Yahoo Tuning Groups Ultimate Backup tuning Temperament names

I'm doing my best to keep up with all the new names for
temperament classes. I'm now scraping these pages:

http://xenharmonic.wikispaces.com/Proposed+names+for+rank+2+temperaments
http://xenharmonic.wikispaces.com/Optimal+patent+val
http://xenharmonic.wikispaces.com/Chromatic+pairs

Older names come from
http://lumma.org/tuning/gws/sevlat.htm but they're in a
static file.

There are now 242 names for rank 2 classes and 84 names for
rank 3 classes, all live on my website.

I noticed that 7-limit Semaphore has been re-named.
"Semaphore" is in Paul Erlich's Middle Path paper, which is
my primary authority. Because of this, I no longer trust
the wiki names to overrule those I already have. Here's the
script's output including all the names it rejects for you
all to pick over.

Semaphore in proposed as Godzilla
Vulture in proposed as Buzzard
Negripent in proposed as Negri
Negrisept in proposed as Negri
Sensipent in proposed as Sensi
Sensisept in proposed as Sensi
Wuerschmidt in proposed as Wurschmidt
Hemithirds in proposed as Hemithird
Hemischismic in proposed as Bischismic
Dimipent in proposed as diminished
Dimisept in proposed as Diminished
5-limit rank two
7-limit rank two
Dimisept in optimal as Diminished
Negrisept in optimal as Negri
Semaphore in optimal as Godzilla
Cynder in optimal as Mothra
Sensisept in optimal as Sensi
Vulture in optimal as Buzzard
Waage in optimal as Compton
Hemischismic in optimal as Bischismic
7-limit rank three
11-limit rank two
Sensi in optimal as Sensus
Hemithird in optimal as Hemithirds
11-limit rank three
13-limit rank two
Valentine in optimal as Lupercalia
Miracle in optimal as Miraculous
Unidec in optimal as Hendec
13-limit rank three
Portent in optimal as Portending
Tyr in optimal as Borneo
Jove in optimal as Jovis
Baldur in optimal as Greenland
Thor in optimal as Thunor
Donner in optimal as Rym
Dominant in chromatic as Supra

I may be missing collisions in subgroup cases because I
don't enforce canonical ordering of harmonics. The
mapping in Hermite normal form will depend on that ordering.

Graham

🔗genewardsmith <genewardsmith@...>

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

> I noticed that 7-limit Semaphore has been re-named.
> "Semaphore" is in Paul Erlich's Middle Path paper, which is
> my primary authority.

My recollection is that "semaphore" was renamed after discussion with some guy named Graham Breed. The idea was that we could use the name instead for the rank three temperament tempering out 49/48.

> Semaphore in proposed as Godzilla

Check with Graham Breed

> Vulture in proposed as Buzzard

Vulture was only proposed as 5-limit.

Rather than go on, I'll wonder why Middle Path is definitive?

> Dominant in chromatic as Supra

Not the same temperament!

🔗Graham Breed <gbreed@...>

"genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...>
> wrote:
>
> > I noticed that 7-limit Semaphore has been re-named.
> > "Semaphore" is in Paul Erlich's Middle Path paper,
> > which is my primary authority.
>
> My recollection is that "semaphore" was renamed after
> discussion with some guy named Graham Breed. The idea was
> that we could use the name instead for the rank three
> temperament tempering out 49/48.

I don't remember it, so you'll have to provide a reference.

> > Vulture in proposed as Buzzard
>
> Vulture was only proposed as 5-limit.

I don't know where this came from. It's in one of my old
lists that I didn't keep citations for.

> Rather than go on, I'll wonder why Middle Path is
> definitive?

Because it's the first paper we tell people to read, the
first paper that was published from the tuning-math
community, and the names represented a tuning-math
consensus. There was a lot of discussion about it at the
time. It also gives a standard set of examples that I've
used since -- with the names.

> > Dominant in chromatic as Supra
>
> Not the same temperament!

The same temperament class. If it wasn't the same, it
wouldn't have been flagged.

Graham

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "genewardsmith" <genewardsmith@...> wrote:
> >
> > --- In tuning@...m, Graham Breed <gbreed@>
> > wrote:
> >
> > > I noticed that 7-limit Semaphore has been re-named.
> > > "Semaphore" is in Paul Erlich's Middle Path paper,
> > > which is my primary authority.
> >
> > My recollection is that "semaphore" was renamed after
> > discussion with some guy named Graham Breed. The idea was
> > that we could use the name instead for the rank three
> > temperament tempering out 49/48.
>
> I don't remember it, so you'll have to provide a reference.

Rather than try to track down who I discussed it with and where, let's see what you have to say about the problem:

(1) Two names for a rank two temperament, godzilla and semaphore

(2) Zero names for a rank three temperament, which tempers out 49/48 and hence splits the fourth in two.

(3) What to do?

