Yahoo Tuning Groups Ultimate Backup tuning-math Linear temperament names?

Have names been proposed for any of the linear microtemperaments below?

The generators and errors are for minimax. The mappings given are
octave equivalent:
[gens_per_3 gens_per_5 gens_per_7 gens_per_11 gens_per_13;
periods_per_3 periods_per_5 etc...]

Limit Period Gen Max gens Max err Prime mapping Rep ET
7-limit 1 oct 193.87 c 16 1.4 c [16 2 5] 99
11-limit 1/2 oct 216.74 c 30 3.1 c [-6 -1 10 -3; 1 1 0 0] 72
11-limit 1/2 oct 183.21 c 30 2.4 c [-6 -11 2 3; 1 0 1 0] 72
15-limit 1/3 oct 83.02 c 48 2.8 c [-6 -5 2 -3 -14; 0 2 2 2 2] 72
15-lm-wo-13 1 oct 193.24 c 35 2.8 c [-15 2 5 -22] 118

These linear temps will appear in the microtempered guitar article I'm
preparing for Xenharmonikon 18.

If you do propose a name, please also say why you think it is
appropriate. If I don't think the name makes much sense I may just
include the temperament without a name.

Others being included, whose names I have accepted, are:
miracle
magic
kleismic
schismic
diaschismic
neutral thirds

My preference is for names that are descriptive of the generator (and
also the period, when it isn't a whole octave). And when the period
isn't an octave then the name might describe any period-equivalent
inversion or extension of the generator.

Graham, have you ever thought of spelling it "majic" since it's
generated by MAJor thirds?

Then the second one above might be called "twin majic" since its
period is a half-octave, and its period minus its gen is a major third.

The third one might be called "twin minor tones".

Perhaps the first one is "semi major thirds" or "semi-majic", except
how will we distinguish it from the last one which also has a gen
which is half a major third, but has a different mapping for the prime 3.

Perhaps the fourth one is "triple minor thirds" or "triple kleismic".

Your thoughts on this will be appreciated.

-- Dave Keenan

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> Have names been proposed for any of the linear microtemperaments below?
>
> The generators and errors are for minimax. The mappings given are
> octave equivalent:
> [gens_per_3 gens_per_5 gens_per_7 gens_per_11 gens_per_13;
> periods_per_3 periods_per_5 etc...]

Graham convinced me to switch to his convention. Do you have a reason
for preferring [generator, period] over [period, generator]? I think
we should try for some degree of standardization. Noreover, you are
ignoring 2, and to me this is simply not acceptable.

> Limit Period Gen Max gens Max err Prime mapping Rep ET
> 7-limit 1 oct 193.87 c 16 1.4 c [16 2 5]

Hemiwuerschmidt. You should give all of the mapping and give it in a
canonical reduced form, or a give a reduced comma basis, or a
wedgie--or best of all, all three.

99
> 11-limit 1/2 oct 216.74 c 30 3.1 c [-6 -1 10 -3; 1 1 0 0]

> 11-limit 1/2 oct 183.21 c 30 2.4 c [-6 -11 2 3; 1 0 1 0]

Unidec.

> 15-limit 1/3 oct 83.02 c 48 2.8 c [-6 -5 2 -3 -14; 0 2 2 2 2]

Trikleismic.

> 15-lm-wo-13 1 oct 193.24 c 35 2.8 c [-15 2 5 -22]

For the 7-limit temperament, I have it listed as Hemithird.

> If you do propose a name, please also say why you think it is
> appropriate.

The names I give are ones which have already been used; they are not
new proposals.

If I don't think the name makes much sense I may just
> include the temperament without a name.

My preference is for you not to sow confusion by introducing new names
for already named and cataloged temperaments; not naming if you object
to a name seems like a plan.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > Have names been proposed for any of the linear microtemperaments
below?
> >
> > The generators and errors are for minimax. The mappings given are
> > octave equivalent:
> > [gens_per_3 gens_per_5 gens_per_7 gens_per_11 gens_per_13;
> > periods_per_3 periods_per_5 etc...]
>
> Graham convinced me to switch to his convention. Do you have a reason
> for preferring [generator, period] over [period, generator]? I think
> we should try for some degree of standardization.

The article deals only with linear temperaments of octave-repeating
octave-equivalent scales, so the reader is only interested in how many
periods there are modulo the number in the octave. So when the period
_is_ the octave these are all zero and I prefer to omit them. It's
easier to omit them without confusion if they come _last_. I do not
want to use any vector or matrix math in the article. It's pitched at
an audience with more basic math skills.

But I agree that for the greatest generality the period should come
first, followed by the generator(s).

> Noreover, you are
> ignoring 2, and to me this is simply not acceptable.

Oh blow it out your ear. :-)

The article deals only with octave-repeating octave-equivalent scales
so why should I bother saying that there are zero generators in the
1:2 every time. And the size of the period, given as a fraction of an
octave, is a bit of a giveaway as to how many of _them_ are in the
1:2. Also I have limited space to fit many things about each LT in
columns across the width of a page.

But I certainly agree that for greatest generality 2 should be
included in all the matrices and vectors.

The main thing is that I explain the format I'm using.

> > Limit Period Gen Max gens Max err Prime mapping
Rep ET
> > 7-limit 1 oct 193.87 c 16 1.4 c [16 2 5]
>
> Hemiwuerschmidt. You should give all of the mapping and give it in a
> canonical reduced form, or a give a reduced comma basis, or a
> wedgie--or best of all, all three.

Commas and wedgies are utterly irrelevant to my article. My canonical
generator is the smallest one (less than half the period), what's yours?

> > 11-limit 1/2 oct 216.74 c 30 3.1 c [-6 -1 10 -3; 1 1 0 0]

No name for this one? Is there any other LT more deserving of being
called "twin thirds"?

> > 11-limit 1/2 oct 183.21 c 30 2.4 c [-6 -11 2 3; 1 0 1 0]
>
> Unidec.

Please explain. Why not call it "twin minortones" since the generator
represents 9:10 in the temperament.

> > 15-limit 1/3 oct 83.02 c 48 2.8 c [-6 -5 2 -3 -14; 0 2 2 2 2]
>
> Trikleismic.

That makes sense, but I would have said "triple kleismic". If you use
the prefix tri- to mean 3 equispaced chains of a generator then what
would you use to mean a single chain of 1/3 of that generator? i.e. in
the way that you use hemi- to mean a single chain of 1/2 a generator?

> > 15-lm-wo-13 1 oct 193.24 c 35 2.8 c [-15 2 5 -22]
>
> For the 7-limit temperament, I have it listed as Hemithird.

Makes sense too. But I don't understand why you use hemi- when it is
already established that semi- is used to halve a musical interval, as
in semitone and semisharp. I've asked you that before, but I don't
remember a satisfactory answer.

> > If you do propose a name, please also say why you think it is
> > appropriate.
>
> The names I give are ones which have already been used; they are not
> new proposals.

So what? They are still only proposals as far as my article is
concerned. I don't have to use the name you give me, and so I'd still
like explanations for the less than obvious ones, like "unidec".

> If I don't think the name makes much sense I may just
> > include the temperament without a name.
>
> My preference is for you not to sow confusion by introducing new
> names for already named and cataloged temperaments;

That's why I'm asking.

How about this one?

