Yahoo Tuning Groups Ultimate Backup tuning Naming subgroups of temperaments

We've decided on a system that names temperaments by commas. This is
simple and works great. However, what sometimes happens is that we
name temperaments based on a particular combination of commas. At this
point, it's like we're naming temperaments by "multicommas," which are
like the wedge products of commas.

Once we assign a name to a temperament eliminating some multicomma,
the naming convention for higher-limit extensions of that multicomma -
perhaps considered to be the wedge product of the multicomma and some
other, new comma - is fairly set out in stone. The lowest badness or
otherwise most notable extension ends up getting the same name as the
temperament it's derived from, and other notable temperaments get
related or offshoot names. Aside from some nitpicking over which is
"the" best extension for a temperament here and there, this is pretty
simple.

However, we now have a new, increasingly common situation, which is
that we have to name temperaments which eliminate -factors- of some
multicomma, rather than the whole thing. As an example, there's
7-limit sensi, and 5-limit sensi, and also 2.5/3.9/7-limit sensi,
which I believe we're now calling "sentry." There is no common comma
eliminated by these three, but they are all -factors- of a temperament
which eliminates a certain multicomma which is important enough to
have a name, which is the full 7-limit "sensi" temperament.

We've been handling this situation by coming up with a new pseudonym
for every single subgroup variation of some temperament. I believe
that this may not always be desirable for three reasons:

1) It leads to an enormous amount of "new temperaments" with "new
names" which we deliberately created by looking at subgroups from
well-known ones
2) Sometimes, defining a "new temperament" isn't even necessary: it
may sometimes be more desirable to work with existing temperaments,
but error-optimize them around a different set of target intervals
than usual
3) Sometimes it leads to schisms in the terminology that people have
been using and the terminology that they're now suddenly supposed to
use

For these reasons I suggest we consider setting it in stone that
subgroup "children" of existing temperaments can use the names of
their parents, so that temperament names can "grow down" from when
define temperaments around multicommas as well as "grow up." This
isn't going to be algorithmically perfect in 100% of the cases, just
like it's not always clear which is "the" 13-limit extension of Catler
temperament, but as a general rule it will solve all of the above
problems.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Dec 17, 2011, at 4:21 PM, Carl Lumma <carl@...> wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> We've decided on a system that names temperaments by commas.
> This is simple and works great.

We did? Since when?

?? Temperaments are defined as things that vanish commas.

> For these reasons I suggest we consider setting it in stone that
> subgroup "children" of existing temperaments can use the names of
> their parents, so that temperament names can "grow down" from when
> define temperaments around multicommas as well as "grow up." This
> isn't going to be algorithmically perfect in 100% of the cases, just
> like it's not always clear which is "the" 13-limit extension of
> Catler temperament, but as a general rule it will solve all of the
> above problems.

Can you give some examples?

For example, the 2.3.5.11 subgroup version of mohajira can just be
2.3.5.11-limit mohajira, instead of mohaha (though you can call it that
too). And all of the numerous subgroup versions of porcupine can just be
x.y.z porcupine, instead of one called "porkupine," and maybe another
called "porkypine," and another called "pocrupnie," or what not. And the
superpyth diatonic scale in 17-edo can actually be superpyth - well, the
2.3.7 version of it - rather than "pepperoni," "supra", "archy," etc. And
the 2.9/7.5/3 245/243 temperament can be identified as a subgroup version
of sensi, rather than calling it "sentry" as we are now.

Now consider: 8-EDO supports this temperament with remarkable accuracy for
only 8 notes. I recommend giving it a whirl on your AXiS. Assuming you
think the 0-450-900 cent chords are halfway decent for writing actual music
in 8-EDO that doesn't sound dark and diminished, which I strongly do, then
there's another reason for you: the more we analyze "bad" EDOs under the
illuminating light of subgroups and dyadic chords, the more we stumble on
subgroup variants of existing temperaments, in the process generating
enormous amounts of names for "new" temperaments which are obviously slight
variants of things we already have. The worst offender I can think of is
17-EDO's "superpyth", which is identical to the usual superpyth except for
the mapping for 5 which is barely ever used at all anyway. So instead we
call it something else and remind people that it's not superpyth, but
rather supra/archy/pepperoni etc.

Of course, there's no problem with the existing names that we have, or
coming up with new ones. It's just that we shouldn't treat them as being
truly separate from the parent temperament they were derived from. For
example, we have wuerschmidt, wurrschmidt, whirrschmidt, and whorrschmidt,
which are all unique extensions of wurrschmidt. But in addition, they're
still "wurrschmidt" as well. I think the same principle should apply to
subgroups.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Dec 17, 2011 at 12:59 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> It seems to me you need to have some way of deciding which temperament something is the child of. Should they always have the same rank, for instance? What things should you look at to decide that mohaha is a child of mohajira and not squares?

For the intervals that mohaha and mohajira have in common, they map to
the same respective positions on both lattices. This isn't true of
squares, where the lattice structure (and hence "generator") changes.
A good time to choose a -DIFFERENT- name would be if some subgroup
causes the generator to double, e.g. where if subgroup(temperament)
causes the lattice to resemble 2-temperament or 3-temperament or so
on. A good example of this is to look at porcupine over the 2.9.7.11
subgroup, where it suddenly becomes 2-porcupine - and we call that
"Orgone" temperament instead.

Another question concerns when a child temperament has more than one
parent. For example, is mohaha a child of mohajira, or beatles, or
maqamic, or migration, or what? One answer to that question is that
mohaha is all of those things, since the phrases "2.3.5.11 mohajira",
"2.3.5.11 beatles", "2.3.5.11 maqamic", and "2.3.5.11 migration" all
give you enough information to uniquely specify mohaha temperament.

If it's desired to have a single standardized name in this case, we
might simply decide to name a subgroup temperament the child of the
lowest-badness temperament of its competitors. So mohajira would win.
And although we can still certainly use the name "mohaha," we now have
the option of also simply calling it "2.3.5.11-limit mohajira", or
just "mohajira" in case where the limit is unambiguous.

Of course, we already have names for these temperaments, many of which
are creative, and "mohaha" is an example. We don't need to get rid of
them or to change the wiki.