> > > Dominant in chromatic as Supra
> >
> > Not the same temperament!
>
> The same temperament class. If it wasn't the same, it
> wouldn't have been flagged.

What's a "temperament class"?

🔗Carl Lumma <carl@...>

Thanks for doing this, Graham. Comments below:

> Semaphore in proposed as Godzilla

7-limit semaphore only, right? I generally prefer unique
names for extensions only when multiple extensions are of
approximately the same badness. Even then I might prefer a
scheme such as "semaphore 7b" etc. However, "godzilla" has
been picked up by a number of people and that should count
for something.

> Wuerschmidt in proposed as Wurschmidt

I personally hate the "ue" Anglicization, for whatever
that's worth.

> Hemithirds in proposed as Hemithird

The plural is definitely for choice.

> Hemischismic in proposed as Bischismic
> Hemischismic in optimal as Bischismic

Is the generator half or twice the size of schismic?
And don't we use "schismatic" now? (However I seem to
recall looking into this and concluding that "matic"
is really no more correct that "mic".)

> 5-limit rank two
> 7-limit rank two
> 7-limit rank three
> 11-limit rank two
> 11-limit rank three
> 13-limit rank two
> 13-limit rank three

Script error or wiki typo?

> Cynder in optimal as Mothra

Should match whatever we decide re. godzilla.

> Waage in optimal as Compton

IIRC Compton had precedence over Waage.

> Valentine in optimal as Lupercalia

WTF is Lupercalia??

> Miracle in optimal as Miraculous

Miraculous... NOT

> Portent in optimal as Portending

ding? NOT

-Carl

🔗Carl Lumma <carl@...>

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

> > Rather than go on, I'll wonder why Middle Path is
> > definitive?
>
> Because it's the first paper we tell people to read, the
> first paper that was published from the tuning-math
> community, and the names represented a tuning-math
> consensus. There was a lot of discussion about it at the
> time. It also gives a standard set of examples that I've
> used since -- with the names.

Agree. There should be a good reason to change something
in Middle Path.

> > Not the same temperament!
>
> The same temperament class. If it wasn't the same, it
> wouldn't have been flagged.

Applying the above logic, please stop using "temperament class".

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

I will really wade in over my head and suggest:

Perhaps a systematic naming convention such as used in the metric system, or
organic chemistry, or IUPAC higher element names?
I know they get ugly and really hard to say. OTOH I think there is something
positive if you can look at even an 8 or 10 syllable name and get an idea of
what it indicates.
In my favor I notice that Ron Sword has been using a convention like this
for his scales.

Right now I can't tell you what Rodan or Godzilla or Father mean except two
appeared in Japanese Sci-Fi movies and the last tried to exorcise a green
pea soup spewing girl.

Disclaimer:

I'm not a tune smith and no asked me - its just a random suggestion.

Chris

On Fri, Apr 8, 2011 at 4:25 PM, Carl Lumma <carl@...> wrote:

>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> > > Rather than go on, I'll wonder why Middle Path is
> > > definitive?
> >
> > Because it's the first paper we tell people to read, the
> > first paper that was published from the tuning-math
> > community, and the names represented a tuning-math
> > consensus. There was a lot of discussion about it at the
> > time. It also gives a standard set of examples that I've
> > used since -- with the names.
>
> Agree. There should be a good reason to change something
> in Middle Path.
>
>
> > > Not the same temperament!
> >
> > The same temperament class. If it wasn't the same, it
> > wouldn't have been flagged.
>
> Applying the above logic, please stop using "temperament class".
>
> -Carl
>
>
>

🔗genewardsmith <genewardsmith@...>

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

> > Wuerschmidt in proposed as Wurschmidt
>
> I personally hate the "ue" Anglicization, for whatever
> that's worth.

There are more than one reasonable extensions of the 5-limit temperament, and Wurschmidt is only proposed for one of them.

> > Hemithirds in proposed as Hemithird
>
> The plural is definitely for choice.

Good.

> > Hemischismic in proposed as Bischismic
> > Hemischismic in optimal as Bischismic
>
> Is the generator half or twice the size of schismic?

The idea here is to use "hemi" only when the generator is split in towo, not when the period is split in two.

> > 5-limit rank two
> > 7-limit rank two
> > 7-limit rank three
> > 11-limit rank two
> > 11-limit rank three
> > 13-limit rank two
> > 13-limit rank three
>
> Script error or wiki typo?

What's the problem?

>
> > Valentine in optimal as Lupercalia
>
> WTF is Lupercalia??

One of several alternative extensions of valentine, higher in error and badness than the main line. Lupercalia, the old Roman holiday, around Valentine's Day.

> > Miracle in optimal as Miraculous
>
> Miraculous... NOT

Another extension with higher error and badness.

> > Portent in optimal as Portending

There are a bunch of extensions of portent with about the same badness.