Period Gen Max gens Max err Prime mapping (no 2s)
1 oct 351.45 c 10 1.9 c [2 25 13]

"cata neutral thirds"?

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> The article deals only with linear temperaments of octave-repeating
> octave-equivalent scales, so the reader is only interested in how
many
> periods there are modulo the number in the octave.

Someone reading about temperaments presumably wants to know what they
are. Your sloppy method means they must work at it even to get the
mapping of primes in terms of period and generator. How can you
simultaneously maintain you are dumbing down *and* increase the
number of mathematical hoops you expect your readers to jump through?
If you want to make things easy, you are going about it in a very,
very bad way.

So when the period
> _is_ the octave these are all zero and I prefer to omit them. It's
> easier to omit them without confusion if they come _last_. I do not
> want to use any vector or matrix math in the article.

It's pitched at
> an audience with more basic math skills.

So that is why you insist on making the math difficult??

> The article deals only with octave-repeating octave-equivalent
scales
> so why should I bother saying that there are zero generators in the
> 1:2 every time.

You should "bother" to give your poor readers a break by explicitly
giving them a mapping to primes. What is this--pledge week for
microtonalists? If they understand your article without the secret
decoder ring they are in? In any case sloppy is sloppy.

> Commas and wedgies are utterly irrelevant to my article.

Commas are irrelevant to explaining temperaments? I don't think so.
Once again, you propose leaving your readers clueless.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
>
> > The article deals only with linear temperaments of octave-repeating
> > octave-equivalent scales, so the reader is only interested in how
> many
> > periods there are modulo the number in the octave.
>
> Someone reading about temperaments presumably wants to know what they
> are.

Yes, but there are many ways to answer that. Those that are best for
mathematicians are not necessarily best for musical types. For musical
types octave-equivalence is a given. It is difficult to consider its
absence.

> Your sloppy method means they must work at it even to get the
> mapping of primes in terms of period and generator.

What sloppy method? You don't even know what my method of explanation is.

Take another look at Graham's temperament catalog.
http://x31eq.com/catalog.htm
He doesn't bother saying that there are zero generators in the octave
every time either, and he doesn't give period mappings at all. I
haven't heard you berating _him_ lately. Sorry Graham :-)

> How can you
> simultaneously maintain you are dumbing down *and* increase the
> number of mathematical hoops you expect your readers to jump through?
> If you want to make things easy, you are going about it in a very,
> very bad way.

You have absolutely no idea how I am going about it. All you know is
the format in which I am tabulating the mappings. I have to say, you
would be the last person I would ask for advice on explaining things
to non-mathematicians.

I was asking for help with the names. That's all. You have chosen not
to explain your proposed names, or point me to earlier explanations,
instead going on with this ridiculous rant. So I may well use my own
names if I think they are sufficiently obvious.

> So when the period
> > _is_ the octave these are all zero and I prefer to omit them. It's
> > easier to omit them without confusion if they come _last_. I do not
> > want to use any vector or matrix math in the article.
>
> It's pitched at
> > an audience with more basic math skills.
>
> So that is why you insist on making the math difficult??

Again you have no idea what math I'm using, so I don't know where you
get off with this sort of arrogant nonsense.

> > The article deals only with octave-repeating octave-equivalent
> scales
> > so why should I bother saying that there are zero generators in the
> > 1:2 every time.
>
> You should "bother" to give your poor readers a break by explicitly
> giving them a mapping to primes.

I know you have trouble grasping this, but they don't actually care
about "primes" per se. Only octave-reduced primes: 3/2, 5/4, 7/4,
11/8, 13/8, etc.

> What is this--pledge week for
> microtonalists? If they understand your article without the secret
> decoder ring they are in? In any case sloppy is sloppy.

How did you get to be such a prick?

> > Commas and wedgies are utterly irrelevant to my article.
>
> Commas are irrelevant to explaining temperaments? I don't think so.
> Once again, you propose leaving your readers clueless.

My article is not intended as a treatise on temperaments in general.
It use temperaments with very specific properties to achieve a very
specific task - guitar fretboard optimisation. Due to limited space,
the use of temperaments will have to be partly in the nature of a
recipe. The understanding of exactly _why_ one is doing certain things
may have to come later. However I do mention commas in general and the
fact that temperaments distribute them. It's just that the knowledge
of which _particular_ commas any given microtemperament distributes
has absolutely no application in the fretboard optimisation method, so
their inclusion would just be clutter.

-- Dave Keenan

🔗monz <monz@attglobal.net>

hi Dave and Gene,

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > How can you simultaneously maintain you are dumbing down
> > *and* increase the number of mathematical hoops you expect
> > your readers to jump through? If you want to make things
> > easy, you are going about it in a very, very bad way.
>
> You have absolutely no idea how I am going about it.
> All you know is the format in which I am tabulating the
> mappings. I have to say, you would be the last person
> I would ask for advice on explaining things to
> non-mathematicians.
>
> <snip>
>
> > > So when the period _is_ the octave these are all zero
> > > and I prefer to omit them. It's easier to omit them
> > > without confusion if they come _last_. I do not
> > > want to use any vector or matrix math in the article.
> >
> > > It's pitched at an audience with more basic math skills.
> >
> > So that is why you insist on making the math difficult??
>
> Again you have no idea what math I'm using, so I don't
> know where you get off with this sort of arrogant nonsense.
>
> <snip>
>
> > What is this--pledge week for microtonalists? If they
> > understand your article without the secret decoder ring
> > they are in? In any case sloppy is sloppy.
>
> How did you get to be such a prick?

first of all, can both of you *PLEASE* take a deep breath
and count to 10 before responding? and if you're still
angry, turn off the computer and respond later.

it would be stupid if you pissed each other off any further.
just cool it, please. there *are* valuable comments being
made in this discussion.

Gene, i'm sorry but i have to agree with Dave that your
explanations are *hardly* the kind non-mathematicians can
make sense out of. i know that when you post a list of
data output from your programs, it's valuable information.

but your presentation of it is so cryptic that if i haven't
read every single word posted to that thread, i don't have
the foggiest idea what those lists of numbers mean, and i
simply file it away for "future reference" ... and unfortunately
have yet to reach the future in which i can understand it.

anyway, aside from personality conflicts, one thing i want
to speak on is the use of vector addition. i have a very
hard time understanding why so many people here consider it
to be "advanced" math. it's just simple addition and subtraction,
and doesn't get more complicated than that unless the reader
*needs* to calculate the ratios from those exponents.

i see no reason why a paper can't simply present a tuning
on a lattice diagram, with a clear explanation of how the
lattice relates to the monzos, and give the reader all the
ratio data in the form of monzos.

*if* the reader is adventurous enough to try calculating the
ratios for himself, fine. if not, then it doesn't get any
more complicated than addition, subtraction, and comparing
results to lattice-points. that's as "dumbed down" as it gets.

-monz

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

I'm sorry about that last message. I lost it.

But you do seem to have that effect on people, Gene. :-)

I should have waited a bit longer before hitting the send button.

You won't believe this, but within minutes of me sending that message
I got a phone call from my mum (mom) telling me about this book she
had just been reading on non-agressive communication! Freaky.

Can we please forget this octave-equivalence war for a moment and just
talk about the names.