-Mike

🔗Graham Breed <gbreed@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> For these reasons I suggest we consider setting it in stone that
> subgroup "children" of existing temperaments can use the names of
> their parents, so that temperament names can "grow down" from when
> define temperaments around multicommas as well as "grow up." This
> isn't going to be algorithmically perfect in 100% of the cases, just
> like it's not always clear which is "the" 13-limit extension of Catler
> temperament, but as a general rule it will solve all of the above
> problems.

I couldn't possibly agree more with this. In fact I think it *can* be made "algorithmically perfect in 100% of cases", by which I mean if I specify a subgroup temperament with a name and a subgroup (of the limit it's already defined on), then either (1) you know exactly what temperament it is, with no ambiguity, or (2) it's nonsense because the temperament is lower rank or contorted on that subgroup.

If I say "31-limit sensi", that's totally ambiguous because you have no idea how all the higher primes are mapped. There is an unlimited number of different mappings of those extra primes, and any assignment of the name "sensi" to one of them involves an arbitrary choice.

What we're suggesting is totally different, because there is no arbitrary choice. If I say "2.5/3.9/7 sensi", there is an algorithm to tell you exactly what temperament I mean, with no other information than that in the known 7-limit mapping matrix of sensi. I can specify the algorithm in as much detail as you like, but in concept it's really simple. You just write down the mapping matrix whose columns are the mappings of those generators {2/1, 5/3, 9/7} in sensi. Next you test if that matrix has full rank and is uncontorted. If so, that's the temperament meant by "2.5/3.9/7 sensi". If not, then you reject the description as nonsense. For example, "2.5/3 sensi" is nonsense, because it's contorted. The description "2.7/5 pajara" is nonsense because it's rank-1 rather than rank-2.

I think this is a really important issue because without this ability to specify a subgroup temperament *unambiguously*, the whole thing falls apart.

Gene, you asked how you could tell that mohaha is a subgroup version of mohajira rather than a subgroup version of squares. I have two things to say in response. First of all, it is not necessary that every subgroup temperament have a unique "parent". The descriptions "2.5/3.9/7 sensor" and "2.5/3.9/7 sensus" refer to the same temperament, and that's OK. (In practice you'd just say "2.5/3.9/7 sensi".) The important thing is NOT that every temperament has a unique name, but that every valid description refers to a unique temperament.

Second of all, although "2.3.5.11 mohajira" makes sense (and refers to the temperament called "mohaha"), "2.3.5.11 squares" is nonsense because squares is contorted on that subgroup. So mohaha could be described as either "2.3.5.11 mohajira" or "2.3.5.11 maqamic", but not as "2.3.5.11 squares" because the latter is contorted nonsense.

Just to be clear:

"2.3.5.11 mohajira" == "2.3.5.11 maqamic" == "mohaha"

"2.3.5.11 squares" is an invalid description that doesn't refer to a temperament

"2.5/3.9/7 sensi" == "2.5/3.9/7 sensus" == "sentry"

"2.3.11 mohajira" == "2.3.11 maqamic" == "2.3.11 hemififths" == "neutraltet"

Keenan

🔗Keenan Pepper <keenanpepper@...>

🔗Carl Lumma <carl@...>

Mike wrote:

> > We've decided on a system that names temperaments by commas.
> > This is simple and works great.
>
> We did? Since when?
>
> ?? Temperaments are defined as things that vanish commas.

When did we "decide on a system that names temperaments
by commas"? Because I think it would be a fantastic idea.

> Can you give some examples?
>
> For example, the 2.3.5.11 subgroup version of mohajira can just
> be 2.3.5.11-limit mohajira, instead of mohaha (though you can
> call it that too). And all of the numerous subgroup versions of
> porcupine can just be x.y.z porcupine, instead of one called
> "porkupine," and maybe another called "porkypine," and another
> called "pocrupnie," or what not. And the superpyth diatonic
> scale in 17-edo can actually be superpyth - well, the 2.3.7
> version of it - rather than "pepperoni," "supra", "archy," etc.
> And the 2.9/7.5/3 245/243 temperament can be identified as a
> subgroup version of sensi, rather than calling it "sentry" as
> we are now.

I dislike the 'change one letter' scheme as much as you
seem to. How is it based on the names of commas??

The last time this came up, which was about a month ago,
Gene said this
/tuning/topicId_101888.html#101889
I said this
/tuning/topicId_101888.html#101894
and Keenan said this
/tuning/topicId_101888.html#101909

-Carl

🔗Carl Lumma <carl@...>

To me, all this looks like the kind of trouble you run
into when you *don't* use a naming scheme based on commas.

-Carl

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

> For the intervals that mohaha and mohajira have in common,
> they map to the same respective positions on both lattices.
> This isn't true of squares, where the lattice structure (and
> hence "generator") changes. A good time to choose a -DIFFERENT-
> name would be if some subgroup causes the generator to double,
[snip]
> Another question concerns when a child temperament has more
> than one parent. For example, is mohaha a child of mohajira, or
> beatles, or maqamic, or migration, or what? One answer to that
> question is that mohaha is all of those things, since the
> phrases "2.3.5.11 mohajira", "2.3.5.11 beatles", "2.3.5.11
> maqamic", and "2.3.5.11 migration" all give you enough
> information to uniquely specify mohaha temperament.
>
> If it's desired to have a single standardized name in this
> case, we might simply decide to name a subgroup temperament
> the child of the lowest-badness temperament of its competitors.
[snip]

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Gene wrote:

> I've started this:
> http://xenharmonic.wikispaces.com/Tree+of+rank+two+temperaments

It's good. I may have seen it before. The names themselves,
though, are still "trivial". I don't think we can or should
replace them, but there's nothing wrong with adding systematic
names and seeing how it goes. Just like caffeine is also
1,3,7-trimethyl-1H-purine-2,6(3H,7H)-dione.

http://en.wikipedia.org/wiki/IUPAC_nomenclature_of_organic_chemistry
http://en.wikipedia.org/wiki/Trivial_name

The tree also doesn't handle subgroups. More precisely, it
doesn't mix temperaments of different rank on the same level.
I would structure it by rank of the reduced kernel basis.
Starting from a big comma search. You'd still need to
specify a subgroup to get a finite mapping (as in Keenan
Pepper's last post) but you wouldn't have to if you wanted
an infinite limit (like Mike was working on a few weeks ago).