🔗Graham Breed <gbreed@...>

On 9 April 2011 00:20, Carl Lumma <carl@...> wrote:
> Thanks for doing this, Graham. Comments below:
>
>> Semaphore in proposed as Godzilla
>
> 7-limit semaphore only, right? I generally prefer unique
> names for extensions only when multiple extensions are of
> approximately the same badness. Even then I might prefer a
> scheme such as "semaphore 7b" etc. However, "godzilla" has
> been picked up by a number of people and that should count
> for something.

7-limit.

There are currently over 300 different names in the database. I
really don't want to promote new names where an old one will do. But
I don't intend to fight new names that have been established somewhere
else. I did add some higher-limit extensions where they were already
coming up in the top tens.

7-limit Semphore isn't an extension of anything, anyway. That it has
4 different names does count for something, but if I call it
Semaphore/Godzilla/Semifourths/Hemifourths the tables get too big.

>> Wuerschmidt in proposed as Wurschmidt
>
> I personally hate the "ue" Anglicization, for whatever
> that's worth.

It's got an umlaut on input, and when I sort out UTF-8 it'll have an
umlaut on output.

>> Hemithirds in proposed as Hemithird
>
> The plural is definitely for choice.

. . . and it doesn't really matter either way.

>> Hemischismic in proposed as Bischismic
>> Hemischismic in optimal as Bischismic
>
> Is the generator half or twice the size of schismic?
> And don't we use "schismatic" now? (However I seem to
> recall looking into this and concluding that "matic"
> is really no more correct that "mic".)

I don't know what this is. There's an argument in the archives for
"semi" to mean dividing an interval, usually the generator, but it
seems not to have been acted on. The logic is that a semitone is half
a tone so semifourths should involve half a fourth.

Schismatic is better because it's closer to what Helmholtz wrote, and
maybe Rieman(n). But longer words tend to end in "schismic" anyway.
"Hemischismatic" is quite a mouthful.

Note that Schismatic itself is largely purged from the database in
favor of Helmholtz, Garibaldi, Cassandra, Pontiac, and maybe others.

>> 5-limit rank two
>> 7-limit rank two
>> 7-limit rank three
>> 11-limit rank two
>> 11-limit rank three
>> 13-limit rank two
>> 13-limit rank three
>
> Script error or wiki typo?

Nothing wrong that I can see. The numbers come from the wiki.

>> Cynder in optimal as Mothra
>
> Should match whatever we decide re. godzilla.

Cynder and Mothra are both in the database. This is a collision at
one particular limit, and I think Erlich 2006 rules on it.

>> Waage in optimal as Compton
>
> IIRC Compton had precedence over Waage.

Again, Compton is certainly in there. This is another higher-limit collision.

>> Valentine in optimal as Lupercalia
>
> WTF is Lupercalia??

Looks like what I thought was the obvious extension of Valentine.
It'll be in "Optimal Patent Vals".

Graham

🔗Graham Breed <gbreed@...>

On 8 April 2011 21:29, genewardsmith <genewardsmith@...> wrote:

> Rather than try to track down who I discussed it with and where, let's see what you have to say about the problem:
>
> (1) Two names for a rank two temperament, godzilla and semaphore

Four, at least.

> (2) Zero names for a rank three temperament, which tempers out 49/48 and hence splits the fourth in two.
>
> (3) What to do?

Follow the same rule as naming 81:80-planar after meantone. But
currently I don't have a name for that either so I don't know what the
rule is. I don't have a big problem with the same name being used at
different ranks.

Alternatively, move "Semifourths" to the planar case.

Graham

🔗Graham Breed <gbreed@...>

On 9 April 2011 06:39, Chris Vaisvil <chrisvaisvil@...> wrote:

> Perhaps a systematic naming convention such as used in the metric system, or organic chemistry, or IUPAC higher element names?
> I know they get ugly and really hard to say. OTOH I think there is something positive if you can look at even an 8 or 10 syllable name and get an idea of what it indicates.
> In my favor I notice that Ron Sword has been using a convention like this for his scales.

Pretty much what Dave Keenan suggested all those years ago on
tuning-math. It ended in an ugly fashion. See:

http://tech.dir.groups.yahoo.com/group/tuning-math/message/7346

> Right now I can't tell you what Rodan or Godzilla or Father mean except two appeared in Japanese Sci-Fi movies and the last tried to exorcise a green pea soup spewing girl.

And that's the problem. These names were created at a furious rate
and now they're out there.

Graham

🔗genewardsmith <genewardsmith@...>

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

> > (2) Zero names for a rank three temperament, which tempers out 49/48 and hence splits the fourth in two.
> >
> > (3) What to do?
>
> Follow the same rule as naming 81:80-planar after meantone.

I called it didymus. Will that do? For 49/48, you could call it slendro, but I think a name which expressed the fact the fourth was divided in two would be better. Semaphore was an example of that idea.

> I don't have a big problem with the same name being used at
> different ranks.

Gaah!

> Alternatively, move "Semifourths" to the planar case.

Anyone else want to weigh in on this?

