point...the general consensus of
this list AS OF NOW is not only that 11-limit+ is good for experienced
microtonalists' ears...but also for the general population's (and please don't
start any rants about what 'general population' means"...we've all been there
before).

Me> Anyhow, it ultimately doesn't matter who said 7-limit was any sort of
listening limit, and either you are going to keep sucking up my thread making
personal accusations...or actually help me get something done.
MikeB>"OK, sorry, but please stop making statements about how dumb everyone else
is."

I was not saying you (all?) are being dumb or are incapable
(intellectually) of answering my question...I was saying you all are CHOOSING to
not answer my original question.

I was sure you all could if you wanted to, but the attitude I'm getting is
from this list seems to be "we're too proud to answer your stupid question".
Which seems to communicate that you think my question is stupid...to the point
you and Carl (by your actions) seemed more eager to start a fight with me than
take the time to answer "what can Blackjack do within 7-limit?"....something I'm
sure you could do if you wanted to.

>"It has some interesting properties in that there's a 10-note MOS that works
>well for melody, but not for harmony. It's apparently common to move the melody
>notes slightly by a tiny blackjack comma-sized step so
that concordant harmonies are formed, but the melodies are still close enough to
the original 10-note MOS to be intelligible and coherent. I don't have a lot of
experience with this but it seems like a really cool concept."

So when going for both harmonies and melodies in Blackjack...the harmonies
are comma-shifted but the melodies are not...got it...interesting. I also got
the part about it being a member of the Miracle sub-group.

>"If I were you I'd ditch the rational version and mess around with the 72-tet
>version of blackjack - looooots of nice 11-limit stuff to play around in there.
>If you want to stick to the 7-limit for some reason
then you can as well. There's also a 13-limit extension or two, but they're less
accurate as far as I know."

Argh...my question concerned what Blackjack could do >within< 7-limit...and
here I am getting tangential options on Blackjack at 11-limit and 13-limit...but
nothing on 7-limit beyond "yes, it can do 7-limit".
-----------------------------
Can anyone (or perhaps more importantly, does anyone WANT to) give me an
answer on what lies in Blackjack that is in the 7th limit?

On Sun, Jan 9, 2011 at 5:44 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"The point was just that 13/10 is already beyond the 7-limit, and Gene's been writing 13-limit music for ages, and Carl's also pretty down with the 11-limit, and so I don't know who said it."
>
>    Ok look...in honesty I do specifically recall someone saying it...specifically saying "11-limit is just weird...man"...I'm not making it up and have/had no reason to.  Anyhow I get your point...the general consensus of this list AS OF NOW is not only that 11-limit+ is good for experienced microtonalists' ears...but also for the general population's (and please don't start any rants about what 'general population' means"...we've all been there before).

But it's silly, from my perspective, that you are using Blackjack as
an example to disprove "the historical consensus of the tuning list
that the 7-limit is as high as is tolerable for the average listener,"
when Blackjack was invented specifically as an 11-limit tuning, on the
tuning list, like a decade ago. And the very people who you keep
saying are the ones who don't believe that the 11-limit is "usable"
are the ones who invented it, and before that George Secor had
previously invented it, or probably more like discovered it.

> Me>   Anyhow, it ultimately doesn't matter who said 7-limit was any sort of listening limit, and either you are going to keep sucking up my thread making personal accusations...or actually help me get something done.
> MikeB>"OK, sorry, but please stop making statements about how dumb everyone else is."
>
>      I was not saying you (all?) are being dumb or are incapable (intellectually) of answering my question...I was saying you all are CHOOSING to not answer my original question.
>
>      I was sure you all could if you wanted to, but the attitude I'm getting is from this list seems to be "we're too proud to answer your stupid question".  Which seems to communicate that you think my question is stupid...to the point you and Carl (by your actions) seemed more eager to start a fight with me than take the time to answer "what can Blackjack do within 7-limit?"....something I'm sure you could do if you wanted to.