So "2.3.5-synotic" would be meantone and "syntonic" would be
the infinite-limit 81/80 temperament. For commas without
historical names, naming the monzos is a bit of a challenge,
as the exponents can be large. Where's the other Keenan when
you need 'im?

-Carl

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> The tree also doesn't handle subgroups. More precisely, it
> doesn't mix temperaments of different rank on the same level.
> I would structure it by rank of the reduced kernel basis.

Just to be clear, by this you mean the codimension, aka dimension of the kernel, aka number of independent commas, right?

> So "2.3.5-synotic" would be meantone and "syntonic" would be
> the infinite-limit 81/80 temperament. For commas without
> historical names, naming the monzos is a bit of a challenge,
> as the exponents can be large. Where's the other Keenan when
> you need 'im?

Organizing temperaments by codimension is an interesting idea, which to me makes just as much sense as organizing them by rank as we (Gene et al.) currently do. It has the advantage that infinite-limit finite-codimension temperaments are trivial to define (as above), whereas infinite-limit finit-rank temperaments are much trickier to define since the definition involves a possibly infinite sequence of arbitrary choices.

However, I think there's a consensus that all these trivial names we currently have refer to finite-rank temperaments (right?). Naming codimension-1 temperaments is easy - just use the name of the single comma that's tempered out (e.g. "syntonic"). But giving sensible trivial names to codimension-2 or greater temperaments, without them being ambiguous with finite-rank ones, might be a problem. They might be stuck with nothing but systematic names, but perhaps everyone's OK with that.

My previous comments in this thread all assumed the paradigm of naming temperaments based on rank.

Keenan

🔗Carl Lumma <carl@...>

Keenan wrote:

> > The tree also doesn't handle subgroups. More precisely, it
> > doesn't mix temperaments of different rank on the same level.
> > I would structure it by rank of the reduced kernel basis.
>
> Just to be clear, by this you mean the codimension, aka
> dimension of the kernel, aka number of independent commas, right?

Yes. We discussed it last time (e.g. the links I posted).

> However, I think there's a consensus that all these trivial
> names we currently have refer to finite-rank temperaments
> (right?).

I suppose so.

> Naming codimension-1 temperaments is easy - just use the
> name of the single comma that's tempered out (e.g. "syntonic").

Not all commas have names. One way to fix this is with
the Hawaiian-like syllabic naming scheme for primes and
exponents I'm currently working out.*

> But giving sensible trivial names to codimension-2 or
> greater temperaments, without them being ambiguous with
> finite-rank ones, might be a problem. They might be stuck
> with nothing but systematic names, but perhaps everyone's
> OK with that.

Each system would be free to produce as many names as it
likes. The comma-based syllabic system can basically name
anything compactly with a subgroup in front.

> My previous comments in this thread all assumed the paradigm
> of naming temperaments based on rank.

I gathered. -Carl

* I don't actually have any time to work on these things.

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > Organizing temperaments by codimension is an interesting idea, which to me makes just as much sense as organizing them by rank as we (Gene et al.) currently do.
>
> Mathematically it does. In practice I think it doesn't. The focus in these parts has always been on rank one or two, with a few lunatics like me spending a lot of time talking about rank three.

But there's a certain kind of music for which it makes perfect sense. Say you're composing something based on 5-limit meantone, so you can use familiar diatonic harmony, but you love throwing in 13 limit chords that are tuned as well as possible given that 81/80 is tempered out. Then logically you're composing in the following temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=17c_19e_19p_12f_7p&limit=13

This is rank-5, but it's silly to think of it that way; really it's codimension-1 and who cares what rank (or limit) it is. It's not supposed to be a novel system with its own coherent scales. All it is is the simplest possible modification to JI that allows for meantone puns, comma pumps, etc.

You could go even further and say 12edo is good enough for the 5 limit, yielding this:

http://x31eq.com/cgi-bin/rt.cgi?ets=24p_12e_12f_12p&limit=13

I think Jon Catler has produced lots of music that's effectively in this codimension-2 temperament, and he'll sell you a guitar designed to play it. (Any extra tempering is merely for convenience and not intrinsic to the music.)

Keenan

🔗genewardsmith <genewardsmith@...>

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

> But there's a certain kind of music for which it makes perfect sense. Say you're composing something based on 5-limit meantone, so you can use familiar diatonic harmony, but you love throwing in 13 limit chords that are tuned as well as possible given that 81/80 is tempered out. Then logically you're composing in the following temperament:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=17c_19e_19p_12f_7p&limit=13
>
> This is rank-5, but it's silly to think of it that way; really it's codimension-1 and who cares what rank (or limit) it is. It's not supposed to be a novel system with its own coherent scales. All it is is the simplest possible modification to JI that allows for meantone puns, comma pumps, etc.

Actually, if you do that the TE/TOP tuning is stable, so you can just keep your favorite POTE fifth for any prime limit. Plus, there is a mathematical advantage to commas: they involve only a finite number of primes, so you don't need to chop them off at the knees at some arbitrary limit. But you still run in to the problem I mentioned: for the most part, people are interested in ranks one and two, and how they relate.

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Dec 18, 2011 at 4:20 PM, Carl Lumma <carl@...> wrote:
>
> Gene wrote:
>
> > I've started this:
> > http://xenharmonic.wikispaces.com/Tree+of+rank+two+temperaments
>
> It's good. I may have seen it before. The names themselves,
> though, are still "trivial". I don't think we can or should
> replace them, but there's nothing wrong with adding systematic
> names and seeing how it goes. Just like caffeine is also
> 1,3,7-trimethyl-1H-purine-2,6(3H,7H)-dione.

That's more or less what I'm suggesting. I don't care if mohaha is
still called "mohaha," but we should also be able to call it
"mohajira" of a certain limit.

One question that should be asked is, if it's arbitrary to name
temperaments, then isn't it arbitrary to name commas as well? Why
don't these names fit your criteria for a systematic naming system?