> Graham
>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> On 9 April 2011 06:39, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > Perhaps a systematic naming convention such as used in the metric system, or organic chemistry, or IUPAC higher element names?

> Pretty much what Dave Keenan suggested all those years ago on
> tuning-math. It ended in an ugly fashion. See:

My objection remains that I don't want to announce to the world I've just composed music in a temperament which sounds like a complex, hideous chemical formula. Some of the ones we have are bad enough as it is.

> And that's the problem. These names were created at a furious rate
> and now they're out there.

If you want a precise naming convention, you could start here:

http://xenharmonic.wikispaces.com/Abstract+regular+temperament

🔗Carl Lumma <carl@...>

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

> > > Wuerschmidt in proposed as Wurschmidt
> >
> > I personally hate the "ue" Anglicization, for whatever
> > that's worth.
>
> There are more than one reasonable extensions of the 5-limit
> temperament, and Wurschmidt is only proposed for one of them.

Oh, maybe this came up before. I vaguely remember something
about someone trying to use these nearly identical words to
refer to two different temperaments. I was trying to repress
that thought, nearly unbearable.

> > > 5-limit rank two
> > > 7-limit rank two
> > > 7-limit rank three
> > > 11-limit rank two
> > > 11-limit rank three
> > > 13-limit rank two
> > > 13-limit rank three
> >
> > Script error or wiki typo?
>
> What's the problem?

These aren't the droids Graham was looking for.

-Carl

🔗Carl Lumma <carl@...>

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

> Schismatic is better because it's closer to what Helmholtz
> wrote, and maybe Rieman(n). But longer words tend to end in
> "schismic" anyway. "Hemischismatic" is quite a mouthful.

That's right, it was the fact the Ellis, at least, wrote
"Skhismic temperament" that got me to think it was OK.
Did Helmholtz do it differently in German?

> Note that Schismatic itself is largely purged from the database in
> favor of Helmholtz, Garibaldi, Cassandra, Pontiac, and maybe others.

Noted, thanks.

> >> 5-limit rank two
> >> 7-limit rank two
> >> 7-limit rank three
> >> 11-limit rank two
> >> 11-limit rank three
> >> 13-limit rank two
> >> 13-limit rank three
> >
> > Script error or wiki typo?
>
> Nothing wrong that I can see. The numbers come from the wiki.

I thought each line was supposed to contain a pair
of different names used for the same wedgie. What's
going on above then?

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Graham, Carl and Gene,

Chemistry (and other sciences) have parallel naming conventions.

Vinegar, acetic acid, and ethanoic acid are the same chemical - the last
name is the IUPAC (official) name. They do, incidentially have the same
Chemical Abstracy Number (CAS #
64-19-7) http://www.commonchemistry.org/ChemicalDetail.aspx?ref=64-19-7
Or course more than one name for something is even more confusing. But when
things get more complex the "official" names are usually the most sensible.

I read the link to Dave's post - I'm not nearly as invested in this
proposal.

An alternative - which may exist on the wiki that I don't recognize, is a
master list that correlates the common names with a more systematic listing
of the temperament or tuning family.

The CAS number serves as that type of index for chemicals. Even though I
don't understand how to make a scale from the wedgie in a sense that is a
type of index, though a fairly complex index for me.

Again, these are some thoughts towards increasing the ability of others to
assimilate the tuning field by systematic ordering. Of course - every major
field of science that has its roots in history (chemistry, geology,
medicine, biology, etc. etc.) has developed what is essentially its own
language. The concepts meant by the language are usually not too hard to
understand when you have a "dictionary" but until that "dictionary" is found
or created the learning curve is pretty steep.

Chris

On Sat, Apr 9, 2011 at 2:33 AM, Graham Breed <gbreed@...> wrote:

>
>
> Pretty much what Dave Keenan suggested all those years ago on
> tuning-math. It ended in an ugly fashion. See:
>
>
>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> An alternative - which may exist on the wiki that I don't recognize, is a
> master list that correlates the common names with a more systematic listing
> of the temperament or tuning family.

That in part is what the optimal patent val page is for. It lists rank two and rank three temperaments from the five to the thriteen limit, and two (in the case of rank two) or three (in the case of rank three) patent vals, using the shorthand notation a&b&c. Since these are patent vals, unlike Graham's use of the same sort of notation they identify the temperament in question, which can easily be found from it. Occasionally when there are not enough patent vals I use the long form and give the normal val list. The a&b or a&b&c system identifies a unique temperament but is non-unique so it doesn't work as a unique name, but it could be modified (say, alphabetical ordering) to provide one.

> The CAS number serves as that type of index for chemicals. Even though I
> don't understand how to make a scale from the wedgie in a sense that is a
> type of index, though a fairly complex index for me.