We would have loved to answer your question if you had just asked
about Blackjack's uses in the 7-limit. But you didn't. You posted a
bunch of other stuff too, which was rather inflammatory. Like this:

> Of course, I did due diligence and used Scala's "compare scale" function...and it turned out my scale was simply a subset of the 21-tone "rational Wilson Grady Blackjack scale". This seems to say that whatever methods I'm using to find optimum scales is in-line with what Mike B and others have been saying all along...that Blackjack is a fantastic scale system. That said, I don't know much about Blackjack...anyone care to elaborate on it and what it can do so far as 7-limit (or less) dyads?

This is a ridiculous statement, because Blackjack was "discovered" by
regular mapping. It's a 21-note MOS of miracle temperament, and the
people who invented the mapping theory and discovered the temperament
and did all the work are the ones who you're trying to disprove by
using their own scale. There is no need to make comments like this. I
posted a 7-tet based 5-limit tuning the other day, and I didn't get
into "despite how Carl and Gene think that 7-tet's fifths are on the
edge of unrecognizability and unusable, I think that this scale proves
something specific about psychoacoustics" and start off a huge
inflammatory rant. I just posted the scale and some useful properties.
Don't post inflammatory statements and people will answer your
questions as you want them to be answered.

> >"It has some interesting properties in that there's a 10-note MOS that works well for melody, but not for harmony. It's apparently common to move the melody notes slightly by a tiny blackjack comma-sized step so
> that concordant harmonies are formed, but the melodies are still close enough to the original 10-note MOS to be intelligible and coherent. I don't have a lot of experience with this but it seems like a really cool concept."
>
>     So when going for both harmonies and melodies in Blackjack...the harmonies are comma-shifted but the melodies are not...got it...interesting.  I also got the part about it being a member of the Miracle sub-group.

I think you'd shift the melodies too. I don't know what you mean by
"Miracle subgroup." The miracle generator is a sharp semitone, roughly
6 out of 72, and there are MOS's at 10, 21, 31, 41, etc notes. The 21
note one is called "blackjack."

> >"If I were you I'd ditch the rational version and mess around with the 72-tet version of blackjack - looooots of nice 11-limit stuff to play around in there. If you want to stick to the 7-limit for some reason
> then you can as well. There's also a 13-limit extension or two, but they're less accurate as far as I know."
>
>    Argh...my question concerned what Blackjack could do >within< 7-limit...and here I am getting tangential options on Blackjack at 11-limit and 13-limit...but nothing on 7-limit beyond "yes, it can do 7-limit".
> -----------------------------
>    Can anyone (or perhaps more importantly, does anyone WANT to) give me an answer on what lies in Blackjack that is in the 7th limit?

Sorry that I threw in a single sentence about the 13-limit. Next time
I'm giving you advice for free about a scale that you could load up
yourself in 30 seconds, I'll be sure to think two steps ahead and
leave out related information that you didn't specifically ask for.

What does Blackjack have in the 7-limit? Jesus man, just load the
scale up and play with it. Like I just told you, ditch the rational
version and load up the 72-tet one. There are 4:5:6:7's pretty much
all over the place, there are 1/(4:5:6:7)'s, there are subminor 7
chords, there's one supermajor 7 chord, there's loads of stuff. All of
your favorite standard 7-limit chords are there.

-Mike

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Making stuff up again, Michael? -Carl"
>
> No I'm not....
> I recall clearly someone on this list said that anything
> over 7-limit, far as scales, would likely sound weird to most
> people...

Someone, or "whole lot of people"?

> it serves me no purpose to
> make something like that up

I completely agree.

> either you are going to keep sucking up my thread making
> personal accusations...or actually help me get something done.

You have to take the first step.

> Why not stay on topic and simply answer my question about what
> uses the Blackjack temperament has far as 7-limit or less dyads
> and chords containing all 7-limit (or less) dyads?