2.3.5.11 81/80 & 121/120
2.3.5.11 ||16 1 -8 -5 8 -2>> (the normalized wedge product of the above)
2.3.5.11 <<2 8 5 8 1 -16|| (wedgie which is Hodge dual to the above
multimonzo, also is 7p^31p)
2.3.5.11 7p & 31p

I used the & operator above because it's just what everyone seems to
be using, but it should be noted that there's some confusion with a
formal definition. One might use 7p ^ 31p instead.

> You'd still need to specify a subgroup to get a finite mapping (as in Keenan
> Pepper's last post) but you wouldn't have to if you wanted
> an infinite limit (like Mike was working on a few weeks ago).
>
> So "2.3.5-synotic" would be meantone and "syntonic" would be
> the infinite-limit 81/80 temperament. For commas without
> historical names, naming the monzos is a bit of a challenge,
> as the exponents can be large. Where's the other Keenan when
> you need 'im?

I still think we should keep on with the infinite limit thing, but I
don't care about anything except categorical perception and the &
operator right now. But "the perfect is the enemy of the good," so we
could perhaps start by looking at and naming 31-limit temperaments.
That ought to do the trick for now until we have all the transfinites
sorted out.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Mon, Dec 19, 2011 at 3:07 PM, Carl Lumma <carl@...> wrote:
>
> Time-weighted namespace for temperaments overwhelmingly
> favors the 5- and 7-limit, no matter when you start timing.
> Or number of mentions on the lists if you prefer. Or number
> of musical recordings if you prefer. Anyway, the naming
> scheme hardly blows up at higher limits as you imply.

That's only because XA isn't being archived, which is a shame.

Anyway, XA seems to overwhelmingly favor subgroup temperaments. Or
more specifically, it favors people thinking in purely scalar terms,
i.e. in terms of MOS's of some EDO, and then us jumping in and
figuring out how to make harmonic use of them using some useful
subgroup. I happen to think this is a good approach. I suppose that in
retrospect, Igs is the guy who's really to thank for this way of doing
things...?

But now the problem is that we're trying to also be technically
correct, so one person will say that a temperament is squares, but
we'll have to explain that it's actually skwares, because there's no
mapping for 5/1. And it's not semaphore, it's semiphore, for the same
reason. And it's not superpyth, it's supra, and so on. And people get
confused and feel like they have to remember a zillion names and give
up.

To be honest, I kind of like the concept of naming temperaments: I
enjoy working things out and giving temperaments poetic names and find
the whole thing very elegant, even though it has no point. So I think
we should still keep doing that. But as a first pass towards arriving
at a more "systematic" way of naming things, one which doesn't require
us all to remember a million variants of names, we can note that most
useful MOS's in most EDOs are subgroups of things already have names.
So we can just use those names, and specify that name with the caveat
that prime xyz doesn't work in this EDO, but that the rest is still
there. That solves all of these problems at once.

And if there's a useful temperament that really doesn't make sense as
a subgroup of something else, then maybe it really should have its own
name, as in Andrew Heathwaite's "Orgone" temperament.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> I didn't mean that we name them after the name of the comma,
> I mean that temperaments are divided up into families based
> on what commas they tempered out,

Ah.

> One question that should be asked is, if it's arbitrary to name
> temperaments, then isn't it arbitrary to name commas as well?

One idea is to make a big table of commas and give them
names like "gimlet" if they don't already have one.
That's still less arbitrary (or at least, more informative)
because the temperament name tells you something rather
than just being "gimlet" itself. It's naming generators
between say 400-415 cents "gimlet" that would be the
equivalent in terms of arbitrariness.

But it goes even better if the comma names encode their
monzos. That's the equivalent (in arbitrariness) to Dave K's
scheme where the generator size range names are descriptive
of their size.

A minor point of course.

> Why don't these names fit your criteria for a systematic
> naming system?
>
> 2.3.5.11 81/80 & 121/120
> 2.3.5.11 ||16 1 -8 -5 8 -2>> (the normalized wedge product of
> the above)
> 2.3.5.11 <<2 8 5 8 1 -16|| (wedgie which is Hodge dual to the
> above multimonzo, also is 7p^31p)
> 2.3.5.11 7p & 31p

They do. Rationals are impractical though, because they
get too big. But even just the numbers in the monzos have
more syllables than something like my Hawaiian scheme.
Wedgies (multivals) are fine but being val-based they
share essential properties with the mapping-based system
currently in use.

> > So "2.3.5-synotic" would be meantone and "syntonic" would be
> > the infinite-limit 81/80 temperament. For commas without
> > historical names, naming the monzos is a bit of a challenge,
> > as the exponents can be large. Where's the other Keenan when
> > you need 'im?
>
> I still think we should keep on with the infinite limit thing,
> but I don't care about anything except categorical perception
> and the & operator right now. But "the perfect is the enemy
> of the good," so we could perhaps start by looking at and
> naming 31-limit temperaments. That ought to do the trick for
> now until we have all the transfinites sorted out.

Keenan gave us a great start on the infinite limit thing.
But we don't have to work out infinite-limit optimal
tunings to reap the benefits of kernelnaming. The thing
about limits is that it forces musicians to say more than
they might want to say. If they use a mapping for the
basic chords but improvise above that, the normal way says
you have to figure out what higher primes were probably
being mapped and then name a temperament for it -- even if
they didn't have any such intention and used the pitches
"chromatically". The regular mapping assumption is the
engine that powers all the xh theory, but it's possible to
over-rely on it. The longer I'm at this the more I think
commas are primary. Petr seems to get good results anyway.

-Carl

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> But now the problem is that we're trying to also be technically
> correct, so one person will say that a temperament is squares, but
> we'll have to explain that it's actually skwares, because there's no
> mapping for 5/1. And it's not semaphore, it's semiphore, for the same
> reason. And it's not superpyth, it's supra, and so on. And people get
> confused and feel like they have to remember a zillion names and give
> up.

As soon as I get to a computer with a real keyboard I'm going to start some kind of glossary that gives all these relationships. It'll be great.

> To be honest, I kind of like the concept of naming temperaments: I
> enjoy working things out and giving temperaments poetic names and find
> the whole thing very elegant, even though it has no point. So I think
> we should still keep doing that. But as a first pass towards arriving
> at a more "systematic" way of naming things, one which doesn't require
> us all to remember a million variants of names, we can note that most
> useful MOS's in most EDOs are subgroups of things already have names.
> So we can just use those names, and specify that name with the caveat
> that prime xyz doesn't work in this EDO, but that the rest is still
> there. That solves all of these problems at once.
>
> And if there's a useful temperament that really doesn't make sense as
> a subgroup of something else, then maybe it really should have its own
> name, as in Andrew Heathwaite's "Orgone" temperament.

