Guaranteed meantone successor

If you look at temperaments with badness less than 20 on the 11-limit catalog, you get, in order of increasing complexity, dicot, augene, meantone, orwell, valentine, myna, miracle, wizard, hemithirds, harry, unidec, tritikleismic, octoid, grendel and hemiennealimmal. Anyone care to pick a guaranteed successor? One strong candidate is meantone as a successor to meantone, as the 11-limit possibilities of meantone (and meanpop) have basically not been explored.

No mohajira or porcupine? I'd have thought one of those.

-Mike

On Tue, Jan 3, 2012 at 9:37 PM, genewardsmith
<genewardsmith@...>wrote:

> **
>
>
> If you look at temperaments with badness less than 20 on the 11-limit
> catalog, you get, in order of increasing complexity, dicot, augene,
> meantone, orwell, valentine, myna, miracle, wizard, hemithirds, harry,
> unidec, tritikleismic, octoid, grendel and hemiennealimmal. Anyone care to
> pick a guaranteed successor? One strong candidate is meantone as a
> successor to meantone, as the 11-limit possibilities of meantone (and
> meanpop) have basically not been explored.
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> No mohajira or porcupine? I'd have thought one of those.

Boost the badness limit up to 22, and you can add august, porcupine, pajara, magic, squares, meanpop, catakleismic, ennealimmic and hemiwürschmidt.

On 1/3/2012 11:06 PM, genewardsmith wrote:
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia<battaglia01@...>
> wrote:
>>
>> No mohajira or porcupine? I'd have thought one of those.
>
> Boost the badness limit up to 22, and you can add august, porcupine,
> pajara, magic, squares, meanpop, catakleismic, ennealimmic and
> hemiw�rschmidt.

I have to question the accuracy of any badness measure that leaves out mohajira and maqamic in favor of dicot, hemithirds (luna), or even meantone and meanpop (which are a bit on the complex side for the accuracy you get in the 11-limit). I've been playing with triforce and I'd expect to see that also on a list of "low badness" temperaments.

I think that TOP error starts to break down around 11-limit and gets worse with higher limits. The reason is that the intervals useful for harmony (such as 11/8 or 11/9) and melody (11/10, 12/11) are so complex that their actual error can be huge. I prefer the results I get from optimizing the superparticular intervals.

My grade A temperament list includes domineering, septimal, dominant, ferrier, porcupine, keemun, mohajira, magic, orwell, hitchcock, miracle, catakleismic, wizard, unidec, harry, supers, octoid, pogo, hemiennealimmal, abigail, and hemienneadecal. Meantone doesn't do as well as you might expect, at grade C, but that's still pretty good as far as temperaments go. I don't know which one you're counting as dicot, but 4&7 is grade A and 4e&7 is grade B.

The grade B list includes arnold, armodue, dichotic, diminished, august, 5e&12e (unnamed dominant), blacksmith, opossum, maqamic, flattone, augene, triforce, 7&27e (unnamed tetracot), pajara, superpyth, meanpop, monkey, valentine, myna, echidna, diaschismic, rodan, garibaldi, zarvo, tritikleismic, guiron, amity, mirkat, and quincy.

I'm thinking of "weasel" for 7&27e because of a comment Neil Haverstick made on the Facebook Xenharmonic Alliance group where he was wondering if there was a "weasel" temperament yet.

I don't expect any of these is likely to displace meantone, but many of them could be worthy competition for augmented and diminished as alternatives to meantone.

On Wed, Jan 4, 2012 at 8:32 PM, Herman Miller <hmiller@...> wrote:
>
> On 1/3/2012 11:06 PM, genewardsmith wrote:
>
> I'm thinking of "weasel" for 7&27e because of a comment Neil Haverstick
> made on the Facebook Xenharmonic Alliance group where he was wondering
> if there was a "weasel" temperament yet.

I suggested "modus" for 7&27e, because of the following reasons:

1) This temperament is absolutely fantastic because of its MODMOS
structure. See the thread I just made about tetracots and weasels for
an analysis.
2) It's far more useful than the actual 5-limit tetracot temperament.
I basically don't ever use "tetracot" by itself.
3) The word "modus" is like "MODMOS."
4) I think that since this is such an important temperament, it should
have a somewhat serious name.

I've lost steam since last night though, when I went on a huge rant
about it. If people really, really want a temperament this good to be
"weasel" temperament, I guess we can do that. But I still think we
should reconsider, even if "modus" isn't the magic bullet.

-Mike

On Wed, Jan 4, 2012 at 8:32 PM, Herman Miller <hmiller@...> wrote:
>
> I have to question the accuracy of any badness measure that leaves out
> mohajira and maqamic in favor of dicot, hemithirds (luna), or even
> meantone and meanpop (which are a bit on the complex side for the
> accuracy you get in the 11-limit). I've been playing with triforce and
> I'd expect to see that also on a list of "low badness" temperaments.

By the way, your list is one of the most sensible I've seen yet. How
are you generating this? You're optimizing around just the
superparticulars in the tonality diamond? How are you weighting
things? Are you factoring prime error into it too?

-Mike

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

> I've lost steam since last night though, when I went on a huge rant
> about it. If people really, really want a temperament this good to be
> "weasel" temperament, I guess we can do that. But I still think we
> should reconsider, even if "modus" isn't the magic bullet.

I've already listed it as modus. If anyone objects, now is the time to do it.

On 1/4/2012 8:44 PM, Mike Battaglia wrote:
> On Wed, Jan 4, 2012 at 8:32 PM, Herman Miller<hmiller@...> wrote:
>>
>> I have to question the accuracy of any badness measure that leaves out
>> mohajira and maqamic in favor of dicot, hemithirds (luna), or even
>> meantone and meanpop (which are a bit on the complex side for the
>> accuracy you get in the 11-limit). I've been playing with triforce and
>> I'd expect to see that also on a list of "low badness" temperaments.
>
> By the way, your list is one of the most sensible I've seen yet. How
> are you generating this? You're optimizing around just the
> superparticulars in the tonality diamond? How are you weighting
> things? Are you factoring prime error into it too?
>

I went over the details in another thread ("Alternative list of best temperaments"). Basically I'm optimizing for all the superparticular intervals from 2/1 to 12/11, without weighting. The practical result of that is that the smaller primes automatically get more weight (since they occur more frequently as factors), but also greater importance is given to the small melodic intervals (which are more sensitive to mistuning), as opposed to theoretical consonances like 11/1.

I also use a different measure for complexity, although it doesn't have a lot of theoretical justification. It does agree pretty well with my intuition as far as which temperaments are more complex, but I still might consider tweaking it if I can come up with better results.