I've searched the tuning-math archive for an explanation of the name
"Unidec" and can find none. I've racked my brains for a reason. I
assume it is an abbreviation for "unidecimal" which means relating to
the number 11. It doesn't give rise to an 11 note DE scale so it can't
be that. It's generator can be described as an approximation to 7:11,
but it can also be described as 11:14 or 5:9 or 9:10, so that doesn't
seem like a good reason. It is a good 11-limit temperament, but so are
many others, so that doesn't seem like a good reason.

"Twin minortones" sure looks like a better name to me.

And I'm interested in your responses (and those of anyone else) to the
other questions I raised regarding prefixes for multiple chains
(fractional-octave periods) versus prefixes for generators which are
fractions of common intervals or other named generators.

I suggest for the former: twin (or double), triple, quadruple,
quintuple, sextuple, septuple, octuple, nonuple, decuple, undecuple,
duodecuple, etc. (as separate words, not prefixes),

and for the latter: semi-, tri-, quarter-, penta-, hexa-, hepta-,
octa-, ennea-, deca-, undeca-, dodeca- etc. as actual prefixes.
Hopefully most of these will be very rare, except semi-.

There is of course a problem with tri- penta- etc. since these usually
mean multiples instead of fractions, but there's a worse problem with
third, fifth etc, since these usually refer to intervals. But I
suggest that third- fifth- etc should be used in place of tri- penta-
etc when applied to the word "tone".

And with the "tuple" words, maybe when it gets big we just say "29
chains of" instead.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Dave and Gene,
> first of all, can both of you *PLEASE* take a deep breath
> and count to 10 before responding?

Done.

> anyway, aside from personality conflicts, one thing i want
> to speak on is the use of vector addition. i have a very
> hard time understanding why so many people here consider it
> to be "advanced" math. it's just simple addition and subtraction,
> and doesn't get more complicated than that unless the reader
> *needs* to calculate the ratios from those exponents.

It isn't only vector addition I'm avoiding, but matrix multiplication.
I deliberately don't even use the word vector, but simply "list",
because the mere introduction of a new word like vector can cause
people to _assume_ there's a whole lot of stuff associated with it
that they will need to know, and don't. So they give up. Probably the
method of fretboard optimisation I'm describing is so complex anyway
that it is futile to explain it to non-mathematicians in the available
space, but it's worth a try. I'm sure you agree that the main thing is
to have lots of diagrams.

> i see no reason why a paper can't simply present a tuning
> on a lattice diagram, with a clear explanation of how the
> lattice relates to the monzos, and give the reader all the
> ratio data in the form of monzos.
>
> *if* the reader is adventurous enough to try calculating the
> ratios for himself, fine. if not, then it doesn't get any
> more complicated than addition, subtraction, and comparing
> results to lattice-points. that's as "dumbed down" as it gets.

Yes. If my reader is to apply my method for themselves they will need
to calculate monzos from ratios, and yes I use lattice diagrams to
illustrate the process.

🔗Carl Lumma <ekin@lumma.org>

>> >For musical types octave-equivalence is a given.
>>
>> It is?
>
>OK. Let me rephrase that.
>
>For most musical types of people who are not mathematicians,
>octave-equivalence is a given.

I don't think that's true. Charles Carpenter, Brian McLaren,
Jeff Scott, Wendy Carlos and many more have used non-octave
scales. All these people have technical backgrounds, but the
general interest on the tuning list has always seemed quite
high to me.

Whether they make sense on guitar is another matter, which I'm
not qualified to address.

Anyway, just a caveat.

>> >I was asking for help with the names. That's all. You have
>> >chosen not to explain your proposed names, or point me to
>> >earlier explanations, instead going on with this ridiculous
>> >rant.
>>
>> Didn't he say he uses names because they have already been used?
>
>Wot, do you mean that if I make up a name for something, give no
>explanation, and use it three times in my own posts (but no one else
>does), that's enough to make it established terminology and everyone
>else ought to just use it from then on? And I should just ignore any
>requests for justification? :-)

That, I can't say. I just took his word that he got the names from
elsewhere. There's a unidecimal (or whatever) comma, IIRC, from
Wilson or earlier.

As for justification, I don't think names need any. If you find
something with no name, it's your right to name it whatever you
like if you're so inclined, with the possible exception of naming
it after yourself.

I know you're one for rigorous ontology. I, on the other hand,
am one for absurd, funny names.

Yet another approach, and one of the more interesting approaches
to naming I've come across, is that of Denny Genovese. He tends
to use very obvious, descriptive multi-word names with no fancy
shortening. Such as, "binary flute", "southeast just intonation
center", etc.

I've always been very fond of Partch's names for instruments.

According to Mark Vonnegut, hippies had an unwritten rule that
everything must have a name. But apparently the emphasis wasn't
on naming classes of things, but on naming particular instances,
often with a tendency toward anthromorphization (such as naming
one's car "Charles").

Now back to your regularly-scheduled flame war.

-Carl

🔗monz <monz@attglobal.net>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I've searched the tuning-math archive for an explanation of the name
> > "Unidec" and can find none. I've racked my brains for a reason.
>
> The generator can be taken to be an 11/7, which Manuel has listed as
> a "unidecimal augmented fifth." It may not be a very good name, but if
> you think that you've waited a long time to say so.

Sorry about that. I guess I was just too busy with other things like
work, family and sagittal, around the time you were posting lists of
11-limit LTs. But it isn't as if lots of people are already using the
name, so I don't see a problem with changing it.

If I use names in my paper that are only my own construction, I will
indicate this. But that doesn't include where I might merely change a
hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic.
I can't see these causing any confusion.

By the way, I have credited you and Graham as follows. Please let me
know if this is not accurate:

Actually finding the linear microtemperaments with the lowest
complexity for a given set of ratios, was extremely difficult until
very recently. In mid 2001, prompted by the rediscovery of the Miracle
temperament, both Graham Breed and Gene Ward Smith wrote computer
programs to search for potentially useful linear temperaments those
having the lowest complexity for a given range of error sizes. Graham
Breed has made this extraordinary facility available free online for
anyone to use at http://x31eq.com/temper/. Gene's software
uses a different method to generate temperament candidates for
testing, and has served as a very important check that Graham's
algorithm is not missing anything important.

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > Yes. If my reader is to apply my method for themselves they will need
> > to calculate monzos from ratios, and yes I use lattice diagrams to
> > illustrate the process.
>
> If they are going to turn monzos into octaves/generators, they will
> need the information a mapping matrix gives, whether or not presented
> as a matrix.

Yes indeed. I'm even using the MATLAB/Octave syntax, since it's the
most compact I know of ("Octave" is a free GNU clone of MATLAB). I'm
just not _calling_ them matrices, and I'm making them
octave-equivalent, which means there are no parameters for the prime
2, and periods are only counted modulo the octave.

> This idea you have rejected with contempt.

Well I wouldn't go that far. But I'm certainly leaving it up to
someone else to teach the readers of Xenharmonicon, matrix arithmetic
in its full generality.

> What to you
> propose as a replacement?

I simply describe the individual scalar arithmetic operations
involved, with examples, without ever ascending to the level of
abstraction of vector or matrix operators. Of course such abstraction
is a truly wonderful thing, and you and Graham have done more than
anyone in helping us to appreciate that on tuning-math, but I don't
have the space to introduce my readers to it. And I don't have the
need since I'm only dealing with the simple cases in my examples -
5-limit, usually with an octave period.

> To be sure, the information can be extracted
> using the generator size in cents, but that, as I pointed out, is
> *harder*.

