Yahoo Tuning Groups Ultimate Backup tuning Improved Horagrams for TOP temperaments and exotemperaments

"tuning files" is a >restricted< group??? eh?

Dante

> -----Original Message-----
> From: wallyesterpaulrus [mailto:paul@stretch-music.com]
> Sent: Tuesday, January 13, 2004 3:04 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Improved Horagrams for TOP temperaments and
> exotemperaments
>
>
> "2 many notes", or "Did grandpa eat a porcupine?":
>
> /tuning/files/Erlich/schismic2.gif
> /tuning/files/Erlich/kleismic2.gif
> /tuning/files/Erlich/diaschismic2.g
> if
> /tuning/files/Erlich/magic2.gif
> /tuning/files/Erlich/meantone2.gif
> /tuning/files/Erlich/augmented2.gif
> /tuning/files/Erlich/porcupine2.gif
> /tuning/files/Erlich/diminished2.gi
> f
> /tuning/files/Erlich/blackwood2.gif
> /tuning/files/Erlich/pelogic2.gif
> /tuning/files/Erlich/dicot2.gif
> /tuning/files/Erlich/father2.gif
> /tuning/files/Erlich/beep2.gif
> /tuning/files/Erlich/grandpa2.gif
> /tuning/files/Erlich/uncle2.gif
> /tuning/files/Erlich/nana2.gif
> /tuning/files/Erlich/eve2.gif
> /tuning/files/Erlich/adam2.gif
> /tuning/files/Erlich/moon2.gif
> /tuning/files/Erlich/earth2.gif
>
> (I hope Gene will check these last seven generators)
>
>
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🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Kurt Bigler <kkb@breathsense.com>

Monz?

on 1/13/04 1:12 AM, Carl Lumma <ekin@lumma.org> wrote:

Yes, this is great. Maybe monz can make a page for these some day, and
include Carl's explantory comments (updated as needed) from his 1/9/04
8:18pm message, without which the diagrams would have been meaningless to
me. (Lacking message numbers via email I thought the date/time would be
useful.)

Several of these files cause a "connection failure" (timeout) when I attempt
to load them. This problem occurs for schismic2 and meantone2. I have not
tried all of them though.

-Kurt

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

TOP tunings for quasi-temperaments.

3/2 [1471.553263, 1471.553263, 2786.313713]

4/3 [1061.073861, 2122.147722, 2786.313713]

5/4 [1289.384577, 1901.955001, 2578.769153]

6/5 [1135.673869, 1800.000495, 2935.674365]

32/25 [1155.684473, 1901.955001, 2889.211181]

9/8 [1233.049025, 1849.573537, 2786.313713]

10/9 [1171.902674, 1946.488209, 2721.073742]

🔗czhang23@aol.com

In a message dated 2004:01:13 08:04:26 AM, paul-e writes:

>"2 many notes", or "Did grandpa eat a porcupine?":

ROTFLMAO bloody damn *ouch* me poor ribs...

explanatory note: there are peeps who actually eat "road-kill"
in the American South... they musta been Cantonese in past life...
or rather, better, they are working _towards_ being Cantonese
in their next ;)

In a message dated 2004:01:13 12:32:07 PM, BooRad*** quotes:

> Only the hand that erases can write the true thing.
>
> Meister Eckhart

Z ;)

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> TOP tunings for quasi-temperaments.
>
> 3/2 [1471.553263, 1471.553263, 2786.313713]
>
> 4/3 [1061.073861, 2122.147722, 2786.313713]
>
> 5/4 [1289.384577, 1901.955001, 2578.769153]
>
> 6/5 [1135.673869, 1800.000495, 2935.674365]
>
> 32/25 [1155.684473, 1901.955001, 2889.211181]

I think you meant to do 32/27.

> 9/8 [1233.049025, 1849.573537, 2786.313713]
>
> 10/9 [1171.902674, 1946.488209, 2721.073742]

It was actually the *generators* I was hoping you would check, since
the above numbers are so easy to derive.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***These are very impressive, although I prefer the ones (let's
just
> take 12-equal as the ready example) that don't go to quite as many
> rings.

