An appeal: can the xenwiki scale articles be written in English?

....and by that I mean, put the technical PhD mathematical terminology 2nd
to a general *musical* description of the structure at hand?

For instance, the xenharmonic wiki on Hobbit scales (
http://xenharmonic.wikispaces.com/Hobbits) defines a "Hobbit" scale as:

"""
Details last edit by [image: genewardsmith]
<http://www.wikispaces.com/user/view/genewardsmith>
genewardsmith<http://www.wikispaces.com/user/view/genewardsmith> Jan
15, 2011 8:23 pm<http://xenharmonic.wikispaces.com/page/diff/Hobbits/193568886>-
14
revisions <http://xenharmonic.wikispaces.com/page/history/Hobbits> [image:
hide details] <http://xenharmonic.wikispaces.com/Hobbits#> Tags

- hobbits <http://xenharmonic.wikispaces.com/tag/view/hobbits>
- math <http://xenharmonic.wikispaces.com/tag/view/math>
- scale <http://xenharmonic.wikispaces.com/tag/view/scale>

edit <http://xenharmonic.wikispaces.com/Hobbits#>
hobbits math scale
Save Cancel <http://xenharmonic.wikispaces.com/Hobbits#>
A *hobbit scale* is a generalization of
MOS<http://xenharmonic.wikispaces.com/MOSScales>for arbitrary regular
temperaments which is a sort of cousin to dwarf
scales <http://xenharmonic.wikispaces.com/Dwarves>; examples may be found on
the Scalesmith <http://xenharmonic.wikispaces.com/Scalesmith> page. Given a
regular temperament and an equal temperament val v which supports (or
belongs to) the temperament, there is a unique scale for the temperament,
which can be tuned to any tuning of the temperament, containing v[1] notes
to the octave.

(AND IT CONTINUES):

To define the hobbit scale we first define a particular
seminorm<http://mathworld.wolfram.com/Seminorm.html>on interval space
derived from a regular temperament, the OE or octave
equivalent seminorm<http://xenharmonic.wikispaces.com/Tenney-Euclidean+metrics>.
This seminorm applies to
monzos<http://xenharmonic.wikispaces.com/Monzos+and+Interval+Space>and
has the property that the seminorm of any comma of the temperament,
and
also of the octave, is 0. This seminorm, for any monzo, is a measure of
complexity of the octave-equivalent pitch class to which the monzo belongs.
Roughly speaking, the hobbit is the scale consisting of the interval of
lowest OE complexity for each scale step mapped to the integer i by the val
v."""

Say What? Whatchu talkin' bout Willis? In English, please?

Okay, so basically, this means it was written for Gene Ward Smith by Gene
Ward Smith (no offense meant, BTW) and some tuning-math compadres, and maybe
a few people who simply swim daily in higher mathematics can parse this
(Paul Hjelmsted, Paul Erlich, etc.).....but can't we simply describe the
properties of these scales according to their *musical* properties? For
example, the size of fifth that makes up this scale can range between blah
and yadda, and it's a hobbit if all the intervals conform to the rule that
bladd yadda bladda, etc, etc......

I fear that this resource will stay useful only to the very very very few,
instead of actually *widening* the scope of musical discovery, we are
narrowing it, and scaring away folks who happen across this page and think
"this stuff is totally for socially clueless geeks and nerds".

Okay, now start throwing the expected tomatoes at me.... ;)

AKJ
--
Aaron Krister Johnson
http://www.akjmusic.com
http://www.untwelve.org

Aaron,

I don't understand most of GWS' math. But,.....

If there is a scala file then its all good. My ear can understand if I find
the tuning useful or not and that is the important part.

Chris

On Mon, Mar 7, 2011 at 4:31 PM, Aaron Krister Johnson <aaron@...>wrote:

>
>
> ....and by that I mean, put the technical PhD mathematical terminology 2nd
> to a general *musical* description of the structure at hand?
>
> For instance, the xenharmonic wiki on Hobbit scales (
> http://xenharmonic.wikispaces.com/Hobbits) defines a "Hobbit" scale as:
>
> """
> Details last edit by [image: genewardsmith]
> <http://www.wikispaces.com/user/view/genewardsmith> genewardsmith<http://www.wikispaces.com/user/view/genewardsmith> Jan
> 15, 2011 8:23 pm<http://xenharmonic.wikispaces.com/page/diff/Hobbits/193568886>- 14
> revisions <http://xenharmonic.wikispaces.com/page/history/Hobbits> [image:
> hide details] <http://xenharmonic.wikispaces.com/Hobbits#> Tags
>
> - hobbits <http://xenharmonic.wikispaces.com/tag/view/hobbits>
> - math <http://xenharmonic.wikispaces.com/tag/view/math>
> - scale <http://xenharmonic.wikispaces.com/tag/view/scale>
>
> edit <http://xenharmonic.wikispaces.com/Hobbits#>
> hobbits math scale
> Save Cancel <http://xenharmonic.wikispaces.com/Hobbits#>
> A *hobbit scale* is a generalization of MOS<http://xenharmonic.wikispaces.com/MOSScales>for arbitrary regular temperaments which is a sort of cousin to dwarf
> scales <http://xenharmonic.wikispaces.com/Dwarves>; examples may be found
> on the Scalesmith <http://xenharmonic.wikispaces.com/Scalesmith> page.
> Given a regular temperament and an equal temperament val v which supports
> (or belongs to) the temperament, there is a unique scale for the
> temperament, which can be tuned to any tuning of the temperament, containing
> v[1] notes to the octave.
>
> (AND IT CONTINUES):
>
> To define the hobbit scale we first define a particular seminorm<http://mathworld.wolfram.com/Seminorm.html>on interval space derived from a regular temperament, the OE or octave
> equivalent seminorm<http://xenharmonic.wikispaces.com/Tenney-Euclidean+metrics>.
> This seminorm applies to monzos<http://xenharmonic.wikispaces.com/Monzos+and+Interval+Space>and has the property that the seminorm of any comma of the temperament, and
> also of the octave, is 0. This seminorm, for any monzo, is a measure of
> complexity of the octave-equivalent pitch class to which the monzo belongs.
> Roughly speaking, the hobbit is the scale consisting of the interval of
> lowest OE complexity for each scale step mapped to the integer i by the val
> v."""
>
> Say What? Whatchu talkin' bout Willis? In English, please?
>
> Okay, so basically, this means it was written for Gene Ward Smith by Gene
> Ward Smith (no offense meant, BTW) and some tuning-math compadres, and maybe
> a few people who simply swim daily in higher mathematics can parse this
> (Paul Hjelmsted, Paul Erlich, etc.).....but can't we simply describe the
> properties of these scales according to their *musical* properties? For
> example, the size of fifth that makes up this scale can range between blah
> and yadda, and it's a hobbit if all the intervals conform to the rule that
> bladd yadda bladda, etc, etc......
>
> I fear that this resource will stay useful only to the very very very few,
> instead of actually *widening* the scope of musical discovery, we are
> narrowing it, and scaring away folks who happen across this page and think
> "this stuff is totally for socially clueless geeks and nerds".
>
> Okay, now start throwing the expected tomatoes at me.... ;)
>
> AKJ
> --
> Aaron Krister Johnson
> http://www.akjmusic.com
> http://www.untwelve.org
>
>
>

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@...> wrote:
>
> ....and by that I mean, put the technical PhD mathematical terminology 2nd
> to a general *musical* description of the structure at hand?

I could give a general sort of explanation of what a hobbit scale is all about, and in fact to some extent I did, but it would be impossible to explain what they actually are without using math.

> Okay, so basically, this means it was written for Gene Ward Smith by Gene
> Ward Smith (no offense meant, BTW) and some tuning-math compadres, and maybe
> a few people who simply swim daily in higher mathematics can parse this
> (Paul Hjelmsted, Paul Erlich, etc.).....but can't we simply describe the
> properties of these scales according to their *musical* properties?

Not in any way that was precise. And I'm writing with the future in mind; the page documents what a hobbit scale is for anyone who might subsequently come along and want to know. Otherwise, people might be left with some scales, but also with a mystery: how were these scales constructed?

For
> example, the size of fifth that makes up this scale can range between blah
> and yadda, and it's a hobbit if all the intervals conform to the rule that
> bladd yadda bladda, etc, etc......

No such description is possible, sorry.

> I fear that this resource will stay useful only to the very very very few,
> instead of actually *widening* the scope of musical discovery, we are
> narrowing it, and scaring away folks who happen across this page and think
> "this stuff is totally for socially clueless geeks and nerds".

I think the cure for that is to write your own pages from your own point of view.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@> wrote:

> > I fear that this resource will stay useful only to the very very very few,
> > instead of actually *widening* the scope of musical discovery, we are
> > narrowing it, and scaring away folks who happen across this page and think
> > "this stuff is totally for socially clueless geeks and nerds".
>
> I think the cure for that is to write your own pages from your own point of view.

That would require that I understand the math enough to translate. I'm not up on 'vals' and so forth. I get "monzos", etc. but the 'val' thing is beyond my understanding and perhaps interest at this point. Maybe Carl or someone like Paul Erlich would be a good candidate for this....we need "tuning math for dummies" at times...

In the meantime, I think one should, ideally, present the scales as cents (IOW, cut to the chase) and then maybe have a *link* (possibly on another page altogether) to the rigorous theory behind it for anyone who happens to be interested. My fear is turning off folks just looking to learn some alternative tunings and finding resources on the wiki only to be scared of by the math wizardry.

AKJ

I'll throw in 2 cents here:
My feeling is things would be best organized like a technical paper,
something like 1) Abstract 2) History, intro, and motivation 3) What was
done very specifically, but as tersely and generally as possible 4) An
example derivation of a particular scale, a written musical example, & an
embedded midi 4) How the tuning is commonly used, its classifications, & its
economy (trade-offs) 5) Future areas to explore 6) Listings of cents,
ratios, related edos 7) Downloadable computer programs in Basic, C, Java,
Maple, Matlab, Maxima, Pari, etc. 8) References

Of course that's not expected, but I was just trying to imagine what format
would make it easiest to understand. Myself, it is frustrating to read a
mathematical description that doesn't describe exactly every algorithm used
so that the tuning is reproducible. The math may be indecipherable at first,
but if someone is interested, they can pick up what bits are necessary -
after all, the motivation for creating a scale often derives directly from
the elegance of the mathematical forms themselves. Scanning back and forth
through the sections in such a format should provide a reader with
everything necessary to understand a given term as well as its desiderata.