No, I'm not trying to do that.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I might merely change a
> >hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic.
> >I can't see these causing any confusion.
>
> Use a little imagination.

Would you care to explain what you mean by that cryptic remark?

Do you mean that you think they _could_ cause confusion? If so, then I
think it would be good if we agreed on some system for distinguishing
a prefix implying a fractional octave period from one that implies a
fractional interval generator. I've made one proposal.

I don't think you can accuse me of insisting on rigour or taking the
fun out of naming when I'm accepting names like miracle and magic and
catakleismic, and some based on commas like schismic and kleismic and
wuerschmidt, and others based on generators. But I think we can only
afford the luxury of totally non-descriptive names for the most common
or the best.

If I come up with some obscure temperament and tell you I'm composing
an algorithmic piece in the "Fart" temperament. The first thing you're
going to ask me is "What's that?", and I'll say, "Oh it's generated by
three chains of generators which are one third of a major third". But
if we had a system and I said I'm composing a piece in the
"triple-trithirds" temperament, you wouldn't even have to ask. And of
course it's possible to have both common _and_ systematic names for
things.

🔗Carl Lumma <ekin@lumma.org>

>> >I might merely change a
>> >hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic.
>> >I can't see these causing any confusion.
>>
>> Use a little imagination.
>
>Would you care to explain what you mean by that cryptic remark?

Sorry, it wasn't meant to be cryptic.

>Do you mean that you think they _could_ cause confusion?

Sure. I can't count the number of times I've checked out a new
subject and observed a terminology difference that wasn't discussed
anywhere. It drives me crazy wondering whether they're actually
the same.

>I don't think you can accuse me of insisting on rigour or taking the
>fun out of naming when I'm accepting names like miracle and magic and
>catakleismic, and some based on commas like schismic and kleismic and
>wuerschmidt, and others based on generators. But I think we can only
>afford the luxury of totally non-descriptive names for the most common
>or the best.

That makes sense. But I don't think generators sizes are important,
especially re. diatonic names. We've been over this before, and it
boggles me how you can support such a program.

In my book commas are the way to name linear temperaments, and what
we actually need is a systematic way of naming commas. Which, IIRC,
you've also tried your hand at. Did it have something to do with
komma and/or quoma? If so, I think that's bad, 'cause it isn't
phonetic. The "a" vs. "ina" thing I thought went over better.

>If I come up with some obscure temperament and tell you I'm composing
>an algorithmic piece in the "Fart" temperament. The first thing you're
>going to ask me is "What's that?", and I'll say, "Oh it's generated by
>three chains of generators which are one third of a major third".

And once I knew that, I wouldn't soon forget it. It's why fantastic
absurdities are so common in advertising.

>But
>if we had a system and I said I'm composing a piece in the
>"triple-trithirds" temperament, you wouldn't even have to ask.

Oh yes I would. I haven't the foggiest idea what this means, and I
hang out here regularly. Does "triple" mean three periods in an
octave? And does "tri" mean 3 times the size of a third, or 1/3rd
the size of a third? And is it a major or minor third? And even
if you answer all these questions I won't necc. be able to get close
to the optimal generator. Really a cent of resolution is needed
here, or it can mean the difference between maps.

-Carl

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> Sorry about that. I guess I was just too busy with other things like
> work, family and sagittal, around the time you were posting lists of
> 11-limit LTs. But it isn't as if lots of people are already using
the
> name, so I don't see a problem with changing it.

I've already have up a posting devoted *solely* to unidec. Moreover,
I rejected names like your proposal for a reason--it is likely to
confuse unidec with the minortone/hemiminortone family. If you decide
to go ahead and start unilaterally renaming things, be warned that I
at least may not agree to it. That will likely sow confusion. If you
propose a renaming, we should have some kind of consensus. To start
with, we need an explanation of why we should want one.

> If I use names in my paper that are only my own construction, I will
> indicate this. But that doesn't include where I might merely change
a
> hemiwuerschmidt to semiwuerschmidt or trikleismic to triple
kleismic.
> I can't see these causing any confusion.

Are you planning to aka these?

> By the way, I have credited you and Graham as follows. Please let me
> know if this is not accurate:

Gene's software
> uses a different method to generate temperament candidates for
> testing, and has served as a very important check that Graham's
> algorithm is not missing anything important.

I used various methods to generate candidates, in order to be self-
checking, but that has little to do with my software beyond the fact
that is able to deal with a variety of methods. This also pretty well
ignores the whole issue of theory, and seems to suggest Graham came
up with a list, and I checked it or something like that. It was a
little more complicated.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Sure. I can't count the number of times I've checked out a new
> subject and observed a terminology difference that wasn't discussed
> anywhere. It drives me crazy wondering whether they're actually
> the same.

Good point.

> >I don't think you can accuse me of insisting on rigour or taking the
> >fun out of naming when I'm accepting names like miracle and magic and
> >catakleismic, and some based on commas like schismic and kleismic and
> >wuerschmidt, and others based on generators. But I think we can only
> >afford the luxury of totally non-descriptive names for the most common
> >or the best.
>
> That makes sense. But I don't think generators sizes are important,
> especially re. diatonic names. We've been over this before, and it
> boggles me how you can support such a program.

So when some minimally-mathematical musician wants to tune up their
synthesizer or whatever, to my new Fart temperament. I should give
them a list of six 19-limit commas and say, "Go to it bud!". Gimme a
break.

> In my book commas are the way to name linear temperaments,

How do you make that work past 5-limit? i.e when there are several commas.

> and what
> we actually need is a systematic way of naming commas. Which, IIRC,
> you've also tried your hand at. Did it have something to do with
> komma and/or quoma? If so, I think that's bad, 'cause it isn't
> phonetic. The "a" vs. "ina" thing I thought went over better.

Nah. I only use the spelling "komma" sometimes when I want to
distinguish the generic term from the term for a specific range of
sizes. Go back and read from
/tuning-math/message/6875
if you want to understand my comma naming system.

> >If I come up with some obscure temperament and tell you I'm composing
> >an algorithmic piece in the "Fart" temperament. The first thing you're
> >going to ask me is "What's that?", and I'll say, "Oh it's generated by
> >three chains of generators which are one third of a major third".
>
> And once I knew that, I wouldn't soon forget it. It's why fantastic
> absurdities are so common in advertising.

You'll remember the name, but why will you remember what it _is_. Did
you find some association, some "reason" for the name? I didn't intend
any. I suppose all the "th" sounds in the description?

Advertising often uses off-the-wall associations, but they _are_
associations.

> >But
> >if we had a system and I said I'm composing a piece in the
> >"triple-trithirds" temperament, you wouldn't even have to ask.
>
> Oh yes I would. I haven't the foggiest idea what this means,

I said "If we had a system". And even if you didn't know the system,
at least you'd only have to learn it once.

> and I
> hang out here regularly. Does "triple" mean three periods in an
> octave?

Yes.

> And does "tri" mean 3 times the size of a third, or 1/3rd
> the size of a third?

Which seems more likely given that we usually give the generator in
lowest terms, or at least significantly smaller than the octave. And
we're usually interested in how many generators make up common
consonances, not the other way 'round.

I admit it's not ideal, but I can't find any short prefixes that
unambiguously indicate a fraction rather than a multiple or a diatonic
interval, except for semi- (or hemi-) and quarter-.

> And is it a major or minor third?