12-equal as the ready example? I don't get it.

I think they're more instructive, and the horagram isn't as
> cluttered.

OK . . . these horagrams were as 'cluttered' as I could make them
without losing readability . . . basically for people like Monz who
tend to be interested in things like schismic-171 and meantone-205.
I'll churn out a less cluttered set next . . .

> I don't see *miracle*? I guess that kind of generator isn't grist
> for this kind of tempermental treatment, correct??

It's just that these are all *5-limit* 'linear' temperaments, and
miracle is hardly worth mentioning in that context. When we get to 7-
limit 'linear' temperaments, you can be sure that both miracle, and
the temperament mentioned in my '22' paper, will make prominent
appearances . . . but if Gene or someone wants to give me the Top 7-
limit Miracle generator and period, I'll give you a 'preview' . . .

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> It was actually the *generators* I was hoping you would check, since
> the above numbers are so easy to derive.

Sorry.

3/2 [[1, 1, 2], [0, 0, -1]] [1471.553263, 156.7928114]

4/3 [[1, 2, 3], [0, 0, -1]] [1061.073861, 396.9078688]

32/25 [[2, 3, 5], [0, 1, 0]] [577.8422363, 168.4282918]

5/4 [[1, 1, 2], [0, 1, 0]] [1289.384577, 612.5704240]

6/5 [[1, 1, 2], [0, 1, 1]] [1135.673869, 664.3266264]

9/8 [[2, 3, 5], [0, 0, -1]] [616.5245122, 296.3088471]

10/9 [[1, 2, 3], [0, -1, -2]] [1171.902674, 397.3171394]

🔗Kurt Bigler <kkb@breathsense.com>

I hate to say it, but "moon" lost all its beauty without the many rings. ;)

-Kurt

on 1/14/04 10:59 AM, wallyesterpaulrus <paul@stretch-music.com> wrote:

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_51707.html#51747

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***These are very impressive, although I prefer the ones (let's
> just
> > take 12-equal as the ready example) that don't go to quite as
many
> > rings.
>
> 12-equal as the ready example? I don't get it.
>

***No... this means nothing. I was just staring at that one because
of it's historical significance. I should have deleted that
parenthesis...

> I think they're more instructive, and the horagram isn't as
> > cluttered.
>
> OK . . . these horagrams were as 'cluttered' as I could make them
> without losing readability . . . basically for people like Monz who
> tend to be interested in things like schismic-171 and meantone-205.
> I'll churn out a less cluttered set next . . .
>

***Well, then some of the *earlier* ones you posted were
more "illuminating" from an educational standpoint... seemed like
that to me, anyway. They're terrific in any case...

> > I don't see *miracle*? I guess that kind of generator isn't
grist
> > for this kind of tempermental treatment, correct??
>
> It's just that these are all *5-limit* 'linear' temperaments, and
> miracle is hardly worth mentioning in that context. When we get to
7-
> limit 'linear' temperaments, you can be sure that both miracle, and
> the temperament mentioned in my '22' paper, will make prominent
> appearances . . . but if Gene or someone wants to give me the Top 7-
> limit Miracle generator and period, I'll give you a 'preview' . . .

***Sure. That would be interesting....

Joseph

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > It was actually the *generators* I was hoping you would check,
since
> > the above numbers are so easy to derive.
>
> Sorry.
>
> 3/2 [[1, 1, 2], [0, 0, -1]] [1471.553263, 156.7928114]

Check.

> 4/3 [[1, 2, 3], [0, 0, -1]] [1061.073861, 396.9078688]

Check.

> 32/25 [[2, 3, 5], [0, 1, 0]] [577.8422363, 168.4282918]

Again, this should be 32/27, not 32/25. I have [389.95, 56.67].

> 5/4 [[1, 1, 2], [0, 1, 0]] [1289.384577, 612.5704240]

Check.