But I'm with Gene, better to get something down than nothing at all.
References can include sites like Graham's that provide a more general
introduction.

I will say I often have an easier time understanding the math of things, including tuning theory, if it's presented as code/algorithm rather than a symbolic abstract relation. Sometimes, seeing things like what Gene is doing as Python code (which I grok much much better than C/C++, because Python is the most cleanly thought out human-readable language in history) for example, will make me say, "oh--okay---it's really quite a simple concept". I guess that why I get annoyed by the culture of needless abstraction in much mathematics.

AKJ

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> I'll throw in 2 cents here:
> My feeling is things would be best organized like a technical paper,
> something like 1) Abstract 2) History, intro, and motivation 3) What was
> done very specifically, but as tersely and generally as possible 4) An
> example derivation of a particular scale, a written musical example, & an
> embedded midi 4) How the tuning is commonly used, its classifications, & its
> economy (trade-offs) 5) Future areas to explore 6) Listings of cents,
> ratios, related edos 7) Downloadable computer programs in Basic, C, Java,
> Maple, Matlab, Maxima, Pari, etc. 8) References
>
> Of course that's not expected, but I was just trying to imagine what format
> would make it easiest to understand. Myself, it is frustrating to read a
> mathematical description that doesn't describe exactly every algorithm used
> so that the tuning is reproducible. The math may be indecipherable at first,
> but if someone is interested, they can pick up what bits are necessary -
> after all, the motivation for creating a scale often derives directly from
> the elegance of the mathematical forms themselves. Scanning back and forth
> through the sections in such a format should provide a reader with
> everything necessary to understand a given term as well as its desiderata.
>
> But I'm with Gene, better to get something down than nothing at all.
> References can include sites like Graham's that provide a more general
> introduction.
>

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

> That would require that I understand the math enough to translate.
> I'm not up on 'vals' and so forth. I get "monzos", etc. but the
> 'val' thing is beyond my understanding and perhaps interest at
> this point. Maybe Carl or someone like Paul Erlich would be a good
> candidate for this....we need "tuning math for dummies" at times...
>
> In the meantime, I think one should, ideally, present the scales
> as cents (IOW, cut to the chase) and then maybe have a *link*
> (possibly on another page altogether) to the rigorous theory
> behind it for anyone who happens to be interested. My fear is
> turning off folks just looking to learn some alternative tunings
> and finding resources on the wiki only to be scared of by the
> math wizardry.

Gene is doing an unbelievable job coming up with stuff and
documenting it. I don't think we should be shy about putting
the math front and center. However I do strongly disagree
with some of Gene's sentiments about it being impossible to
explain stuff in musical terms too. I personally miss
Paul Erlich's unique ability to do that on tuning-math. I do
the best I can on these lists. I've been avoiding the wiki
because it seems like a major new timesink, though I have made
some edits there. Also I'm wary of putting a lot of effort
into wikispaces' system, though this gives some reassurance

http://xenharmonic.wikispaces.com/backing+up+this+wiki

-Carl

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

> In the meantime, I think one should, ideally, present the scales as cents (IOW, cut to the chase) and then maybe have a *link* (possibly on another page altogether) to the rigorous theory behind it for anyone who happens to be interested.

Isn't that what I've done?

> My fear is turning off folks just looking to learn some alternative tunings and finding resources on the wiki only to be scared of by the math wizardry.

I'll repeat my suggestion: write the articles you think are needed.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
Also I'm wary of putting a lot of effort
> into wikispaces' system, though this gives some reassurance
>
> http://xenharmonic.wikispaces.com/backing+up+this+wiki

There's also this:

http://xenharmonic.wikispaces.com/WebCite+citations

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "akjmicro" <aaron@> wrote:
>
> > That would require that I understand the math enough to translate.
> > I'm not up on 'vals' and so forth. I get "monzos", etc. but the
> > 'val' thing is beyond my understanding and perhaps interest at
> > this point. Maybe Carl or someone like Paul Erlich would be a good
> > candidate for this....we need "tuning math for dummies" at times...
> >
> > In the meantime, I think one should, ideally, present the scales
> > as cents (IOW, cut to the chase) and then maybe have a *link*
> > (possibly on another page altogether) to the rigorous theory
> > behind it for anyone who happens to be interested. My fear is
> > turning off folks just looking to learn some alternative tunings
> > and finding resources on the wiki only to be scared of by the
> > math wizardry.
>
> Gene is doing an unbelievable job coming up with stuff and
> documenting it.

Sure, sure!

> I don't think we should be shy about putting
> the math front and center.

I do. But I guess I'm coming at it from the point-of-view of a musician, and that's supposed to be the purpose of a tuning system.

> However I do strongly disagree
> with some of Gene's sentiments about it being impossible to
> explain stuff in musical terms too. I personally miss
> Paul Erlich's unique ability to do that on tuning-math.

I suspect it probably is possible, too. Maybe we can rope Paul back into the fold.

AKJ

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I've been avoiding the wiki
> because it seems like a major new timesink, though I have made
> some edits there.

The wiki is probably a much more fruitful place than these lists at this point. I look at it as the accumulation (in a nutshell) of the basic thrust of activity here.

In any event, having a central location for tuning knowledge like that is a gift, we all owe Jacob Barton a hearty thank you for setting it up. Beats the hell out of search function in Yahoo, that's for sure.

AKJ

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

> In any event, having a central location for tuning knowledge
> like that is a gift, we all owe Jacob Barton a hearty thank
> you for setting it up. Beats the hell out of search function
> in Yahoo, that's for sure.

I don't know when you last used it, but it was upgraded recently
and is now basically the best search function of any website
that I use.

-Carl

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

> > Also I'm wary of putting a lot of effort
> > into wikispaces' system, though this gives some reassurance
> >
> > http://xenharmonic.wikispaces.com/backing+up+this+wiki
>
> There's also this:
>
> http://xenharmonic.wikispaces.com/WebCite+citations

That's pretty cool. -Carl

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

> Also I'm wary of putting a lot of effort
> into wikispaces' system, though this gives some reassurance
>
> http://xenharmonic.wikispaces.com/backing+up+this+wiki

You know, if you were to become more involved you could not only write comprehensible articles, you could save backups.

Aaron wrote:

> That would require that I understand the math enough to
> translate. I'm not up on 'vals' and so forth. I get "monzos",
> etc. but the 'val' thing is beyond my understanding and perhaps
> interest at this point.

If you understand monzos you know what vals are! They form
an isomorphic dual Z-module to the monzos. Just as an interval
may be regarded as a Z-linear combination of basis elements
representing the prime numbers, a val may be regarded as a
Z-linear combination of a dual basis, consisting of the p-adic valuations (from which vals take their name).

That's how Gene might say it, though I probably made a gaffe
stitching it together. Here's how I would say it:

A monzo tells you the size of a just intonation ratio in
terms of primes. A val tells you the size of a temperament's
generator in terms of primes. If you multiply a val and a
monzo, you get the size of the ratio in steps of the temperament.

-Carl

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

> A monzo tells you the size of a just intonation ratio in
> terms of primes. A val tells you the size of a temperament's
> generator in terms of primes.

A monzo tells you the prime factorization of a JI ratio is one way to put it, but Aaron already has that figured out. A val gives you an integer when applied to a monzo, and therefore when applied to a p-limit just intonation ratio. For example, <12 19 28| is a val, and if you apply it to |-1 1 0>, the monzo for 3/2 = 2^(-1) 3^1 5^0, you get
<12 19 28|-1 1 0> = -12+19 = 7, and that tells you that there are seven steps in 12et to get to the fifth from the unison. Also, <0 1 4| is a val, and that counts generator steps in meantone. These are typical examples, and you can see they are quite different.

If you multiply a val and a
> monzo, you get the size of the ratio in steps of the temperament.

Calling the inner product "multiplication" is like calling a Debussy prelude a "song"; meaning, it's something which should not be done. Though I admit it's called a "product", so the fault may lie with mathematicians. If you want to make it into a multiplication, you would need to consider a val to be a 1xn integral matrix and a monzo an nx1 integral matrix, so the result would be a 1x1 integral matrix, which you would treat as an integer. Sort of a headache, and not standard. More standard would be row vectors and column vectors, but that gets us back to the problem that it's called a "product" but not "multiplication".

Gene wrote:

> > A monzo tells you the size of a just intonation ratio in
> > terms of primes. A val tells you the size of a temperament's
> > generator in terms of primes.
>
> A monzo tells you the prime factorization of a JI ratio is one
> way to put it, but Aaron already has that figured out.

Uh... you have to say something they already know to fix
the words you're using.

>> If you multiply a val and a monzo, you get the size of the
>> ratio in steps of the temperament.
>
> Calling the inner product "multiplication" is like calling a
> Debussy prelude a "song"; meaning, it's something which should
> not be done.

OK thanks, I'll use "product" in the future.

The important point is that you don't offer things like this
to people like Aaron. It's important because you have great
ideas that only you understand. My guess is you don't because
your brain just doesn't work that way. But that is not how
everyone explains such failure. And there are experts writing
things in places who do not have this excuse.
See also: http://www.youtube.com/watch?v=hpjwotips7E

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
My guess is you don't because
> your brain just doesn't work that way.

My brain certainly doesn't work like Feynmann's who had an ability to simplify problems matched by no one else I can think of. But as for that lecture, I'd take some of what was said with a grain of salt; Feynmann in one of his books talked of a similar intellectual battle with mathematicians over the Banach-Tarski paradox where he declared victory. But just because he was willing to declare victory does not mean that in any meaningful sense he proved his original intuition, which was that it couldn't be true. Susskind seemed to think Feynmann scored a victory over a couple of philosophers on one occasion, and perhaps he did. But some of the rest of what he said was garbage, frankly, so who knows.

