Laka 17-limit minimax planar temperament

Hi gang.

I'd like to play around with Laka, the 17-limit minimax planar temperament sketched at URLs like these:

http://xenharmonic.wikispaces.com/Hemifamity+family#Laka
http://xenharmonic.wikispaces.com/152edo
http://xenharmonic.wikispaces.com/205edo
http://xenharmonic.wikispaces.com/Optimal+patent+val

Unfortunately I don't follow hyperconcise math wizardese well enough to translate the sketch into, say, a Scala file with pitches and cents. Can anyone help bring me up to speed?

Thanks!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
>
> Hi gang.
>
> I'd like to play around with Laka, the 17-limit minimax planar temperament sketched at URLs like these:
>
> http://xenharmonic.wikispaces.com/Hemifamity+family#Laka
> http://xenharmonic.wikispaces.com/152edo
> http://xenharmonic.wikispaces.com/205edo
> http://xenharmonic.wikispaces.com/Optimal+patent+val

Are you looking for a scale, and if so, of about what size?

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

> Are you looking for a scale, and if so, of about what size?
>

Here's a 17-note scale to start you off:

! laka-dwarf.scl
!
Laka tempered (205et) dwarf(<17 27 40 48 59 63 70|)
17
!
52.68293
105.36585
204.87805
245.85366
345.36585
386.34146
474.14634
550.24390
591.21951
702.43902
743.41463
842.92683
907.31707
971.70732
1047.80488
1088.78049
2/1
!
! laka-dwarf.scl
!
! Dwarf((<17 27 40 48 59 63 70|)
! 17
!
! 33/32
! 17/16
! 9/8
! 147/128
! 39/32
! 5/4
! 21/16
! 11/8
! 45/32
! 3/2
! 49/32
! 13/8
! 27/16
! 7/4
! 117/64
! 15/8
! 2/1

Thank you, Gene. I'll noodle around with that for a bit. In the meantime, how many more notes per octave would the next step into greater note density have?

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > Are you looking for a scale, and if so, of about what size?
> >
>
> Here's a 17-note scale to start you off:
>
> ! laka-dwarf.scl
> !
> Laka tempered (205et) dwarf(<17 27 40 48 59 63 70|)
> 17
> !
> 52.68293
> 105.36585
> 204.87805
> 245.85366
> 345.36585
> 386.34146
> 474.14634
> 550.24390
> 591.21951
> 702.43902
> 743.41463
> 842.92683
> 907.31707
> 971.70732
> 1047.80488
> 1088.78049
> 2/1
> !
> ! laka-dwarf.scl
> !
> ! Dwarf((<17 27 40 48 59 63 70|)
> ! 17
> !
> ! 33/32
> ! 17/16
> ! 9/8
> ! 147/128
> ! 39/32
> ! 5/4
> ! 21/16
> ! 11/8
> ! 45/32
> ! 3/2
> ! 49/32
> ! 13/8
> ! 27/16
> ! 7/4
> ! 117/64
> ! 15/8
> ! 2/1
>

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
>
> Thank you, Gene. I'll noodle around with that for a bit. In the meantime, how many more notes per octave would the next step into greater note density have?

I'm not sure what you are asking, but you might try 29 notes.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> >
> > Thank you, Gene. I'll noodle around with that for a bit. In the meantime, how many more notes per octave would the next step into greater note density have?
>
> I'm not sure what you are asking, but you might try 29 notes.

Here's a 29-note scale extracted from this:

http://xenharmonic.wikispaces.com/Gallery+of+Z-polygon+transversals#x2)5 Dekany 1.3.5.7.11 (1.3 tonic)

! dekany_laka205.scl
!
Dekany laka convex closure of the 2)5 Dekany 1.3.5.7.11 (1.3 tonic)
29
!
29.26829
93.65854
117.07317
181.46341
204.87805
234.14634
269.26829
321.95122
386.34146
409.75610
474.14634
526.82927
550.24390
591.21951
614.63415
655.60976
679.02439
702.43902
731.70732
819.51220
883.90244
907.31707
971.70732
1024.39024
1047.80488
1088.78049
1112.19512
1176.58537
2/1

Okay, here's one of the things I don't get about planar temperaments. Compared with laka-dwarf this 29-note laka breaks up one step of 15 degrees of 205ed2 (about 88 cents) between 66 and 81 degrees \205 by inserting a note at 70\205 to produce 11- and 4-degree steps, but then lets another step of precisely 15\205 remain between 125 and 140 degrees.

Keeping in mind that I personally don't remember how to do the mathematical operations by which planar temperaments are produced, why is that sort of thing legit? :-)
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> > >
> > > Thank you, Gene. I'll noodle around with that for a bit. In the meantime, how many more notes per octave would the next step into greater note density have?
> >
> > I'm not sure what you are asking, but you might try 29 notes.
>
> Here's a 29-note scale extracted from this:
>
> http://xenharmonic.wikispaces.com/Gallery+of+Z-polygon+transversals#x2)5 Dekany 1.3.5.7.11 (1.3 tonic)
>
> ! dekany_laka205.scl
> !
> Dekany laka convex closure of the 2)5 Dekany 1.3.5.7.11 (1.3 tonic)
> 29
> !
> 29.26829
> 93.65854
> 117.07317
> 181.46341
> 204.87805
> 234.14634
> 269.26829
> 321.95122
> 386.34146
> 409.75610
> 474.14634
> 526.82927
> 550.24390
> 591.21951
> 614.63415
> 655.60976
> 679.02439
> 702.43902
> 731.70732
> 819.51220
> 883.90244
> 907.31707
> 971.70732
> 1024.39024
> 1047.80488
> 1088.78049
> 1112.19512
> 1176.58537
> 2/1
>

"manuphonic" <manuphonic@...> wrote:
> Hi gang.
>
> I'd like to play around with Laka, the 17-limit minimax
> planar temperament sketched at URLs like these:
>
> http://xenharmonic.wikispaces.com/Hemifamity+family#Laka
> http://xenharmonic.wikispaces.com/152edo
> http://xenharmonic.wikispaces.com/205edo
> http://xenharmonic.wikispaces.com/Optimal+patent+val

Or this:

http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=41p+53p+58

> Unfortunately I don't follow hyperconcise math wizardese
> well enough to translate the sketch into, say, a Scala
> file with pitches and cents. Can anyone help bring me up
> to speed?

One interesting thing about Laka is that there's a two-way,
one-to-one mapping with 5-limit just intonation. Not all
rank 3 temperaments do this. You can find a 5-limit
interval that has to be equally divided. So, Laka doesn't
require this, you can use any 5-limit notation you like and
apply a Laka tuning map. I don't know if that does make
Scala easier. If you can think of a way of writing it with
Lilypond note names, I'll implement it.

The other thing about Laka is that it doesn't look very
interesting. There are a lot of rank 3 temperaments
that come out better by my scoring. It has the one-to-one
5-limit property, but to get 17-limit harmony from a convex
scale on the 5-limit lattice, you need a heck of a lot of
notes. There are plenty of 17-limit alternatives (maybe
100) with the same property that look better.

Laka's more competitive in the 13-limit. Here are
alternatives with the one-to-one 5-limit property that
score more highly:

Marvel (31&53&72)
http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13

Hecate (41&53&72)
http://x31eq.com/cgi-bin/rt.cgi?ets=41_72_53&limit=13

Pele (41&58&87)
http://x31eq.com/cgi-bin/rt.cgi?ets=41_58_87&limit=13

Marvel and Hecate are both extensions of 11-limit Marvel.
Pele is another member of the Hemifamity family.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> Marvel (31&53&72)
> http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13

I can't find this listed, though clearly it should be. Want to propose a marvelous name?

"genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...>
> wrote:
>
> > Marvel (31&53&72)
> > http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13
>
> I can't find this listed, though clearly it should be.
> Want to propose a marvelous name?

It's called "Marvel" and has been since May of last year.

Graham

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>
> > Marvel (31&53&72)
> > http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13
>
> I can't find this listed, though clearly it should be. Want to propose a marvelous name?

Yeah? There's also Hecate, which has been called marvel in the 13-limit.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> > > Marvel (31&53&72)
> > > http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13
> >
> > I can't find this listed, though clearly it should be. Want to propose a marvelous name?
>
> Yeah? There's also Hecate, which has been called marvel in the 13-limit.

We have:

"Marvel"
Commas: 225/224, 385/384, 351/350
Optimal patent val: 103
10^5 * badness: 68.997

Hecate
Commas: 225/224, 385/384, 325/324
Optimal patent val: 166
10^5 * badness: 72.113

Marvell
Commas: 225/224, 385/384, 1573/1568
Optimal patent val: 166
10^5 * badness: 86.160

Isis
Commas: 225/224, 385/384, 275/273
Optimal patent val: 94
10^5 * badness: 86.583

Deecee
Commas: 225/224, 385/384, 364/363
Optimal patent val: 72
10^5 * badness: 92.048

My vote would be for a separate name for 13-limit "marvel". Anyone else care to weigh in?

"genewardsmith" <genewardsmith@...> wrote:

> Yeah? There's also Hecate, which has been called marvel
> in the 13-limit.

Don't hide behind an agentless passive. It looks like *you*
added "13-limit marvel" to an obscure wiki page because you
didn't check my website to see that the name was taken:

http://xenharmonic.wikispaces.com/page/diff/Marvel+family/214238270

And you didn't add it to one of the pages I was scraping,
so I didn't see the clash. I announced Hecate here:

/tuning-math/message/19204

You replied to the message. Within two months you added
"Hecate" to the wiki. And now, after a few more months,
you're saying my name from over a year ago is up for
discussion because you made a mistake.

You can check what's in my database like this:

http://x31eq.com/cgi-bin/uv.cgi?limit=13&uvs=225:224+384:385

The URL format isn't documented but it should be easy
enough to get there from the unison vector box.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> /tuning-math/message/19204
>
> You replied to the message. Within two months you added
> "Hecate" to the wiki. And now, after a few more months,
> you're saying my name from over a year ago is up for
> discussion because you made a mistake.

Oh, blow it out your ears and rub it in your hair. You failed to state you were claiming "marvel" for any temperament on the page you cite, and now you want to blame your oversight on me. And I think the question of whether we should use "marvel" for that temperament could use some input if anyone else wants to give some, though since you've decided to turn this into a food-fight and pizzas and hamburgers are flying though the air, that may be less likely. You don't have much of a prior claim for your name proposal that I can see, in case that matters, since you never published it. In any case, I want to wait a bit before editing the page to reflect a name which as far as I am concerned has only been proposed now.

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
>
> Okay, here's one of the things I don't get about planar temperaments. Compared with laka-dwarf this 29-note laka breaks up one step of 15 degrees of 205ed2 (about 88 cents) between 66 and 81 degrees \205 by inserting a note at 70\205 to produce 11- and 4-degree steps, but then lets another step of precisely 15\205 remain between 125 and 140 degrees.

This is describing how the scale Gene posted fails to be a "constant structure" (or "epimorphic", which implies "constant structure").

> Keeping in mind that I personally don't remember how to do the mathematical operations by which planar temperaments are produced, why is that sort of thing legit? :-)

It's "legit" as long as your definition of "legit" doesn't include "constant structure" or "epimorphic". =)

It's really interesting that you posted about this, because we "math wizards" are currently trying to find out what the specific "steps into greater note density" (as you wrote in a previous post) should be for planar temperaments. Right now, nobody knows what they should be.

For linear (rank 2) temperaments it's very clear that the answer is MOSes. MOSes have all these desirable properties, but unfortunately it's not possible to have a single structure that generalizes all of them to planar (rank 3) and higher rank temperaments. So we're currently debating what the important properties are, proving theorems about which properties imply which others, etc.

Anyone who's interested about this stuff can tune into tuning-math.

Keenan

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Oh, blow it out your ears and rub it in your hair. You failed to state you were claiming "marvel" for any temperament on the page you cite, and now you want to blame your oversight on me. And I think the question of whether we should use "marvel" for that temperament could use some input if anyone else wants to give some,
>

I do.

> though since you've decided to turn this into a food-fight and pizzas and hamburgers are flying though the air, that may be less likely.
>

The only one I see resorting to verbal abuse here is you, Gene.