> 6/5 [[1, 1, 2], [0, 1, 1]] [1135.673869, 664.3266264]

Looks right except you're violating the "smallest possible generator"
convention, using its inversion instead.

> 9/8 [[2, 3, 5], [0, 0, -1]] [616.5245122, 296.3088471]

Check.

> 10/9 [[1, 2, 3], [0, -1, -2]] [1171.902674, 397.3171394]

Check!

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_51707.html#51747
>
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > ***These are very impressive, although I prefer the ones (let's
> > just
> > > take 12-equal as the ready example) that don't go to quite as
> many
> > > rings.
> >
> > 12-equal as the ready example? I don't get it.
> >
>
> ***No... this means nothing. I was just staring at that one
because
> of it's historical significance.

Staring at which one? There's no 12-equal horagram, of course.
Meantone has the most historical significance, but I obviously had
way too many rings there, going all the way to 205 notes per
octave . . . so I'm wondering what you were referring to . . .

> > I think they're more instructive, and the horagram isn't as
> > > cluttered.
> >
> > OK . . . these horagrams were as 'cluttered' as I could make them
> > without losing readability . . . basically for people like Monz
who
> > tend to be interested in things like schismic-171 and meantone-
205.
> > I'll churn out a less cluttered set next . . .
> >
>
> ***Well, then some of the *earlier* ones you posted were
> more "illuminating" from an educational standpoint... seemed like
> that to me, anyway.

But they were lacking the step sizes.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> > 6/5 [[1, 1, 2], [0, 1, 1]] [1135.673869, 664.3266264]
>
> Looks right except you're violating the "smallest possible
generator"
> convention, using its inversion instead.

I used my existing code, which refers to the rms solution to reduce,
to find a mapping, and then found generators for that mapping.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> > but if Gene or someone wants to give me the Top 7-
> > limit Miracle generator and period, I'll give you
> >a 'preview' . . .
>
>
> ***Sure. That would be interesting....
>
> Joseph

According to Gene, Top miracle is exactly the same whether you're
talking about 7-limit, 11-limit, or even the 5-limit "ampersand"
temperament:

/tuning/files/miracle.gif

And Kalle, if you're reading this:

/tuning/files/pajara.gif

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_51707.html#51822

> Staring at which one? There's no 12-equal horagram, of course.
> Meantone has the most historical significance, but I obviously had
> way too many rings there, going all the way to 205 notes per
> octave . . . so I'm wondering what you were referring to . . .
>

***I meant the meantone one, which seemed a logical place to *start*
in understanding them... That's all..

> > > I think they're more instructive, and the horagram isn't as
> > > > cluttered.
> > >
> > > OK . . . these horagrams were as 'cluttered' as I could make
them
> > > without losing readability . . . basically for people like Monz
> who
> > > tend to be interested in things like schismic-171 and meantone-
> 205.
> > > I'll churn out a less cluttered set next . . .
> > >
> >
> > ***Well, then some of the *earlier* ones you posted were
> > more "illuminating" from an educational standpoint... seemed like
> > that to me, anyway.
>
> But they were lacking the step sizes.

***Sure, but now you've seemed to "compromise" to a degree with the
very newest ones, which seem the best visuals of all...

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_51707.html#51833

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > > but if Gene or someone wants to give me the Top 7-
> > > limit Miracle generator and period, I'll give you
> > >a 'preview' . . .
> >
> >
> > ***Sure. That would be interesting....
> >
> > Joseph
>
> According to Gene, Top miracle is exactly the same whether you're
> talking about 7-limit, 11-limit, or even the 5-limit "ampersand"
> temperament:
>
> /tuning/files/miracle.gif
>

***Wow... this makes for an interesting comparison of the miracle ETs!

🔗Kurt Bigler <kkb@breathsense.com>

on 1/15/04 1:02 PM, wallyesterpaulrus <paul@stretch-music.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> I hate to say it, but "moon" lost all its beauty without the many
> rings. ;)
>>
>> -Kurt
>
> I'm amazed that you were actually looking!