In any case, if you are assuming the definition of for example how a hobbit is constructed could be radically simplified based on some anecdotes about Feynmann's exploits, you are assuming way too much. And definitions can get so much more difficult than that it's dubious to pick on me as a bad example. Try the definitions of a vertex operator algebra or a scheme, to give two very important mathematical definitions, if you don't believe me. if no one has radically simplified these, despite their importance, could it be because it can't be done?

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

> Feynmann in one of his books talked of a similar intellectual
> battle with mathematicians over the Banach-Tarski paradox where
> he declared victory. But just because he was willing to declare
> victory does not mean that in any meaningful sense he proved his
> original intuition, which was that it couldn't be true.

Funny you should mention that
http://www.youtube.com/watch?v=SczraSQE3MY

> But some of the rest of what he said was garbage, frankly,
> so who knows.

Feynman or Susskind?

> In any case, if you are assuming the definition of for example
> how a hobbit is constructed could be radically simplified based
> on some anecdotes about Feynmann's exploits, you are assuming
> way too much.

I don't know why you say that - hobbits are quite simple.

> Try the definitions of a vertex operator algebra or a scheme,
> to give two very important mathematical definitions, if you
> don't believe me. if no one has radically simplified these,
> despite their importance, could it be because it can't be done?

I doubt it.

-Carl

I've read a fair amount of stuff on the wiki, and while I'm not averse
to math, this is math with which I'm not familiar, which makes it hard
to relate to. To learn about vals, you have to go to another page to
learn about abelian groups, and that page presumes a knowledge of
set-theoretical notation, etc.

If it's possible to add content that explains the concepts without
requiring a background in all the notation, and if the explanation of
certain concepts (e.g., abelian groups) can be done in a way that
excises the stuff most of us don't need, that would help. The
Wikipedia article on abelian groups is for the general mathematician;
it seems that the xenharmonic wiki should give an article that's for
xenharmonic musicians.

Of course, I'm depending on the work of others to get that done, so
I'm grateful for whatever I get.

Speaking of grateful, Gene's giving examples, and I want to thank him
for that. :)

Gene said:
> For example, <12 19 28| is a val, and if you
> apply it to |-1 1 0>, the monzo for 3/2
> = 2^(-1) 3^1 5^0, you get
> <12 19 28|-1 1 0> = -12+19 = 7, and that
> tells you that there are seven steps in 12et
> to get to the fifth from the unison.

This is good, in a monkey-see-monkey-do sort of way (which is,
honestly, what I'm looking for).

Octave monzo: 2/1 = (2^1)*(3^0)*(5^0), or |1 0 0>.
Product of octave monzo and the 12TET val: 1*12 + 0*19 + 0*28 = 12
steps to an octave.

M3 monzo: 5/4 = (2^-2)*(3^0)*(5^1), or |-2 0 1>.
Product: -2*12 + 0*19 + 1*28 = 4 steps to the M3.

m3 monzo: 6/5 = |1 1 -1>.
Product: <12 19 28| 1 1 -1> = 12*1 + 19*1 + 28*-1 = 31-28 = 3 steps to the m3.

Good! That's really cool. I don't know why it works, but I was an
engineer, not a mathematician, and I'm willing to press the "I
believe" button. :)

I don't get how this works if you extend to other primes, though.

Here's the septimal m3 I love so much:
7/6 = 2^-1 3^-1 5^0 7^1, or |-1 -1 0 1>. It should land on Eb, the 3rd
step of 12TET.

But, in my monkey-see-monkey-do way, it looks like <12 19 28 |-1 -1 0
1> would be -12-19 = -31. (I'm presuming that there's an implied zero
in the spot for 7.) 31 steps down from C is F, so it's not just
weird-looking: I must be wrong. Interestingly, though perhaps
coincidentally, 31-28 = 3, which would have been the right answer.

It seems like I need to understand the val better. How are 2^12, 3^19,
and 5^28 related to a generator for 12TET?

And do I need to extend the val if I'm working with monzos with more primes?

> Also, <0 1 4| is a val, and that counts
> generator steps in meantone. These are
> typical examples, and you can see they are
> quite different.

I'm sure someone can see. :)

M3 monzo: 5/4 = |-2 0 1>.
Product: <0 1 4| -2 0 1> = 0*-2 + 1*0 + 4*1 = 4 steps to the M3. Good!
But is it just coincidence?

Octave monzo: 2/1 = |1 0 0>.
Product of octave monzo and the meantone val: <0 1 4|1 0 0> = 0*1 +
1*0 + 4*0 = 0. Bad.

m3 monzo: 6/5 = |1 1 -1>.
Product: <0 1 4| 1 1 -1> = 0*1 + 1*1 + 4*-1 = -3. Bad.

I clearly don't get it.

Regards,
Jake

On 3/8/11, genewardsmith <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
>> A monzo tells you the size of a just intonation ratio in
>> terms of primes. A val tells you the size of a temperament's
>> generator in terms of primes.
>
> A monzo tells you the prime factorization of a JI ratio is one way to put
> it, but Aaron already has that figured out. A val gives you an integer when
> applied to a monzo, and therefore when applied to a p-limit just intonation
> ratio. For example, <12 19 28| is a val, and if you apply it to |-1 1 0>,
> the monzo for 3/2 = 2^(-1) 3^1 5^0, you get
> <12 19 28|-1 1 0> = -12+19 = 7, and that tells you that there are seven
> steps in 12et to get to the fifth from the unison. Also, <0 1 4| is a val,
> and that counts generator steps in meantone. These are typical examples, and
> you can see they are quite different.
>
> If you multiply a val and a
>> monzo, you get the size of the ratio in steps of the temperament.
>
> Calling the inner product "multiplication" is like calling a Debussy prelude
> a "song"; meaning, it's something which should not be done. Though I admit
> it's called a "product", so the fault may lie with mathematicians. If you
> want to make it into a multiplication, you would need to consider a val to
> be a 1xn integral matrix and a monzo an nx1 integral matrix, so the result
> would be a 1x1 integral matrix, which you would treat as an integer. Sort of
> a headache, and not standard. More standard would be row vectors and column
> vectors, but that gets us back to the problem that it's called a "product"
> but not "multiplication".
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

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

> > But some of the rest of what he said was garbage, frankly,
> > so who knows.
>
> Feynman or Susskind?

Susskind.

> I don't know why you say that - hobbits are quite simple.

Unless you simply want to present a lot of unmotivated matrix computations, you will need to explain the idea behind it, which means to explain in some manner or another octave-equivalent Tenney-Euclidean complexity. The best way I know to understand that is geometrically. So how do you make it simple?

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:

> If it's possible to add content that explains the concepts without
> requiring a background in all the notation, and if the explanation of
> certain concepts (e.g., abelian groups) can be done in a way that
> excises the stuff most of us don't need, that would help.

I could try, but it's my explanations people are complaining about in the first place. If someone knows of where I could find simple explanations of, for instance, what "abelian group" means it would surely help.

> I don't get how this works if you extend to other primes, though.

It's based on the fact that in 12edo, the 2 takes 12 steps, the 3 19 steps, and the 5 28 steps. So, if you wanted to find what 12 uses for a 7, you could try 12*log2(7) = 33.688, which rounds to 34. This, in fact, is the correct answer, so the 12et septimal val is <12 19 28 34|. If you look at 11, 12*log2(11) = 41.513, which is just about half way between 41 and 42, so it's not so clear which one to pick. However, if you look at 5 and 7, they are rounded up (are sharp), so you would round up to 42. This gives the correct unidecimal val for 12, which happens to be the "patent val", the one obtained by rounding to the nearest integer: <12 19 28 34 42|.

> Here's the septimal m3 I love so much:
> 7/6 = 2^-1 3^-1 5^0 7^1, or |-1 -1 0 1>. It should land on Eb, the 3rd
> step of 12TET.

Except you need to use the septimal val, so it's <12 19 28 34|-1 -1 0 1> = -12-19+0+34 = 3.

> It seems like I need to understand the val better. How are 2^12, 3^19,
> and 5^28 related to a generator for 12TET?

They aren't; vals are not monzos.

> M3 monzo: 5/4 = |-2 0 1>.
> Product: <0 1 4| -2 0 1> = 0*-2 + 1*0 + 4*1 = 4 steps to the M3. Good!
> But is it just coincidence?
>
> Octave monzo: 2/1 = |1 0 0>.
> Product of octave monzo and the meantone val: <0 1 4|1 0 0> = 0*1 +
> 1*0 + 4*0 = 0. Bad.

Nope, good. If C is 0, then C' had better be 0 also, because you don't go up or down the chain of fifths to reach it.

>
> m3 monzo: 6/5 = |1 1 -1>.
> Product: <0 1 4| 1 1 -1> = 0*1 + 1*1 + 4*-1 = -3. Bad.

Again, good. Going down the chain of fifths, C to F to Bb to Eb goes -3 generator steps if a fifth is the generator.

I get it. The val relates to the number of generator-sized steps for each prime; it's not like the monzo, in which you're relating things to the powers of primes, and it's not related to steps of the scale (except indirectly).

Gene, this was great, and has helped me immensely. Although it'll take a little time, I'll try writing some of it up for newbies on the wiki.