Not the best possible example, because orgone == 2.7.11 superkleismic. But there are a few temperaments I really couldn't find a "full version" for, for example bridgetown, bossier, and silver.

Keenan

🔗Carl Lumma <carl@...>

Mike wrote:

> > Time-weighted namespace for temperaments overwhelmingly
> > favors the 5- and 7-limit, no matter when you start timing.
> > Or number of mentions on the lists if you prefer. Or number
> > of musical recordings if you prefer. Anyway, the naming
> > scheme hardly blows up at higher limits as you imply.

> That's only because XA isn't being archived, which is a shame.

Ok, if you start and finish timing anywhere between
2000 BCE to 2010.

Yes, it is a shame. A terrible one in my view.

> Anyway, XA seems to overwhelmingly favor subgroup temperaments.

As the first person in this galaxy to do anything serious
with subgroups, I insist on royalties.

> I suppose that in retrospect, Igs is the guy who's really to
> thank for this way of doing things...?

*cough*

> But now the problem is that we're trying to also be technically
> correct, so one person will say that a temperament is squares, but
> we'll have to explain that it's actually skwares, because there's
> no mapping for 5/1. And it's not semaphore, it's semiphore, for
> the same reason. And it's not superpyth, it's supra, and so on.
> And people get confused and feel like they have to remember a
> zillion names and give up.

That's because you're not using kernelnaming.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Dec 20, 2011 at 2:28 AM, Carl Lumma <carl@...> wrote:
>
> But it goes even better if the comma names encode their
> monzos. That's the equivalent (in arbitrariness) to Dave K's
> scheme where the generator size range names are descriptive
> of their size.

What is Dave K's scheme? If it uses 12-EDO based categorical names for
everything I don't like it.

> They do. Rationals are impractical though, because they
> get too big. But even just the numbers in the monzos have
> more syllables than something like my Hawaiian scheme.
> Wedgies (multivals) are fine but being val-based they
> share essential properties with the mapping-based system
> currently in use.

You should make a Wiki page of things you wish existed that you don't
have time to work on. Some of us have a lot of time these days. Then
it'll be ensured that you get credit for the ideas you came up with
and etc.

> The thing about limits is that it forces musicians to say more than
> they might want to say. If they use a mapping for the
> basic chords but improvise above that, the normal way says
> you have to figure out what higher primes were probably
> being mapped and then name a temperament for it -- even if
> they didn't have any such intention and used the pitches
> "chromatically". The regular mapping assumption is the
> engine that powers all the xh theory, but it's possible to
> over-rely on it. The longer I'm at this the more I think
> commas are primary. Petr seems to get good results anyway.

The more time goes on, and the more I play and write more actual
music, the more I think that temperaments are multifaceted objects
with lots of neat uses, and whichever one predominates for you will
depend on your compositional style and on what you care about when you
look at a temperament.

If what you care about is the structure of the lattice, e.g. what
comma pumps there are and what tempers out what, then you'll view
temperaments in terms of things like comma pumps and primes and so on.
There's quite a lot to be said for this approach, because it can turn
a temperament with the most complex and crappiest MOS structure
possible into a unique and useful musical construct. A temperament
that eliminates an absurdly large comma with a triangular distance of
64 from the origin is now a through-composed 32-bar chord progression
with a chord change every half note. But if you don't care about the
MOS's and work directly with pumps and primes and so on, then 5-limit
sensi and 2.9/7.5/3 sensi have almost nothing in common at all.

On the other hand, if you care about scales and rank order matrices
and melodies, the above means nothing at all to you, because ratios
are nothing more than a way to "intone" the sounds you're hearing in
as pleasantly a way as possible. If you're this guy, then at the end
of the day what you care about are scale categories. You might want to
find "different ways to intone" 5L3s and "different temperaments that
support" 4L3s and all that. You couldn't care less about
diatonic-based music in superpyth temperament. You have no idea what
point the Bach retunings I just did are supposed to prove. So to you,
there's a very obvious connection between 5-limit sensi and
2.9/7.5/3-limit sensi: they're the same thing, except for some higher
primes that you probably don't care about.

There are merits to both approaches. And when things like MODMOS's get
involved, they start to come together. But the problem is that they
come from different paradigms. And until we as theorists integrate
them into one overarching paradigm of music, then never the twain
shall meet.* And we're stuck trying to force-fit names that are built
around lattices into ideas that are built around scales.

I think that sooner or later we will have such a theory, but until
then, a nice solution is just for us to allow subgroups of
higher-limit temperaments to be named after their parents. And
besides, the people on the first side of the fence caused their own
problems by naming temperaments after multicommas and not after
individual commas in the first place.

-Mike

*I explored the difference between the two approaches a bit in this
composition - http://soundcloud.com/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/

The tonality is built around 7:9:11 in 11-EDO, and more complex things
in other temperaments, but what my ears really care about is that the
scale be 4L3s as intended and proper. The whole thing falls apart in
15-EDO and 26-EDO, where this is not the case, and I have to keep
remembering that this smaller interval is actually a "fourth" with a
half and two whole steps leading up to it, whereas this larger
interval is a "third" with only two whole steps. The whole thing
starts to break down at that point, with intonation being secondary.

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Mike wrote:

> > As the first person in this galaxy to do anything serious
> > with subgroups, I insist on royalties.
>
> Were you? What did you do?

The earliest serious work on subgroups I know of was by
Bohlen (and later Pierce), with no-2s.

Wilson worked with CPSs based on more intricate subgroups,
and mapping them to linear chains, no later than 1989
(examples appear in D'Alessandro).

On the lists, people would occasionally mention things
like "25 is a good no-3s ET" and point out that Paul
Rapoport's music made use of this fact. For example, I
said that in May 1998 -- so old it's not in the Yahoo
archives.

But Graham/Paul/Dave/Gene were remarkably focused on
complete prime or odd limits. I always wanted to get rid
of them. In Jan 2004
/tuning-math/message/8529
I asked whether TOP tunings converged to zeta tunings,
for instance.