[head explodes]

-Carl

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

> Can anyone (or perhaps more importantly, does anyone WANT to) give me an
> answer on what lies in Blackjack that is in the 7th limit?
>

Tetrads in miracle have a Graham complexity of 13, so there are 21-13 = 8 otonal tetrads and an equal number of utonal tetrads. Similar calculations can be made for other chords. Meantone does a bit better, but is much less accurate, and the chord relationships are entirely different. Here are some examples of 7-limit Blackjack:

http://www.archive.org/details/RachmaninoffPlaysBlackjack
http://www.archive.org/details/StainedGlass

MikeB>"But it's silly, from my perspective, that you are using Blackjack as an
example to disprove "the historical consensus of the tuning list that the
7-limit is as high as is tolerable for the average listener,""

Look, THE POINT IS if I want to do a fair analysis on making "well received"
scales...I need to try a bit of everything...and one thing I have not tried a
lot of is 7-limit....If anything I'm admitting >I< need/want to be more
open-minded to what may/.may-not work and go beyond simply my old 11-limit+
experiments....yes that's right, I'm saying I, and not any of you, want help
with being more open-minded.
If anything, I'm experimenting with the idea that maybe my past experiments,
which resolve a lot around 11-limit...have equally useful equivalents in
7-limit. I never said "11-limit is not a good answer"...my point is..."7-limit
may be a good answer for some people who dismiss 11-limit". Though, on the
other hand, some people may well prefer 11-limit to 7-limit. I'm trying to be
open-minded here.And the very people who you keep

>the ones who don't believe that the 11-limit is "usable" are the ones who
>invented it, and before that George Secor had previously invented it, or
>probably more like discovered it."
Look, I'm not here to fight about who I attributed what to...fine, I may well
be wrong in saying who said what, I have no ball in that game...my "game" is to
find scales good for 7-limit and learn their options...and then see how they
fair with listeners...including NOT well if that turns out to be the case!

MikeB>"You posted a bunch of other stuff too, which was rather inflammatory.
Like this:"

Michael>"Of course, I did due diligence and used Scala's "compare scale"
function...and it turned out my scale was simply a subset of the 21-tone
"rational Wilson Grady Blackjack scale". This seems to say that whatever methods
I'm using to find optimum scales is in-line with what Mike B and others have
been saying all along...that Blackjack is a fantastic scale system."
What I was doing was ADMITTING THE SCALE I CAME UP WITH WAS NOT MINE IE
GIVING FAIR CREDIT (BOTH TO THE CREATORS OF THE SCALE AND PEOPLE WHO I RECALL
RECOMMENDING IT)!
Now why on earth are you picking on me FOR my honest attempt to give fair
credit (even if you say don't, in fact, like Blackjack and I misread you)?

MikeB>I think you'd shift the melodies too. I don't know what you mean by
"Miracle subgroup." The miracle generator is a sharp semitone, roughly 6 out of
72, and there are MOS's at 10, 21, 31, 41, etc notes. The 21
note one is called "blackjack."

Cool...this is useful tuning information...not random bullying...thank you.
When I said "subgroup", I did mean "subgroup...of a generator".

>"What does Blackjack have in the 7-limit? Jesus man, just load the scale up and
>play with it. Like I just told you, ditch the rational version and load up the
>72-tet one. There are 4:5:6:7's pretty much all over the place, there are
>1/(4:5:6:7)'s, there are subminor 7 chords, there's one supermajor 7 chord,
>there's loads of stuff. All of
your favorite standard 7-limit chords are there."

So your tone of voice is needlessly hostile but, yes, that was actually an
on-topic useful answer now that you finally chose to give it....case closed
(unless someone else has other answers along the same lines). Now was it really
that hard to "lower yourself" to saying that answer?

Gene>"Tetrads in miracle have a Graham complexity of 13, so there are 21-13 = 8
otonal tetrads and an equal number of utonal tetrads. Similar calculations can
be made for other chords. Meantone does a bit better, but is much less accurate,
and the chord relationships are entirely different."

Good info...gives a good picture of what to expect on the whole from
Blackjack vs. the somewhat standard meantone system...IE less chords than
meantone...but much more accuracy.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jan 9, 2011 at 5:06 PM, Michael <djtrancendance@...> wrote:
> >
> > >"Making stuff up again, Michael? -Carl"
> >
> > No I'm not....
> >     I recall clearly someone on this list said that anything over 7-limit, far as scales, would likely sound weird to most people...it serves me no purpose to make something like that up (especially since such a statement would go AGAINST much of the work I've done lately on my 11+ limit scales).
>
> I don't ever remember someone saying that, but okay. If they said
> that, then they aren't really part of the mainstream view around here.
> I think Blackjack is a fantastic scale system, but it was developed
> right here on this list, so...