Regards,
Jake

> --- In tuning@yahoogroups.com, Jake Freivald<jdfreivald@...> wrote:
>
>> If it's possible to add content that explains the concepts without
>> requiring a background in all the notation, and if the explanation of
>> certain concepts (e.g., abelian groups) can be done in a way that
>> excises the stuff most of us don't need, that would help.
> I could try, but it's my explanations people are complaining about in the first place. If someone knows of where I could find simple explanations of, for instance, what "abelian group" means it would surely help.
>
>> I don't get how this works if you extend to other primes, though.
> It's based on the fact that in 12edo, the 2 takes 12 steps, the 3 19 steps, and the 5 28 steps. So, if you wanted to find what 12 uses for a 7, you could try 12*log2(7) = 33.688, which rounds to 34. This, in fact, is the correct answer, so the 12et septimal val is<12 19 28 34|. If you look at 11, 12*log2(11) = 41.513, which is just about half way between 41 and 42, so it's not so clear which one to pick. However, if you look at 5 and 7, they are rounded up (are sharp), so you would round up to 42. This gives the correct unidecimal val for 12, which happens to be the "patent val", the one obtained by rounding to the nearest integer:<12 19 28 34 42|.
>
>> Here's the septimal m3 I love so much:
>> 7/6 = 2^-1 3^-1 5^0 7^1, or |-1 -1 0 1>. It should land on Eb, the 3rd
>> step of 12TET.
> Except you need to use the septimal val, so it's<12 19 28 34|-1 -1 0 1> = -12-19+0+34 = 3.
>
>> It seems like I need to understand the val better. How are 2^12, 3^19,
>> and 5^28 related to a generator for 12TET?
> They aren't; vals are not monzos.
>
>> M3 monzo: 5/4 = |-2 0 1>.
>> Product:<0 1 4| -2 0 1> = 0*-2 + 1*0 + 4*1 = 4 steps to the M3. Good!
>> But is it just coincidence?
>>
>> Octave monzo: 2/1 = |1 0 0>.
>> Product of octave monzo and the meantone val:<0 1 4|1 0 0> = 0*1 +
>> 1*0 + 4*0 = 0. Bad.
> Nope, good. If C is 0, then C' had better be 0 also, because you don't go up or down the chain of fifths to reach it.
>
>> m3 monzo: 6/5 = |1 1 -1>.
>> Product:<0 1 4| 1 1 -1> = 0*1 + 1*1 + 4*-1 = -3. Bad.
> Again, good. Going down the chain of fifths, C to F to Bb to Eb goes -3 generator steps if a fifth is the generator.
>
>
>

Gene wrote:

>>> But some of the rest of what he said was garbage, frankly,
>>> so who knows.
>>
>> Feynman or Susskind?
>
> Susskind.

I'd like to know what. Write me offlist if you feel it's
more appropriate.

>> I don't know why you say that - hobbits are quite simple.
>
> Unless you simply want to present a lot of unmotivated matrix
> computations, you will need to explain the idea behind it,
> which means to explain in some manner or another octave-
> equivalent Tenney-Euclidean complexity. The best way I know to
> understand that is geometrically. So how do you make it simple?

I worked out a suggestion and posted it to the talk page, but
the wikispaces talk page is useless. I just checked out wikia
and it's somewhat better, though still not as good as a real
mediawiki instance.

For now, I continue here:

**Hobbits**

In 2001 it was discovered that [MOS] scales correspond to rank 2 regular temperamnts. For a regular temperament of arbitrary rank, there is a corroseponding hobbit scale (named for their relationship to [dwarf scales]). Examples may be found on the [Scalesmith] page.

*Definition*

Given a regular tempearment, we first find an equal temperament [val] v which supports it. Next, we define an [octave equivalent seminorm] for the temperament. This seminorm applies to monzos and sends any comma of the temperament, and also the octave, to zero. It measures the complexity of the octave-equivalent pitch class to which a monzo belongs. For example, in meantone temperament, the OE seminorm of 3/2 is ___ and of 3/1 is ___ and of 25/16 is ___. Roughly speaking, the hobbit is the scale consisting of the lowest OE complexity for each scale step mapped to the integer i by v (see [epimorphic] for details).

In the rank 2 case, the hobbit for v is identical to the MOS for v because...

*Examples*

Consider the 7-note hobbit for meantone temperament ... yields the familiar diatonic scale (MOS)...

Next, consider the 22-note hobbit for minerva temperament...

*Details*

Denoting the OE seminorm...

-Carl

On 9 March 2011 10:22, Carl Lumma <carl@...> wrote:

> **Hobbits**
>
> In 2001 it was discovered that [MOS] scales correspond to rank 2 regular temperamnts. For a regular temperament of arbitrary rank, there is a corroseponding hobbit scale (named for their relationship to [dwarf scales]).  Examples may be found on the [Scalesmith] page.

It's not clear to me what wasn't already obvious in 2000 or why
anybody should care in an introduction to hobbits.

> *Definition*
>
> Given a regular temperament, we first find an equal temperament [val] v which supports it. Next, we define an [octave equivalent seminorm] for the temperament. This seminorm applies to monzos and sends any comma of the temperament, and also the octave, to zero. It measures the complexity of the octave-equivalent pitch class to which a monzo belongs. For example, in meantone temperament, the OE seminorm of 3/2 is ___ and of 3/1 is ___ and of 25/16 is ___. Roughly speaking, the hobbit is the scale consisting of the lowest OE complexity for each scale step mapped to the integer i by v (see [epimorphic] for details).

I don't think this is superior to the equivalent paragraph on the
wiki. What use are the examples? You won't understand temperamental
complexity from two data points. (It should be obvious that 3/2 and
3/1 are octave equivalent.)

> In the rank 2 case, the hobbit for v is identical to the MOS for v because...

... any seminorm applied to an octave-equivalent rank 2 temperament
will be counting generator steps.

> *Details*
>
> Denoting the OE seminorm...

That's it, isn't it? You make it simple by hiding all the difficult bits.

My opinion is that hobbits are an extremely advanced concept. In
musical terms, they require regular temperaments of rank three or
higher. They assume you've chosen such a temperament without knowing
what scale you want to use. Mathematically, they require you to find
a string of short vectors in a way that I haven't worked out and I'm
not sure if even Gene has automated. I don't think it's the jargon
that's holding us back.

It's a lousy example of an obscure page. You need a high level of
mathematical ability to calculate hobbits. If the page doesn't
explain that clearly, somebody needs to criticize it from a point of
view of understanding the mathematics. If you don't understand the
mathematics it won't be helpful to you. It isn't cloaking some
musically intuitive concept in jargon.

What would help is a short introduction on the Scalesmith page.

Graham

Graham wrote:

>> In 2001 it was discovered that [MOS] scales correspond to
>> rank 2 regular temperamnts. For a regular temperament of
>> arbitrary rank, there is a corroseponding hobbit scale
>> (named for their relationship to [dwarf scales]).  Examples
>> may be found on the [Scalesmith] page.
>
> It's not clear to me what wasn't already obvious in 2000 or
> why anybody should care in an introduction to hobbits.

2001 was a place holder. I haven't gone back and looked.
The key discovery was 2000, but IIRC not all the pieces
regarding fractional-octave periods, rank vs codimension, etc
were in place.

It's there because hobbits are generalizations of MOS for
arbitrary ranks.

> I don't think this is superior to the equivalent paragraph on
> the wiki. What use are the examples?

Noted. Your track record of writing impenetrable pedagogical
materials is also noted.

> (It should be obvious that 3/2 and 3/1 are octave equivalent.)

It's a lot like unit testing. You write tests even when
the answer's obvious (to you).

>> In the rank 2 case, the hobbit for v is identical to the
>> MOS for v because...
>
> ... any seminorm applied to an octave-equivalent rank 2
> temperament will be counting generator steps.

Good. Another sentence or two would wrap up the paragraph.

>> *Details*
>>
>> Denoting the OE seminorm...
>
> That's it, isn't it? You make it simple by hiding all the
> difficult bits.

I don't hid them, I just don't retype them.

> My opinion is that hobbits are an extremely advanced concept.

My opinion is that if you can't explain scales of rank 3
temperaments to brilliant musicians and Python hackers like
Aaron, you should quit music theory for life.

> In musical terms, they require regular temperaments of rank
> three or higher.

Since you seem to be corroborating my guess that they are
equivalent to MOS in rank 2, that is hardly the case.

> They assume you've chosen such a temperament without knowing
> what scale you want to use.

...which is the whole point of doing temperament searches.

> Mathematically, they require you to find a string of short
> vectors in a way that I haven't worked out and I'm not sure
> if even Gene has automated. I don't think it's the jargon
> that's holding us back.

Aaron doesn't need to generate them himself, since Gene's
got a page full of them. He isn't the first reasonable,
intelligent, sincere microtonal musician to complain about
the writing on the xenwiki.

-Carl

On 9 March 2011 12:23, Carl Lumma <carl@...> wrote:

> Noted.  Your track record of writing impenetrable pedagogical
> materials is also noted.

Thanks for the gratuitous insult.

>>> Denoting the OE seminorm...
>>
>> That's it, isn't it?  You make it simple by hiding all the
>> difficult bits.
>
> I don't hid them, I just don't retype them.

I can't see them.

>> My opinion is that hobbits are an extremely advanced concept.
>
> My opinion is that if you can't explain scales of rank 3
> temperaments to brilliant musicians and Python hackers like
> Aaron, you should quit music theory for life.

And another insult!

Show me your code for calculating hobbits.

>> In musical terms, they require regular temperaments of rank
>> three or higher.
>
> Since you seem to be corroborating my guess that they are
> equivalent to MOS in rank 2, that is hardly the case.

Why would you be reading a page on hobbits to learn about MOS?

>> They assume you've chosen such a temperament without knowing
>> what scale you want to use.
>
> ...which is the whole point of doing temperament searches.

Is not.

> Aaron doesn't need to generate them himself, since Gene's
> got a page full of them.  He isn't the first reasonable,
> intelligent, sincere microtonal musician to complain about
> the writing on the xenwiki.

Right, he doesn't need to generate them. So his complaint has no merit.

Graham

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

> I can't see them.

They're already on the xenwiki page in question.

> Why would you be reading a page on hobbits to learn about MOS?

I can't decide which wrongheaded aspect of this question
to address.

>>> They assume you've chosen such a temperament without knowing
>>> what scale you want to use.
>>
>> ...which is the whole point of doing temperament searches.
>
> Is not.

To make music you need a scale. Temperament searches are
supposed to tell us what scales to use and how to use them.

>> Aaron doesn't need to generate them himself, since Gene's
>> got a page full of them.  He isn't the first reasonable,
>> intelligent, sincere microtonal musician to complain about
>> the writing on the xenwiki.
>
> Right, he doesn't need to generate them. So his complaint
> has no merit.