On October 1st 2006, I suggested finding the best subgroup
for each ET from 5 to 100.
/tuning-math/message/15770

By the 6th, Graham had sent me (offlist) the results of
this search. I wasn't satisfied with his approach though,
and I had just started at Apple and wasn't doing much
with music theory.

In early 2008, Petr posted about a no-3s no-7s temperament
in 87-ET (and may have worked with other subgroups earlier,
thanks to his natural kernel-based approach). This
inspired me to do these posts, fixing what I didn't like
about Graham's earlier calculation
http://lumma.org/music/theory/subgroup/
It should still be the definitive guide rank 1 AFAIK.

In 2009 or 2010, Igs started asking about rank 2 in
connection with his EDO primer, and I worked with him on
it extensively offlist, through Sept 2010. I haven't
been involved much since then.

-Carl

🔗Carl Lumma <carl@...>

Mike wrote:

> > But it goes even better if the comma names encode their
> > monzos. That's the equivalent (in arbitrariness) to Dave K's
> > scheme where the generator size range names are descriptive
> > of their size.
>
> What is Dave K's scheme? If it uses 12-EDO based categorical
> names for everything I don't like it.

Me either. I don't like enshrining these categories, and
I don't like generator-based naming schemes. Here's the
proposal for the record (Mar 2002)

/tuning-math/message/3685

and here's how Dave would handle commas, which I should
have a fresh look at tonight in connection with
kernelnaming:
/tuning-math/message/6880
/tuning-math/message/7458

> > They do. Rationals are impractical though, because they
> > get too big. But even just the numbers in the monzos have
> > more syllables than something like my Hawaiian scheme.
> > Wedgies (multivals) are fine but being val-based they
> > share essential properties with the mapping-based system
> > currently in use.
>
> You should make a Wiki page of things you wish existed that
> you don't have time to work on. Some of us have a lot of time
> these days. Then it'll be ensured that you get credit for the
> ideas you came up with and etc.

Heh. :)

> On the other hand, if you care about scales and rank order
> matrices and melodies, the above means nothing at all to you,
> because ratios are nothing more than a way to "intone" the
> sounds you're hearing in as pleasantly a way as possible.
> If you're this guy, then at the end of the day what you care
> about are scale categories. You might want to find "different
> ways to intone" 5L3s and "different temperaments that support"
> 4L3s and all that.

Sure, the beauty of RMP is that it unifies these two
approaches that had been separate. With kernelnaming, the
tool is geometric algebra. With MOS, combinatorics.
I love how Keenan P. showed some deep connections there
recently. And for naming, I like Igs' MOS naming scheme.
But ultimately I do believe kernelnaming should be
simpler.

> And besides, the people on the first side of the fence caused
> their own problems by naming temperaments after multicommas
> and not after individual commas in the first place.

Gene invented comma lists in 2002 or something, and I've been
begging him to take them more seriously ever since.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> What is Dave K's scheme? If it uses 12-EDO based categorical names for
> everything I don't like it.

What are 12-EDO based categorical names?

I suspect you mean the standard interval names based on staff positions. Or equivalently, based on diatonic scales. These have no necessary relationship to 12-EDO. They were used prior to the invention of 12-EDO. They were, and still are, used with Pythagorean, meantone and 5-limit JI tunings.

When extended for finer categories with the additional prefixes "sub", "neutral" and "super" they map quite nicely to at least the 11-limit consonances and their approximations.

Carl, I understand your objections. We've discussed them in the past. But for better or worse, I'm afraid they already are fairly well "enshrined".

I've come to see them as a valid _universal_ system by seeing the initial seven categories as the (almost?) inevitable result of the relationship between the first two prime numbers and human psychoacoustic limitations. And it seems quite fortuitous that it can be extended in such a simple way to encompass further primes.

http://dkeenan.com/Music/IntervalNaming.htm

A few days ago I found myself seated next to a retired concert pianist and music teacher at dinner. I told her about the consonant "subminor seventh". She immediately understood where she would find it, and merely confirmed that I didn't mean a diminished seventh, but something in between.

Of course that won't do her much good with her piano. Fortunately she also teaches cello. :-)

🔗Mike Battaglia <battaglia01@...>

On Tue, Dec 20, 2011 at 2:47 PM, Carl Lumma <carl@...> wrote:
>
> > On the other hand, if you care about scales and rank order
> > matrices and melodies, the above means nothing at all to you,
> > because ratios are nothing more than a way to "intone" the
> > sounds you're hearing in as pleasantly a way as possible.
> > If you're this guy, then at the end of the day what you care
> > about are scale categories. You might want to find "different
> > ways to intone" 5L3s and "different temperaments that support"
> > 4L3s and all that.
>
> Sure, the beauty of RMP is that it unifies these two
> approaches that had been separate. With kernelnaming, the
> tool is geometric algebra. With MOS, combinatorics.
> I love how Keenan P. showed some deep connections there
> recently. And for naming, I like Igs' MOS naming scheme.
> But ultimately I do believe kernelnaming should be
> simpler.

Is kernelnaming your Hawaiian scheme? How does it use geometric
algebra? By geometric algebra do you mean the formal definition of
"geometric algebra," which is that it's the Clifford algebra over the
field of reals?

One interesting way I think that MOS's are related to temperaments are
that they turn this

[5]
[7]

into this

[5 8 12]
[7 11 16]

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Dec 20, 2011 at 9:01 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > What is Dave K's scheme? If it uses 12-EDO based categorical names for
> > everything I don't like it.
>
> What are 12-EDO based categorical names?
>
> I suspect you mean the standard interval names based on staff positions. Or equivalently, based on diatonic scales. These have no necessary relationship to 12-EDO. They were used prior to the invention of 12-EDO. They were, and still are, used with Pythagorean, meantone and 5-limit JI tunings.

I mean the perceptual "interval categories" that exist for western
listeners, with names like "major third" and "minor third" and all
that, which do not have their ultimate origin in any particular
intonational ratio. See here

http://soundcloud.com/mikebattagliamusic/sets/the-categorical-experiments/

> When extended for finer categories with the additional prefixes "sub", "neutral" and "super" they map quite nicely to at least the 11-limit consonances and their approximations.