Maybe it was me? 11-limit chords are just weird, man. I mean, I like them for a lot of things, but I'd have a hard time being convinced that "Joe Radio" on the street would find them any less than cringe-worthy. Even an 11-limit otonal pentad sounds like nails on a chalkboard to me. And this is ME we're talking about.

-Igs

Igs>"Maybe it was me? 11-limit chords are just weird, man."

Quite likely that was you...you said it precisely how I remember it being
said: "11-limit chords are just weird, man". So I attributed the wrong
person...it's not like I intended to at all. Of course, apologies about the
"Making Stuff Up Again?!" statement would make sense...though I have my doubts
anyone will actually apologize maturely considering they started fight against
me on a perfectly honest question...

Far as Blackjack...I've been experimenting with it, both in and beyond
7-limit...and I can see why it would be a favorite scale common among bunch of
people on this list. I'd like to give thanks for those I RECALL suggesting it
in honest gratitude, but that would probably start another flame war (hey, it
did the first time I tried to give thanks and due credit...apparently, that act
is a real fire-starter on this list)! :-S

Igs>"Maybe it was me? 11-limit chords are just weird, man."

Another note...I guess the only "audience" I'm playing to by looking for a scale
with very accurate 7-limit (or less) dyads within to octave IE including the
following list of dyads:
3/2
4/3
5/3
5/4
6/5
7/4
7/5
7/6
8/7
9/7
10/7
12/7
-----plus the additional intervals of---------
15/8
15/14

Is Igs. So, Igs (since you're the only one who seems to think 11-limit as
inappropriate for the "average Joe" scale...apparently), look at the below scale

1/1
15/14
8/7
5/4
10/7
12/7
2/1

.....does it strike you as loaded with "just weird man" chords...and, if so,
where are they? :-D
And again, I'm not saying 11-limit+ chords or scales are bad but, rather, trying
to entertain the possibility of a hopefully quite efficient 7-limit scale. And
if any of you have suggestions for 7-limit scales of any sort...suggestions are
welcome...

Michael <djtrancendance@...> wrote:
> Another note...I guess the only "audience" I'm playing to
> by looking for a scale with very accurate 7-limit (or
> less) dyads within to octave IE including the following
> list of dyads: 3/2

> 9/7

That's 9-limit -- outside the 7-limit. So if you're happy
with one 9-limit interval, how about 9/8, 10/9, and friends?

Graham

Graham>"That's 9-limit -- outside the 7-limit. So if you're happy with one
9-limit interval, how about 9/8, 10/9, and friends?"

Hmm...I actually think I threw that one in by mistake and meant 10/7.

Come to think of it, if I cut myself some slack on the "all dyads must be good"
restriction I can get a 7-tone scale of

2/1
12/7
3/2 (new tone)
10/7
5/4
8/7
15/14
1/1

Although that gives me an issue with the octave above 8/7 (IE 8/7 * 2) being
an ugly 32/21 interval above 3/2 and the 10/7 an octave above being 19/10 above
3/2...and the 3/2 over 8/7 giving 21/16. That's 3 "bad" intervals, in my book.

The question that comes up in my mind is...is there a good way to "temper
this out" to a temperament that would kill some of those really high limit dyads
(IE put them within 8 cents of a 7-or-less limit dyad if possible)?

Michael <djtrancendance@...> wrote:
> Graham>"That's 9-limit -- outside the 7-limit. So if
> Graham>you're happy with one
> 9-limit interval, how about 9/8, 10/9, and friends?"
>
> Hmm...I actually think I threw that one in by mistake
> and meant 10/7.

Okay.

> Come to think of it, if I cut myself some slack on the
> "all dyads must be good" restriction I can get a 7-tone
> scale of
>
> 2/1
> 12/7
> 3/2 (new tone)
> 10/7
> 5/4
> 8/7
> 15/14
> 1/1

It's 7-limit except for the 15/14. Why 10/7 instead of 7/5?

> Although that gives me an issue with the octave above
> 8/7 (IE 8/7 * 2) being an ugly 32/21 interval above 3/2
> and the 10/7 an octave above being 19/10 above 3/2...and
> the 3/2 over 8/7 giving 21/16. That's 3 "bad" intervals,
> in my book.