These unique identifiers tend to be. The normal comma list often has big, nasty commas, the a&b&c system doesn't always work, the wedgie is long and complex past the seven-limit, the Frobenius projection map is fairly horrendous. The normal val list is easier, and Graham is using either that or something similar (I haven't checked.) Graham's suggestion of reduced row echelon form would also work, but not be as meaningful to the eye.

🔗Petr Parízek <petrparizek2000@...>

Chris wrote:

> Chemistry (and other sciences) have parallel naming conventions.
>
> Vinegar, acetic acid, and ethanoic acid are the same chemical - the last
> name is the IUPAC (official) name. They do, incidentially have the same
> Chemical Abstracy Number (CAS #
> 64-19-7) http://www.commonchemistry.org/ChemicalDetail.aspx?ref=64-19-7
> Or course more than one name for something is even more confusing. But > when
> things get more complex the "official" names are usually the most > sensible.

I don't think anything like this is actually possible.

I'm not sure how you'd like to apply this concept to something like regular temperaments where you have hundreds of possible explanations for particular generator sizes (a generator like ~233 cents may approximate something in one temperament and something else in another).

And then, there's the strong divide of oppinions over what we should to characterize the temperament with, in the first place. While Gene or Graham prefers EDO combinations in order to describe the possible "melodic properties" of the temperament, I prefer vanishing intervals because they can clearly explain the harmonical (or let's call it "chordal") possibilities of the temperament. The thing here is that something like "19&34" doesn't tell me that six minor thirds approximate a 3/1 here, which the ratio of 15625/15552 explains clearly.

Petr

🔗Daniel Nielsen <nielsed@...>

On Sat, Apr 9, 2011 at 11:44 AM, Petr Parízek <petrparizek2000@...>wrote:

And then, there's the strong divide of opinions over what we should to
> characterize the temperament with, in the first place. While Gene or Graham
>
> prefers EDO combinations in order to describe the possible "melodic
> properties" of the temperament, I prefer vanishing intervals because they
> can clearly explain the harmonical (or let's call it "chordal")
> possibilities of the temperament. The thing here is that something like
> "19&34" doesn't tell me that six minor thirds approximate a 3/1 here, which
>
> the ratio of 15625/15552 explains clearly.
>

What metric is used to determine these edo combinations?
I have a very notional idea of a systemization for edos; however, it is not
based on the factorization of the edo number, so I don't know how valid it
might be. Anyway, it gives the first favored edos as
2,4,7,9,12,14,17,19,22,24,27,29,31,34,36,39. Does this set seem reasonable?

🔗Petr Parízek <petrparizek2000@...>

Daniel wrote:

> What metric is used to determine these edo combinations?
> I have a very notional idea of a systemization for edos; however, it is > not
> based on the factorization of the edo number, so I don't know how valid it
> might be. Anyway, it gives the first favored edos as
> 2,4,7,9,12,14,17,19,22,24,27,29,31,34,36,39. Does this set seem > reasonable?

Probably not.
34-EDO and 19-EDO both temper out 15625/15552 -- i.e. in both of them, the nearest interval to 3/1 is 6 times larger than the nearest interval to 6/5. That means that both of them can be used as for "hanson temperament". You could also say this about 53-EDO or 72-EDO.
OTOH, 12-EDO cannot be used for hanson since the nearest interval to 3/1 is one step larger than 6 minor thirds.
This means that you get hanson by combining temperaments like 19&34 or 34&53 or 53&72 but not 19&12.
If you combine 19&12, you get meantone, because in both of these, the interval closest to 5/1 is 4 times larger than the interval closest to 3/2 -- i.e. they both temper out 81/80.
The obvious thing worth noting here is that a 2D temperament is not defined by an unique pair of EDOs -- for example, 19&31 also gives you meantone and 31&50 as well.
In contrast, the vanishing interval is still 81/80 and there's only one such interval there (unless you want to include its integer powers like 6561/6400 or some such).

Petr

🔗Daniel Nielsen <nielsed@...>

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Thanks Chris, for pointing out that the problem we're trying to
solve is very similar to the one solved by the CAS system.

Like Petr, I prefer the normal comma list to the normal val
list or the two-ETs method. However, there are so many commas
I don't see how to create a prefix lingo for them.

Dave's solution was to use the size of the generator (e.g.
"hemithirds"). The problem is that the same generator can be
used with different mappings. Also, "half a major third" is
not very precise.

So I think the best solution is the colorful names (e.g.
"godzilla") with a lookup page that tells you the normal
comma list and wedgie. Ideally this page would be a tree,
based on comma sequences.

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Graham, Carl and Gene,
[snip]

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Carl,

It sounds like a many to one relationship database layout. So then one
could arrive at the same tuning regardless of point of entry into the
database.