This is more insulting than anything I wrote.

-Carl

On 9 March 2011 12:41, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>> Right, he doesn't need to generate them.  So his complaint
>> has no merit.
>
> This is more insulting than anything I wrote.

I don't see an insult. I addressed the argument, not the man. I've
done that consistently. In this thread so far, you've told me I'm not
competent to do my job, that I'm not a reasonable, intelligent,
sincere musician and that I should quit music theory. I'm not
continuing this argument under those circumstances.

Graham

On 8 March 2011 03:36, akjmicro <aaron@...> wrote:
> I will say I often have an easier time understanding the math of things, including tuning theory, if it's presented as code/algorithm rather than a symbolic abstract relation. Sometimes, seeing things like what Gene is doing as Python code (which I grok much much better than C/C++, because Python is the most cleanly thought out human-readable language in history) for example, will make me say, "oh--okay---it's really quite a simple concept". I guess that why I get annoyed by the culture of needless abstraction in much mathematics.

I hope you know, then, that I have a lot of Python code here:

http://x31eq.com/temper/regular.zip

It covers a fair bit. It uses vals a lot but I don't use the term
"val" anywhere that I can remember. It doesn't do hobbits. That's
because I'm genuinely unable to generate hobbits in Python. I think
it's difficult. Maybe one day you or I or somebody else will write
the code and then we can look at it to decide how difficult the
problem really is.

You may be able to adapt the code for finding mappings to give
hobbits. I think they're analogous problems. Unfortunately, that
code isn't at all simple :-(

I've got somewhere with Pari/GP. The code for that is here:

http://x31eq.com/parametric.gp

Naturally, anything that can be done with Pari can also be done with
Sage, where Python is the scripting language. I don't have Sage
installed here and now so I haven't done that. I don't think it would
make much difference. GP isn't as nice as Python but there isn't much
syntax involved.

The (semi)norm that hobbits minimize is temperamental complexity. The
functions are there in GP to calculate it. By trial and error you can
find the intervals of minimal complexity for a given number of scale
steps. I don't have a cleaner way of finding the hobbit.

The octave equivalent function isn't there. That's because I'm not
happy with it. You can find my comments on tuning-math. Or, use
Gene's alternative method for getting hobbit pitches within the octave
from an octave-specific function.

Gene has said that finding each pitch of the hobbit maps to finding
the shortest vector in a lattice. I haven't been able to work that
out. Maybe it isn't that difficult, but it is at least more
appropriate for tuning-math.

Note that the "meantone scale" in my GP code is solving a hobbit-like
problem. Maybe that could be adapted to produce hobbits with
octave-equivalent vectors. Have a look at it if you like. Note, at
least, that Pari is capable of finding shortest vectors in certain
lattices. I don't have such functions in Python -- other than by
accessing Pari through Sage.

Graham

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

> I don't see an insult. I addressed the argument, not the man.
> I've done that consistently. In this thread so far, you've
> told me I'm not competent to do my job, that I'm not a
> reasonable, intelligent, sincere musician and that I should
> quit music theory. I'm not continuing this argument under
> those circumstances.

I said none of those things. I said you have a track record
of writing impenetrable materials, which is true. I will also
say that your attitude from your first reply has been piss poor.
Your remark that Aaron's request has no merit may or may not
be construed as an insult to Aaron, but it certainly is a
grade A example of the elitist bullshit you claim tuning-math
is not suffering from.

-Carl

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

> > > But some of the rest of what he said was garbage, frankly,
> > > so who knows.
> >
> > Feynman or Susskind?
>
> Susskind.

I haven't gotten anything from you, and I would genuinely
like to know. It seemed to me he only relayed a few anecdotes,
and explained two technical things (one on liquid helium, one
on QCD). -Carl

Gene wrote:

> I'll repeat my suggestion: write the articles you think are needed.

Yeah, Aaron, simply write the content you are trying to learn.
Duh!

> You know, if you were to become more involved you could not only
> write comprehensible articles, you could save backups.

I'd love to. You can see, however, that my good-faith effort to
improve an article after someone criticized it has been met with
silence and contempt. Shall I give up?

-Carl

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

> > Susskind.
>
> I haven't gotten anything from you, and I would genuinely
> like to know. It seemed to me he only relayed a few anecdotes,
> and explained two technical things (one on liquid helium, one
> on QCD). -Carl

He said that these two philosophers were being pretentious because they were using terms like "idealism", which is exactly like saying physicists are pretentious for using terms like "photon". He also said that since the question of when a machine is or isn't conscious is a scientific question, Feynmann could easily demolish his opponents. But the question has not yet been reduced to one of science, and may never be. It's easy to see that a finite state automaton can reproduce any behavior, which suggests it may be impossible in principle to determine consciousness from behavior.

Scientists as amateur philosophers are no better than any other educated person from what I have seen, and are quite likely to think they are better at it than they are.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > I'll repeat my suggestion: write the articles you think are needed.
>
> Yeah, Aaron, simply write the content you are trying to learn.
> Duh!

Aaron is perfectly capable of adding content. It hardly needs to be attempts to explain mathemematical terminology.

Major DUH!

> I'd love to. You can see, however, that my good-faith effort to
> improve an article after someone criticized it has been met with
> silence and contempt. Shall I give up?

I've paid attention to what you said about the hobbit article. I'll see if I can improve it.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > > But some of the rest of what he said was garbage, frankly,
> > > so who knows.
> >
> > Feynman or Susskind?
>
> Susskind.
>
> > I don't know why you say that - hobbits are quite simple.
>
> Unless you simply want to present a lot of unmotivated matrix computations, you will need to explain the idea behind it, which means to explain in some manner or another octave-equivalent Tenney-Euclidean complexity. The best way I know to understand that is geometrically. So how do you make it simple?
>

A picture? :) I'm thinking something like what Ikea does in their instructions for building furniture---they use no words. It's often very powerful, if the picture is well drawn, which sometimes it isn't...

AKJ

Thanks Graham,

I'll have a look at this when I have the time.

It's an interesting question whether a complex thing like Hobbits can be meaningfully conveyed in simpler terms. I always default to the idea that a picture is worth a thousand words. The brain is hard-wired to immediately pick up meaning in visual shapes that would be lost in mounds of symbolic data. I wonder if someone could explain the math of hobbit-construction visually?

I appreciate your willingness to share code, and I'm sorry to have inadvertantly started a flame-war between you and Carl...not my intention. I'm grateful for the authors of the xenwiki for what they've done, I'm just seeking for ways to maybe allowing it to communicate to a less-specialized audience.

Best,
AKJ

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> On 8 March 2011 03:36, akjmicro <aaron@...> wrote:
> > I will say I often have an easier time understanding the math of things, including tuning theory, if it's presented as code/algorithm rather than a symbolic abstract relation. Sometimes, seeing things like what Gene is doing as Python code (which I grok much much better than C/C++, because Python is the most cleanly thought out human-readable language in history) for example, will make me say, "oh--okay---it's really quite a simple concept". I guess that why I get annoyed by the culture of needless abstraction in much mathematics.
>
> I hope you know, then, that I have a lot of Python code here:
>
> http://x31eq.com/temper/regular.zip
>
> It covers a fair bit. It uses vals a lot but I don't use the term
> "val" anywhere that I can remember. It doesn't do hobbits. That's
> because I'm genuinely unable to generate hobbits in Python. I think
> it's difficult. Maybe one day you or I or somebody else will write
> the code and then we can look at it to decide how difficult the
> problem really is.
>
> You may be able to adapt the code for finding mappings to give
> hobbits. I think they're analogous problems. Unfortunately, that
> code isn't at all simple :-(
>
> I've got somewhere with Pari/GP. The code for that is here:
>
> http://x31eq.com/parametric.gp
>
> Naturally, anything that can be done with Pari can also be done with
> Sage, where Python is the scripting language. I don't have Sage
> installed here and now so I haven't done that. I don't think it would
> make much difference. GP isn't as nice as Python but there isn't much
> syntax involved.
>
> The (semi)norm that hobbits minimize is temperamental complexity. The
> functions are there in GP to calculate it. By trial and error you can
> find the intervals of minimal complexity for a given number of scale
> steps. I don't have a cleaner way of finding the hobbit.
>
> The octave equivalent function isn't there. That's because I'm not
> happy with it. You can find my comments on tuning-math. Or, use
> Gene's alternative method for getting hobbit pitches within the octave
> from an octave-specific function.
>
> Gene has said that finding each pitch of the hobbit maps to finding
> the shortest vector in a lattice. I haven't been able to work that
> out. Maybe it isn't that difficult, but it is at least more
> appropriate for tuning-math.
>
> Note that the "meantone scale" in my GP code is solving a hobbit-like
> problem. Maybe that could be adapted to produce hobbits with
> octave-equivalent vectors. Have a look at it if you like. Note, at
> least, that Pari is capable of finding shortest vectors in certain
> lattices. I don't have such functions in Python -- other than by
> accessing Pari through Sage.
>
>
> Graham
>

Hye Gene,

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > Gene wrote:
> >
> > > I'll repeat my suggestion: write the articles you think are needed.
> >
> > Yeah, Aaron, simply write the content you are trying to learn.
> > Duh!
>
> Aaron is perfectly capable of adding content. It hardly needs to be attempts to explain mathemematical terminology.
>
> Major DUH!

No DUHS and counter-DUHS are necessary---I regret another tuning flame war.... :)

I'm intrigued by the idea that Hobbits, to use the example I first "complained" about, are difficult to code in a general scripting language...Gene, what tools do you use, and maybe you are willing to share algorithms, or best yet---COMMENTED code?

Graham says it's difficult in Python, and he does it in Pari, which he can access through Python. I know Carl is a Scheme wiz, Carl---do you have any idea where to start doing this in scheme? I know enough Scheme that I could probably translate it to Python, which I'm much more fluent in.