The 21:16 can approximate 13:10. The only simpler target
would be 4:3, which means 8/7 becomes 9/8, and so 64:63
tempered out. My website says this is consistent with
Dominant, Pajara, Blacksmith, Augene, Superpyth, Porcupine,
a Dicot variant, Beatles, Schism, and Mother.

How do you get a 19-limit interval between two 7-limit
intervals? 2*10/7*2/3 = 40/21. Or an interval of 21:20
between 10/7 and 3/2.

If you want something like a tritone along with a 3/2,
you're going to have to have something like a semitone
between them. Use 7/5 instead of 10/7, and that would be
15:14.

> The question that comes up in my mind is...is there a
> good way to "temper this out" to a temperament that would
> kill some of those really high limit dyads (IE put them
> within 8 cents of a 7-or-less limit dyad if possible)?

64:63 is a 27.3 cent interval made up of three 7-limit
intervals. The optimal tempering-out of it would be
27.3/3=9.1 cents out. That's the best you can do if you
want to avoid the 21:16. Superpyth gets pretty close:
minimax error of 9.8 cents.

http://x31eq.com/cgi-bin/rt.cgi?ets=5_22&limit=7

Graham

Graham>"It's 7-limit except for the 15/14. Why 10/7 instead of 7/5?"

Right...the semitones are not 7-limit...just as they are not 5-limit in
"5-limit" meantone. Isn't it true/obvious? though, that any ratio smaller than
7/6 is going to be more than 7-limit?

As for why I'm using the 10/7 and not the simpler 7/5....it turns out 7/5
causes problems as it forms a near-11/9-interval with 12/7 and forms a similar
one with 8/7 (assuming octave equivalence). There are a lot of 7-limit
intervals that look great from the 1/1 root...but cause problems when assuming
other roots.

So far the best result I've managed is
1/1
16/15
8/7
4/3
10/7
3/2
12/7

The catches?
I get a 9-limit "septimal minor sixth" of sorts around 14/9 between 12/7 and
4/3 (really not too bad), a seventh from 3/2 to the next octave around 19/10,
and a rather sharp fifth nearing 50/33. The "hopelessly sharp" fifth I can well
tolerate, but the 19/10 and 14/9 much less so.

>"The 21:16 can approximate 13:10. The only simpler target would be 4:3, which
>means 8/7 becomes 9/8, and so 64:63 tempered out."
Good idea...I'll likely make a second scale where I swap the 8/7 with a
9/8...

>" My website says this is consistent with Dominant, Pajara, Blacksmith, Augene,
>Superpyth, Porcupine,
a Dicot variant, Beatles, Schism, and Mother."
...and try it in those tunings.

>"How do you get a 19-limit interval between two 7-limit intervals?"
I'm using the term 19-limit lightly.

>"2*10/7*2/3 = 40/21"
Right...and the difference between 40/21 and 19/10...around 4 a mere
cents...and, yes, I'm being an optimist and saying the two are virtually
equivalent. Admittedly, I'm thinking more in terms of "psuedo-JI" (as decribed
in Monzo's online dictionary of microtonal terms) than JI.

>"64:63 is a 27.3 cent interval made up of three 7-limit intervals. The optimal
>tempering-out of it would be
27.3/3=9.1 cents out. That's the best you can do if you want to avoid the
21:16. Superpyth gets pretty close:
minimax error of 9.8 cents." http://x31eq.com/cgi-bin/rt.cgi?ets=5_22&limit=7

Indeed...that is really close (plus I acknowledge Superpyth has been getting a
lot of attention on here lately)...I will definitely try that: thank you for the
tip.

Michael <djtrancendance@...> wrote:
> Graham>"It's 7-limit except for the 15/14. Why 10/7
> Graham>instead of 7/5?"
>
> Right...the semitones are not 7-limit...just as they
> are not 5-limit in "5-limit" meantone. Isn't it
> true/obvious? though, that any ratio smaller than 7/6 is
> going to be more than 7-limit?

Meantone temperaments can be used for 5-limit harmony. But
that doesn't mean every interval in the scale has to be
5-limit. You can write music with strictly 5-limit chords.