> You don't have much of a prior claim for your name proposal that I can see, in case that matters, since you never published it. In any case, I want to wait a bit before editing the page to reflect a name which as far as I am concerned has only been proposed now.
>

Gene, I think everyone on this list has been more than patient with you in many ways, including allowing you to name or rename all and sundry, so I do think you might be a little more gracious in allowing the occasional claim by someone else.

-- Dave Keenan

On Fri, Sep 23, 2011 at 8:39 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
> >
> > Okay, here's one of the things I don't get about planar temperaments. Compared with laka-dwarf this 29-note laka breaks up one step of 15 degrees of 205ed2 (about 88 cents) between 66 and 81 degrees \205 by inserting a note at 70\205 to produce 11- and 4-degree steps, but then lets another step of precisely 15\205 remain between 125 and 140 degrees.
>
> This is describing how the scale Gene posted fails to be a "constant structure" (or "epimorphic", which implies "constant structure").

How does epimorphicity imply constant structure? I thought that
constant structure is defined as any scale which doesn't have
intervals that are Rothenberg ambiguous. As epimorphicity is something
to do with abstract regular temperaments, and constant structure has
to do with the tuning that you give a particular temperament, how can
the two be the same? The 3-limit Fokker block eliminating the
2187/2048 is epimorphic, but it's not CS if you tune the generator to
700 cents.

-Mike

On Fri, Sep 23, 2011 at 6:41 PM, genewardsmith
<genewardsmith@...> wrote:
>
> Oh, blow it out your ears and rub it in your hair. You failed to state you were claiming "marvel" for any temperament on the page you cite, and now you want to blame your oversight on me. And I think the question of whether we should use "marvel" for that temperament could use some input if anyone else wants to give some,

My two cents are that it's the lowest-badness 13-limit extension for
marvel, so it's a good candidate to call marvel. Why do you think the
one called "Hecate" should be marvel if it's higher in badness? And
even more so if Graham's already named it Hecate?

-Mike

Mike Battaglia <battaglia01@...> wrote:

> My two cents are that it's the lowest-badness 13-limit
> extension for marvel, so it's a good candidate to call
> marvel. Why do you think the one called "Hecate" should
> be marvel if it's higher in badness? And even more so if
> Graham's already named it Hecate?

The thing I'm calling Marvel is has the lowest
Tenney-Euclidean (TE) badness for all (reasonable)
parameters. That follows from it having the lowest TE
complexity. But TE complexity is an abstract thing, and
won't always correlate with real world complexity. In
these cases, the tempered 13-limit lattices are isomorphic
with the 5-limit JI lattice, so you're likely to borrow a
notation for 5-limit JI. In that case, 2-3-5 is a
privileged basis and we don't need the "scalar" property of
TE complexity that it doesn't depend on the choice of
generators.

The 5-limit basis of 13-limit Marvel (coinciding with
hermite normal form) is:

[<1 0 0 -5 12 -4]
<0 1 0 2 -1 -1]
<0 0 1 2 -3 4]>

The addition of 13:1 means you need two more steps of 5:1
beyond what you needed for the 11-limit, but no additional
steps of 2:1 or 3:1. In notational terms, that means you
keep the same note names but you need more comma shifts,
which is relatively expensive.

The corresponding basis for Hecate is:

[<1 0 0 -5 12 2]
<0 1 0 2 -1 4]
<0 0 1 2 -3 -2]>

This need two more steps of 3:1 relative to the 11-limit,
but no more steps of 2:1 or 5:1. That saves us comma
shifts, so it appears to be simpler than Marvel.

I chose Marvel to be the mapping with lower TE complexity
because it fills in gaps in some badness listings. That
looks like as good a reason as any. While it isn't a
compelling name, I do object to changing it now because
I've been assigning names to these temperaments over the
past year when I was trying to understand them and reading
up on mythology to find good names. Changing the names now
puts up another barrier to my understanding.

Anyway, let's try and understand the alternatives relative
to the 5-limit. One thing we can do is transform the
mappings into Kelley's chromatic/diatonic/arp format and
work out what a 13:8 looks like. The results are:

Marvel --> [9 4 2>
Hecate --> [8 5 3>
Tripod --> [9 4 3>
Isis --> [8 6 1>

Note that Hecate is the only one where the neutral sixth
is written as a sixth. Most extended notations measure
pitches relative to a Pythagorean diatonic. Lets fix C as
the 1/1. Then the relative section of the scale is

G --> [7 4 2>
A --> [9 5 3>
B --> [11 6 4>

Using # and b for sharp and flat (approximating 25:24) and +
and - to raise or lower by a comma (approximating 81:80), we
can write 13:8 above C according to the different mappings

Marvel --> G##
Hecate --> Ab
Tripod --> G##+
Isis --> Bbbb---

Hecate is the simplest spelling although Tripod is the
simplest mapping. (And, yes, Tripod temperament is simple
to write in Tripod Notation.)

Unfortunately, the Pythagorean sharp doesn't approximate
25:24. It comes out as <1 0 2] in terms of chromatic,
diatonic, and arp steps. This changes our spellings.

Marvel --> G##----
Hecate -> Ab++
Tripod -> G##---
Isis -> Bbbb+++

For all of them, you're likely to want specialist
accidental symbols. That makes the complexity harder to
estimate.

We can also look at 13:8 relative to 5-limit intervals. In
Hecate, 13:8 is written as a minor sixth. The 5-limit
minor sixth, 8:5, is [8 5 2>. That means 13:8 approximates
as a comma sharp of an 8:5 minor sixth in Hecate. In
Marvel, 13:8 is a diesis flat of a 5:3 major sixth mapping
as [9 5 2>. That might be convenient if you have a symbol
for diesis shifts.

In Isis, the 11:9 and 16:13 neutral thirds add up to a 3:2
perfect fifth. The spelling of the 16:13 is ugly because
so is 11:9. In 11-limit Marvel, 11:9 maps to
chromatic/diatonic/arp as [3 3 0>. The 11:9 above C would
be written as Fbb+++. And that's equally ugly for all of
the 13-limit alternatives.

Maybe you'd define a "quartertone" symbol for the [1 -1 2>
by which Fb+++ is flat of E. (E above C is [4 2 2>. [4 2
2> - [1 -1 2> = 3 3 0>.) A guess would be that 16:13 is
2> the quartertone above Eb. That means [4 2 2> - [1 0 2>
2> + <1 -1 2] = <4 1 2]. This difference between this and
2> the octave is <12 7 3] - <4 1 2] = <8 6 1]. Hence this
2> corresponds to the Isis mapping.

If we want a new name for 13-limit Marvel, one option is to
name it relative to Hecate. (I think Hecate is a good
name, and Isis is already related.) Marvel (as it is now)
and Hecate have similar complexity and error so it makes
sense to pair them. One option is Demeter. She was in the
pantheon and doesn't currently have any temperaments named
after her. According to Wikipedia, she was, like Hecate, a
triune goddess:

http://en.wikipedia.org/wiki/Demeter#Greek_mythology

Hecate has counterparts in related cultures:

http://en.wikipedia.org/wiki/Hecate#Cross-cultural_parallels

Isis and Artemis are already (deliberately) taken. There's
also Ereshkigal, which is good in that she was important
and outside Greece (if anybody worries about a Greek bias),
but bad in that it's quite a long name. Juno gets mentioned
in the Apuleius quote as well. Funnily enough, we currently
have neither Juno nor Hera temperaments. But if we did
maybe they should be related to Zeus or Jove.

And there's Hermes, a god related (if accidentally) to
magicians and alchemists. Maybe not to replace Marvel, but
9&53&72 is still unnamed:

http://x31eq.com/cgi-bin/rt.cgi?ets=9_72_53&limit=13

Graham

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > This is describing how the scale Gene posted fails to be a "constant structure" (or "epimorphic", which implies "constant structure").
>
> How does epimorphicity imply constant structure? I thought that
> constant structure is defined as any scale which doesn't have
> intervals that are Rothenberg ambiguous. As epimorphicity is something
> to do with abstract regular temperaments, and constant structure has
> to do with the tuning that you give a particular temperament, how can
> the two be the same? The 3-limit Fokker block eliminating the
> 2187/2048 is epimorphic, but it's not CS if you tune the generator to
> 700 cents.

This is a good point, so let me clarify my statement and explain why it does apply in this case (and if we want to talk about it any more than this I suggest we take it over to tuning-math).

Epimorphicity means that any two intervals that subtend different numbers of scale steps also map to different numbers under the val. So in JI they could not possibly be the same. In fact, the only way they could be the same is if the interval between them - which does not map to 0 under the val - is tempered out.

If our scale consists of notes from some temperament that can be expressed as a wedge product of vals, one of which is the particular val v corresponding to scale steps, then all the commas of the temperament must have v(c) = 0. So if no other commas are "accidentally" tempered out, epimorphicity implies constant structure.

In other words, epimorphicity does imply constant structure as long as the actual temperament you're using can be expressed as a wedge product *that includes the val under which the scale is epimorphic*.

In your example, if you tuned the generator to 3/2, you'd have the Pythagorean[7] MOS, which is CS because it is epimorphic (per above). However, if you tune the generator to *exactly* 700 cents, then you're "accidentally" tempering out 531441/524288, so the "augmented fourth" and "diminished fifth" both become 600 cents and it's no longer CS.

In other words, if the generator is 3/2 your temperament is rank-2 Pythagorean, which can be expressed as the wedge product of vals 7 ^ 12. But if the generator is exactly 700 cents it becomes a rank-1 temperament, which can only be expressed as the single val 12. The 7 val is no longer part of it, so it's no longer guaranteed to be CS.

If Gene had given a scale in Laka temperament that was epimorphic under the val, let's see... 29efggg, then it would be easy to make it constant structure simply by choosing a tuning that doesn't temper out any commas other than those of Laka itself. But instead the scale he gave was neither epimorphic nor constant structure, hence manuphonic's question.

Keenan

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:

> > though since you've decided to turn this into a food-fight and pizzas and hamburgers are flying though the air, that may be less likely.
> >
>
> The only one I see resorting to verbal abuse here is you, Gene.

Jocular comments like "blow it out your ears and rub it in your hair" and references to flying pizzas is "verbal abuse"? There's this thing called a "sense of humor". You might look it up.

> Gene, I think everyone on this list has been more than patient with you in many ways, including allowing you to name or rename all and sundry, so I do think you might be a little more gracious in allowing the occasional claim by someone else.

I'm perfectly happy with a claim by someone else. I am NOT happy with someone getting in my face about a naming proposal which was never made. Putting a name in his software doesn't count unless it's clear it's an actual proposal, rather than a nonce term, which is something Graham often does, or at least that's how I've been taking it. Considering the same term may be used for different temperaments of the same rank and limit, I don't see how else *to* take it. And in any case it's hardly the same as putting it up publically. When you give a long list of proposals and leave one off, how does the one you left off count as a proposal?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Sep 23, 2011 at 6:41 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > Oh, blow it out your ears and rub it in your hair. You failed to state you were claiming "marvel" for any temperament on the page you cite, and now you want to blame your oversight on me. And I think the question of whether we should use "marvel" for that temperament could use some input if anyone else wants to give some,
>
> My two cents are that it's the lowest-badness 13-limit extension for
> marvel, so it's a good candidate to call marvel. Why do you think the
> one called "Hecate" should be marvel if it's higher in badness? And
> even more so if Graham's already named it Hecate?

I'm not claiming it should be called "marvel", I'm saying it used to be called that. And there's very little difference in badness, but "marvel" is slightly lower, just as there's very little difference in tuning damage, but hecate is slightly lower. "Marvel" in fine with me. I DO object to being kicked in the ass with comments like "passive agressive" and bogus claims about a mistake I supposedly made, because Graham thinks I should have read his mind as well as his posting on tuning-math, and I likewise object to Keenan (who has, after all, done his own share of naming) piling on.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> If we want a new name for 13-limit Marvel, one option is to
> name it relative to Hecate. (I think Hecate is a good
> name, and Isis is already related.) Marvel (as it is now)
> and Hecate have similar complexity and error so it makes
> sense to pair them. One option is Demeter.

I'd prefer Demeter, because the claim to be "the" 13-limit extension of marvel is pretty hard to sustain. But I'm happy with "Marvel" if that's what people want.

I really appreciate the trouble all of you are taking to create scales and explain some of the issues involved in planar temperaments.