I wonder if it wouldn't be nice to add a 'code' section to the wiki so that people might be able to grok tuning-math concepts in the language of their choice? Maybe that's a far off goal, but I know many of us, myself included, already have scripts for doing tuning-math. I have a whole library of stuff, and I'd say it's safe to say that the tuning-math I really get is the stuff I've coded scripts for. So, maybe if I can code Hobbit-creation, I'll get hobbits....

I share Carl's optimism that there is a simpler way of speaking about these things, or visualizing them, than what is symbolically there on the wiki as of today. But who can say for sure unitl it's actually done?

>
> > I'd love to. You can see, however, that my good-faith effort to
> > improve an article after someone criticized it has been met with
> > silence and contempt. Shall I give up?
>
> I've paid attention to what you said about the hobbit article. I'll see if I can improve it.

Thanks for your not-unnoticed work, Gene. Really, I mean that. You've created, like Erv Wilson before you, entire universes that might take many generations of musicians to even begin exploring. It's daunting.

Ars Longa, Vida Breve.

AKJ

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

> A picture? :) I'm thinking something like what Ikea does in their instructions for building furniture---they use no words. It's often very powerful, if the picture is well drawn, which sometimes it isn't...

If someone who was good with pictures wanted to try making one, it might help.

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

> I'm intrigued by the idea that Hobbits, to use the example I first "complained" about, are difficult to code in a general scripting language...Gene, what tools do you use, and maybe you are willing to share algorithms, or best yet---COMMENTED code?
>
> Graham says it's difficult in Python, and he does it in Pari, which he can access through Python. I know Carl is a Scheme wiz, Carl---do you have any idea where to start doing this in scheme? I know enough Scheme that I could probably translate it to Python, which I'm much more fluent in.
>
> I wonder if it wouldn't be nice to add a 'code' section to the wiki so that people might be able to grok tuning-math concepts in the language of their choice? Maybe that's a far off goal, but I know many of us, myself included, already have scripts for doing tuning-math. I have a whole library of stuff, and I'd say it's safe to say that the tuning-math I really get is the stuff I've coded scripts for. So, maybe if I can code Hobbit-creation, I'll get hobbits....

> I share Carl's optimism that there is a simpler way of speaking about these things, or visualizing them, than what is symbolically there on the wiki as of today. But who can say for sure unitl it's actually done?

I've been considering how to fully automate the process, but if I did, it would be in Maple.

> Thanks for your not-unnoticed work, Gene. Really, I mean that. You've created, like Erv Wilson before you, entire universes that might take many generations of musicians to even begin exploring. It's daunting.

Thanks, Aaron. As you say, a person could spend a lifetime just exploring 19edo. But I'm always interested to hear what someone can make of a new scale or tuning.

Gene wrote:

> He said that these two philosophers were being pretentious
> because they were using terms like "idealism"

Thanks.

>> Yeah, Aaron, simply write the content you are trying to learn.
>> Duh!
>
> Aaron is perfectly capable of adding content. It hardly needs
> to be attempts to explain mathemematical terminology.

I think you should have another look at that.

> I've paid attention to what you said about the hobbit article.
> I'll see if I can improve it.

Believe it or not I once made a living explaining things
to people in writing, and hiring and editing the work of
other authors to do the same.

-Carl

Aaron wrote:

> It's an interesting question whether a complex thing like
> Hobbits can be meaningfully conveyed in simpler terms.

There's no question about it. Read Feynman's lectures.
Some of them are very involved, but I have no doubt that
anyone of reasonable intelligence, with a little effort,
could succeed with them. Or read any of Paul Erlich's
tutorials or papers. I can't say the same thing about
the xenwiki content. So there's no question of if, only
why not.

> I always default to the idea that a picture is worth a
> thousand words.

Pictures are very helpful, and Paul Erlich has made some
truly great visualizations of this stuff. But there is no
substitute for words and numbers. Ideally we'd have all
three. I stink at visualizations but I'm willing to work
hard to improve the words.

-Carl

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

> Graham says it's difficult in Python, and he does it in Pari,
> which he can access through Python. I know Carl is a Scheme
> wiz, Carl---do you have any idea where to start doing this
> in scheme?

There are probably things like Pari for Scheme, but they're
probably not as good as Pari. You could probably call Pari
from Scheme, but then you might as well use Python.

There are two things here: first, understanding what problem
hobbits try to solve, and roughly how they are constructed.
Then, being able to construct them yourself. Gene and/or
Graham seem to be sayingt you should learn the latter first,
or the former not at all, or something like that, which is
extremely wrong.

-Carl

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

> There's no question about it. Read Feynman's lectures.
> Some of them are very involved, but I have no doubt that
> anyone of reasonable intelligence, with a little effort,
> could succeed with them.

You can read Feynmann's QED from cover to cover and have not one single clue how to actually calculate anything. No one, including Feynmann, has ever made Feynmann's path integral formulation of quantum field theory easy, and no one ever will.

Gene wrote:

> You can read Feynmann's QED from cover to cover and have not
> one single clue how to actually calculate anything. No one,
> including Feynmann, has ever made Feynmann's path integral
> formulation of quantum field theory easy, and no one ever will.

I didn't say anything could be made easy. I said anything
can be explained without making it harder. I also said:

> There are two things here: first, understanding what problem
> hobbits try to solve, and roughly how they are constructed.
> Then, being able to construct them yourself. Gene and/or
> Graham seem to be saying you should learn the latter first,
> or the former not at all, or something like that, which is
> extremely wrong.

-Carl

On Tue, Mar 8, 2011 at 4:22 PM, genewardsmith
<genewardsmith@...> wrote:
>
> In any case, if you are assuming the definition of for example how a hobbit is constructed could be radically simplified based on some anecdotes about Feynmann's exploits, you are assuming way too much. And definitions can get so much more difficult than that it's dubious to pick on me as a bad example. Try the definitions of a vertex operator algebra or a scheme, to give two very important mathematical definitions, if you don't believe me. if no one has radically simplified these, despite their importance, could it be because it can't be done?

Is this an alternative way to look at hobbits that makes sense?

1) Pick an n-limit regular temperament
2) For every ET that supports that temperament, a hobbit scale exists
3) To find the hobbit scale, start with that ET

Now an intermediate step I'm introducing for conceptual simplicity:

4) Regress the scale to JI: for each scale step in that ET, pick the
simplest possible JI ratio that corresponds to it (and just leave it
at that for now!)

And then
5) Now re-temper the resultant JI scale according to your original
regular temperament.

You now have a tempered scale that isn't tempered as much as the ET
you started with, but tempered more than JI; this is the hobbit scale
and it generalizes MOS

Is that not a decent way to explain Hobbits for Dummies? You kind of
just gloss over -how- you find the simplest possible JI ratio that
corresponds to each scale step, but that statement can be made more
rigorous for power users.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> Is this an alternative way to look at hobbits that makes
> sense?
>
> 1) Pick an n-limit regular temperament
> 2) For every ET that supports that temperament, a hobbit
> scale exists 3) To find the hobbit scale, start with that
> ET

That's all good.

> Now an intermediate step I'm introducing for conceptual
> simplicity:
>
> 4) Regress the scale to JI: for each scale step in that
> ET, pick the simplest possible JI ratio that corresponds
> to it (and just leave it at that for now!)

That's an interesting idea, and conceptually simple. I
don't believe it leads to a hobbit. You could look into it
and see how the scales it does give look (including how
likely they are to coincide with hobbits).

Graham

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Is that not a decent way to explain Hobbits for Dummies?

Also to be included: why is it called hobbit? There is nothing there in the wiki. It says it is "sort of a cousin of dwarf scales", but, naturally, the entry on dwarf scales says nothing about why they are called dwarf scales.

Psychologists would probably have a field day with the purposeful obscurity of an awful lot of this.

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

> Also to be included: why is it called hobbit? There is nothing
> there in the wiki. It says it is "sort of a cousin of dwarf
> scales", but, naturally, the entry on dwarf scales says nothing
> about why they are called dwarf scales.
> Psychologists would probably have a field day with the purposeful
> obscurity of an awful lot of this.

It's hard to come up with names for all this stuff, but the
names do help. Dwarfs are named because each note is a
JI ratio with the shortest "Tenney height" among the notes
that could fit in that spot. Hobbits use a different 'height'
related to temperaments.

As I understand it, Mike's procedure actually gives tempered
dwarfs. I share Graham's skepticism but they probably at least
correspond to hobbits some of the time. Gene may have more to
say on that. -Carl

"akjmicro" <aaron@...> wrote:

> Graham says it's difficult in Python, and he does it in
> Pari, which he can access through Python. I know Carl is
> a Scheme wiz, Carl---do you have any idea where to start
> doing this in scheme? I know enough Scheme that I could
> probably translate it to Python, which I'm much more
> fluent in.

The difficult part is that it involves finding the shortest
vector in a lattice. That's hard in the sense that it's
believed to be impossible by any algorithm in polynomial
time. Still, it's not something to be frightened of.

The problem of finding regular temperaments also amounts to
a lattice minimization, and I'll guess it's a little harder
than finding a hobbit. In my publicly available code,
that's done by parametric.py (367 lines) with help from
regutils.py (507 lines, not all relevant). The somewhat
less readable regular_terse.py does the same job in 66
lines. For comparison, microcsound20101231.py is 523
generally longer lines.

Actually, as far as I've got with hobbits now I think the
code could be translated to Python easily enough. You'll
need a matrix library. I included a free one in my
code bundle. I think you can then convert the code from
parametric.gp easily enough. I could also do it, of
course, and maybe I will if you have difficulty.

In GP, * is a matrix product, ~ is a transpose, matdet is a
determinant, and matadjoint(X)/matdet(X) is an inverse.
Other things are explained in the tutorial -- it's all free
software.

The things you can't easily duplicate from that file are
the lattice minimizations and the clever function to
convert between mappings (vals) and unison vectors
(commas). You don't need them to understand hobbits.

Warning: I calculate temperamental complexity using a norm
on intervals in a temperament. Gene prefers a seminorm on
monzos (JI-like vectors). He may document both. (I'm not
sure, I didn't do my research for this post, how naughty.)
I think you can get the octave-equivalent version from
either by throwing away the 2 dimension. Given that, I
think Gene's instructions are understandable.