Why were you amazed? Because you know I am so overwhelmed and far behind
that I never get to most things I talk about, and so would probably never
follow many of these links? Or because you feared all the work you did
might never be justified by people actually looking at it?

-Kurt

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> According to Gene, Top miracle is exactly the same whether you're
> talking about 7-limit, 11-limit, or even the 5-limit "ampersand"
> temperament:
>
> /tuning/files/miracle.gif
>
> And Kalle, if you're reading this:
>
> /tuning/files/pajara.gif

Yes. I'd like to try 22 out of Pajara with my 22-tone keyboard. I
already created a file in Scala for that. Now, how should I map
this "scale" into the keys? Does that depend whether I want to use
symmetrical or pentachordal decatonics?

And what about that 22-equal, what's the TOP version?

Kalle

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> And what about that 22-equal, what's the TOP version?

Depends on your prime limit (if you want to get around that, there is
always zeta tuning.)

5-limit

<1198.718302 1907.051844 2778.846973|

7-limit

<1198.655597 1906.952086 2778.701611 3378.029410|

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
>
> > And what about that 22-equal, what's the TOP version?
>
> Depends on your prime limit

Yes, I knew it. I'm not sure why I asked about *the* TOP version.

> (if you want to get around that, there is always zeta tuning.)

No need to. Is zeta tuning related to Riemann's zeta function?

> 5-limit
>
> <1198.718302 1907.051844 2778.846973|
>
> 7-limit
>
> <1198.655597 1906.952086 2778.701611 3378.029410|

Many thanx, Gene!

How about 11-limit?

Kalle

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >5-limit
> >
> ><1198.718302 1907.051844 2778.846973|
> >
> >7-limit
> >
> ><1198.655597 1906.952086 2778.701611 3378.029410|
>
> Hey, you *are* writing these as vals. Good.

They're points in val space, so why not?

Now, there
> used to be this hN (h12, etc) notation around, though I
> don't see mention of it on your "Intervals and Vals" page.
> What is this notation?

I use hn to mean the "standard" n-val, meaning what you get by
rounding log2(p) for each prime p to the nearest integer. This still
has advantages--rounding off the top tuning means the standard vals
in different limits might not be compatible, and rounding off the
zeta tuning means you would first have to compute it.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_51707.html#51833
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > > but if Gene or someone wants to give me the Top 7-
> > > > limit Miracle generator and period, I'll give you
> > > >a 'preview' . . .
> > >
> > >
> > > ***Sure. That would be interesting....
> > >
> > > Joseph
> >
> > According to Gene, Top miracle is exactly the same whether you're
> > talking about 7-limit, 11-limit, or even the 5-limit "ampersand"
> > temperament:
> >
> > /tuning/files/miracle.gif
> >
>
> ***Wow... this makes for an interesting comparison of the miracle
ETs!
>
> JP

I don't see any ETs on this diagram . . . ;)

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 1/15/04 1:02 PM, wallyesterpaulrus <paul@s...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >
> >> I hate to say it, but "moon" lost all its beauty without the many
> > rings. ;)
> >>
> >> -Kurt
> >
> > I'm amazed that you were actually looking!
>
> Why were you amazed? Because you know I am so overwhelmed and far
behind
> that I never get to most things I talk about, and so would probably
never
> follow many of these links?

I meant anyone, not you in particular.

> Or because you feared all the work you did
> might never be justified by people actually looking at it?

If I had feared it, then I would have simply been comforted. But
actually, I was amazed that someone took the time to look at so many
of those links.

Sorry if I seemed to be saying something about you in particular,
particularly if it was negative,

Paul

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > According to Gene, Top miracle is exactly the same whether you're
> > talking about 7-limit, 11-limit, or even the 5-limit "ampersand"
> > temperament:
> >
> > /tuning/files/miracle.gif
> >
> > And Kalle, if you're reading this:
> >
> > /tuning/files/pajara.gif
>
> Yes. I'd like to try 22 out of Pajara with my 22-tone keyboard.