But there is clearly something which an interval like a "major third",
in the context of common practice harmony, truly "is" which is
independent of its intonation. For instance, in some of the sharper
retunings above, the augmented fourth is closer to 3/2 than the actual
generator, and around 22 to 27-EDO the augmented second in harmonic
minor is about 5/4, and that doesn't seem to make any difference. The
only difference it made is on how pleasant the piece sounds on an
"intonational" layer. (I expect that difference will become more
important on the overall sound for my next set of retunings, which
will be slower and use more chords).

This entire dimension of experience, which to the best of my knowledge
is still poorly understood in comparison to the honorary Ph. D's
everyone around here should all be getting in psychoacoustics, is what
is truly enshrined in names like "major third" and "minor third."

From now on, I'm going to call 5/4 an augmented second, because that's
what it is in 5-limit superpyth temperament. Its essential character
is that it's dissonant and needs to resolve outward in harmonic minor.
This is the essential nature of augmented seconds, of which the best
possible intonation is 5/4.

> Carl, I understand your objections. We've discussed them in the past. But for better or worse, I'm afraid they already are fairly well "enshrined".
>
> I've come to see them as a valid _universal_ system by seeing the initial seven categories as the (almost?) inevitable result of the relationship between the first two prime numbers and human psychoacoustic limitations. And it seems quite fortuitous that it can be extended in such a simple way to encompass further primes.

FWIW, I wrote this throwaway piece here to explore what it all means

http://soundcloud.com/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/

This is written in the LLsLsLs MOS of Orgone temperament. The
"tonality" is built around 7:9:11 instead of 4:5:6 here.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

Hi Dave,

> Carl, I understand your objections. We've discussed them in the
> past. But for better or worse, I'm afraid they already are fairly
> well "enshrined".

Actually your systematic names failed to catch on. Trivial
names won the day. But I've come around on your point about
how systematic names are a good idea. I still don't think
that naming the things from tuning space (generators) is the
way to go.

> I've come to see them as a valid _universal_ system by seeing
> the initial seven categories as the (almost?) inevitable result
> of the relationship between the first two prime numbers and
> human psychoacoustic limitations.

I can certainly see the case for that, but don't tell it to
people like Igs and Mike who are testing the viability of
radically different categories.

-Carl

🔗Carl Lumma <carl@...>

Mike wrote:

> Is kernelnaming your Hawaiian scheme?

It just means naming kernels. The Hawaiian approach is
just one way to do it that might result in compact, decent-
sounding names.

> How does it use geometric algebra? By geometric algebra do
> you mean the formal definition of "geometric algebra,"

Sorry; Grassmann algebra.

> > Big mistake, it seems to me. Herman Miller posted what
> > plots of what the generator tuning thresholds look like...
> > way wonky compared to comma families.
>
> But if you classify generators by what MOS's they generate, rather
> than by how they relate to 12-EDO categories, then I think it isn't
> arbitrary at all. An MOS is something which might someday actually
> lead to a new categorical perception if you're lucky enough.

As you yourself point out, MOSs aren't so crucial.
When you get into MODMOSs that blows up, but the kernel
approach keeps going strong, all the way to untempered
Fokker blocks. Of course something obscene happens to
the generators make such a transition, too...

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Dec 20, 2011 at 10:13 PM, Carl Lumma <carl@...> wrote:
>
> As you yourself point out, MOSs aren't so crucial.
> When you get into MODMOSs that blows up, but the kernel
> approach keeps going strong, all the way to untempered
> Fokker blocks. Of course something obscene happens to
> the generators make such a transition, too...

I should add that I don't really understand how categories work. But I
do think the kernel approach happens to sync up with categories mostly
by accident. Or rather, I believe that one could build categories
around many different sorts of Fokker block, but that such things will
always be prone to perceptual distortions such that the same
categorical structure might apply to more than one Fokker block, even
in cases that are nontrivial (i.e. cases beyond obvious ones like
Fokker blocks in which all of the 5/4's are replaced with
5001/4000's).

This is why I think that kernel naming is mostly useful for looking at
things like comma pumps and such. These things, I believe, model a
completely different facet of categorical perception: the part whereby
the perception of pelog or mavila[5] changes once you realize there's
a string of "empats" (or 3/2s) running around the whole thing. So far
both myself, Keenan, and Ron have noticed this effect. I've
particularly noticed that the sound of the mavila 5/2 changes when I
know that there are three "perfect fourths" leading into it.

I'm not entirely sure that when I learn that a "major tenth" is three
"perfect fourths," what I'm specifically learning is that "a 5/2" is
three "4/3's." There are other facets of the concept of "major tenth"
and "perfect fourth" I could be relating instead, and I don't even
know what they are. But, kernel naming handles all of this nicely if
one makes the assumption that a listener is going to try to build
interval categories around harmonic ratios. In that case, the name
"4/3" doesn't just refer to a particular intonation, but also to a
category that you just so happen to have assigned a ratio-based name
to. I believe this is the "default interpretation" of regular
temperament theory for a lot of people.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Wed, Dec 21, 2011 at 12:38 AM, Mike Battaglia <battaglia01@...> wrote:
>
> This is why I think that kernel naming is mostly useful for looking at
> things like comma pumps and such. These things, I believe, model a
> completely different facet of categorical perception: the part whereby
> the perception of pelog or mavila[5] changes once you realize there's
> a string of "empats" (or 3/2s) running around the whole thing. So far
> both myself, Keenan, and Ron have noticed this effect. I've
> particularly noticed that the sound of the mavila 5/2 changes when I
> know that there are three "perfect fourths" leading into it.
>
> I'm not entirely sure that when I learn that a "major tenth" is three
> "perfect fourths," what I'm specifically learning is that "a 5/2" is
> three "4/3's." There are other facets of the concept of "major tenth"
> and "perfect fourth" I could be relating instead, and I don't even
> know what they are. But, kernel naming handles all of this nicely if
> one makes the assumption that a listener is going to try to build
> interval categories around harmonic ratios. In that case, the name
> "4/3" doesn't just refer to a particular intonation, but also to a
> category that you just so happen to have assigned a ratio-based name
> to. I believe this is the "default interpretation" of regular
> temperament theory for a lot of people.