That would be part of the "system" too, only being allowed to drop the
"major" and "perfect" off interval names. This is something we already
do in several existing temperament names.

> And even
> if you answer all these questions I won't necc. be able to get close
> to the optimal generator. Really a cent of resolution is needed
> here, or it can mean the difference between maps.

That's true. But you can only pack so much information into a name. At
least it does get you in the right ballpark.

🔗Carl Lumma <ekin@lumma.org>

>> That makes sense. But I don't think generators sizes are important,
>> especially re. diatonic names. We've been over this before, and it
>> boggles me how you can support such a program.
>
>So when some minimally-mathematical musician wants to tune up their
>synthesizer or whatever, to my new Fart temperament. I should give
>them a list of six 19-limit commas and say, "Go to it bud!". Gimme a
>break.

No, you should give them the size of the generator in cents, and
probably the entire scale, and probably the entire fretboard, and
probably the name of a good luthier. :)

>> In my book commas are the way to name linear temperaments,
>
>How do you make that work past 5-limit? i.e when there are several
>commas.

I was thinking of using the one that's not tempered out. Of
course this can be expressed in oompteen ways. One probably just
chooses the way with the lowest complexity, but I admit this
weakens my suggestion somewhat.

>Go back and read from
>/tuning-math/message/6875
>if you want to understand my comma naming system.

>> >If I come up with some obscure temperament and tell you I'm composing
>> >an algorithmic piece in the "Fart" temperament. The first thing you're
>> >going to ask me is "What's that?", and I'll say, "Oh it's generated by
>> >three chains of generators which are one third of a major third".
>>
>> And once I knew that, I wouldn't soon forget it. It's why fantastic
>> absurdities are so common in advertising.
>
>You'll remember the name, but why will you remember what it _is_.

Because I have a hook.

>Did you find some association, some "reason" for the name? I didn't
>intend any. I suppose all the "th" sounds in the description?

I don't think association has to be logical. At least not for me.

>> And does "tri" mean 3 times the size of a third, or 1/3rd
>> the size of a third?
>
>Which seems more likely given that we usually give the generator in
>lowest terms, or at least significantly smaller than the octave. And
>we're usually interested in how many generators make up common
>consonances, not the other way 'round.

I thought you were using tertia for division, or some such.

>> And even
>> if you answer all these questions I won't necc. be able to get close
>> to the optimal generator. Really a cent of resolution is needed
>> here, or it can mean the difference between maps.
>
>That's true. But you can only pack so much information into a name. At
>least it does get you in the right ballpark.

C'mon. You could just say "700 cents". But that's not much of a
name. So you've got to dress it up, and make it more ambiguous in
the process. Seems pretty silly to me.

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> > But it isn't as if lots of people are already using the
> > name, so I don't see a problem with changing it.
>
> I've already have up a posting devoted *solely* to unidec.

Yes. I saw that one. The only posts containing the word "Unidec" come
from you. In most cases, the name is buried in a great list of
temperaments and their vectors and matrices. It seems no one ever
responded regarding that particular temperament, and as far as I can
tell, you never volunteered any reason for the name until now.

You can't assume that a lack of response means that everyone assents
to a name forever. I think you've gone overboard in naming so many
things long before anyone actually _needed_ a name for them.

Is it a territorial thing? You've gone and peed on all these
temperaments and commas and now you think another doggie-come-lately
is trying to overpower your scent? :-)

All I'm asking is - if you have a system for the more descriptive
names (in particular those based on the generator and period) what is
it? And if you don't, can we make some improvements in that direction?

> Moreover,
> I rejected names like your proposal for a reason--it is likely to
> confuse unidec with the minortone/hemiminortone family.

OK! At last we're getting into the kind of discussion I had hoped for,
when instead I got a rant about how "sloppy" I was being by assuming
octave equivalence or something.

What are the mappings for minortone and hemiminortone?

> If you decide
> to go ahead and start unilaterally renaming things,

I never wanted to _unilaterally_ name anything. _That_ is what you
seem to have done. I wanted to discuss your names. You apparently
refused until now.

> be warned that I
> at least may not agree to it. That will likely sow confusion. If you
> propose a renaming, we should have some kind of consensus.

Gee I wish I'd thought of that? :-)

> To start
> with, we need an explanation of why we should want one.

One what? A consensus? Oh I guess you mean the renaming of Unidec?

Well in a way it's _worse_ than a meaningless name like "Fart",
because it _looks_ like it is descriptive, but in fact it tells you
nothing about the temperament that it doesn't have in common with
zillions of others.

> > If I use names in my paper that are only my own construction, I will
> > indicate this. But that doesn't include where I might merely change
> a
> > hemiwuerschmidt to semiwuerschmidt or trikleismic to triple
> kleismic.
> > I can't see these causing any confusion.
>
> Are you planning to aka these?

Carl has convinced me to do so. But I'd prefer we just agreed on a few
principles to make some of these names a little more systematic. Do
you have some such principles that I am not understanding? I don't
understand why you are unwilling to discuss this.

> I used various methods to generate candidates, in order to be self-
> checking, but that has little to do with my software beyond the fact
> that is able to deal with a variety of methods. This also pretty well
> ignores the whole issue of theory, and seems to suggest Graham came
> up with a list, and I checked it or something like that.

What is it about the theory that you think I should mention?

> It was a little more complicated.

It always is. But I'm not writing a history article. Please feel free
to suggest alternate wording.

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> Yes. I saw that one. The only posts containing the word "Unidec"
come
> from you.

Until now, I seem to have been the only person to take an interest in
the temperament. Is that my fault?

> You can't assume that a lack of response means that everyone assents
> to a name forever. I think you've gone overboard in naming so many
> things long before anyone actually _needed_ a name for them.

If you want to blame someone for that, why not pick on Paul, who has
named 5-limit nanotemperaments no one could possibly ever use in
practice. I have NOT named things needlessly; I want to talk about
temperaments, and while the wedgie or TM comma basis might supply a
name, they really don't work with human beings. You can't tell someone
"Oh yes, that's the [12, 22, -4, -6, 7, -40, -51, -71, -90, -3]
temperament"; but saying "Oh yes, that's unidec" gives something you
might be able to associate with.

> Is it a territorial thing? You've gone and peed on all these
> temperaments and commas and now you think another doggie-come-lately
> is trying to overpower your scent? :-)

Oh, please. I've accomodated you by adopting a number of your names
for temperaments on my lists of temperaments, which in some cases
meant I changed the name I had listed, despite the fact that I don't
much like how you name things. Your names tend to be boring and
difficult to remember. However, if you are going to adopt an Only
Dave Keenan Names attitude, don't expect me to play along. I prefer
calling things vulture, like Paul does, to calling them things which
sound like an explosion in a chemical factory.

> All I'm asking is - if you have a system for the more descriptive
> names (in particular those based on the generator and period) what
is
> it? And if you don't, can we make some improvements in that
direction?

If you want to propose a completely systematic naming proceedure,
then have at it. Name everything the Keenan way, and make every name
tell you just exactly what the temperament is. Maybe people will like
it, and adopt your scheme. However, I see little point in half-
measures.

> > Moreover,
> > I rejected names like your proposal for a reason--it is likely to
> > confuse unidec with the minortone/hemiminortone family.
>
> OK! At last we're getting into the kind of discussion I had hoped
for,
> when instead I got a rant about how "sloppy" I was being by assuming
> octave equivalence or something.
>
> What are the mappings for minortone and hemiminortone?