To find the hobbit, what you have to do is try every
possible interval that gives the right number of scale
steps. As such, that's impossible, but Gene says rounding
each element of the vector up and down similar to Fokker
blocks (coded in Python) is good enough. That's an
exponential time algorithm, but still, don't be frightened
of it.

> I wonder if it wouldn't be nice to add a 'code' section
> to the wiki so that people might be able to grok
> tuning-math concepts in the language of their choice?
> Maybe that's a far off goal, but I know many of us,
> myself included, already have scripts for doing
> tuning-math. I have a whole library of stuff, and I'd say
> it's safe to say that the tuning-math I really get is the
> stuff I've coded scripts for. So, maybe if I can code
> Hobbit-creation, I'll get hobbits....

You can copy any of my code there.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> It's hard to come up with names for all this stuff, but the
> names do help.

I understand the former, and agree with the latter, but it is all *completely* moot and useless if the name doesn't have *some* kind of explanation. If one puts an encyclopedic entry for an entity, you'd think the naming of that entity would be right up front.

Because, as I'm sure you can see, they just become a miasma of curious but obscure, referential terms.

> Is this an alternative way to look at hobbits that makes sense?

I think this focus on hobbits, though well-intentioned, is a little misplaced. If you were teaching traditional music theory, and someone said, "But how do I make a M7b5 chord easy to understand?" I'd suggest that you don't worry about how to teach that chord. Focus on triads, 7th chords, tritones, and leading tones first, because that's what most students need first; M7b5 chords are for the advanced musician, so almost by definition you don't need a beginner's explanation for them.

By the way: because I now know that hobbits are an advanced topic, I can ignore them for a while. As I was first trying to make sense of the xenharmonic wiki, I didn't know they were an advanced topic, and I struggled to understand them. (I still don't understand them, but I no longer struggle because I know enough to know that I don't need to know them yet.) George Secor said about 11-EDO that there's low contrast between the high- and low-dissonance intervals; analogously, the xenharmonic wiki is currently written in 11-EDO, where there's low contrast between high- and low-complexity topics. There's nothing wrong with 11-EDO, but it's a rare tune that will be written that way that reaches a general audience. I don't think the wiki should be written in 12-EDO, but it should probably be written in something more like 19. :)

So, if you're trying to figure out how to make things easier for non-mathematicians, don't start with something that complex. Start instead by coming up with simple examples of the basic things that you do, e.g., commas, vals, monzos, tempering. Use them in several examples that would be immediately useful to the beginner, e.g., translating this:

----
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125

POTE generator: ~11/10 = 156.055

Map: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 77, 100
----

...into a scale or set of scales that someone can play with. (That's the "Greeley" Chromatic Pair on the new Chromatic Pairs page, by the way.) Give a sense of why you'd want to temper those commas; help people understand how those EDOs support Greeley, and why more than one does so; explain what a generator is (or what the different types of generators are).

Even if the way you use these things is mechanical -- say I don't understand what a subgroup is yet, but I can use the generator and the vals given to generate the scale -- that's better than making sure I understand what a subgroup is. Because if a musician gets a scale he can play, he can start to make music, which will make all the other stuff worth digging into. Until he gets to that point, Greeley is just a blob of numbers.

Maybe that's not possible. But if it is, that's the approach I'd take.

I'm very grateful to those who have stocked the wiki with so much information, and to people like Gene and Igs who have provided information on this list. Getting good information, even if opaque to the average musician, is a very important start. I'm willing to help simplify and write (where I think I understand something) to give something back to the community.

Regards,
Jake

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

> I said none of those things. I said you have a track
> record of writing impenetrable materials, which is true.
> I will also say that your attitude from your first reply
> has been piss poor. Your remark that Aaron's request has
> no merit may or may not be construed as an insult to
> Aaron, but it certainly is a grade A example of the
> elitist bullshit you claim tuning-math is not suffering
> from.

I'm sorry about my first reply. My attitude, in fact, was
to get it sent off before lunch on a morning when I had to
get up early, and so I was in a bit of a haze. Note that
I did have one positive contribution to make -- about the
rank 2 case -- and I wanted you to get that. I didn't say
what I meant to say. The context was this paragraph from
Gene:

"Unless you simply want to present a lot of unmotivated
matrix computations, you will need to explain the idea
behind it, which means to explain in some manner or another
octave-equivalent Tenney-Euclidean complexity. The best way
I know to understand that is geometrically. So how do you
make it simple?"

All you did is tinker with the wording. And, yes, your
wording is better and I should have said so. But you
haven't dealt with the underlying complexity and you
haven't explained octave-equivalent Tenney-Euclidean
complexity (OETEC) which I think is difficult to explain.
So I meant to back Gene up on that. While all kinds of
things can be improved there are still concepts like vals
and norms that you need to bring in under one name or
another.

I vote for you committing your changes to the wiki (if you
haven't already -- I haven't checked) and I'll take it from
there.

On the point of examples, I do think you need more than
three. You also need to choose carefully which examples to
give, which isn't a simple matter, but let's do it. The
example I've given before is 5-limit meantone. Here's the
mapping:

[<31, 49, 72], < 12, 19, 28]>

Here's the reduced basis:

[<1, 1, 0], <0, 1, 4]>

Here's the matrix that determines temperamental TE
complexity in terms of the reduced basis.

( 0.247 -0.029)
(-0.029 0.102)

Note: because one of the generators is the period, I
believe the octave-equivalent metric amounts to the number
0.102. That is, you remove the first column and first row
from the metric and only consider the octave-equivalent
generator. That means the OETEC becomes

sqrt(n*0.102*n) = abs(n)*sqrt(0.102)

for n generator steps. This is obviously counting
generator steps and shows why rank 2 hobbits are also MOS.

Note also that my normalization is probably different to
Gene's, and so the number 0.102 really has no meaning.

Anyway, here are the examples of the octave-specific
complexity with the above metric:

2:1 0.497
3:2 0.320
4:3 0.638
5:4 1.759
9:8 0.879
6:5 0.960

I think you need at least this number of intervals to show
the pattern. Would 7-limit Marvel (225/224-planar) be a
good example for OETEC?

Graham

On Thu, Mar 10, 2011 at 4:54 AM, Graham Breed <gbreed@...> wrote:
>
> > 4) Regress the scale to JI: for each scale step in that
> > ET, pick the simplest possible JI ratio that corresponds
> > to it (and just leave it at that for now!)
>
> That's an interesting idea, and conceptually simple. I
> don't believe it leads to a hobbit. You could look into it
> and see how the scales it does give look (including how
> likely they are to coincide with hobbits).

You cut out step 5, which was to retemper according to the chosen
regular temperament. Gene's algorithm seems like he's doing exactly
what I wrote above, except instead of detempering all the way to JI
and then retempering, he just uses a complexity metric for tempered
intervals right off the bat.

Since the OE seminorm isn't actually defined in the hobbit algorithm,
but is rather left open such that one can use any seminorm that one
wants, then my algorithm would be a hobbit with the OE seminorm
defined as

OE(i) = min(geomean(S_i))

Where S_i is the set of all intervals that are tempered to be
equivalent to it, geomean yields a new set with the geometric mean of
the old site, and min takes the lowest value. AKA you do exactly what
I said, which is you find the simplest JI interval that corresponds to
the scale step you're looking at. So this is a hobbit scale with that
norm defined, yes? I believe the difference between this and Gene's
implementation is that he used an octave-equivalent TE norm with
tempering built in right off the bat.

-Mike

On Thu, Mar 10, 2011 at 5:24 AM, Carl Lumma <carl@...> wrote:
>
> As I understand it, Mike's procedure actually gives tempered
> dwarfs. I share Graham's skepticism but they probably at least
> correspond to hobbits some of the time. Gene may have more to
> say on that. -Carl

Don't dwarves always give quote unquote "otonal" ratios, though? As
in, a 12-note 5-limit dwarf will put 25/16 in there over 8/5 for the
base mode of the scale (e.g. the one that the algorithm spits out by
default, with no permutations).

I asked Gene a while ago if one could start with an ET and then
"detemper" to get a hobbit, and he said yes, so that's basically what
I based my algorithm on.

-Mike

Mike Battaglia <battaglia01@...> wrote:
> On Thu, Mar 10, 2011 at 4:54 AM, Graham Breed
> <gbreed@...> wrote:
> >
> > > 4) Regress the scale to JI: for each scale step in
> > > that ET, pick the simplest possible JI ratio that
> > > corresponds to it (and just leave it at that for now!)
<snip>

> You cut out step 5, which was to retemper according to
> the chosen regular temperament. Gene's algorithm seems
> like he's doing exactly what I wrote above, except
> instead of detempering all the way to JI and then
> retempering, he just uses a complexity metric for
> tempered intervals right off the bat.

Yes, but it still doesn't work. I've thought of some
counterexamples. Any rank 2 case where you don't get a 9:8
in the MOS will break. 3:2 and 4:3 are the simplest
intervals within the octave. Except for a really
pathological case where 9:8 is tempered out, one degree
will have 3/2 as its simplest ratio and another will have
4/3. The interval between them will be 9:8. When you
temper it, you'll find the tempered version of 9:8 in
there, and if that shouldn't be in the MOS what you have
can't be an MOS. A hobbit should be. Examples are 10
notes of Miracle, 9 notes of Orwell, and 7 notes of Magic.

Also, think about the decimal scale of Miracle. 6 steps
will be best approximated by 3/2. That means you must have
6 secors counting from the tonic. Three secors should give
the approximation to 11/9. But 5/4 will come out as
simpler for this degree. The 4:5:6 chord is too complex to
fit in the decimal scale, but with your algorithm it's
irresistible.