Yes, it's obvious that no 7 note scale can be fully
7-limit, because the steps would have to be too small.
Although 8:7 is the smallest allowable, not 7:6. That would
limit you to a pentatonic scale. I know of two pentatonics
that lie within the 9-limit: the usual meantone pentatonic
(no 7s) and the 5 note MOS from Bogey (no 5s, 19&24 or every
other note of Negri). Probably 5-equal (the scale of
nature) is the only way to approximate the strict 7-limit.

What I can see working here is the usual diatonic scale in
Dominant temperament (12&5). It's a bit of a shocker
though: worst error 25 cents. The whole tone approximates
as 8:7 and the tritone as either 7:5 or 10:7.

> As for why I'm using the 10/7 and not the simpler
> 7/5....it turns out 7/5 causes problems as it forms a
> near-11/9-interval with 12/7 and forms a similar one with
> 8/7 (assuming octave equivalence). There are a lot of
> 7-limit intervals that look great from the 1/1 root...but
> cause problems when assuming other roots.

Yes, and those neutral thirds approximate 11/9 with Miracle
temperament.

> Good idea...I'll likely make a second scale where I
> swap the 8/7 with a 9/8...

Is 9:8 allowed now?

Graham

Graham>"Yes, it's obvious that no 7 note scale can be fully 7-limit, because the
steps would have to be too small. Although 8:7 is the smallest allowable, not
7:6."
Right...my mistake, the minimum allowed is 8/7.

>"Yes, it's obvious that no 7 note scale can be fully 7-limit, because the steps
>would have to be too small."
Exactly/agreed.

>"I know of two pentatonics that lie within the 9-limit: the usual meantone
>pentatonic
(no 7s) and the 5 note MOS from Bogey (no 5s, 19&24 or every other note of
Negri). Probably 5-equal (the scale of nature) is the only way to approximate
the strict 7-limit."
Need to look up the 5 note MOS (or "Negri")...what's its .scl file name in
Scala and, if you happen to know off the top of your head...how many notes have
an error over 10 cents or so? Have tried 5 equal...but it seems rather off so
far as the third and 5th.

>"What I can see working here is the usual diatonic scale in Dominant temperament
>(12&5). It's a bit of a shocker though: worst error 25 cents."
Interesting...the thing is 25 cents, to me, is an unforgivable sin (unless it
happens to be for only, say, two dyads or less out of all possible dyads). :-D

Me> "Good idea...I'll likely make a second scale where I swap the 8/7 with a
9/8..."
Graham>"Is 9:8 allowed now?"

Certainly is...the more ratio swapping I do to try and optimize things for a
7-tone scale "mostly in 7-limit"...the more I run into 9-limit dyads...looks
like 9-limit is here to stay (at least, unless I go for 5-tone scales). Look
for my best shot at a similar scale but using 9/8 rather than 8/7 soon...

Michael <djtrancendance@...> wrote:

> >"I know of two pentatonics that lie within the 9-limit:
> >the usual meantone pentatonic
> (no 7s) and the 5 note MOS from Bogey (no 5s, 19&24 or
> every other note of Negri). Probably 5-equal (the scale
> of nature) is the only way to approximate the strict
> 7-limit." Need to look up the 5 note MOS (or
> "Negri")...what's its .scl file name in Scala and, if you
> happen to know off the top of your head...how many notes
> have an error over 10 cents or so? Have tried 5
> equal...but it seems rather off so far as the third and
> 5th.

Bogey is here:

http://x31eq.com/cgi-bin/rt.cgi?ets=19+5&limit=2.3.7

You can get Scala files from those pages now. Hopefully
the 5 note ones make sense.

I'm not sure how the errors are distributed. It's not the
best because it has to equate 7:6 and 8:7. But it can't be
much worse than 19-equal. From what I remember, the
tuning's very close to 19-equal, also supporting 24 and 29.

The minimax 7- or 9-limit error for Negri is 17.8 cents.
(It's the same for both limits.) I can't calculate Bogey's
right now, but it can't be worse.

> >"What I can see working here is the usual diatonic scale
> >in Dominant temperament (12&5). It's a bit of a shocker
> >though: worst error 25 cents."
> Interesting...the thing is 25 cents, to me, is an
> unforgivable sin (unless it happens to be for only, say,
> two dyads or less out of all possible dyads). :-D

It's not quite 12-equal pretending to be 7-limit, but it's
not much better.