There is of course a qualitative difference when you go from 1 size
step to 2 step sizes, etc. (there is a chemistry analogy I'll leave
out)

Those cases would logically have a different "colorful" index - but
the analogous CAS index value, if built right, could be the same. I
think (if I even have a clue) it would work like a wedgie where a
"field" in the CAS index would indicate different things.
for instance an index number like 2-32-2.5 would indicate 2 step
sizes, 32 steps, a two and a half octave period. One could even
encode scales into a number. This would take some more thinking on my
part but for instance in 12 equal a major scale is 1101110 in binary
(whole step =1 and half step = 2) but more compactly can be
represented as 110 decimal - but even better, 6E as hex. This specific
example is limited however - I think it illustrates a way of encoding
the information. Since I will plead ignorance (and I do apologize Gene
- you have tried) of the details of the wedgie all of this may be
covered already. However, the main idea is to create a unique
identifier that can describe any tuning and perhaps scale that we can
conceive at this time. Doing that we have a handle on organizing,
ranking, categorizing, and eventually dividing and concurring.

A lot of the graphs I see Paul generating seem to organize in
geometric way though I don't have a good handle on the meaning yet.

Chris

On Sat, Apr 9, 2011 at 5:19 PM, Carl Lumma <carl@...> wrote:
>

> So I think the best solution is the colorful names (e.g.
> "godzilla") with a lookup page that tells you the normal
> comma list and wedgie. Ideally this page would be a tree,
> based on comma sequences.
>
> -Carl
>

🔗Daniel Nielsen <nielsed@...>

>
>
> Favored why? I can't see the reasoning behind this list.
>
>
It's numerology, but the difference pattern 3,2,3,2,.. with some certain
variations in the pattern at certain places in the sequence seems to me
potentially to crop up in other important wave-based phenomena and in
certain areas of number theory, though it's both too notional and a little
too involved an explanation to be worthwhile putting on-list at the moment.
Still, it's something I am interested in investigating and would like to
present if it attains even a little more "rule of thumb" validity.

I'm still a microtonal neophyte. Gene, would you have a ready list of EDOs
that you consider preferred in a general context of human composition and
listening and wouldn't mind taking your time to share?

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Daniel,

If it helps (and you didn't know already) I've improvised / written in a lot
of different tunings and organized them here:

http://micro.soonlabel.com/

Do *not* feel obligated to comment on anything.

While I of course enjoy comments the vast majority of these pieces are one
off exploration improvisations for my own education. So its no big deal - I
hope they help. And of course the Wiki has links to even more examples by
other composers. (And I host some work of other composers [with permission]
as well on the above link)

Chris

On Sat, Apr 9, 2011 at 7:14 PM, Daniel Nielsen <nielsed@...> wrote:

>
>
>
>> Favored why? I can't see the reasoning behind this list.
>>
>>
> It's numerology, but the difference pattern 3,2,3,2,.. with some certain
> variations in the pattern at certain places in the sequence seems to me
> potentially to crop up in other important wave-based phenomena and in
> certain areas of number theory, though it's both too notional and a little
> too involved an explanation to be worthwhile putting on-list at the moment.
> Still, it's something I am interested in investigating and would like to
> present if it attains even a little more "rule of thumb" validity.
>
> I'm still a microtonal neophyte. Gene, would you have a ready list of EDOs
> that you consider preferred in a general context of human composition and
> listening and wouldn't mind taking your time to share?
>
>

🔗Herman Miller <hmiller@...>

On 4/9/2011 2:36 PM, Petr Parï¿½zek wrote:
> Daniel wrote:
>
>> What metric is used to determine these edo combinations?
>> I have a very notional idea of a systemization for edos; however, it is
>> not
>> based on the factorization of the edo number, so I don't know how valid it
>> might be. Anyway, it gives the first favored edos as
>> 2,4,7,9,12,14,17,19,22,24,27,29,31,34,36,39. Does this set seem
>> reasonable?
>
> Probably not.
> 34-EDO and 19-EDO both temper out 15625/15552 -- i.e. in both of them, the
> nearest interval to 3/1 is 6 times larger than the nearest interval to 6/5.
> That means that both of them can be used as for "hanson temperament". You
> could also say this about 53-EDO or 72-EDO.
> OTOH, 12-EDO cannot be used for hanson since the nearest interval to 3/1 is
> one step larger than 6 minor thirds.
> This means that you get hanson by combining temperaments like 19&34 or 34&53
> or 53&72 but not 19&12.
> If you combine 19&12, you get meantone, because in both of these, the
> interval closest to 5/1 is 4 times larger than the interval closest to
> 3/2 -- i.e. they both temper out 81/80.
> The obvious thing worth noting here is that a 2D temperament is not defined
> by an unique pair of EDOs -- for example, 19&31 also gives you meantone and
> 31&50 as well.
> In contrast, the vanishing interval is still 81/80 and there's only one such
> interval there (unless you want to include its integer powers like 6561/6400
> or some such).

The nice thing about labels like "19&31" or "31&50" is that they clear up any ambiguity when you're trying to extend temperaments like "meantone" to higher limits. They're the same as 12&19 in 7-limit meantone, but in 11-limit you've got 12&31 "meantone" and 19&31 "meanpop" (which includes 31&50). In the 17-limit, the two varieties of "meanpop" (19&31, 31&50) are distinct.