> Since the OE seminorm isn't actually defined in the
> hobbit algorithm, but is rather left open such that one
> can use any seminorm that one wants, then my algorithm
> would be a hobbit with the OE seminorm defined as
>
> OE(i) = min(geomean(S_i))

That's an interesting interpretation of the algorithm. The
seminorm is, at least, constrained. It should give unison
vectors zero size. If it's octave equivalent, it should
give octaves zero size. For rank 2 that leaves you with no
degrees of freedom.

> Where S_i is the set of all intervals that are tempered
> to be equivalent to it, geomean yields a new set with the
> geometric mean of the old site, and min takes the lowest
> value. AKA you do exactly what I said, which is you find
> the simplest JI interval that corresponds to the scale
> step you're looking at. So this is a hobbit scale with
> that norm defined, yes? I believe the difference between
> this and Gene's implementation is that he used an
> octave-equivalent TE norm with tempering built in right
> off the bat.

The seminorm is really a norm on intervals in tempered
coordinates along with the transformation from ratio space
to tempered coordinates. The norm it transforms to is RxR
for rank R temperaments. Any imposition of octave
equivalence has to reduce the rank by 1. What you're
talking about is a JI hobbit, where no intervals are
tempered out, that you then temper.

Graham

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

> I asked Gene a while ago if one could start with an ET and then
> "detemper" to get a hobbit, and he said yes, so that's basically what
> I based my algorithm on.

Yes, but you are detempering in your own way, which leads to a different scale. At least, if I understand correctly you are proposing to first detemper to a Tenney-reduced JI scale for the val in question, and then retemper to whatever lower rank temperament you had in mind. If someone were able to make good 2D lattice diagrams it might help; as I said, there are some pictures which might be helpful.

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

> > It's hard to come up with names for all this stuff, but the
> > names do help.
>
> I understand the former, and agree with the latter, but it is
> all *completely* moot and useless if the name doesn't have
> *some* kind of explanation. If one puts an encyclopedic entry
> for an entity, you'd think the naming of that entity would be
> right up front.

It's in the first sentence!
http://xenharmonic.wikispaces.com/Hobbits

And had you followed the link to
http://xenharmonic.wikispaces.com/Dwarves
what I just shared about Tenney height is there. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> It's in the first sentence!
> http://xenharmonic.wikispaces.com/Hobbits

You dork - I quoted that in my original post! :) All it says is that it is related to dwarf scales. If that is *all* it is, well, ok. I note that the notion of "dwarve" isn't mentioned until the very last sentence of the dwarve entry, which strikes me as not very communicative. Seems like an encyclopedic entry might start with "Dwarve, so named because..."

Ah, well. It is probably hard to see this when you've been knee deep in it as long as a few of you had, but on the outside, it seems like a lot of priestly obfuscation. I appreciate the whimsy and effort going into all the names, but when only a handful of people bandy about said names, it becomes rather cult-like. I was hoping there was a bit of clarity to be found.

Meh. This is small potatos. Or potatoes. Carry on.

Addendum -

Carl, I've just found:

http://xenharmonic.wikispaces.com/MOSNamingScheme
http://xenharmonic.wikispaces.com/DwarfNamingScheme

Nevermind. I mean, really, never mind! :)

"A hobbit scale is a generalization of MOS for arbitrary regular temperaments which is a sort of cousin to dwarf scales; examples may be found on the Scalesmith page. The idea is that MOS scales give us a means of contructing scales for a rank two regular temperament which gives priority to the intervals of least complexity in that temperament, and so makes efficient use of it; a hobbit does the same in higher ranks, and so using them is one way to make higher ranks, including especially the interesting rank three case, accessible for musical purposes. "

So basically a Hobbit is to higher-rank temperaments as MOS is to rank-2. What could be clearer?

I would consider myself in sufficient intuitive understanding of hobbits if the following questions were answered:

Do you use the generators of the temperament to produce hobbits?

Is the size of a hobbit arbitrary, or are there "moments of hobbitry"?

Related: do all hobbits have [rank] step-sizes--i.e. will all rank-3 hobbits have 3 step-sizes?

-Igs

--- In tuning@yahoogroups.com, "akjmicro" <aaron@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > > But some of the rest of what he said was garbage, frankly,
> > > > so who knows.
> > >
> > > Feynman or Susskind?
> >
> > Susskind.
> >
> > > I don't know why you say that - hobbits are quite simple.
> >
> > Unless you simply want to present a lot of unmotivated matrix computations, you will need to explain the idea behind it, which means to explain in some manner or another octave-equivalent Tenney-Euclidean complexity. The best way I know to understand that is geometrically. So how do you make it simple?
> >
>
>
> A picture? :) I'm thinking something like what Ikea does in their instructions for building furniture---they use no words. It's often very powerful, if the picture is well drawn, which sometimes it isn't...
>
> AKJ
>

Graham wrote:

> I'm sorry about my first reply. My attitude, in fact, was
> to get it sent off before lunch on a morning when I had to
> get up early, and so I was in a bit of a haze.

Sorry for escalating. My kids have been sick for two weeks
and I haven't gotten anything resembling sleep in as long.

> All you did is tinker with the wording. And, yes, your
> wording is better and I should have said so. But you
> haven't dealt with the underlying complexity and you
> haven't explained octave-equivalent Tenney-Euclidean
> complexity (OETEC) which I think is difficult to explain.

I didn't mean to devalue difficult concepts (though it's
true I'm not a fan of the word "difficult"). I meant to
improve the high-level explanation. I do think it's a big
mistake to not put effort into high-level explanations, or
tell people they have no need of them, or that no high-level
explanation is possible. I'd try to improve the details
too, but I'll need to understand them myself first.

> So I meant to back Gene up on that. While all kinds of
> things can be improved there are still concepts like vals
> and norms that you need to bring in under one name or
> another.

I'm not against terminology or equations, as I do not
think they are sources of difficulty. In fact I despise
pop physics books that deal in meaningless analogies in an
effort to avoid math. I'm against bad explanations. Not
nearly enough effort is spent in our society on good
explanations. Take Paul's gentle intro to Fokker blocks,
which I used back in the thread on rank 3 scales. It was
absolutely effortless to follow and implement. At least it
didn't feel like effort.

I hate to keep bringing up Feynman, but this story by
Thinking Machines founder Danny Hills is really great if
you haven't read it
http://longnow.org/essays/richard-feynman-connection-machine/
Note what he says about the dumbed-down article Hills wrote
for Scientific American.
Then there's this Dyson quote:
"Dick was also a profoundly original scientist. He refused
to take anybody's word for anything. This meant that he was
forced to rediscover or reinvent for himself almost the whole
of physics. It took him five years of concentrated work to
reinvent quantum mechanics. **He said that he couldn't
understand the official version of quantum mechanics that was
taught in textbooks,** and so he had to begin afresh from the
beginning. That was a heroic enterprise. He worked harder
during those years than anybody else I ever knew. At the end
he had a version of quantum mechanics that he could understand.
The calculation that I did for Hans Bethe, using the orthodox
theory, took me several months of work and several hundred
sheets of paper. Dick could get the same answer, calculating
on a blackboard, in half an hour." [emphasis added]

If something like "learning styles" exist, I bet I'm in the
same bucket as Feynman (only at the bottom). And I bet there
are a lot of others too, who get washed out of the system
before they're even counted. Probably some go on to become
musicians, only to encounter the xenwiki. ;)

And it's not just an issue for students. Browsing arxiv.org,
I often muse that better theories must be lurking in there,
just not assembled in one place.

> I vote for you committing your changes to the wiki (if you
> haven't already -- I haven't checked) and I'll take it from
> there.

Great, I'll do so (probably tomorrow).

> On the point of examples, I do think you need more than
> three. You also need to choose carefully which examples to
> give, which isn't a simple matter, but let's do it. The
> example I've given before is 5-limit meantone. Here's the
> mapping:
> [<31, 49, 72], < 12, 19, 28]>
> Here's the reduced basis:
> [<1, 1, 0], <0, 1, 4]>
> Here's the matrix that determines temperamental TE
> complexity in terms of the reduced basis.
> ( 0.247 -0.029)
> (-0.029 0.102)

Looks good, though I don't have time to check it now. I'll
let you do that once I commit my thing to the wiki.

One thing to note is that I stopped to give examples of the
seminorm just to illustrate the two properties mentioned,
without showing other details. First I illustrate octave
ignorance with 3/2 and 3/1 (IIRC) and then the complexity
with 25/16. So I agree that choosing the right examples is
critical. If you've ever worked at a shop that practices
rigorous TDD then I suggest you think of it that way.
My wife once practiced her spiel on me as I implemented a
spell checker in Python. She had me write absolutely trivial
tests - and make them fail - before letting me write a line
of code. Her job is to make big-ego programmers do this on
a daily basis. The fact that she makes twice what they do
suggests it works. There's nothing against fully worked
examples at the bottom, but they don't replace the kind of
inline, incremental examples I'm advocating here.

> Note: because one of the generators is the period, I
> believe the octave-equivalent metric amounts to the number
> 0.102. That is, you remove the first column and first row
> from the metric and only consider the octave-equivalent
> generator.
> That means the OETEC becomes
> sqrt(n*0.102*n) = abs(n)*sqrt(0.102)
> for n generator steps. This is obviously counting
> generator steps and shows why rank 2 hobbits are also MOS.

I got this far in my mind when you said it last time, but
I was unable to convince myself that it always leads to MOS.
If I worked it on paper I probably could close the gap...

> Note also that my normalization is probably different to
> Gene's, and so the number 0.102 really has no meaning.

Just a constant, sure.

> Anyway, here are the examples of the octave-specific
> complexity with the above metric:
> 2:1 0.497
> 3:2 0.320
> 4:3 0.638
> 5:4 1.759
> 9:8 0.879
> 6:5 0.960
> I think you need at least this number of intervals to show
> the pattern.

I still don't see why 2:1 is 0.497. And you should probably
show something like 3:1 again too.

> Would 7-limit Marvel (225/224-planar) be a good example
> for OETEC?

Usually for any of this stuff I like to see at least 3
examples: rank 1 codimension 2, rank 2 codimension 1, and
rank 2 codimension 2. Marvel is rank 3 codimension 1 but
it can't hurt.

-Carl