Eh, left out an important sentence here. The point is that if one
makes this assumption, then the kernel name that applies to the effect
we've all noticed with pelog is "135/128."

-Mike

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

Oh nice. I wasn't aware. The only thing I'd say is that you missed my
beloved 4:7:9:11 subgroup, mostly because you missed 9. But being as
it took about 8 years for us all to catch up, I guess I can't complain
too much.

-Mike

On Tue, Dec 20, 2011 at 2:30 PM, Carl Lumma <carl@...> wrote:
>
>
>
> Mike wrote:
>
> > > As the first person in this galaxy to do anything serious
> > > with subgroups, I insist on royalties.
> >
> > Were you? What did you do?
>
> The earliest serious work on subgroups I know of was by
> Bohlen (and later Pierce), with no-2s.
>
> Wilson worked with CPSs based on more intricate subgroups,
> and mapping them to linear chains, no later than 1989
> (examples appear in D'Alessandro).
>
> On the lists, people would occasionally mention things
> like "25 is a good no-3s ET" and point out that Paul
> Rapoport's music made use of this fact. For example, I
> said that in May 1998 -- so old it's not in the Yahoo
> archives.
>
> But Graham/Paul/Dave/Gene were remarkably focused on
> complete prime or odd limits. I always wanted to get rid
> of them. In Jan 2004
> /tuning-math/message/8529
> I asked whether TOP tunings converged to zeta tunings,
> for instance.
>
> On October 1st 2006, I suggested finding the best subgroup
> for each ET from 5 to 100.
> /tuning-math/message/15770
>
> By the 6th, Graham had sent me (offlist) the results of
> this search. I wasn't satisfied with his approach though,
> and I had just started at Apple and wasn't doing much
> with music theory.
>
> In early 2008, Petr posted about a no-3s no-7s temperament
> in 87-ET (and may have worked with other subgroups earlier,
> thanks to his natural kernel-based approach). This
> inspired me to do these posts, fixing what I didn't like
> about Graham's earlier calculation
> http://lumma.org/music/theory/subgroup/
> It should still be the definitive guide rank 1 AFAIK.
>
> In 2009 or 2010, Igs started asking about rank 2 in
> connection with his EDO primer, and I worked with him on
> it extensively offlist, through Sept 2010. I haven't
> been involved much since then.
>
> -Carl
>
>

🔗Carl Lumma <carl@...>

🔗gbreed@...

You can get Fokker blocks from normalized lists of unison vectors (commas), segregating those inside and outside the temperament. But you can do the same thing with val lists (mappings). That follows from them being dual to each other.
There are some ways vals are easier to work with. Ranks don't go above three very often but codimensions can. I can't get Cangwu badness working with sets of unison vectors.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Wednesday, December 21, 2011 3:15:17 AM GMT-0000
Subject: [tuning] Re: Naming subgroups of temperaments

I wrote:

> As you yourself point out, MOSs aren't so crucial.
> When you get into MODMOSs that blows up, but the kernel
> approach keeps going strong, all the way to untempered
> Fokker blocks. Of course something obscene happens to
> the generators make such a transition, too...

Typos edited:

> As you yourself point out, MOSs aren't so crucial.
> When you get into MODMOSs, the MOS approach blows up,
> but the kernel approach keeps going strong all the way
> to untempered Fokker blocks. Of course something
> obscene happens to the generators during such a
> transition, too...

-C.

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🔗Carl Lumma <carl@...>

Gene wrote:

> It still seems to me you've got to pay attention to rank two.

11-limit rank 2 temperaments could have up to 30 syllables in
their Hawaiian-inspired name, but I think I can do better.
In fact I'm ready to make a bona fide suggestion.

I reckon there are probably fewer than 500 unique commas in
the comma sequences of all named temperaments so far. We can
put them in a database and give them three-letter names, of
the form consonant-vowel-consonant. Using the 17 unambiguous
consonants and five vowels, we can name over 1400 commas.
The names could be random but could also use a scheme like
the following:

The vowel could encode the largest prime factor in the comma,
a = 3, e = 5, i = 7, o = 11, u = all others

The leading and trailing consonants could encode the
unweighted triangular lattice distance of the comma, and its
size in cents, respectively. Just bin the master comma list
into 17 equal-size bins for each. As long as any peaks in
the true distribution of commas are wide compared to these
bins, commas can be added to the database incrementally
without causing too many problems. (Of course collisions
aren't forbidden, but could be resolved by bumping the last
letter to the neighboring bin with fewest members, and then
bumping the first letter if necessary, then bumping the last
letter two places, and so on.)

Fokker blocks can be accommodated by changing the length of
the vowels, thus

tempered, untempered
written "spoken"
a "mat", aa "mate"
e "pet", ee "Pete"
i "twin", ii "twine"
o "not", oo "note"
u "cub", uu "cube"

11-limit rank 2 temperaments all have three syllables in
this system. As before, infinite systems have only a
syllabic name whereas finite systems add a subgroup prefix,
e.g. "2.3.5.7-gimletpop". For true prime limit subgroups,
the shorthand "plim" would be provided; "7lim-gimletpop".

-Carl

🔗dkeenanuqnetau <d.keenan@...>

Hi Carl,

Sorry to take so long to notice this response. I'm aware that this has become the "Obscure Naming of Arkane Notions"-ism list and so no systematic naming of anything has much of a chance, but which of my systematic naming proposals were you referring to?

I wasn't actually referring to any proposal of mine being already "enshrined". I was referring to the common usage of "major third", "perfect fifth", "diminished fifth" etc.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Dave,
>
> > Carl, I understand your objections. We've discussed them in the
> > past. But for better or worse, I'm afraid they already are fairly
> > well "enshrined".
>
> Actually your systematic names failed to catch on. Trivial
> names won the day. But I've come around on your point about
> how systematic names are a good idea. I still don't think
> that naming the things from tuning space (generators) is the
> way to go.
>
> > I've come to see them as a valid _universal_ system by seeing
> > the initial seven categories as the (almost?) inevitable result
> > of the relationship between the first two prime numbers and
> > human psychoacoustic limitations.
>
> I can certainly see the case for that, but don't tell it to
> people like Igs and Mike who are testing the viability of
> radically different categories.
>
> -Carl
>