Graham, your point about Laka being less interesting than many other tunings raises the question of why I'd bother to noodle around with it. Well, I do my noodling around on a Tonal Plexus where the default tuning that shaped the keyboard layout is 2^(n/205). Although the board can be tuned otherwise I prefer to explore either the default or its 41ed2 core. The wiki mentions Laka among the temperaments that 205ed2 can deliver.

Also, Laka is described as a 17-limit minimax temperament. The word minimax reminds me of Miracle, which I consider great fun. Meanwhile, my studies of overtone beating phenomena among notes of the harmonic series has taught me that 17 can usefully be grouped with all the primes that are less than 2^4, such that the 17-limit can make harmonic sense. (This contradicted my earlier inclination, which was to jump from 13 to a prime limit of 23 or higher.) So those three points == 205, minimax and 17 == all made Laka attractive enough that I'd ask about it.

So, if you were going to noodle around on a 205ed2 keyboard, which temperaments would you prefer to explore if not Laka?

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "manuphonic" <manuphonic@...> wrote:
> > Hi gang.
> >
> > I'd like to play around with Laka, the 17-limit minimax
> > planar temperament sketched at URLs like these:
> >
> > http://xenharmonic.wikispaces.com/Hemifamity+family#Laka
> > http://xenharmonic.wikispaces.com/152edo
> > http://xenharmonic.wikispaces.com/205edo
> > http://xenharmonic.wikispaces.com/Optimal+patent+val
>
> Or this:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=41p+53p+58
>
> > Unfortunately I don't follow hyperconcise math wizardese
> > well enough to translate the sketch into, say, a Scala
> > file with pitches and cents. Can anyone help bring me up
> > to speed?
>
> One interesting thing about Laka is that there's a two-way,
> one-to-one mapping with 5-limit just intonation. Not all
> rank 3 temperaments do this. You can find a 5-limit
> interval that has to be equally divided. So, Laka doesn't
> require this, you can use any 5-limit notation you like and
> apply a Laka tuning map. I don't know if that does make
> Scala easier. If you can think of a way of writing it with
> Lilypond note names, I'll implement it.
>
> The other thing about Laka is that it doesn't look very
> interesting. There are a lot of rank 3 temperaments
> that come out better by my scoring. It has the one-to-one
> 5-limit property, but to get 17-limit harmony from a convex
> scale on the 5-limit lattice, you need a heck of a lot of
> notes. There are plenty of 17-limit alternatives (maybe
> 100) with the same property that look better.
>
> Laka's more competitive in the 13-limit. Here are
> alternatives with the one-to-one 5-limit property that
> score more highly:
>
> Marvel (31&53&72)
> http://x31eq.com/cgi-bin/rt.cgi?ets=53_72_31&limit=13
>
> Hecate (41&53&72)
> http://x31eq.com/cgi-bin/rt.cgi?ets=41_72_53&limit=13
>
> Pele (41&58&87)
> http://x31eq.com/cgi-bin/rt.cgi?ets=41_58_87&limit=13
>
> Marvel and Hecate are both extensions of 11-limit Marvel.
> Pele is another member of the Hemifamity family.
>
>
> Graham
>

"genewardsmith" <genewardsmith@...> wrote:

> I'm not claiming it should be called "marvel", I'm saying
> it used to be called that.<snip>

Yes, you say that, and the way you say it is misleading.
It makes it look like your usage is accepted, when it only
seems to consist of one mention on a wiki page. (I say
"seems", of course, because you don't supply any evidence.
You're forcing me to do the research.)

> And there's very little
> difference in badness, but "marvel" is slightly lower,
> just as there's very little difference in tuning damage,
> but hecate is slightly lower. "Marvel" in fine with me. I
> DO object to being kicked in the ass with comments like
> "passive agressive" and bogus claims about a mistake I
> supposedly made, because Graham thinks I should have read
> his mind as well as his posting on tuning-math, and I
> likewise object to Keenan (who has, after all, done his
> own share of naming) piling on.

Marvel also has a standout 17-limit mapping, so I've made
that official. I notice there are also 17-limit
extensions of Tripod and Isis that I must have added at
some point:

http://x31eq.com/cgi-bin/uv.cgi?limit=17&uvs=225:224&page=3

There are 17-limit Hecates here, but the Marvel line
*looks* superior:

http://x31eq.com/cgi-bin/uv.cgi?limit=17&uvs=225:224&page=0

I don't think you should have read my mind. I think you
should have checked my website before you decided a name
wasn't taken. I keep a central database with sanity checks
and some of the names in it were pulled directly from the
wiki. Sometimes my checks flag errors in the wiki, and I
correct them. That makes my database reliable and
comprehensive, and you can easily query it. Except that
it's "software" so for some reason it's inferior to the
wiki pages you work on.

I object to terminology disputes when there's no need for
them. I also object to you blaming other people for
disputes you started.

While this is current, I've also added a Mercury:

http://x31eq.com/cgi-bin/rt.cgi?ets=22p_9_10p&limit=13

It's related to Hecate and Minerva, which has mythological
support. It's also the name of an element, so it's on the
border between two naming conventions. I sketched a chord
using this mapping a while ago. It's an easy way of
writing 13-limit harmony in tripod notation. While it
isn't particularly accurate as a temperament, there can be
reasons for using such mappings anyway. It's consistent
with Blair and Sorcery.

Graham

"manuphonic" <manuphonic@...> wrote:

> Also, Laka is described as a 17-limit minimax
> temperament. The word minimax reminds me of Miracle,
> which I consider great fun. Meanwhile, my studies of
> overtone beating phenomena among notes of the harmonic
> series has taught me that 17 can usefully be grouped with
> all the primes that are less than 2^4, such that the
> 17-limit can make harmonic sense. (This contradicted my
> earlier inclination, which was to jump from 13 to a prime
> limit of 23 or higher.) So those three points == 205,
> minimax and 17 == all made Laka attractive enough that
> I'd ask about it.

Any regular temperament can be tuned to optimize a
minimax. This isn't a special connection between Miracle
and Laka.

> So, if you were going to noodle around on a 205ed2
> keyboard, which temperaments would you prefer to explore
> if not Laka?

I started searching rank 2 temperaments, and I found
something called Quanic:

http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=111+94

The 17-limit minimax generator is 140.461 cents. Here's an
octave of it:

0.000
3.335
6.671
15.498
18.833
27.661
30.996
39.824
43.159
51.986
55.322
64.149
67.484
70.820
79.647
82.982
91.810
95.145
103.973
107.308
116.135
119.471
128.298
131.634
140.461
143.796
147.132
155.959
159.294
168.122
171.457
180.285
183.620
192.447
195.783
204.610
207.945
211.281
220.108
223.443
232.271
235.606
244.434
247.769
256.596
259.932
268.759
272.095
280.922
284.257
287.593
296.420
299.755
308.583
311.918
320.746
324.081
332.908
336.244
345.071
348.406
351.742
360.569
363.904
372.732
376.067
384.895
388.230
397.058
400.393
409.220
412.556
421.383
424.718
428.054
436.881
440.216
449.044
452.379
461.207
464.542
473.369
476.705
485.532
488.867
492.203
501.030
504.365
513.193
516.528
525.356
528.691
537.519
540.854
549.681
553.017
561.844
565.179
568.515
577.342
580.677
589.505
592.840
601.668
605.003
613.830
617.166
625.993
629.328
632.664
641.491
644.827
653.654
656.989
665.817
669.152
677.980
681.315
690.142
693.478
702.305
705.640
708.976
717.803
721.138
729.966
733.301
742.129
745.464
754.291
757.627
766.454
769.789
773.125
781.952
785.288
794.115
797.450
806.278
809.613
818.441
821.776
830.603
833.939
842.766
846.101
849.437
858.264
861.599
870.427
873.762
882.590
885.925
894.752
898.088
906.915
910.250
913.586
922.413
925.749
934.576
937.911
946.739
950.074
958.902
962.237
971.064
974.400
983.227
986.562
989.898
998.725
1002.060
1010.888
1014.223
1023.051
1026.386
1035.213
1038.549
1047.376
1050.711
1054.047
1062.874
1066.210
1075.037
1078.372
1087.200
1090.535
1099.363
1102.698
1111.525
1114.861
1123.688
1127.023
1130.359
1139.186
1142.521
1151.349
1154.684
1163.512
1166.847
1175.674
1179.010
1187.837
1191.173
1200.000

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> I don't think you should have read my mind. I think you
> should have checked my website before you decided a name
> wasn't taken.

I should have checked your website to see if your posting on tuning-math was not complete? Why should I have assumed it might not be? And as I've explained, I can't assume a name like "marvel" is "taken" from your website, or is just a nonce name, by any means known to me. At what point was I supposed to check this, and what, exactly, was I supposed to check, and why? It's a bit absurd to complain I didn't first check before NOT doing something!

I keep a central database with sanity checks
> and some of the names in it were pulled directly from the
> wiki. Sometimes my checks flag errors in the wiki, and I
> correct them. That makes my database reliable and
> comprehensive, and you can easily query it.

And I'm supposed to query it at random, or is your complaint that I said a name wasn't listed when in fact it was in your database? Saying a name isn't listed on the Xenwiki hardly strikes me as a major crime, or even a peccadillo, so I presume the crime in question is that by asking for a name proposal I suggested it hadn't already been named, whereas if I had fed the right commas into your app it would have come up as "marvel", and if I was a mind-reader I would have known you were proposing that as a name, and not simply making nonce use of it. This whole thing is ridiculous.

> I object to terminology disputes when there's no need for
> them. I also object to you blaming other people for
> disputes you started.

Sorry, but you were the one who started off the blaming and accusing. Take some responsibility.

> It's consistent
> with Blair and Sorcery.

When you mention a name like Sorcery I have no way of finding out what it is. Since apps are so much superior to wikis or Yahoo groups, I presume this is an oversight and you will correct it.

Yes, there are very nice versions of Quanic, one stage having 17 notes per octave. Distributionally even, with a trick of closing in on the 5/4 and 15/8 overtones from opposite sides as the note density increases.

Thanks for the 17-limit minimax generator. I never did have the knack of calculating those.

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "manuphonic" <manuphonic@...> wrote:
>
> > Also, Laka is described as a 17-limit minimax
> > temperament. The word minimax reminds me of Miracle,
> > which I consider great fun. Meanwhile, my studies of
> > overtone beating phenomena among notes of the harmonic
> > series has taught me that 17 can usefully be grouped with
> > all the primes that are less than 2^4, such that the
> > 17-limit can make harmonic sense. (This contradicted my
> > earlier inclination, which was to jump from 13 to a prime
> > limit of 23 or higher.) So those three points == 205,
> > minimax and 17 == all made Laka attractive enough that
> > I'd ask about it.
>
> Any regular temperament can be tuned to optimize a
> minimax. This isn't a special connection between Miracle
> and Laka.
>
> > So, if you were going to noodle around on a 205ed2
> > keyboard, which temperaments would you prefer to explore
> > if not Laka?
>
> I started searching rank 2 temperaments, and I found
> something called Quanic:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=111+94
>
> The 17-limit minimax generator is 140.461 cents. Here's an
> octave of it:
>
> 0.000
> 3.335
> 6.671
> 15.498
> 18.833
> 27.661
> 30.996
> 39.824
> 43.159
> 51.986
> 55.322
> 64.149
> 67.484
> 70.820
> 79.647
> 82.982
> 91.810
> 95.145
> 103.973
> 107.308
> 116.135
> 119.471
> 128.298
> 131.634
> 140.461
> 143.796
> 147.132
> 155.959
> 159.294
> 168.122
> 171.457
> 180.285
> 183.620
> 192.447
> 195.783
> 204.610
> 207.945
> 211.281
> 220.108
> 223.443
> 232.271
> 235.606
> 244.434
> 247.769
> 256.596
> 259.932
> 268.759
> 272.095
> 280.922
> 284.257
> 287.593
> 296.420
> 299.755
> 308.583
> 311.918
> 320.746
> 324.081
> 332.908
> 336.244
> 345.071
> 348.406
> 351.742
> 360.569
> 363.904
> 372.732
> 376.067
> 384.895
> 388.230
> 397.058
> 400.393
> 409.220
> 412.556
> 421.383
> 424.718
> 428.054
> 436.881
> 440.216
> 449.044
> 452.379
> 461.207
> 464.542
> 473.369
> 476.705
> 485.532
> 488.867
> 492.203
> 501.030
> 504.365
> 513.193
> 516.528
> 525.356
> 528.691
> 537.519
> 540.854
> 549.681
> 553.017
> 561.844
> 565.179
> 568.515
> 577.342
> 580.677
> 589.505
> 592.840
> 601.668
> 605.003
> 613.830
> 617.166
> 625.993
> 629.328
> 632.664
> 641.491
> 644.827
> 653.654
> 656.989
> 665.817
> 669.152
> 677.980
> 681.315
> 690.142
> 693.478
> 702.305
> 705.640
> 708.976
> 717.803
> 721.138
> 729.966
> 733.301
> 742.129
> 745.464
> 754.291
> 757.627
> 766.454
> 769.789
> 773.125
> 781.952
> 785.288
> 794.115
> 797.450
> 806.278
> 809.613
> 818.441
> 821.776
> 830.603
> 833.939
> 842.766
> 846.101
> 849.437
> 858.264
> 861.599
> 870.427
> 873.762
> 882.590
> 885.925
> 894.752
> 898.088
> 906.915
> 910.250
> 913.586
> 922.413
> 925.749
> 934.576
> 937.911
> 946.739
> 950.074
> 958.902
> 962.237
> 971.064
> 974.400
> 983.227
> 986.562
> 989.898
> 998.725
> 1002.060
> 1010.888
> 1014.223
> 1023.051
> 1026.386
> 1035.213
> 1038.549
> 1047.376
> 1050.711
> 1054.047
> 1062.874
> 1066.210
> 1075.037
> 1078.372
> 1087.200
> 1090.535
> 1099.363
> 1102.698
> 1111.525
> 1114.861
> 1123.688
> 1127.023
> 1130.359
> 1139.186
> 1142.521
> 1151.349
> 1154.684
> 1163.512
> 1166.847
> 1175.674
> 1179.010
> 1187.837
> 1191.173
> 1200.000
>
>
> Graham
>