Oh yeah -- the one you modified yourself, right? Where are the
pictures of that again?

> I
> already created a file in Scala for that. Now, how should I map
> this "scale" into the keys?

The same way as before, I'd say.

> Does that depend whether I want to use
> symmetrical or pentachordal decatonics?

It seems the symmetrical would fall on the black keys, while that
wouldn't make sense with the pentachordal. But if you have a
different idea, let me know.

For the other 12 notes, I'd probably just use something like what the
horagram says. So the '10' ring is the symmetrical decatonic (your
black keys), and the '22' ring is those 10 plus the 12 to put on your
white keys.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_51707.html#51860

> > > /tuning/files/miracle.gif
> > >
> >
> > ***Wow... this makes for an interesting comparison of the miracle
> ETs!
> >
> > JP
>
> I don't see any ETs on this diagram . . . ;)

***0h... I guess when I see the number 72, I get a "knee jerk"
reaction that it's 72-tET. I see it's frequently off by a cent about
every other step...

Thanks!

🔗Kurt Bigler <kkb@breathsense.com>

on 1/16/04 4:26 PM, wallyesterpaulrus <paul@stretch-music.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 1/15/04 1:02 PM, wallyesterpaulrus <paul@s...> wrote:
>>
>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>>
>>>> I hate to say it, but "moon" lost all its beauty without the many
>>> rings. ;)
>>>>
>>>> -Kurt
>>>
>>> I'm amazed that you were actually looking!
>>
>> Why were you amazed? Because you know I am so overwhelmed and far
> behind
>> that I never get to most things I talk about, and so would probably
> never
>> follow many of these links?
>
> I meant anyone, not you in particular.
>
>> Or because you feared all the work you did
>> might never be justified by people actually looking at it?
>
> If I had feared it, then I would have simply been comforted. But
> actually, I was amazed that someone took the time to look at so many
> of those links.
>
> Sorry if I seemed to be saying something about you in particular,
> particularly if it was negative,

No, I took it very lightly. Since you took the time to post a message
expressing your amazement, I just wanted to find out what you actually
meant. I gave a couple of alternatives just to try to encourage you not to
be shy about it, and so I included the possibility that you meant me in
particular, just in case. ;)

-Kurt

>
> Paul

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> > Yes. I'd like to try 22 out of Pajara with my 22-tone keyboard.
>
> Oh yeah -- the one you modified yourself, right?

Yup.

> Where are the pictures of that again?

They are on Graham's site:

http://x31eq.com/instrum.htm

> > I
> > already created a file in Scala for that. Now, how should I map
> > this "scale" into the keys?
>
> The same way as before, I'd say.

But I have only used 22-equal previously. I meant Pajara[22]
with "scale".

> > Does that depend whether I want to use
> > symmetrical or pentachordal decatonics?
>
> It seems the symmetrical would fall on the black keys, while that
> wouldn't make sense with the pentachordal. But if you have a
> different idea, let me know.
>
> For the other 12 notes, I'd probably just use something like what
the
> horagram says. So the '10' ring is the symmetrical decatonic (your
> black keys), and the '22' ring is those 10 plus the 12 to put on
your
> white keys.

Yes, I figured it out. It works more nicely than meantone in 12-tone
keyboard because there's an even number of white keys. So one can
have an equal number of sharp and flat keys, right?

However, I made brief comparisons between TOP Pajara, standard 22-
equal and TOP 7-limit 22-equal by playing around with them in FM7.
This shows that one needs very static and bright timbres to really
appreciate their differences but I guess that was to be expected.
Especially noticeable were the smoother fifths in TOP Pajara.