19&31: [<1 2 4 7 -2 10 2|, <0 -1 -4 -10 13 -15 5|]
31&50: [<1 2 4 7 -2 10 15|, <0 -1 -4 -10 13 -15 -26|]

The biggest problem is that a few temperaments can't be labeled this way, or at least not easily. Take these other 17-limit versions of meanpop for instance:

[<1 2 4 7 -2 2 2|, <0 -1 -4 -10 13 4 5|]
[<1 2 4 7 -2 10 7|, <0 -1 -4 -10 13 -15 -7|]

While not a huge problem in 7-limit temperaments, it does seem that more of these tend to show up in higher limits. I use a method for labeling these temperaments that adds letter suffixes to the basic ET numbers:

no suffix - the nearest approximations of all primes
b - a less accurate approximation of prime 3
c - a less accurate approximation of prime 5

etc.

for instance, "12" without a suffix represents <12 19 28 34 42 44 49|, but "12e" represents <12 19 28 34 41 44 49|. With these I can label temperaments like those 17-limit versions of meanpop:

12e&19: [<1 2 4 7 -2 2 2|, <0 -1 -4 -10 13 4 5|]
19g&31g: [<1 2 4 7 -2 10 7|, <0 -1 -4 -10 13 -15 -7|]

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Thanks Chris, for pointing out that the problem we're trying to
> solve is very similar to the one solved by the CAS system.

When giving names to prescription drugs, chemical names are not used. Instead, a plethora of made-up names is the system. The drug with the generic name Warfarin is also known as Cumadin, Jantoven, Marfarin, Marevan, Lowarin, Warfan and Warfant, for instance, and considered as rat poison is usually called Warfarin. No one seems to want to call it
(RS)-4-hydroxy- 3-(3- oxo- 1-phenylbutyl)- 2H- chromen- 2-one for some reason.

My point is, I don't think we need see these types of names as in competition, as they serve different purposes, and we can survive more than one name.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> >
> >
> > Favored why? I can't see the reasoning behind this list.
> >
> >
> It's numerology, but the difference pattern 3,2,3,2,.. with some certain
> variations in the pattern at certain places in the sequence seems to me
> potentially to crop up in other important wave-based phenomena and in
> certain areas of number theory, though it's both too notional and a little
> too involved an explanation to be worthwhile putting on-list at the moment.

starting from 5, we could get a pattern going like that of 5, 7, 9, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, ..., 41, ..., 46, ..., 53, ..., 58, ..., 68, ..., 72, ..., 77, 80, ..., 84, 87, ..., 94, ... 99.

If you check the corresponding edo pages (except for 12, of course) on the Xenwiki:

http://xenharmonic.wikispaces.com/edo

you will find examples of music in 5, 7, 9, 15, 17, 19, 22, 29 (if I can find find Igs and fix the link), 31, 36, 46, 53, 72, 87 and 99. Plenty to consider there, and opportunities to explore what hasn't been much, if at all, explored. I could use some more links--why is the only link for 72 to something I wrote? That can't be right.

If you want examples of 12edo music, check around.

🔗Carl Lumma <carl@...>

--- "genewardsmith" <genewardsmith@...> wrote:
>
> > Thanks Chris, for pointing out that the problem we're trying to
> > solve is very similar to the one solved by the CAS system.
>
> When giving names to prescription drugs, chemical names are not
> used. Instead, a plethora of made-up names is the system. The
> drug with the generic name Warfarin is also known as Cumadin,
> Jantoven, Marfarin, Marevan, Lowarin, Warfan and Warfant, for
> instance, and considered as rat poison is usually called
> Warfarin. No one seems to want to call it
> (RS)-4-hydroxy- 3-(3- oxo- 1-phenylbutyl)- 2H- chromen- 2-one
> for some reason.
>
> My point is, I don't think we need see these types of names

I agreed, in fact, in the part of my message you clipped.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

With all due respect I don't think you understood my point.

(RS)-4-hydroxy- 3-(3- oxo- 1-phenylbutyl)- 2H- chromen- 2-one in theory
tells you what it is and how to make it.

Cumadin, Jantoven, Marfarin, Marevan, Lowarin, Warfan and Warfant give you
*no* information as to what the drug is, how its made, or even what it
contains unless you read the manufacture's information - maybe.

But, please understand I do not wish to argue the point. I was only offering
a suggestion. I don't make the tunings, I use them so its the realm of the
tune smiths to decide the names and I have no problem with that being the
case.