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

> > I started searching rank 2 temperaments, and I found
> > something called Quanic:
> >
> > http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=111+94

Quanic is closely associated to 205edo, as 205 gives the optimal patent val for 7, 11, 13, 17 and 19 limit quanic. It's pretty complex, but the tonal plexus has a lot of notes. The quanic generator of 24\205 is an approximate 13/12 and you need to go at least to the 13-limit to get the most out of this temperament. Semiconvergents for 24\205 tell us that 17, 26, 43, 60, 77 and 94 note MOS would make sense for quanic, but I don't know enough about the tonal plexus to know what would make sense for it.

"genewardsmith" <genewardsmith@...> wrote:

> I should have checked your website to see if your posting
> on tuning-math was not complete? Why should I have
> assumed it might not be? And as I've explained, I can't
> assume a name like "marvel" is "taken" from your website,
> or is just a nonce name, by any means known to me. At
> what point was I supposed to check this, and what,
> exactly, was I supposed to check, and why? It's a bit
> absurd to complain I didn't first check before NOT doing
> something!

I don't know what tuning-math post should have listed
13-limit Marvel. The only post where I tried to give a
complete list of my additions was this one:

/tuning/topicId_97783.html#98166

It does mention 13-limit Marvel, with a link, so what's your
complaint?

I think you should have checked my website for names of
Marvel family members before you wrote about them on the
Xenwiki. That seems like a reasonable amount of research
to me. You could also list whatever names you want on one
of the pages I scrape, and leave me to deal with the
collisions. I'd prefer you didn't do that because it
pushes the work onto me, but you can still do it. I think
you should also check for higher-limit extensions before you
give one of them the default name. (Note: my database has
duplicates of 13-limit Squares. You could look into that.)

You're also quite welcome to put names on obscure Xenwiki
pages that happen to clash with names in my database. When
the inconsistency is pointed out you're then welcome to
chill out and quietly make the correction. If you decide
to start a dispute, that's when I might get annoyed. And I
really object to you making a vague statement about a name
"being in use" so that I have to put in the work to
research it, and then attacking me when I do this research.

And on top of this, you could avoid making stupid arguments.
I mean, you know of no means to check if something was on
my website? Really?

> I keep a central database with sanity checks
> > and some of the names in it were pulled directly from
> > the wiki. Sometimes my checks flag errors in the wiki,
> > and I correct them. That makes my database reliable and
> > comprehensive, and you can easily query it.
>
> And I'm supposed to query it at random, or is your
> complaint that I said a name wasn't listed when in fact
> it was in your database? Saying a name isn't listed on
> the Xenwiki hardly strikes me as a major crime, or even a
> peccadillo, so I presume the crime in question is that by
> asking for a name proposal I suggested it hadn't already
> been named, whereas if I had fed the right commas into
> your app it would have come up as "marvel", and if I was
> a mind-reader I would have known you were proposing that
> as a name, and not simply making nonce use of it. This
> whole thing is ridiculous.

It's fine for a name not to be listed on the Xenwiki. The
rules regarding my database and the Xenwiki are very
simple. I scrape these pages:

http://xenharmonic.wikispaces.com/proposed+names+for+rank+2+temperaments

http://xenharmonic.wikispaces.com/optimal+patent+val

http://xenharmonic.wikispaces.com/chromatic+pairs

Anything listed in a consistent format on one of those
pages will get picked up. Anything else won't. So if you
start using a name, please put it on one of those pages,
and I'll know about it. If you don't, then I won't know
about it, which is fine but don't then get in my ear about
it being in use.

This business of "nonce use" is a diversion you invented.
You don't know if it's a "nonce use" and neither does
anybody else. So it's reasonable to assume that the name
might be picked up, and respect any precedent unless you
have a good reason to say otherwise. Which means it would
be nice if any name being used *were* on a page I scrape. I
know that isn't the case because I found some I'm missing
here:

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

Now I know about them, I can add them. But I don't know
what else might be lurking on the family pages and I don't
plan to go through them all. So don't assume that such
names are "being used".

> > It's consistent
> > with Blair and Sorcery.
>
> When you mention a name like Sorcery I have no way of
> finding out what it is. Since apps are so much superior
> to wikis or Yahoo groups, I presume this is an oversight
> and you will correct it.

Of course you have a way of finding out. The most obvious
one is to look at the page on my website that lists the
temperament names. If you're having a problem with it,
you'll have to tell me about it. I can't correct it
otherwise.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> I don't know what tuning-math post should have listed
> 13-limit Marvel. The only post where I tried to give a
> complete list of my additions was this one:

The tuning-math post where you introduce other marvel names is what I am talking about, but this would have been find except it told me I'd already done the needed fix.

> I think you should have checked my website for names of
> Marvel family members before you wrote about them on the
> Xenwiki.

This is a new complaint. Who says I didn't? I often do, may have overlooked something, but what is it now?

That seems like a reasonable amount of research
> to me. You could also list whatever names you want on one
> of the pages I scrape,

You scrape Optimal patent vals, so I do this up to the 13 limit.

and leave me to deal with the
> collisions. I'd prefer you didn't do that because it
> pushes the work onto me, but you can still do it. I think
> you should also check for higher-limit extensions before you
> give one of them the default name. (Note: my database has
> duplicates of 13-limit Squares. You could look into that.)

I think that's been taken care of.

> You're also quite welcome to put names on obscure Xenwiki
> pages that happen to clash with names in my database. When
> the inconsistency is pointed out you're then welcome to
> chill out and quietly make the correction. If you decide
> to start a dispute, that's when I might get annoyed.

And this has what connection, if any, to the problem being discussed?

> And on top of this, you could avoid making stupid arguments.
> I mean, you know of no means to check if something was on
> my website? Really?

Yes, really. Don't know how to find a name on your website.

> Anything listed in a consistent format on one of those
> pages will get picked up. Anything else won't. So if you
> start using a name, please put it on one of those pages,
> and I'll know about it. If you don't, then I won't know
> about it, which is fine but don't then get in my ear about
> it being in use.

And this has what connection to the topic under discussion? What, *specifically*, are you talking about? What *specific* name or names?

> This business of "nonce use" is a diversion you invented.
> You don't know if it's a "nonce use" and neither does
> anybody else.

Bah. You use the same name all over the place for different things. If I tried to follow that, it would create a new mess.

> http://xenharmonic.wikispaces.com/Cataharry+family

Ah, finally something specific. Is your point nothing should get a name unless it's something which should be listed on the Optimal patent vals page? I'm not the only one coming up with names, by the way. If this is a big problem maybe there should be a place to put such names, whether the temperament involved is good, bad or ugly.

> > When you mention a name like Sorcery I have no way of
> > finding out what it is. Since apps are so much superior
> > to wikis or Yahoo groups, I presume this is an oversight
> > and you will correct it.
>
> Of course you have a way of finding out. The most obvious
> one is to look at the page on my website that lists the
> temperament names.

That would be fine if I knew there was such a page. I didn't. I don't recall you mentioning it. Nor do I know as I write this how to find it, though I'll take a look.

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

> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:

> > Of course you have a way of finding out. The most obvious
> > one is to look at the page on my website that lists the
> > temperament names.
>
> That would be fine if I knew there was such a page. I didn't. I don't recall you mentioning it. Nor do I know as I write this how to find it, though I'll take a look.

I looked and I found the old "Catalog of linear temperaments" page. You need to give a url to the listing you speak of.

Gene wrote:

> That would be fine if I knew there was such a page. I didn't.
> I don't recall you mentioning it. Nor do I know as I write
> this how to find it, though I'll take a look.

Graham's website isn't a website, it's a web application, and
an unnavigable one at that. The only way to get around is to
reverse engineer an obtuse URL format. Keenan's posted some
travails of doing that - I've been complaining about it for a
while now. If the argument is 'you should have checked
Graham's website' it seems to me a poor one. I know of no
index of anything there, only 3 ways to summon a computation.

That said, this petty business of naming every 13-limit rank 4
temperament is really, really dumb. I should have listened to
Dave Keenan when he objected to this naming business back in
the day. I didn't imagine naming much more than the best 20
or so rank 2 systems, and had Dave based his scheme on comma
families instead of generator size, I probably would have
subscribed to it.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> That said, this petty business of naming every 13-limit rank 4
> temperament is really, really dumb.

We're talking about rank 3 temperaments, at least I hope we are. And you can't very well stop people from naming things, the best you can do is to nag them to get everything on one page. But I strongly suspect that Graham has no idea Mike Battaglia has been devising names; I don't know if that is a crime in his book or not.

"genewardsmith" <genewardsmith@...> wrote:

> I looked and I found the old "Catalog of linear
> temperaments" page. You need to give a url to the listing
> you speak of.

There's a temperament called Ennealimmal, isn't there? And
you're looking for Sorcery. You can expect this page to
include both Ennealimmal and Sorcery. How many pages does
Google give you that look like that?

Graham

"Carl Lumma" <carl@...> wrote:

> Graham's website isn't a website, it's a web application,
> and an unnavigable one at that. The only way to get
> around is to reverse engineer an obtuse URL format.
> Keenan's posted some travails of doing that - I've been
> complaining about it for a while now. If the argument is
> 'you should have checked Graham's website' it seems to me
> a poor one. I know of no index of anything there, only 3
> ways to summon a computation.

Yeah, yeah, insult my professional competence while you're
at it. Pretend search engines don't exist. And don't worry
that nobody bothered to link to this page on their sites.

Graham

On Mon, Sep 26, 2011 at 2:06 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > That said, this petty business of naming every 13-limit rank 4
> > temperament is really, really dumb.
>
> We're talking about rank 3 temperaments, at least I hope we are. And you can't very well stop people from naming things, the best you can do is to nag them to get everything on one page. But I strongly suspect that Graham has no idea Mike Battaglia has been devising names; I don't know if that is a crime in his book or not.

He knows. I've made sure to add every name I come up with to the
"proposed rank-2 temperament" page. I always double check to make sure
that everything ends up on the temperament finder as well. The only
thing that really posed a problem was all the 7-limit mavila
extensions a while ago, but it's all sorted out now.

Also, might as well open this can of worms - what Graham's temperament
finder calls "Semaphore" is called "Godzilla" on the wiki, and what
the temperament finder calls "Cynder" is called "Mothra" on the wiki.
I've been using the names "Semaphore" and "Cynder" for the rank-2
7-limit versions respectively, but there's a growing schizophrenia
around these tunings I can't ignore.