Kalle

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_51707.html#51860
>
> > > > /tuning/files/miracle.gif
> > > >
> > >
> > > ***Wow... this makes for an interesting comparison of the
miracle
> > ETs!
> > >
> > > JP
> >
> > I don't see any ETs on this diagram . . . ;)
>
>
> ***0h... I guess when I see the number 72, I get a "knee jerk"
> reaction that it's 72-tET. I see it's frequently off by a cent
about
> every other step...
>
> Thanks!
>
> JP

Close enough -- but there are no other close-to-ETs there. Blackjack
*is* there, though.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> Yes, I figured it out. It works more nicely than meantone in 12-
tone
> keyboard because there's an even number of white keys. So one can
> have an equal number of sharp and flat keys, right?

Yup.

> However, I made brief comparisons between TOP Pajara, standard 22-
> equal and TOP 7-limit 22-equal by playing around with them in FM7.
> This shows that one needs very static and bright timbres to really
> appreciate their differences but I guess that was to be expected.
> Especially noticeable were the smoother fifths in TOP Pajara.

Yeah, and this was always the biggest complaint about it. I suppose
you lose some of the extra justness in 7:6 in TOP but it seems worth
it. However, we're tempering the octaves significantly, which may be
objectionable to some. For them, we hope to soon have an octave-
equivalent version of TOP, where there can be no benefit to tempering
the octaves at all . . .

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_51707.html#51901

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > /tuning/topicId_51707.html#51860
> >
> > > > > /tuning/files/miracle.gif
> > > > >
> > > >
> > > > ***Wow... this makes for an interesting comparison of the
> miracle
> > > ETs!
> > > >
> > > > JP
> > >
> > > I don't see any ETs on this diagram . . . ;)
> >
> >
> > ***0h... I guess when I see the number 72, I get a "knee jerk"
> > reaction that it's 72-tET. I see it's frequently off by a cent
> about
> > every other step...
> >
> > Thanks!
> >
> > JP
>
> Close enough -- but there are no other close-to-ETs there.
Blackjack
> *is* there, though.

***Well, that's very neat... and I see the two small adjacent 33 cent
steps on each side of the octave...

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> Yeah, and this was always the biggest complaint about it. I suppose
> you lose some of the extra justness in 7:6 in TOP but it seems worth
> it. However, we're tempering the octaves significantly, which may be
> objectionable to some. For them, we hope to soon have an octave-
> equivalent version of TOP, where there can be no benefit to tempering
> the octaves at all . . .

Here's octave-equivalent TOP (in the sense of restricting TOP to have
pure octaves) for three key temperaments. Annoyingly, I find that the
31&43 version of meantone is like septimal meantone if we restrict to
pure octaves, and the 31&50 version is like it if we don't. What's
annoying about that is that I want a clear justification for calling
one or the other of them "meantone".

Meantone

7 limit: [1200.000000, 1897.645847, 2790.583387, 3376.458469]

11 limit: [1200.000000, 1896.901014, 2787.604056,
3369.010141, 4140.286817]

11 limit, 31&43 version: [1200.000000, 1897.645847, 2790.583387,
3376.458469, 4157.625244]

Pajara

7 limit: [1200.000000, 1909.184471, 2781.631060, 3381.631060]

11 limit: [1200.000000, 1909.184471, 2781.631060, 3381.631060,
4144.893178]

Miracle

7 limit: [1200.000000, 1899.955786, 2783.384916, 3366.681404]

11 limit: [1200.000000, 1899.955786, 2783.384916, 3366.681404,
4149.889465]

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Yeah, and this was always the biggest complaint about it. I
suppose
> > you lose some of the extra justness in 7:6 in TOP but it seems
worth
> > it. However, we're tempering the octaves significantly, which may
be
> > objectionable to some. For them, we hope to soon have an octave-
> > equivalent version of TOP, where there can be no benefit to
tempering
> > the octaves at all . . .
>
> Here's octave-equivalent TOP (in the sense of restricting TOP to
have
> pure octaves) for three key temperaments.

I would call that something else (see below) -- for example, "octave-
restricted TOP", "octave-constrained-TOP", "just-octave TOP", or
perhaps something more technical that abandons the diatonically-
biased term "octave".

