1029

A long time ago, in a galaxy far far away, Gene wrote:

>1. Sonata #52 in E flat, Matty Weimar
>
>This was retuned by sending the meantone generator of ~3/2 to an approximate
>7/4, and then reducing the result to the range of an octave. This sends a
>1--5/4--3/2 chord to a 1--7/6--7/4 chord; {2,3,5} meantone harmony to a
>{2,3,7} subgroup of miracle; and 81/80 to 1029/1024.

So it looks like Igs has been using something like this no-5s
miracle in 18-ET

""
After having slept most of the day, here's
the mapping

2 9 21
0 3 1 gen (466.7)
1 2 4 period (1200.0)

If you plug the 2.9.21 subgroup in here with 5 cents target error
http://x31eq.com/temper/pregular.html
you get it right on top as being the best choice
http://x31eq.com/cgi-bin/rt.cgi?ets=18_5&error=5.0&limit=2_9_21&invariant=3_1_1_2_4

The optimal rank 2 tuning is 467.871, 1200.297. Essentially 18-ET.
The rank 1 stretch is only 0.7 cents/octave. Is there any ET you
like better for this than 18? Because there shouldn't be (41 is
just slightly more accurate).
[snip]
So 1029/1024 vanishes. That makes it something like a no-5s
miracle.
""

Igs declined to name it. I suggested "pseudonym" temperament.
Gene, is that sonata on archive.org or somewhere?

-Carl

Looks like Igs has also been using Octokeidecal/Octokaidecal
without knowing it (in 18-ET)

http://xenharmonic.wikispaces.com/Trienstonic+clan

The 8-note/oct MOS/DES scale is sweet. There are alternating
5:6:7 and 7:6:10 chords on 1_2_4, and they're a cinch to transpose
around on the halberstadt as the first three tones of what
would be a wholetone scale there.

There are also revolving 6:7:9, 10:12:15, and 5:6:8 chords
on 1_2_5. And many of these can be extended to 1_2_5_7 chords.

Notes:

* Can Graham and the wiki be synchronized on the spelling?

* Why are generators on the wiki sometimes bigger than
periods? What kind of mappings are these?

Anyway, great work Graham and Gene.

-Carl

On 15 January 2011 10:20, Carl Lumma <carl@lumma.org> wrote:

> * Can Graham and the wiki be synchronized on the spelling?

I can copy the wiki page and get all updates on my website at the
weekend. (No, it isn't the weekend now.) Currently the names from
Gene's original web pages take precedence. That can easily be changed
if we agree that the Wiki's authoritative.

Graham

>> * Can Graham and the wiki be synchronized on the spelling?
>
>I can copy the wiki page and get all updates on my website at the
>weekend. (No, it isn't the weekend now.) Currently the names from
>Gene's original web pages take precedence. That can easily be changed
>if we agree that the Wiki's authoritative.

I don't care one way or the other, but your way (with the e)
looks more Greek to me. Is there are right or wrong way on it? -C.

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
> Igs declined to name it. I suggested "pseudonym" temperament.
> Gene, is that sonata on archive.org or somewhere?
>
> -Carl
>
I did not decline, I needed to think on it. Then I came up with "A-Team" because that sounds like "Eighteen" (since 18-EDO is very close to an optimal tuning of this temperament) and the tuning world needs more Mr. T references.

-Igs

On 1/15/2011 2:40 AM, Carl Lumma wrote:
>>> * Can Graham and the wiki be synchronized on the spelling?
>>
>> I can copy the wiki page and get all updates on my website at the
>> weekend. (No, it isn't the weekend now.) Currently the names from
>> Gene's original web pages take precedence. That can easily be changed
>> if we agree that the Wiki's authoritative.
>
> I don't care one way or the other, but your way (with the e)
> looks more Greek to me. Is there are right or wrong way on it? -C.

I'm pretty sure it's "kai" in Greek.

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

> Igs declined to name it. I suggested "pseudonym" temperament.
> Gene, is that sonata on archive.org or somewhere?

I'll see if I can dig it up on the composition contest site.

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

> * Why are generators on the wiki sometimes bigger than
> periods? What kind of mappings are these?

That can happen if you go for the most interesting generator--eg, 3/2--instead of the smallest. Why shouldn't it be larger?

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

> I don't care one way or the other, but your way (with the e)
> looks more Greek to me. Is there are right or wrong way on it? -C.
>

I think with the "a" is more correct.

Gene:
>> * Why are generators on the wiki sometimes bigger than
>> periods? What kind of mappings are these?
>
>That can happen if you go for the most interesting generator--eg,
>3/2--instead of the smallest. Why shouldn't it be larger?

I thought we'd agreed on a standard form for these things,
which is all I care about. Do you have a precise method for
choosing what is "most interesting"?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Gene:
> >> * Why are generators on the wiki sometimes bigger than
> >> periods? What kind of mappings are these?
> >
> >That can happen if you go for the most interesting generator--eg,
> >3/2--instead of the smallest. Why shouldn't it be larger?
>
> I thought we'd agreed on a standard form for these things,
> which is all I care about. Do you have a precise method for
> choosing what is "most interesting"?

The mapping under "Map" is the normal val list, a modified Hermite normal form. For the generator for POTE tunings, I pick something I like; I don't see why a standard is required there. When it isn't clear what the generator is approximating, I note that.

Gene wrote:
>The mapping under "Map" is the normal val list, a modified Hermite
>normal form. For the generator for POTE tunings, I pick something I
>like; I don't see why a standard is required there. When it isn't
>clear what the generator is approximating, I note that.

Silly me, I assumed the generator and period tunings would be
ones that worked with the map given.

-Carl

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

> Silly me, I assumed the generator and period tunings would be
> ones that worked with the map given.

I don't bother to give period tunings, and I'm assuming that if someone sees a number like "385.647" they will be able to see it's approximately a major third without me holding their hand. Maybe I shouldn't do that, as not everyone speaks cents. You'd like the using the generator tunings from the map even less, it seems to me, as they can exceed an octave. Of course one can just give the tuning map.

>> Silly me, I assumed the generator and period tunings would be
>> ones that worked with the map given.
>
>I don't bother to give period tunings, and I'm assuming that if
>someone sees a number like "385.647" they will be able to see it's
>approximately a major third without me holding their hand. Maybe I
>shouldn't do that, as not everyone speaks cents. You'd like the using
>the generator tunings from the map even less, it seems to me, as they
>can exceed an octave. Of course one can just give the tuning map.

To me the most useful format would be

name: Hedgehog
family: Porcupine
wedgie: <<6 10 10 2 -1 -5||

2 3 5 7
< . . . . | period (1201.4 cents)
< . . . . | gen1 (164.3 cents)

commas: p1/q1, p2/q2...
eigenmonzos: n1/d1, n2/d2...
MOS: 7, 8, 15, 22...

TE tuning: < 1201.4 1901.6 ... |
TE error: 5.1 cents
TE complexity: etc.
TE badness: etc.

It's a lot like Graham's output, but with the wedgie, commas,
and eigenmonzos, the generator tunings up next to the map, and
a precision of 0.1 cents.

I forget the good properties of the normal val list, but to me
the most useful mapping in working with these things is always
the one with the generator smaller than half the period. It is
easier to construct MOS from, and to look at the map and the
generator tunings and plot it out in my head.

I realize others may have different priorities. I also realize
the above rigid format might impose on the more literary style
of the wiki, which I can sometimes appreciate if I try.

-Carl

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

> I also realize
> the above rigid format might impose on the more literary style
> of the wiki, which I can sometimes appreciate if I try.

The xenwiki has a wide range of styles; part of its charm.