-Mike

PS - part of my goal with this JS tuning library is to facilitate the
creation of a central naming database, so that sites can AJAX it and
so on. It's going to be a while before I can get it off the ground
though, as work + moving is a bit too soul-crushing right now to do
anything fun.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "genewardsmith" <genewardsmith@...> wrote:
>
> > I looked and I found the old "Catalog of linear
> > temperaments" page. You need to give a url to the listing
> > you speak of.
>
> There's a temperament called Ennealimmal, isn't there? And
> you're looking for Sorcery. You can expect this page to
> include both Ennealimmal and Sorcery. How many pages does
> Google give you that look like that?

(1) I should look on an Ennealimmal page for Sorcery because...?

Mike Battaglia <battaglia01@...> wrote:

> Also, might as well open this can of worms - what
> Graham's temperament finder calls "Semaphore" is called
> "Godzilla" on the wiki, and what the temperament finder
> calls "Cynder" is called "Mothra" on the wiki. I've been
> using the names "Semaphore" and "Cynder" for the rank-2
> 7-limit versions respectively, but there's a growing
> schizophrenia around these tunings I can't ignore.

Semaphore and Cynder are both in A Middle Path. I'm not
sure what the situation is with Waage and Compton. Other
clashes are a matter of spelling: whether you use the
umlaut in Würschmidt and whether there's a "i" in Semaphore.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Also, might as well open this can of worms - what
> > Graham's temperament finder calls "Semaphore" is called
> > "Godzilla" on the wiki, and what the temperament finder
> > calls "Cynder" is called "Mothra" on the wiki. I've been
> > using the names "Semaphore" and "Cynder" for the rank-2
> > 7-limit versions respectively, but there's a growing
> > schizophrenia around these tunings I can't ignore.
>
> Semaphore and Cynder are both in A Middle Path.

I've taken them to be 5-limit temperament names.

I'm not
> sure what the situation is with Waage and Compton. Other
> clashes are a matter of spelling: whether you use the
> umlaut in Würschmidt and whether there's a "i" in Semaphore.

Semiphore is not semaphore.

Graham wrote:

> Yeah, yeah, insult my professional competence while you're
> at it. Pretend search engines don't exist. And don't worry
> that nobody bothered to link to this page on their sites.

I didn't mean to insult your professional competence. Your
calculator is amazing and like anything else around here, that
you found the time to bring it into existence is a miracle.
But don't yell at people for not linking to the URLs it
produces.

I had no idea this page existed
http://x31eq.com/catalog2.html
and only found it by just now trying the google search you
patronizingly described in your previous post. I only knew
about the first incarnation and, come to that, I prefer it
to this one, since it doesn't try to crash my browser by
being the longest web page on the internet. And for what?
So that every single system can have an obscure name so that
everyone on this list can claim to have discovered something?

-Carl

Gene wrote:

> We're talking about rank 3 temperaments, at least I hope
> we are.

I was obviously being figurative, and obviously there are
even more rank 3 systems if you want to make it worse for
yourself.

> And you can't very well stop people from naming things,

No, and you don't have to craft an artificial intelligence
that takes any and everyone's suggested names and enshines
them in a "catalog", either.

-Carl

"Carl Lumma" <carl@...> wrote:

> I had no idea this page existed
> http://x31eq.com/catalog2.html
> and only found it by just now trying the google search you
> patronizingly described in your previous post. I only
> knew about the first incarnation and, come to that, I
> prefer it to this one, since it doesn't try to crash my
> browser by being the longest web page on the internet.
> And for what? So that every single system can have an
> obscure name so that everyone on this list can claim to
> have discovered something?

Sure, I should have linked to it. I didn't. I forgot.

It isn't a big deal but if you want a list of all the
names, there it is.

Graham

Gene wrote:

> Semiphore is not semaphore.

Shame on whoever made this error! -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I had no idea this page existed
> http://x31eq.com/catalog2.html
> and only found it by just now trying the google search you
> patronizingly described in your previous post.

Can I put up a link to this page on the Xenwiki?

"genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...>
> wrote:
>
> > I had no idea this page existed
> > http://x31eq.com/catalog2.html
> > and only found it by just now trying the google search
> > you patronizingly described in your previous post.
>
> Can I put up a link to this page on the Xenwiki?

Of course you can!

Graham

There's also a "semephore" too.

-Mike

On Mon, Sep 26, 2011 at 3:03 PM, Carl Lumma <carl@...> wrote:
>
>
>
> Gene wrote:
>
> > Semiphore is not semaphore.
>
> Shame on whoever made this error! -Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
>
> > > I started searching rank 2 temperaments, and I found
> > > something called Quanic:
> > >
> > > http://x31eq.com/cgi-bin/rt.cgi?limit=17&ets=111+94
>
> Quanic is closely associated to 205edo, as 205 gives the optimal patent val for 7, 11, 13, 17 and 19 limit quanic. It's pretty complex, but the tonal plexus has a lot of notes. The quanic generator of 24\205 is an approximate 13/12 and you need to go at least to the 13-limit to get the most out of this temperament. Semiconvergents for 24\205 tell us that 17, 26, 43, 60, 77 and 94 note MOS would make sense for quanic, but I don't know enough about the tonal plexus to know what would make sense for it.

Hmm, even the 9-note quanic MOS is enough to provide the 13/1 overtone opv, though not the 5/1, not with opv precision anyway. Evidently the 60-note MOS gets you through 17/1, but the 77-note doesn't quite reach the 19/1 opv; 94 notes are required for that. So the complexity cost of raising the prime limit precisely in quanic is high. Tolerate imprecision and embrace beating in certain overtones, however, and the 17-note quanic may suffice or even shine.

Those 24\205 and 13\205 intervals found in quanic seem to play a role in laka-dwarf as well, yes?

"manuphonic" <manuphonic@...> wrote:

> Hmm, even the 9-note quanic MOS is enough to provide the
> 13/1 overtone opv, though not the 5/1, not with opv
> precision anyway. Evidently the 60-note MOS gets you
> through 17/1, but the 77-note doesn't quite reach the
> 19/1 opv; 94 notes are required for that. So the
> complexity cost of raising the prime limit precisely in
> quanic is high. Tolerate imprecision and embrace beating
> in certain overtones, however, and the 17-note quanic may
> suffice or even shine.

You've got 205 notes on your keyboard. Even with Quanic
being fairly complicated, 73% of the 17-limit chords are
"in tune". Never mind that "in tune" is barely an
improvement on equal temperament . . .

The problem is, 205 isn't that great a division. It was
chosen because it's a multiple of 41, and 41 is good. If
you want something simpler, you can look to 41, extend it
beyond 41 notes if you like, and duplicate keys if you
don't.

In the 17-limit, 41 notes work well with extensions of
Miraculous (10&31), Superkleismic (26&41p), Octacot
(41p&27eg or 41p&27effg), Magic (19p&41p), and Cassandra
(41p&12f or 41p&12fg). In the 13-limit there's also
Hemififths (41&58), Manna (41&72), and Rodan (41&46).

> Those 24\205 and 13\205 intervals found in quanic seem to
> play a role in laka-dwarf as well, yes?

Quanic is a special case of Laka, although the 17-limit
Quanic I gave disagrees with the 17-limit mapping you gave
for Laka.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> The problem is, 205 isn't that great a division. It was
> chosen because it's a multiple of 41, and 41 is good.

It depends on what you use it for. It's a great division not only for quanic and laka, but 5-limit amity, where it delivers 5-limit microtempering with a temperament which is not too terribly complex, and gets you away from the circle-of-fifths of helmholtz or the double circle of diaschismic, with more accuracy than diaschismic or hanson. It's also pretty good for hemithirds.

As an owner of a Tonal Plexus, I'm interested in this but I'm afraid the learning curve of regular temperament theory and terminology is rather steep for me. Could you help me a little bit? You list a number of temperaments that would be approximated well by 205tet, right?
For instance, what's the double cicle of diaschismic temperament? And what are hemithirds?
How many notes do those scales have? If less than 205, then the pitches belonging to the scale would have to be found among the 205 keys (the other keys could be re-tuned to duplicates). If more than 205, some kind of selection would have to be made. (Using what principle?)

Unless you are only talking about the 205 keys of the keyboard (midi notes), and what temperaments could be mapped onto them.

My experience with the TPX is that even though any tunings can be mapped to the keys, and even though in the default tuning, transposed patterns have similar shapes, it is not really a genralized keyboard; it definitely works best with the default 205tet tuning. With that tuning, it's an excellent tool for trying out harmonies and melodies.
The 41tet fifths are practically pure, and you can approximate any other interval with a maximun error of 3 cents. That's part of the reasoning behind 205 but it has also to do with the keyboard layout. It's divided into 41 areas that each have 5 keys, and the keys are physically different so that moving on a 41-chain of fifths you always move to a corresponding, same-shaped key in another area. So the middle keys of these areas make up a chain of 41 virtully pure fifths, and to make a correction (ca. 6 or 12 cents up or down) from those 41tet pitches you play a key one or twor steps lower or higher than the middle key.

Juhani

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>
> > The problem is, 205 isn't that great a division. It was
> > chosen because it's a multiple of 41, and 41 is good.
>
> It depends on what you use it for. It's a great division not only for quanic and laka, but 5-limit amity, where it delivers 5-limit microtempering with a temperament which is not too terribly complex, and gets you away from the circle-of-fifths of helmholtz or the double circle of diaschismic, with more accuracy than diaschismic or hanson. It's also pretty good for hemithirds.
>

Don't overestimate my math skills. If my Laka mapping "disagrees" with yours, Graham, it's probably just that mine is wrong. :-)
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "manuphonic" <manuphonic@...> wrote:
>
> > Hmm, even the 9-note quanic MOS is enough to provide the
> > 13/1 overtone opv, though not the 5/1, not with opv
> > precision anyway. Evidently the 60-note MOS gets you
> > through 17/1, but the 77-note doesn't quite reach the
> > 19/1 opv; 94 notes are required for that. So the
> > complexity cost of raising the prime limit precisely in
> > quanic is high. Tolerate imprecision and embrace beating
> > in certain overtones, however, and the 17-note quanic may
> > suffice or even shine.
>
> You've got 205 notes on your keyboard. Even with Quanic
> being fairly complicated, 73% of the 17-limit chords are
> "in tune". Never mind that "in tune" is barely an
> improvement on equal temperament . . .
>
> The problem is, 205 isn't that great a division. It was
> chosen because it's a multiple of 41, and 41 is good. If
> you want something simpler, you can look to 41, extend it
> beyond 41 notes if you like, and duplicate keys if you
> don't.
>
> In the 17-limit, 41 notes work well with extensions of
> Miraculous (10&31), Superkleismic (26&41p), Octacot
> (41p&27eg or 41p&27effg), Magic (19p&41p), and Cassandra
> (41p&12f or 41p&12fg). In the 13-limit there's also
> Hemififths (41&58), Manna (41&72), and Rodan (41&46).
>
> > Those 24\205 and 13\205 intervals found in quanic seem to
> > play a role in laka-dwarf as well, yes?
>
> Quanic is a special case of Laka, although the 17-limit
> Quanic I gave disagrees with the 17-limit mapping you gave
> for Laka.
>
>
> Graham
>

Juhani, I totally validate your insight that the Tonal Plexus is best used with its master tuning. I'll say also that the tactile & visual cues of its layout are most conducive to the Garibaldi linear temperament. The bowl-topped center keys of the black & white keystrips are identical with Garibaldi 17. This offers excellent "backwards compatibility" with familiar diatonic & chromatic music, Ellis & Pythagoras, while including some nice higher harmonics. If you choose prime limit 7 & odd limit 27, as I did, then Garibaldi is impressively symmetrical in terms of the chords possible in each of its key signatures. Start in plus-A-flat & you'll be amazed.

However, I prefer my temperaments to come without steps as narrow as 1\41, so I'm dismissing the spectacular advantages of Garibaldi (for now) in favor of searching out higher harmonics & wider steps. Magic 19 is a good 2^(n/41) example of the kind of temperament I seek, but does 2^(n/205) offer anything better?

Cribbing some numbers from work done by Jake Freivald, I've rediscovered or possibly even discovered at least one temperament that could qualify. Its generator, which approximates 8/7, is 39 degrees of 2^(n/205). Do any of you recognize this as a temperament that's already extant?