Minortone is the 5-limit 50031545098999707/50000000000000000
comma system, extendible to 7-limit. 17 10/9's make up a 6, and 35 a
40.

> > If you decide
> > to go ahead and start unilaterally renaming things,
>
> I never wanted to _unilaterally_ name anything. _That_ is what you
> seem to have done.

I said renaming.

I wanted to discuss your names. You apparently
> refused until now.

What gives you that idea?

Do
> you have some such principles that I am not understanding? I don't
> understand why you are unwilling to discuss this.

Yes, pick memorable names.

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
>
> > Yes. I saw that one. The only posts containing the word "Unidec"
> > come from you.
>
> Until now, I seem to have been the only person to take an interest in
> the temperament. Is that my fault?

Of course not. That wasn't my point. I remind you:

You wrote: "It may not be a very good name, but if you think that
you've waited a long time to say so."

I wrote: "... But it isn't as if lots of people are already using the
name, so I don't see a problem with changing it."

You wrote: "I've already have up a posting devoted *solely* to unidec."

I wrote: Yes. I saw that one. The only posts containing the word
"Unidec" come from you.

My point is that it wasn't actually necessary to name it back then
because there was only one person interested in it.

When in 1998 I wrote a whole article with extensive diagrams about
what is now called kleismic, it had already been discussed on the
tuning list by at least four people, but we apparently saw no need to
name it at that stage, unless you count "chain of minor thirds" as a
name. The word "kleismic" does not appear in the article, although of
course the kleisma gets a mention.

It took another 3 years before the term "kleismic" was applied to it.

> > You can't assume that a lack of response means that everyone assents
> > to a name forever. I think you've gone overboard in naming so many
> > things long before anyone actually _needed_ a name for them.
>
> If you want to blame someone for that, why not pick on Paul, who has
> named 5-limit nanotemperaments no one could possibly ever use in
> practice.

OK. Sorry if I've unfairly "picked on" you. I wasn't aware these had
come from Paul. Paul, please consider yourself "picked on".

Whoever started it, it looks like everyone has gotten a bit carried
away with the fun of giving cute names to every temperament or comma
in sight.

I think that may be unfair to those who may come after us. They may
not have a clue what we were talking about. Such names are far more in
need of a "secret decoder ring" than systematic names are.

I'm thinking maybe we've had our fun now, and we should do like in
chemistry. First you use only the systematic name (or no name at all,
just a description in terms of period and generators, in cents if
necessary), and only if a particular temperament becomes a hot topic
of conversation, particularly if someone actually uses it for music or
notation or instrument building, _then_ those people can look at
giving it a less boring common name.

> I have NOT named things needlessly; I want to talk about
> temperaments,

As above.

> and while the wedgie or TM comma basis might supply a
> name, they really don't work with human beings. You can't tell someone
> "Oh yes, that's the [12, 22, -4, -6, 7, -40, -51, -71, -90, -3]
> temperament";

I totally agree.

> but saying "Oh yes, that's unidec" gives something you
> might be able to associate with.

Well I dunno about anyone else, but saying "two chains of 183 c
generators" is something I can associate with a helluvalot better, and
if that can be condensed systematically into a name then it's a better
name in my book. I'm sorry if that's boring, but excitement isn't
always the most important thing to me. You seem to rarely give optimum
generator sizes in cents in your posted lists of temperaments.

> > All I'm asking is - if you have a system for the more descriptive
> > names (in particular those based on the generator and period) what
> is
> > it? And if you don't, can we make some improvements in that
> direction?
>
> If you want to propose a completely systematic naming proceedure,
> then have at it. Name everything the Keenan way, and make every name
> tell you just exactly what the temperament is. Maybe people will like
> it, and adopt your scheme. However, I see little point in half-
> measures.

As you should realise by now, I'm not proposing "half-measures", but
double measures. Systematic names _and_ common names. Although most
temperaments would automatically _have_ systematic names, there would
of course be no point in using them for really common things like
meantone or schismic. But for temperaments that have been discovered,
but not extensively discussed or used, the systematic name should
probably be the only name. Other temperaments would be at an in
between stage where we might need to use both their systematic and
common names for a while. So we'd need two "name" columns in any
temperament database.

The same situation occurs not only in chemistry, but also biology
(taxonomy). Athough in taxonomy there is an unfortunate fondness for
eponyms (naming after the discoverer) among the more descriptive
terminology. What's more, common names tend to differ from place to
place. People not on the tuning lists may have discovered and named
some of these temperaments, and I suppose they would be entitled to
keep using their common names, but systematic names would be, well,
systematic.

Is this a dumb idea?

Now of course I would rather such a system was obtained by consensus
(at least of those on this list who have an interest), and so would
you. You're just saying go ahead and do it the "Keenan" way because
you're still sore at me.

> Minortone is the 5-limit 50031545098999707/50000000000000000
> comma system, extendible to 7-limit. 17 10/9's make up a 6, and 35 a
> 40.

This brings up a good point. Log-flat badness isn't much good for
deciding which temperament gets a particular name, because you'll
always be able to go far enough out in complexity that you will find a
"less-bad" mapping with a generator that's very close to the one
you're trying to name.

IMHO the 5-limit temperament you describe above is so complex it
doesn't need a name at all. Whether we have sharp cutoffs or gradual
rolloffs on error and complexity, there has to be _some_ such for
naming purposes. Doesn't there?

My views on that are already on record. This temperament has more than
twice the weighted rms complexity of 10 that I must have imagined some
of us had agreed on as a reasonable cutoff for 5-limit (_if_ you must
have a sharp cutoff).

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> > > You can't assume that a lack of response means that everyone
assents
> > > to a name forever. I think you've gone overboard in naming so
many
> > > things long before anyone actually _needed_ a name for them.
> >
> > If you want to blame someone for that, why not pick on Paul, who
has
> > named 5-limit nanotemperaments no one could possibly ever use in
> > practice.
>
> OK. Sorry if I've unfairly "picked on" you. I wasn't aware these had
> come from Paul. Paul, please consider yourself "picked on".

Despite his opinion above, Gene first gave the data for all of these,
as well as much more complex ones, and i just named the ones simpler
than the atom of Kirnberger so that one would have something other
than numbers, numbers, numbers, to refer to on Monz's ET page.

> Well I dunno about anyone else, but saying "two chains of 183 c
> generators" is something I can associate with a helluvalot better,

But it doesn't uniquely signify a temperament. I believe Graham has
discussed 13-limit generators which are fifths within a fraction of a
cent in optimal size. In order to actually temper, a temperament must
have a mapping associated with it.

> IMHO the 5-limit temperament you describe above is so complex it
> doesn't need a name at all.

It describes 46, 125, 171, 217 equal temperaments, barely used so far
but why not? Look, if it'll make you happy i'll replace all the names
on Monz's page with SINGLE LETTERS except for meantone and schismic
(or whatever you say) . . . that way the *signification purpose* is
not lost . . .

> Whether we have sharp cutoffs or gradual
> rolloffs on error and complexity, there has to be _some_ such for
> naming purposes. Doesn't there?

The atom of kirnberger is of historical interest as a result of the
means of setting one of its associated temperaments, namely 12-equal.
It's a bit outside the usual direct application of temperament, which
is why i put 12 in paretheses in the table.