Annoyingly, I find that the
> 31&43 version of meantone is like septimal meantone if we restrict
to
> pure octaves, and the 31&50 version is like it if we don't. What's
> annoying about that is that I want a clear justification for calling
> one or the other of them "meantone".

I'd be more comfortable with 'neither'! And I would
say 'Huygens/Fokker meantone' or something when you mean 'Augmented
Sixths' . . .

> Meantone
>
> 7 limit: [1200.000000, 1897.645847, 2790.583387, 3376.458469]

This is an interesting result, similar to 1/5-comma meantone. One
possible objection here, I feel, is that the assumption of octave-
equivalence is not being fully carried through. Full octave-
equivalence means any set of intervals octave-equivalent to one
another have to be treated as equally complex and equally sensitive
to mistuning.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Annoyingly, I find that the
> > 31&43 version of meantone is like septimal meantone if we
restrict
> to
> > pure octaves, and the 31&50 version is like it if we don't. What's
> > annoying about that is that I want a clear justification for
calling
> > one or the other of them "meantone".
>
> I'd be more comfortable with 'neither'!

Why? They both are versions of meantone.

And I would
> say 'Huygens/Fokker meantone' or something when you mean 'Augmented
> Sixths' . . .

Why again? Huygens/Fokker meantone is another name for 31-equal
meantone, and has no particular monopoly on augmented sixths, which I
think is an absurd name anyway for the 7th harmonic.

> This is an interesting result, similar to 1/5-comma meantone. One
> possible objection here, I feel, is that the assumption of octave-
> equivalence is not being fully carried through. Full octave-
> equivalence means any set of intervals octave-equivalent to one
> another have to be treated as equally complex and equally sensitive
> to mistuning.

Is it a bug or a feature? It looks like the latter to me.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Annoyingly, I find that the
> > > 31&43 version of meantone is like septimal meantone if we
> restrict
> > to
> > > pure octaves, and the 31&50 version is like it if we don't.
What's
> > > annoying about that is that I want a clear justification for
> calling
> > > one or the other of them "meantone".
> >
> > I'd be more comfortable with 'neither'!
>
> Why? They both are versions of meantone.

Yes -- *versions* of meantone.

> And I would
> > say 'Huygens/Fokker meantone' or something when you
mean 'Augmented
> > Sixths' . . .
>
> Why again? Huygens/Fokker meantone is another name for 31-equal
> meantone,

Not what I had in mind.

> and has no particular monopoly on augmented sixths,

Huygens, I believe, was the first to suggest that the 7th harmonic
was relevant in (then-) existing music, and identified it with the
augmented sixth (when octave-reduced, of course) . . .

> which I
> think is an absurd name anyway for the 7th harmonic.

If there is a version of meantone named "Dominant Sevenths", why
isn't there one named "Augmented Sixths"?

> > This is an interesting result, similar to 1/5-comma meantone. One
> > possible objection here, I feel, is that the assumption of octave-
> > equivalence is not being fully carried through. Full octave-
> > equivalence means any set of intervals octave-equivalent to one
> > another have to be treated as equally complex and equally
sensitive
> > to mistuning.
>
> Is it a bug or a feature? It looks like the latter to me.

Is not assuming full octave-equivalence a bug or a feature? Well, it
depends. For example, there are those (say, Partch) who consider 8:5
(and 6:5 equally) consonant and 7:5 somewhat more dissonant. This
could be explained by full octave-equivalence, for example with
octave-equivalent harmonic entropy. Applying *this* assumption to
temperament in a TOP-like way is what I've been itching about on the
tuning-math list for like a year.

Improved Horagrams for TOP temperaments and exotemperaments

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Dante Rosati <dante@interport.net>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Kurt Bigler <kkb@breathsense.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗czhang23@aol.com

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

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🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Kurt Bigler <kkb@breathsense.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

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🔗Gene Ward Smith <gwsmith@svpal.org>

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🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

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🔗Gene Ward Smith <gwsmith@svpal.org>

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🔗Gene Ward Smith <gwsmith@svpal.org>

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