It has a haplotonic MOS at 5 notes per octave, an albitonic MOS at 11, a quite chromatic MOS at 16, & a hyperchromatic MOS at 21 notes per octave. The last of these has no steps narrower than 9\205 & it closely approximates every 31-limit overtone. Today & over the next few days I'll be programming its intervals & chords into TPXE & learning to play it.

Here it is in degrees of 2^(n/205):

9
19
29
39
48
58
68
78
87
97
107
117
126
136
146
156
166
175
185
195
205

If this has no name yet, I'm not sure if Jake or I should be the one to suggest a name, nor am I sure what naming conventions are best followed in such a case. If we can use names of metals & if the name isn't already taken I'd like to suggest Chromium.

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "Juhani" <jnylenius@...> wrote:
>
> As an owner of a Tonal Plexus, I'm interested in this but I'm afraid the learning curve of regular temperament theory and terminology is rather steep for me. Could you help me a little bit? You list a number of temperaments that would be approximated well by 205tet, right?
> For instance, what's the double cicle of diaschismic temperament? And what are hemithirds?
> How many notes do those scales have? If less than 205, then the pitches belonging to the scale would have to be found among the 205 keys (the other keys could be re-tuned to duplicates). If more than 205, some kind of selection would have to be made. (Using what principle?)
>
> Unless you are only talking about the 205 keys of the keyboard (midi notes), and what temperaments could be mapped onto them.
>
> My experience with the TPX is that even though any tunings can be mapped to the keys, and even though in the default tuning, transposed patterns have similar shapes, it is not really a genralized keyboard; it definitely works best with the default 205tet tuning. With that tuning, it's an excellent tool for trying out harmonies and melodies.
> The 41tet fifths are practically pure, and you can approximate any other interval with a maximun error of 3 cents. That's part of the reasoning behind 205 but it has also to do with the keyboard layout. It's divided into 41 areas that each have 5 keys, and the keys are physically different so that moving on a 41-chain of fifths you always move to a corresponding, same-shaped key in another area. So the middle keys of these areas make up a chain of 41 virtully pure fifths, and to make a correction (ca. 6 or 12 cents up or down) from those 41tet pitches you play a key one or twor steps lower or higher than the middle key.
>
> Juhani
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> > > The problem is, 205 isn't that great a division. It was
> > > chosen because it's a multiple of 41, and 41 is good.
> >
> > It depends on what you use it for. It's a great division not only for quanic and laka, but 5-limit amity, where it delivers 5-limit microtempering with a temperament which is not too terribly complex, and gets you away from the circle-of-fifths of helmholtz or the double circle of diaschismic, with more accuracy than diaschismic or hanson. It's also pretty good for hemithirds.
> >
>

"manuphonic" <manuphonic@...> wrote:
> Don't overestimate my math skills. If my Laka mapping
> "disagrees" with yours, Graham, it's probably just that
> mine is wrong. :-) == MLV aka Manu Phonic

It isn't that simple. There's one obvious 13-limit Laka,
but there are different ways of extending it to the
17-limit. To find them, note that Laka tempers out
352:352, 540:539, 640:637, and 729:728. (My website tells
you this now.) Then, go to

http://x31eq.com/temper/uv.html

put them in the box, and ask for the 17-limit.

Here's a URL to take you straight there:

http://tinyurl.com/6yk5v53

The first three names as Laka+ all look viable. Your one,
I think is the second.

http://x31eq.com/cgi-bin/rt.cgi?ets=53p_58_41p&limit=17

It looks like it has the simplest mapping, and the new
intervals of 17 will fit in the section of the 5-limit
lattice that you're already using to map the 13-limit. But
it's listed as the most complex of the three. Maybe the
winner would be more interesting:

http://x31eq.com/cgi-bin/rt.cgi?ets=94_58_53p&limit=17

But the reduced mapping *looks* a lot more complicated than
your option. The 17:16 is three steps of the approximate
5:1 when all the lower primes only need one step in one
direction or another. So you'll need a much bigger chunk
of the 5-limit lattice to cover this temperament that's
supposed to be simpler.

What's happening is that the TE complexity is considering
all possible choices of basis. So the optimal Laka can be
easier to use, but you have to choose the appropriate
basis. The TLLL-reduced basis, which is mathematically
optimized to do this, is:

[<1, 2, 4, 2, 8, 7, 0],
<1, 1, -3, 1, 0, 2, 1],
<0, 0, 1, 1, -1, -1, 3]]

The numbers are generally smaller than the Hermite basis
given on the website, but in practical terms, your mapping
will be simpler.

But what's really happening is that Laka isn't that good in
the 17-limit, so you have to choose from different mediocre
extensions. Here's a fairly long list of rank 3
temperaments that target an error of around 2 cents:

http://x31eq.com/cgi-bin/more.cgi?r=3&limit=17&error=2

No kind of Laka makes it. But the Ragismic+++ near the top
does work without dividing 5-limit intervals:

http:/x31eq.com/cgi-bin/rt.cgi?ets=27eg_72_46&limit=17

Or there's Marvel:

http://x31eq.com/cgi-bin/rt.cgi?ets=22p_72_31&limit=17

I don't really trust any of these listings, but they're
still giving an indication that there are better things
than Laka out there.

Graham

"manuphonic" <manuphonic@...> wrote:

> However, I prefer my temperaments to come without steps
> as narrow as 1\41, so I'm dismissing the spectacular
> advantages of Garibaldi (for now) in favor of searching
> out higher harmonics & wider steps. Magic 19 is a good
> 2^(n/41) example of the kind of temperament I seek, but
> does 2^(n/205) offer anything better?

One thing about Magic is that there are 5 generators to a
fifth, so you could map it as five Pythagorean scales. That
would give you the full 205 notes. There wouldn't be much
difference between the five different tunings, but still,
they would be different.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "manuphonic" <manuphonic@...> wrote:
>
> > However, I prefer my temperaments to come without steps
> > as narrow as 1\41, so I'm dismissing the spectacular
> > advantages of Garibaldi (for now) in favor of searching
> > out higher harmonics & wider steps. Magic 19 is a good
> > 2^(n/41) example of the kind of temperament I seek, but
> > does 2^(n/205) offer anything better?
>
> One thing about Magic is that there are 5 generators to a
> fifth, so you could map it as five Pythagorean scales. That
> would give you the full 205 notes. There wouldn't be much
> difference between the five different tunings, but still,
> they would be different.

This beings to mind 41&205 temperament, which you may as well do in 205edo. It tempers out (in the 13 limit) 352/351, 540/539, 847/845 and 203125/201684. The generator can be construed as the 66\205 major third (with period 1\41) but of course you could use 145\451 if you happened to have a 451edo keyboard lying around.

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
> Cribbing some numbers from work done by Jake Freivald, I've rediscovered or possibly even discovered at least one temperament that could qualify. Its generator, which approximates 8/7, is 39 degrees of 2^(n/205). Do any of you recognize this as a temperament that's already extant?
>
> It has a haplotonic MOS at 5 notes per octave, an albitonic MOS at 11, a quite chromatic MOS at 16, & a hyperchromatic MOS at 21 notes per octave. The last of these has no steps narrower than 9\205 & it closely approximates every 31-limit overtone. Today & over the next few days I'll be programming its intervals & chords into TPXE & learning to play it.

I don't see how this "closely approximates every 31-limit overtone". For starters, where is overtone 3, which is supposed to be 120 steps? Is 117 (or 118, found between 48 and 166) close enough?

Where is overtone 5, which is supposed to be 66 steps? Is 68 close enough?

These don't seem like close approximations to me.

Keenan

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

Incidentally, I should mention that another talent of 205edo is tempering out the huntma, 640/637, and having good huntmic chords:

http://xenharmonic.wikispaces.com/huntmic+chords

Not that these are the only essentially tempered chords it does well for.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> > Cribbing some numbers from work done by Jake Freivald, I've rediscovered or possibly even discovered at least one temperament that could qualify. Its generator, which approximates 8/7, is 39 degrees of 2^(n/205). Do any of you recognize this as a temperament that's already extant?
> >
> > It has a haplotonic MOS at 5 notes per octave, an albitonic MOS at 11, a quite chromatic MOS at 16, & a hyperchromatic MOS at 21 notes per octave. The last of these has no steps narrower than 9\205 & it closely approximates every 31-limit overtone. Today & over the next few days I'll be programming its intervals & chords into TPXE & learning to play it.
>
> I don't see how this "closely approximates every 31-limit overtone". For starters, where is overtone 3, which is supposed to be 120 steps? Is 117 (or 118, found between 48 and 166) close enough?
>
> Where is overtone 5, which is supposed to be 66 steps? Is 68 close enough?

Yes, 117 & 68 were the ones I meant.

>
> These don't seem like close approximations to me.
>
> Keenan
>

Yet the otonal variances in this tuning to prime & odd limit 31 are comparable to or better than some in some other scales under discussion here, like Quanic 17. Nothing to that limit is more than 4\205 off in "Chromium" 21 if I've not miscalculated. Still, I believe you when you suggest I'm overselling this tuning a bit, since I'm known for the occasional excess of enthusiasm. :-)

What description of "Chromium" do you think would be more justifiable? Or, no need to focus on "Chromium"; what linear or planar temperament of 205tet with fewer than 24 notes per octave & no steps any smaller than 9\205 would you say we Plexus players can more profitably explore?

Cheers!
==
MLV aka Manu Phonic

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

what linear or planar temperament of 205tet with fewer than 24 notes per octave & no steps any smaller than 9\205 would you say we Plexus players can more profitably explore?

Some obvious choices are the hemithirds generator, 33\205, with MOS of 13 or 19 (or 25, if you go that high) notes, or the amity generator, 58\205, with MOS of 11, 18 and (again) 25 notes. If you use the amity generator with the <205 325 476 577| val, you get to use 225/224 tempering, though with a 7 getting on towards nine cents sharp.

>
> Incidentally, I should mention that another talent of 205edo is tempering out the huntma, 640/637, and having good huntmic chords:

Meaning, that on the Tonal Plexus, you play 5/4 and 13/8 of 7/4 of 7/4 on the same key? Hey, so it is! But to arrive at that I had to take both 7/4's as four keys flat from 16/9's, so here the septimal comma is played as 4 steps, not 5 as you suggested a while ago in some other situation. The harmonic seventh falls almost in the middle of steps and either one can be used, according to context. Five is simplest to play, as it stays in the same 41-cycle. Four is a little closer approximation but then 81/80 and 64/63 will have the same number of key steps (so 5120/5103 is tempered out, n'est-ce pas?).

I originally thought that the less-than-perfect approximation of septimal intervals in 205tet is its weakness but I begin to see now that these various choices between commas-to-be-temepered-out may be interesting in themselves.

juhani

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
> > I don't see how this "closely approximates every 31-limit overtone". For starters, where is overtone 3, which is supposed to be 120 steps? Is 117 (or 118, found between 48 and 166) close enough?
> >
> > Where is overtone 5, which is supposed to be 66 steps? Is 68 close enough?
>
> Yes, 117 & 68 were the ones I meant.

In that case, this is "gorgo" temperament, tempering out 1029/1024 and 36/35. Mike Battaglia and Ron Sword are fond of its 16edo incarnation, but 21edo is closer to optimal.

My personal opinion is that it's an out-of-tune bastardization of slendric. But I can see why some people like it.

> Yet the otonal variances in this tuning to prime & odd limit 31 are comparable to or better than some in some other scales under discussion here, like Quanic 17. Nothing to that limit is more than 4\205 off in "Chromium" 21 if I've not miscalculated. Still, I believe you when you suggest I'm overselling this tuning a bit, since I'm known for the occasional excess of enthusiasm. :-)
>
> What description of "Chromium" do you think would be more justifiable? Or, no need to focus on "Chromium"; what linear or planar temperament of 205tet with fewer than 24 notes per octave & no steps any smaller than 9\205 would you say we Plexus players can more profitably explore?

I'm unclear why it needs to be a subset of 205edo. That seems like a pretty weird restriction to me. Why can't you just use the tonal plexus as a midi controller and use a synth that lets you make the notes whatever you want?

Keenan

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

> I originally thought that the less-than-perfect approximation of septimal intervals in 205tet is its weakness but I begin to see now that these various choices between commas-to-be-temepered-out may be interesting in themselves.