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

Paul Erlich wrote:
> Despite his opinion above, Gene first gave the data for all of these,
> as well as much more complex ones, and i just named the ones simpler
> than the atom of Kirnberger so that one would have something other
> than numbers, numbers, numbers, to refer to on Monz's ET page.

To remind other readers: We're talking about the diagram and table in
http://sonic-arts.org/dict/eqtemp.htm

Dave Keenan:
> > Whether we have sharp cutoffs or gradual
> > rolloffs on error and complexity, there has to be _some_ such for
> > naming purposes. Doesn't there?

Paul Erlich:
> The atom of kirnberger is of historical interest as a result of the
> means of setting one of its associated temperaments, namely 12-equal.
> It's a bit outside the usual direct application of temperament, which
> is why i put 12 in paretheses in the table.

I think these parentheses are a bit subtle - easily missed. An
asterisk and corresponding footnote might be better. However ...

The atom of Kirnberger may be of historical interest, but why would
anyone be interested in using the 5-limit linear temperament in which
it vanishes, as opposed to using an ET that happens to be a member of
it? If all 12 chains were extended equally you'd need 108 notes before
a single minor third appeared!

Even if this linear temperament (and not just its comma) is of
interest because the comma was used in the tuning of 12-equal, I don't
see why that should imply that all less-complex 5-limit temperaments
are also of interest.

I'm suspecting that blind faith in log-flat badness measures may have
something to do with this.

I think we should take some account of the fact that we're supposed to
be considering musical purposes for actual human beings here, not pure
mathematics.

Please explain to me why anyone would want to make musical use of any
5-limit linear temperament where you need more than 10 generators to
approximate some 5-limit ratio, when we have schismic that can get us
errors of less than a quarter of a cent, with only 9 generators?

I'll grant that Aristoxenean is a special case and might be included
despite needing 12 generators, because of its relationship to 12-ET.

Don't bother with a "you just never know" type of answer, because if
you're going to clutter an already cluttered (but very clever) diagram
with lines corresponding to them, and give them meaningless or cryptic
names and fill up a huge table (43 temperaments!), then you'd better
do a lot better than that. Particularly given the fact that we can now
generate temperaments on demand, for specific purposes, using Graham's
Breed's online temperament finder. http://x31eq.com/temper/

The same goes for 5-limit linear temperaments having any error greater
than the one that uses the same neutral third generator as both major
and minor third. Why would anyone care about such so-called 5-limit
temperaments?

-------

Now we're talking about the one called "minortone" in the
abovementioned table.

Dave Keenan:
> > Well I dunno about anyone else, but saying "two chains of 183 c
> > generators" is something I can associate with a helluvalot better,

Paul Erlich:
> But it doesn't uniquely signify a temperament. I believe Graham has
> discussed 13-limit generators which are fifths within a fraction of a
> cent in optimal size. In order to actually temper, a temperament must
> have a mapping associated with it.

Sure. But giving a period and generator (and odd-limit) gets you to a
small list of possible mappings which can easily be ranked by error or
complexity. The best one (within reasonable limits (or rolloffs) of
error and complexity) can be given the simplest name, e.g.
"minortone", and the less accurate ones can be called "inaccurate
minortone", "super-inaccurate minortone" and the more complex ones
"complex minortone", "supercomplex minortone", etc. That way it would
be rare to ever need to refer to those with the longer names.

Dave Keenan:
> > IMHO the 5-limit temperament you describe above is so complex it
> > doesn't need a name at all.

Paul Erlich:
> It describes 46, 125, 171, 217 equal temperaments, barely used so far
> but why not?

So it includes some interesting ETs, but these ET's are also included
in many other temperaments. It's what's special about the actual
temperament (the line between the ETs) that we should be asking here.
And the answer is "practically nothing".

> Look, if it'll make you happy i'll replace all the names
> on Monz's page with SINGLE LETTERS except for meantone and schismic
> (or whatever you say) . . . that way the *signification purpose* is
> not lost . . .

I earlier wrote:
"I certainly don't want you to use letters instead of names in those
wonderful diagrams. I'm just saying I think it has gone far enough,
and besides there is at least _some_ kind of logic to most of those
names."

But I hadn't looked very closely at that stage, and I think I just
wanted out, with no hard feelings. Now I want to address those
temperaments where the names you've given have no discernable logic
(and a few that do).

These are (25): father, beep, misty, escapade, amity, parakleismic,
semisuper, vulture, enneadecal, semithirds, vavoom, tricot,
counterschismic, ennealimmal (5-limit), minortone, kwazy, astro,
whoosh, monzismic, egads, senior, gross, pirate, raider, atomic. Note
that this includes everything that comes after schismic in the table.

In my opinion, the diagram (and table) would be greatly improved if
these did not appear at all, because they are either too inaccurate or
too complex to be of any likely musical use. By removing these you
would reduce clutter on the diagram and focus attention on the
temperaments that deserve it.

If anyone really wants a 5-limit temperament that has an error less
than a thousanth of a cent, and they don't mind if they need more
notes than a grand piano to get a single triad, then you can direct
them to Graham's temperament finder.

But if you really think these 25 should stay, then I'll take you up on
your offer and ask that you refer to them with single letters, except
where they are 5-limit subsets of higher-limit temperaments that _do_
deserve a name, in which case their names should be followed by
"(5-limit)".

Carl Lumma wrote:
> Nooooooooooooooooooooooo!

Thanks Carl. Rest assured that I've taken this carefully reasoned
defense into account in the above. ;-)

-- Dave Keenan

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> I'm suspecting that blind faith in log-flat badness measures may
have
> something to do with this.

blind faith in log-flat badness and believing it's a useful measure
for any purpose are two completely different issues.

> Don't bother with a "you just never know" type of answer, because if
> you're going to clutter an already cluttered (but very clever)
diagram
> with lines corresponding to them, and give them meaningless or
cryptic
> names and fill up a huge table (43 temperaments!),

going to? i already did! or do you think i'm going to add further
clutter (since you said already cluttered . . .)?

> then you'd better
> do a lot better than that.

monz made tables for ETs as large as 4296 so i wanted to show how
those ETs were related to one another. perhaps the best solution is
to make different versions of the table to go with the different zoom
levels, so that it's never presented as that huge.

> The same goes for 5-limit linear temperaments having any error
greater
> than the one that uses the same neutral third generator as both
major
> and minor third. Why would anyone care about such so-called 5-limit
> temperaments?

for example, one can regard a given temperament as 'lame' in the
sense of not fully functioning, to help understand the structures
inherent in a distributionally even scale that is not equally
tempered. if nothing else, the temperament will signify that a
certain ratio is operating as a chromatic unison vector for
distributionally even scales of interest with cardinalities that
appear as numbers along the line representing the temperament.

> In my opinion, the diagram (and table) would be greatly improved if
> these did not appear at all,

they pretty much don't appear in the diagrams you would be looking
at! it's only at the zoom levels that don't interest you anyway where
you would see these lines.

> But if you really think these 25 should stay, then I'll take you up
on
> your offer and ask that you refer to them with single letters,
except
> where they are 5-limit subsets

you don't really mean subsets, but rather 'incarnations', right?

> of higher-limit temperaments that _do_
> deserve a name, in which case their names should be followed by
> "(5-limit)".

ok, if monz is on board we'll proceed to strip the personality out of
this page :). i have no qualms about doing so.