> Me> "Good idea...I'll likely make a second scale where
> Me> I swap the 8/7 with a
> 9/8..."
> Graham>"Is 9:8 allowed now?"
>
> Certainly is...the more ratio swapping I do to try
> and optimize things for a 7-tone scale "mostly in
> 7-limit"...the more I run into 9-limit dyads...looks like
> 9-limit is here to stay (at least, unless I go for 5-tone
> scales). Look for my best shot at a similar scale but
> using 9/8 rather than 8/7 soon...

You could try Negri, starting from that Bogey pentatonic
and dividing the 8:7 steps equally.

Graham

On Sun, Jan 9, 2011 at 6:36 PM, Michael <djtrancendance@...> wrote:
>
>    What I was doing was ADMITTING THE SCALE I CAME UP WITH WAS NOT MINE IE GIVING FAIR CREDIT (BOTH TO THE CREATORS OF THE SCALE AND PEOPLE WHO I RECALL RECOMMENDING IT)!
>   Now why on earth are you picking on me FOR my honest attempt to give fair credit (even if you say don't, in fact, like Blackjack and I misread you)?

I have no idea what's an honest attempt. I'm not psychic, and I can't
read your mind. It seemed at the time like you were badmouthing
people, and I was defending them. Sorry if I misjudged.

> MikeB>I think you'd shift the melodies too. I don't know what you mean by "Miracle subgroup." The miracle generator is a sharp semitone, roughly 6 out of 72, and there are MOS's at 10, 21, 31, 41, etc notes. The 21
> note one is called "blackjack."
>
>    Cool...this is useful tuning information...not random bullying...thank you.  When I said "subgroup", I did mean "subgroup...of a generator".

I don't think you're using the right terminology - a subgroup
temperament is generally something that "skips" a prime, like how
24-equal is really good for something like 2.3.5.11 but less good for
2.3.5.7.11. Or you can do something like 2.3.7/5.

-Mike

MikeB>"It seemed at the time like you were badmouthing people, and I was
defending them. Sorry if I misjudged."

I wasn't, I was simply trying to give credit to people I thought had very
good ideas which I was deciding to investigate more deeply because I thought
they were good...seriously. :-(

Thank you for the apology and, hey, next time if you're not sure, please just
ask first and I'll try my best to clarify.

>"I don't think you're using the right terminology - a subgroup temperament is
>generally something that "skips" a prime, like how 24-equal is really good for
>something like 2.3.5.11 but less good for 2.3.5.7.11."

Got it...I'm trying to say a scale that fits under a categorization so far as
how it is generated IE it is grouped under said categorization. Being under a
larger group made me think of the term "subgroup"...I didn't know the meaning
you just mentioned about estimating up to a certain prime but not including all
primes below that prime before of the same name IE "subgroup".

On Tue, Jan 11, 2011 at 12:11 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"It seemed at the time like you were badmouthing people, and I was defending them. Sorry if I misjudged."
>
>    I wasn't, I was simply trying to give credit to people I thought had very good ideas which I was deciding to investigate more deeply because I thought they were good...seriously. :-(
>    Thank you for the apology and, hey, next time if you're not sure, please just ask first and I'll try my best to clarify.
>
> >"I don't think you're using the right terminology - a subgroup temperament is generally something that "skips" a prime, like how 24-equal is really good for something like 2.3.5.11 but less good for 2.3.5.7.11."
>
>   Got it...I'm trying to say a scale that fits under a categorization so far as how it is generated IE it is grouped under said categorization.  Being under a larger group made me think of the term "subgroup"...I didn't know the meaning you just mentioned about estimating up to a certain prime but not including all primes below that prime before of the same name IE "subgroup".

Well, in this case, blackjack is an "MOS" of miracle temperament,
because it has only two step sizes and is generated by the miracle
generator, called the "secor." You're using the rational version, but
like I said, if you ditch it and mess with the tempered version, of
which 72-tet is a great example, you'll find extremely accurate 7 and
11-limit harmony all over the place. It's accurate to within like 3
cents, which I guess is part of why they called it "miracle"
temperament.

-Mike