Absolutely. 205 gets the 5-limit almost dead on, but it's lots of fun to figure if you'd rather temper out 6144/6125, 5120/5103 and 4375/4374, like 99edo, or possibly 1029/1024 and 3136/3125, like 87 or 118. Or even 225/224.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> I'm unclear why it needs to be a subset of 205edo. That seems like a pretty weird restriction to me. Why can't you just use the tonal plexus as a midi controller and use a synth that lets you make the notes whatever you want?

Apparently it's a little easier that way. I'm all in favor of giving the virtues of 205edo a try; it's not as if it's thouroughly explored. Why not a focus on hemithirds or amity?

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

> Apparently it's a little easier that way. I'm all in favor of giving the virtues of 205edo a try; it's not as if it's thouroughly explored. Why not a focus on hemithirds or amity?
>

Some other thoughts:

119\205, 696.585, is an excellent meantone fifth
53\205, 310.244, is an excellent myna generator

On Sun, Oct 2, 2011 at 10:41 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > Apparently it's a little easier that way. I'm all in favor of giving the virtues of 205edo a try; it's not as if it's thouroughly explored. Why not a focus on hemithirds or amity?
> >
>
> Some other thoughts:
>
> 119\205, 696.585, is an excellent meantone fifth
> 53\205, 310.244, is an excellent myna generator

See, this is the problem with giant EDOs - there are so many decent
vals that you could use that there's never any end to the number of
temperaments that they support. How can we narrow it down?

Doesn't look like it does too well with porcupine though. Of course,
all it's going to take for us to change our tune about that is for
some guy to come along who's completely down with using 205-EDO as a
circulating temperament for porcupine, and views us as being trapped
in our own preconceptions for not using it that way, and we'll start
looking at functions that map porcupine onto 205-EDO. (I was trying to
come up with some hip mathematical phrasing for this, preferably one
using the term "image," but I gave up)

-Mike

> Absolutely. 205 gets the 5-limit almost dead on, but it's lots of fun to figure if you'd rather temper out 6144/6125, 5120/5103 and 4375/4374, like 99edo, or possibly 1029/1024 and 3136/3125, like 87 or 118. Or even 225/224.
>
Great, thanks! This will keep me busy with my keyboard (&calculator) for a while.
Juhani

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> > > I don't see how this "closely approximates every 31-limit overtone". For starters, where is overtone 3, which is supposed to be 120 steps? Is 117 (or 118, found between 48 and 166) close enough?
> > >
> > > Where is overtone 5, which is supposed to be 66 steps? Is 68 close enough?
> >
> > Yes, 117 & 68 were the ones I meant.
>
> In that case, this is "gorgo" temperament, tempering out 1029/1024 and 36/35. Mike Battaglia and Ron Sword are fond of its 16edo incarnation, but 21edo is closer to optimal.

Gorgo it is, then. Thanks for clearing that up.

> My personal opinion is that it's an out-of-tune bastardization of slendric. But I can see why some people like it.

If equal, near-equal, proportional & near-proportional beating phenomena fascinate you, as they do me, even when the beat rates are as high as 15.659 Hz, you start to recognize nontonics as "approximating" a harmonic (say 3/2) across much of the range in which they beat against the corresponding overtone of the tonic note.

Keenan, your reactions may be more like those of a JI purist who perceives approximation only across the narrow center of that range where beating slows to almost nothing.

<snip>

> > What description of "Chromium" do you think would be more justifiable? Or, no need to focus on "Chromium"; what linear or planar temperament of 205tet with fewer than 24 notes per octave & no steps any smaller than 9\205 would you say we Plexus players can more profitably explore?
>
> I'm unclear why it needs to be a subset of 205edo. That seems like a pretty weird restriction to me. Why can't you just use the tonal plexus as a midi controller and use a synth that lets you make the notes whatever you want?

Just to be clear, the Tonal Plexus itself comes equipped with many tunings, including favorites of mine, & can be programmed for many more. I didn't expect to stick with the 2^(n/205) master tuning when I bought the keyboard. I thought I'd probably switch tunings every few minutes!

But in practice I found I just don't like trying to play other tunings on the Plexus, an unexpected response I now know other Plexus players have also reported. When I'm ready to play in 15 or 22 equal divisions of some stretched octave or another I'll get a different instrument. Meanwhile, since I have the Plexus, I'd like to make the most of it. Its TPXE software includes a reprogrammable "Shapes" function that helps me memorize the modes & chords of my choice, & that function is easier to reprogram if I stick with 205 or 41tet. That may seem restrictive but, if Darreg & Blackwood have taught us anything, it's that practically any EDO has musical possibilities worth exploring.

> Keenan

Cheers!
==
MLV aka Manu Phonic

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

> See, this is the problem with giant EDOs - there are so many decent
> vals that you could use that there's never any end to the number of
> temperaments that they support. How can we narrow it down?

Not really true. It's only at the low complexity, high error end of the scale that you are going to be assured of finding something. When you get to more accurate temperaments like myna and meantone, finding a really good generator is worthy of note, and for low error temperaments like amity or hemithirds, you must go with what's on offer.

> Doesn't look like it does too well with porcupine though.

What's wrong with 28\205? That's actually pretty damned good, it seems to me. Maybe I should add it to the 205edo article.

The biggest problem I noticed was that sometimes, the generator you get is a 41edo one. Now, 41 does a fine job for magic, but how well does it work on the Tonal Plexus to stick with just 41?

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
> > My personal opinion is that it's an out-of-tune bastardization of slendric. But I can see why some people like it.
>
> If equal, near-equal, proportional & near-proportional beating phenomena fascinate you, as they do me, even when the beat rates are as high as 15.659 Hz, you start to recognize nontonics as "approximating" a harmonic (say 3/2) across much of the range in which they beat against the corresponding overtone of the tonic note.
>
> Keenan, your reactions may be more like those of a JI purist who perceives approximation only across the narrow center of that range where beating slows to almost nothing.

No way, man, I love me some beating. I play with Gamelan Sekar Jaya, the best gamelan this side of the equator.* Mike recently got me to try blackwood temperament, which I think is pretty neat now. It's just that "slendric" (which is unrelated to slendro btw) is one of my all-time favorite temperaments because it does the 2.3.7 subgroup so accurately yet simply. Gorgo seems like throwing that all away for the sake of a crappy 5.

(* And by this I mean, if you disagree, we'll come mebarung your gamelan. We're going to LA this weekend to mebarung Burat Wangi and they're not gonna know what hit them.)

> > I'm unclear why it needs to be a subset of 205edo. That seems like a pretty weird restriction to me. Why can't you just use the tonal plexus as a midi controller and use a synth that lets you make the notes whatever you want?
>
> Just to be clear, the Tonal Plexus itself comes equipped with many tunings, including favorites of mine, & can be programmed for many more. I didn't expect to stick with the 2^(n/205) master tuning when I bought the keyboard. I thought I'd probably switch tunings every few minutes!
>
> But in practice I found I just don't like trying to play other tunings on the Plexus, an unexpected response I now know other Plexus players have also reported. When I'm ready to play in 15 or 22 equal divisions of some stretched octave or another I'll get a different instrument. Meanwhile, since I have the Plexus, I'd like to make the most of it. Its TPXE software includes a reprogrammable "Shapes" function that helps me memorize the modes & chords of my choice, & that function is easier to reprogram if I stick with 205 or 41tet. That may seem restrictive but, if Darreg & Blackwood have taught us anything, it's that practically any EDO has musical possibilities worth exploring.

Okay, that's cool. In that case I would make sure to try the wonderful temperaments 41-equal has to offer first. In particular, you got miracle (if you're looking for a 21-note scale, why not try blackjack??), you got magic, you got rodan (aka the GOOD version of slendric)... See http://xenharmonic.wikispaces.com/41edo for more. Then you can start on the cornucopia I'm sure is available in the full 205.

Keenan

>
> Just to be clear, the Tonal Plexus itself comes equipped with many tunings, including favorites of mine, & can be programmed for many more. I didn't expect to stick with the 2^(n/205) master tuning when I bought the keyboard. I thought I'd probably switch tunings every few minutes!

My experience has been very similar to yours. I'd assumed I would be using it with numerous JI mappings of my own design, as well as for 31, 53 etc. But as a composer who mainly writes in JI, I've found the master tuning the best way to try out intervals and harmonies on the TPX. As I explained here: /tuning/topicId_101682.html#101738 , the keyboard design is not as generalized as that of other array keyboards but it's physically and visually tied to the 5*41 principle.
What I have done however, is that I've created tunings for specific pieces of mine, ones that use maybe 35 pitch classes in Just Intonation, so that I've replaced the keys that those pitches would be played on in the master 205tet tuning with the precise, untempered notes. (Of course this won't work in those few cases where the same key represents two ratios). This way, when coaching singers, for example, I can give them the exact note but I don't have to learn new keyboard mappings.

>
> But in practice I found I just don't like trying to play other tunings on the Plexus, an unexpected response I now know other Plexus players have also reported. When I'm ready to play in 15 or 22 equal divisions of some stretched octave or another I'll get a different instrument.

Again - same here! I've been considering an C-thru Axis for those purposes.

>Meanwhile, since I have the Plexus, I'd like to make the most of it. Its TPXE software includes a reprogrammable "Shapes" function that helps me memorize the modes & chords of my choice, & that function is easier to reprogram if I stick with 205 or 41tet. That may seem restrictive but, if Darreg & Blackwood have taught us anything, it's that practically any EDO has musical possibilities worth exploring.
>

Oh and thanks for the Garibaldi 17 suggestion! It shows how there are subsets in the TPX keyboard layout that are really logical and neat visually and physically for certain tunings.
In one tuning I myself made use of the fact that there are 12 large yellow keys per octave and mapped 12tet to those so as to be able to quickly compare anything to 12TET.

Juhani

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

> Oh and thanks for the Garibaldi 17 suggestion! It shows how there are subsets in the TPX keyboard layout that are really logical and neat visually and physically for certain tunings.

I've added a bunch of stuff here

http://xenharmonic.wikispaces.com/205edo

which might prove useful.

Keenan wrote:

> (* And by this I mean, if you disagree, we'll come mebarung
> your gamelan.

What does that mean? Is there, in traditional Indonesian
music, a culture of rivalry and boasting like in rap and
b-boying?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Keenan wrote:
>
> > (* And by this I mean, if you disagree, we'll come mebarung
> > your gamelan.
>
> What does that mean? Is there, in traditional Indonesian
> music, a culture of rivalry and boasting like in rap and
> b-boying?

A mebarung is a musical battle -- the culture of gamelan in Bali loves a good competition. In most parts of Bali, two groups will face off and trade pieces one by one, sometimes heckling each other over their mistakes. Jegog groups in Jembrana take it a bit farther -- when one group finishes a piece, they launch into a repeating musical cycle as a challenge to the other group . . . who respond by jumping back onto their instruments and playing their own cycle. At this point both jegog groups try to drown each other out, stay together with their compatriots through the unholy noise, and be the one to outlast the other in a contest of stamina.

http://www.festivalofsacredmusic.org/event/mebarung

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> > What does that mean? Is there, in traditional Indonesian
> > music, a culture of rivalry and boasting like in rap and
> > b-boying?
>
> A mebarung is a musical battle

Sure sounded like it! Rap started in "battles", as did b-boying.

Do women traditionally play instruments in the gamelan?
I'm guessing dancing and singing only.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Sure sounded like it! Rap started in "battles", as did b-boying.
>
> Do women traditionally play instruments in the gamelan?
> I'm guessing dancing and singing only.

You're correct. Unfortunately there's still some stigma about it in Bali too. There's no shortage of papers about it:

http://muse.jhu.edu/journals/asian_theatre_journal/v025/25.2.diamond.html

http://scholarspace.manoa.hawaii.edu/handle/10125/19378
(this one by our illustrious Director, Emiko Saraswati Susilo)

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> > > My personal opinion is that it's an out-of-tune bastardization of slendric. But I can see why some people like it.
> >
> > If equal, near-equal, proportional & near-proportional beating phenomena fascinate you, as they do me, even when the beat rates are as high as 15.659 Hz, you start to recognize nontonics as "approximating" a harmonic (say 3/2) across much of the range in which they beat against the corresponding overtone of the tonic note.
> >
> > Keenan, your reactions may be more like those of a JI purist who perceives approximation only across the narrow center of that range where beating slows to almost nothing.
>
> No way, man, I love me some beating. I play with Gamelan Sekar Jaya, the best gamelan this side of the equator.* Mike recently got me to try blackwood temperament, which I think is pretty neat now. It's just that "slendric" (which is unrelated to slendro btw) is one of my all-time favorite temperaments because it does the 2.3.7 subgroup so accurately yet simply. Gorgo seems like throwing that all away for the sake of a crappy 5.