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Carl Lumma <ekin@lumma.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
>
> > I'm suspecting that blind faith in log-flat badness measures may
> > have something to do with this.
>
> blind faith in log-flat badness and believing it's a useful measure
> for any purpose are two completely different issues.

That depends how I take the word "any" here. If I interpret it as
"some" then I agree. Sure, it's useful for some purposes, and I'm very
grateful to Gene for providing us with that tool.

> > Don't bother with a "you just never know" type of answer, because if
> > you're going to clutter an already cluttered (but very clever)
> diagram
> > with lines corresponding to them, and give them meaningless or
> cryptic
> > names and fill up a huge table (43 temperaments!),
>
> going to? i already did! or do you think i'm going to add further
> clutter (since you said already cluttered . . .)?

I'm sorry. "Going to" was just a manner of speaking. I was imagining a
time before all the more complex or inaccurate temperaments were added.

> > then you'd better
> > do a lot better than that.
>
> monz made tables for ETs as large as 4296 so i wanted to show how
> those ETs were related to one another. perhaps the best solution is
> to make different versions of the table to go with the different zoom
> levels, so that it's never presented as that huge.

I don't think that would help. The question would still remain as to
why anyone would care that, for example, 4296-ET and 3125-ET are
related by a linear temperament in which the comma [71 -99, 37]
vanishes (or has any of its other given properties), since one can
come up with a linear temperament for _any_ pair of 5-limit ETs, and
you're clearly not proposing to list them all.

> > The same goes for 5-limit linear temperaments having any error
> greater
> > than the one that uses the same neutral third generator as both
> major
> > and minor third. Why would anyone care about such so-called 5-limit
> > temperaments?
>
> for example, one can regard a given temperament as 'lame' in the
> sense of not fully functioning, to help understand the structures
> inherent in a distributionally even scale that is not equally
> tempered. if nothing else, the temperament will signify that a
> certain ratio is operating as a chromatic unison vector for
> distributionally even scales of interest with cardinalities that
> appear as numbers along the line representing the temperament.

Hmm. Do you really think people will appreciate that from the mere
inclusion of such a temperament on the diagram and in the table? I'm
still having trouble figuring out what you mean, from what you've
written above. I suspect this is a bit subtle or esoteric as a reason
for including them here.

> > In my opinion, the diagram (and table) would be greatly improved if
> > these did not appear at all,
>
> they pretty much don't appear in the diagrams you would be looking
> at! it's only at the zoom levels that don't interest you anyway where
> you would see these lines.

Hmm. 7 of them appear on the default zoom:10 level and 13 of them on
the zoom:100 level. These are the levels of most interest to me, and I
suspect of most interest to most musicians.

> > But if you really think these 25 should stay, then I'll take you up
> on
> > your offer and ask that you refer to them with single letters,
> except
> > where they are 5-limit subsets
>
> you don't really mean subsets, but rather 'incarnations', right?

I suppose so. I mean where their prime-mapping matrix is a sub-matrix
of the higher limit one that does deserve a name.

> > of higher-limit temperaments that _do_
> > deserve a name, in which case their names should be followed by
> > "(5-limit)".
>
> ok, if monz is on board we'll proceed to strip the personality out of
> this page :). i have no qualms about doing so.

I guess you don't have any qualms, because you know that anyone who
does would hold _me_ responsible, not you. You've out-bluffed me here. :-)

I really don't think you had the right to make the offer you made
(regarding replacing names with letters). I'm pretty sure that was the
feeling behind Carl's "Nooooooooooooooooooooooo!".

So I thought I'd call your bluff. But I've lost my nerve for this
game, and I couldn't bear Carl's anguish if you actually went ahead
with it.

So please leave it as it is. I'm happy that you've at least heard me out.

Actually, I'd be _really_ happy if you'd just change the name of the
one you call "minortone" to something silly. Maybe Carl can suggest
one? This is because I'd like to use the name "minortone" in the
naming of an actually useful higher-limit temperament whose mapping is
not a superset of that one.

I've come to the conclusion that if you're going to give names to
meaningless temperaments, they should be meaningless names, so as to
leave the meaningful names to do real work elsewhere.

By the way, I've said it before, but I'll say it again: Those diagrams
really are marvelous. So much information at a glance. The idea of
making the numerals smaller as the numbers get bigger was particularly
brilliant.

Regards,
-- Dave Keenan

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> > wrote:
> >
> > > I'm suspecting that blind faith in log-flat badness measures
may
> > > have something to do with this.
> >
> > blind faith in log-flat badness and believing it's a useful
measure
> > for any purpose are two completely different issues.
>
> That depends how I take the word "any" here. If I interpret it as
> "some" then I agree. Sure, it's useful for some purposes, and I'm
very
> grateful to Gene for providing us with that tool.

yes, it's just what was needed to complement a series of 10x-zooms on
the ET chart.

> > > Don't bother with a "you just never know" type of answer,
because if
> > > you're going to clutter an already cluttered (but very clever)
> > diagram
> > > with lines corresponding to them, and give them meaningless or
> > cryptic
> > > names and fill up a huge table (43 temperaments!),
> >
> > going to? i already did! or do you think i'm going to add further
> > clutter (since you said already cluttered . . .)?
>
> I'm sorry. "Going to" was just a manner of speaking. I was
imagining a
> time before all the more complex or inaccurate temperaments were
added.

at that time, there were lines temperaments with much more badness,
and those have been removed.

> > monz made tables for ETs as large as 4296 so i wanted to show how
> > those ETs were related to one another. perhaps the best solution
is
> > to make different versions of the table to go with the different
zoom
> > levels, so that it's never presented as that huge.
>
> I don't think that would help. The question would still remain as to
> why anyone would care that, for example, 4296-ET and 3125-ET are
> related by a linear temperament in which the comma [71 -99, 37]
> vanishes (or has any of its other given properties), since one can
> come up with a linear temperament for _any_ pair of 5-limit ETs, and
> you're clearly not proposing to list them all.

i don't think it hurts, though, given that if someone cares enough
about 4296-ET or 3125-ET to zoom that far into the chart, they should
be equally interested in linear temperaments of that level of
complexity.

> > > The same goes for 5-limit linear temperaments having any error
> > greater
> > > than the one that uses the same neutral third generator as both
> > major
> > > and minor third. Why would anyone care about such so-called 5-
limit
> > > temperaments?

> Hmm. Do you really think people will appreciate that from the mere
> inclusion of such a temperament on the diagram and in the table?

no, more text would be needed.

> > > In my opinion, the diagram (and table) would be greatly
improved if
> > > these did not appear at all,
> >
> > they pretty much don't appear in the diagrams you would be
looking
> > at! it's only at the zoom levels that don't interest you anyway
where
> > you would see these lines.
>
> Hmm. 7 of them appear on the default zoom:10 level and 13 of them on
> the zoom:100 level. These are the levels of most interest to me,
and I
> suspect of most interest to most musicians.

ok, list these 7 and 13.

why is the zoom 100 level of such interest to you?

> By the way, I've said it before, but I'll say it again: Those
diagrams
> really are marvelous. So much information at a glance. The idea of
> making the numerals smaller as the numbers get bigger was
particularly
> brilliant.

there's more text that needs to be added to explain the scale-tree
character of what you're seeing here, and how it implies all sorts of
wonderful DE scales at a glance.