Oh, I misjudged you here pretty badly, didn't I? Knowing better now really cheers me up. :-) Gorgo had some unpleasant surprises for me too when I started following the vals in a proper fashion instead of just noticing the notes that were nearest to the overtones I wanted. Slendric (I did think from the name that it had a slendro connection, so thanks for correcting that misimpression) may be something I should investigate further.

> (* And by this I mean, if you disagree, we'll come mebarung your gamelan. We're going to LA this weekend to mebarung Burat Wangi and they're not gonna know what hit them.)
>
> > > I'm unclear why it needs to be a subset of 205edo. That seems like a pretty weird restriction to me. Why can't you just use the tonal plexus as a midi controller and use a synth that lets you make the notes whatever you want?
> >
> > Just to be clear, the Tonal Plexus itself comes equipped with many tunings, including favorites of mine, & can be programmed for many more. I didn't expect to stick with the 2^(n/205) master tuning when I bought the keyboard. I thought I'd probably switch tunings every few minutes!
> >
> > But in practice I found I just don't like trying to play other tunings on the Plexus, an unexpected response I now know other Plexus players have also reported. When I'm ready to play in 15 or 22 equal divisions of some stretched octave or another I'll get a different instrument. Meanwhile, since I have the Plexus, I'd like to make the most of it. Its TPXE software includes a reprogrammable "Shapes" function that helps me memorize the modes & chords of my choice, & that function is easier to reprogram if I stick with 205 or 41tet. That may seem restrictive but, if Darreg & Blackwood have taught us anything, it's that practically any EDO has musical possibilities worth exploring.
>
> Okay, that's cool. In that case I would make sure to try the wonderful temperaments 41-equal has to offer first. In particular, you got miracle (if you're looking for a 21-note scale, why not try blackjack??), you got magic, you got rodan (aka the GOOD version of slendric)... See http://xenharmonic.wikispaces.com/41edo for more. Then you can start on the cornucopia I'm sure is available in the full 205.

Trying temperaments of 41tet first is exactly what I've been doing. Blackjack would be perfect if I could reliably pitch my voice at step sizes like 1\41. I'd be happier with Garibaldi then too. Since I cannot, Magic suits me better.

> Keenan

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > See, this is the problem with giant EDOs - there are so many decent
> > vals that you could use that there's never any end to the number of
> > temperaments that they support. How can we narrow it down?
>
> Not really true. It's only at the low complexity, high error end of the scale that you are going to be assured of finding something. When you get to more accurate temperaments like myna and meantone, finding a really good generator is worthy of note, and for low error temperaments like amity or hemithirds, you must go with what's on offer.
>
> > Doesn't look like it does too well with porcupine though.
>
> What's wrong with 28\205? That's actually pretty damned good, it seems to me. Maybe I should add it to the 205edo article.
>
> The biggest problem I noticed was that sometimes, the generator you get is a 41edo one. Now, 41 does a fine job for magic, but how well does it work on the Tonal Plexus to stick with just 41?

That's easy enough that you can do it in the dark, thanks to tactile cues. All the 41edo keys have concave "bowl" tops.

Cheers!
==
MLV aka Manu Phonic

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

> > The biggest problem I noticed was that sometimes, the generator you get is a 41edo one. Now, 41 does a fine job for magic, but how well does it work on the Tonal Plexus to stick with just 41?
>
> That's easy enough that you can do it in the dark, thanks to tactile cues. All the 41edo keys have concave "bowl" tops.

What I wondered about is that you don't get to use all of the keys. In terms of temperaments starting with "m", that means you can use more keys with meantone or myna than with miracle or magic. I'd be interested to hear if anyone has taken up the suggestion of using myna or porcupine on the Tonal Plexus, and how well that worked, BTW.

--- In tuning@yahoogroups.com, "manuphonic" <manuphonic@...> wrote:
> Oh, I misjudged you here pretty badly, didn't I? Knowing better now really cheers me up. :-) Gorgo had some unpleasant surprises for me too when I started following the vals in a proper fashion instead of just noticing the notes that were nearest to the overtones I wanted. Slendric (I did think from the name that it had a slendro connection, so thanks for correcting that misimpression) may be something I should investigate further.

Basically the only thing slendro and slendric have in common is that they both have scales with 5 roughly equal steps in an octave. Slendric is very accurate, but slendro, like all gamelan scales, is very inaccurate and based on an aesthetic of ever-present beating. Slendro is an irregular circulating temperament where all five empat intervals are used as strong consonances; slendric only really gets good when you have at least 11 notes.

They're both really beautiful in their own ways.

> Trying temperaments of 41tet first is exactly what I've been doing. Blackjack would be perfect if I could reliably pitch my voice at step sizes like 1\41. I'd be happier with Garibaldi then too. Since I cannot, Magic suits me better.

Hmm, yeah, I guess that is how blackjack works out in 41. That's a shame.

Keenan

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

<snip>

> > The biggest problem I noticed was that sometimes, the generator you get is a 41edo one. Now, 41 does a fine job for magic, but how well does it work on the Tonal Plexus to stick with just 41?
>
> That's easy enough that you can do it in the dark, thanks to tactile cues. All the 41edo keys have concave "bowl" tops.

The tactile cues only apply when using the 205edo master tuning.

I should add that, with the press of an easily reached button, all Tonal Plexus keys, not just the concave ones, play 41edo. The board is divided into 5-key strips. One of the "factory"-installed tunings assigns the same 41edo pitch to every key in any given strip, so that it doesn't matter which key in a strip your finger hits, as long as it lands in the right strip.

This redundancy allows faster fingerwork on the same note, using two or more fingers hitting adjacent keys, than is allowed by tunings where adjacent keys always play different notes.

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
>
> > > The biggest problem I noticed was that sometimes, the generator you get is a 41edo one. Now, 41 does a fine job for magic, but how well does it work on the Tonal Plexus to stick with just 41?
> >
> > That's easy enough that you can do it in the dark, thanks to tactile cues. All the 41edo keys have concave "bowl" tops.
>
> What I wondered about is that you don't get to use all of the keys. In terms of temperaments starting with "m", that means you can use more keys with meantone or myna than with miracle or magic. I'd be interested to hear if anyone has taken up the suggestion of using myna or porcupine on the Tonal Plexus, and how well that worked, BTW.
>

Gene, I really appreciate those temperaments you (& anyone else?) added to the 205edo wikipage. I'm slowly programming them all into my TPXE Shapes function. I"ll probably start noodling around with Myna fairly soon. "Soon" by the standards of a 51-year-old guy whose family, job & long commute keep him pretty busy, anyway. If I come up with anything sparkly maybe I'll post a vid on YouTube.

I also keep trying to tweak Laka, the planar temperament that began this conversation. I never did remember to ask what a 13-limit Laka looks like in 205edo. Graham said something about the 13-limit version being more easily worked out than the 17-limit? Fewer decision or inflection points or something?

Cheers!
==
MLV aka Manu Phonic

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "manuphonic" <manuphonic@> wrote:
> >
> > Trying temperaments of 41tet first is exactly what I've been doing. Blackjack would be perfect if I could reliably pitch my voice at step sizes like 1\41. I'd be happier with Garibaldi then too. Since I cannot, Magic suits me better.
>
> Hmm, yeah, I guess that is how blackjack works out in 41. That's a shame.

Theoretically the best equal temperament for blackjack is what, 202 equal divisions of 7/1, with t = 652.24? At least that's closer to the local peak in the Riemann-Siegel Z(t) curve than 72ed2, with t = 652.66. Not that I'd be likely to notice the difference on any note other than maybe the octave.

http://web.viu.ca/pughg/RiemannZeta/RiemannZetaLong.html#ZPlotter

> Keenan

Cheers!
==
MLV aka Manu Phonic

"manuphonic" <manuphonic@...> wrote:

> I also keep trying to tweak Laka, the planar temperament
> that began this conversation. I never did remember to ask
> what a 13-limit Laka looks like in 205edo. Graham said
> something about the 13-limit version being more easily
> worked out than the 17-limit? Fewer decision or
> inflection points or something?

I don't have a high-level theory for it. It's the way the
numbers fall. The Laka geometry happens to work reasonably
well in the 13-limit but not so well in the 17-limit.
There isn't one obvious 17-limit extension and none of them
are competitive with other 17-limit temperaments. This
isn't a deficiency of 205-EDO because I notice it gets very
close to 17:16.

You can certainly follow the work Gene (if it be he) is
doing with 205 note scales. From the search I did, it
looks like nothing really stands out, and you may as well
stay with equal temperament, or some circulating
temperament that focuses on the chords you're most
interested in, if the problem is to find a way of tuning
those 205 keys for 17-limit harmony.

If the question is to find some simple scales with 17-limit
harmony that work with the keyboard, that's where 41 comes
in. 41 is a great meeting point for regular temperaments.
Some you might be interested in are:

Miraculous
http://x31eq.com/cgi-bin/rt.cgi?ets=10_31&limit=17

Superkleismic
http://x31eq.com/cgi-bin/rt.cgi?ets=26_15g&limit=17

Octacot
http://x31eq.com/cgi-bin/rt.cgi?ets=27eg_41p&limit=17

Magic
http://x31eq.com/cgi-bin/rt.cgi?ets=22f_19p&limit=17

Two extensions of Cassandra:
http://x31eq.com/cgi-bin/rt.cgi?ets=29g_12fg&limit=17
http://x31eq.com/cgi-bin/rt.cgi?ets=12f_41p&limit=17

Another extension of Octacot:
http://x31eq.com/cgi-bin/rt.cgi?ets=14cf_41p&limit=17

Graham

On Wed, Oct 5, 2011 at 8:16 AM, Keenan Pepper <keenanpepper@...> wrote:
>
> Basically the only thing slendro and slendric have in common is that they both have scales with 5 roughly equal steps in an octave. Slendric is very accurate, but slendro, like all gamelan scales, is very inaccurate and based on an aesthetic of ever-present beating. Slendro is an irregular circulating temperament where all five empat intervals are used as strong consonances; slendric only really gets good when you have at least 11 notes.

Does the actual slendro even make sense if viewed as 1L4s? I vaguely
remember hearing that it was more like 3L2s or something.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Oct 5, 2011 at 8:16 AM, Keenan Pepper <keenanpepper@...> wrote:
> >
> > Basically the only thing slendro and slendric have in common is that they both have scales with 5 roughly equal steps in an octave. Slendric is very accurate, but slendro, like all gamelan scales, is very inaccurate and based on an aesthetic of ever-present beating. Slendro is an irregular circulating temperament where all five empat intervals are used as strong consonances; slendric only really gets good when you have at least 11 notes.
>
> Does the actual slendro even make sense if viewed as 1L4s? I vaguely
> remember hearing that it was more like 3L2s or something.

This is a tough question.

My personal pet theory predicts that the Platonic ideal slendro is 3L2s (or, alternatively, indistinguishable from 5-equal, but that contradicts the observation that the modes are distinguishable), but in practice I don't know. The gamelan angklung scale, which is basically 4 notes out of slendro, definitely sounds like ssL within a 3/2, which would imply that the full slendro scale is a superpyth-like 2L3s.

I'm sure that if you gave a gender or something tuned perfectly to 1L4s slendric to most Balinese musicians, they wouldn't even bat an eye. They'd say "of course it's slendro, what else could it be?". But of course this doesn't mean that 1L4s is the ideal slendro tuning; it only means that the requirements for being an acceptable slendro tuning are none too strict.

There's no shortage of papers about slendro tuning. This one: lit.gfax.ch/Indonesian%20Music--slendro_balungan_tunings.pdf says there are more than 2 step sizes, so it's something like 1L3m1s or 2L2m1s.

All I can say for sure about slendro is that:

* The five steps are so similar in size that you can't tell for sure what the scale imprint is.

* But, the different modes have distinguishable flavors.

* All five "empat" intervals (~3/2) are used similarly; none is treated as a dissonance.

Maybe this means that the "conceptual" scale imprint is simply aaaaa, even though each 'a' is not exactly equal.

Keenan