On Sat, Apr 9, 2011 at 9:45 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > Thanks Chris, for pointing out that the problem we're trying to
> > solve is very similar to the one solved by the CAS system.
>
> When giving names to prescription drugs, chemical names are not used.
> Instead, a plethora of made-up names is the system. The drug with the
> generic name Warfarin is also known as Cumadin, Jantoven, Marfarin, Marevan,
> Lowarin, Warfan and Warfant, for instance, and considered as rat poison is
> usually called Warfarin. No one seems to want to call it
> (RS)-4-hydroxy- 3-(3- oxo- 1-phenylbutyl)- 2H- chromen- 2-one for some
> reason.
>
> My point is, I don't think we need see these types of names as in
> competition, as they serve different purposes, and we can survive more than
> one name.
>
>
>
>

🔗Carl Lumma <carl@...>

🔗lobawad <lobawad@...>

🔗Daniel Nielsen <nielsed@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

You are most welcome. Also hang out on http://www.nonoctave.com/forum/
on occasion as some interesting conversations and musical examples pop
up there as well.

Also, if you are on facebook feel free to friend me (chris vaisvil)
and also look up the xenharmonic alliance group which will help you
get into the loop of things.

My blog is www.chrisvaisvil.com
Carlo Serafini 's blog is http://www.seraph.it/index.html

On Sun, Apr 10, 2011 at 10:48 AM, Daniel Nielsen <nielsed@...> wrote:
>
>
>
> Thank you, Gene & Carl, that's very helpful in this aim. Thanks also, Chris, these collections of musical pieces and examples are generally interesting - but even more so as I will be trying to play microtonally (likely beginning with mostly edos) and get up to speed on the implications of Sethares and HE.
>

🔗Daniel Nielsen <nielsed@...>

🔗Carl Lumma <carl@...>

🔗Daniel Nielsen <nielsed@...>

On Mon, Apr 11, 2011 at 1:46 PM, Carl Lumma <carl@...> wrote:

>
>
> --- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
> >
> > Nice! (wondering if AndR at nonoctave.com is And Rosta from the
> > Conlang-L list)
>
> Not sure who you're replying to, but there's been definite
> crossover with the conlang community (Herman Miller comes
> to mind... John Chalmers dabbled in Loglan). -Carl
>

Right, I'd recognized John Chalmers' name at one point, and Graham's page -
along with some of my own little experiments and a couple of posts on
netnewmusic.net/reblog - led me here. (On second thought, though, I'd highly
doubt a confirmation of my original thought about that particular list
member.)

🔗Chris Vaisvil <chrisvaisvil@...>

I'm thinking AndR is Andrew Heathwaite from Urbana IL. There is a microtonal
community there - Jacob Barton of Udderbot fame is there as well.

If you are anywhere near to Urbana you should stop by for an event. The next
event is coming up towards the end of this month.
http://www.nonoctave.com/forum/messages/9678.html?n=0

Chris

On Mon, Apr 11, 2011 at 5:56 PM, Daniel Nielsen <nielsed@...> wrote:

>
>
>
>
> On Mon, Apr 11, 2011 at 1:46 PM, Carl Lumma <carl@...> wrote:
>
>>
>>
>> --- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>> >
>> > Nice! (wondering if AndR at nonoctave.com is And Rosta from the
>> > Conlang-L list)
>>
>> Not sure who you're replying to, but there's been definite
>> crossover with the conlang community (Herman Miller comes
>> to mind... John Chalmers dabbled in Loglan). -Carl
>>
>
> Right, I'd recognized John Chalmers' name at one point, and Graham's page
> - along with some of my own little experiments and a couple of posts on
> netnewmusic.net/reblog - led me here. (On second thought, though, I'd
> highly doubt a confirmation of my original thought about that particular
> list member.)
>
>

🔗Graham Breed <gbreed@...>

On 10 April 2011 05:39, Herman Miller <hmiller@...> wrote:

> While not a huge problem in 7-limit temperaments, it does seem that more
> of these tend to show up in higher limits. I use a method for labeling
> these temperaments that adds letter suffixes to the basic ET numbers:
>
> no suffix - the nearest approximations of all primes
> b - a less accurate approximation of prime 3
> c - a less accurate approximation of prime 5
>
> etc.
>
> for instance, "12" without a suffix represents <12 19 28 34 42 44 49|,
> but "12e" represents <12 19 28 34 41 44 49|. With these I can label
> temperaments like those 17-limit versions of meanpop:
>
> 12e&19: [<1 2 4 7 -2 2 2|, <0 -1 -4 -10 13 4 5|]
> 19g&31g: [<1 2 4 7 -2 10 7|, <0 -1 -4 -10 13 -15 -7|]

So, we've got to naming equal temperaments now. That would work if we
remember the names, or the logic behind them.

I'll suggest the no suffix case should refer to an unambiguous mapping
-- the definition of which I'll leave hanging for now. Where there is
ambiguity, a "p" can mean the nearest approximation of all primes.
The "p" is for either "prime" or "patent".

Follow tuning-math for examples.

Graham

🔗Graham Breed <gbreed@...>

On 9 April 2011 11:33, genewardsmith <genewardsmith@...> wrote:

>> Follow the same rule as naming 81:80-planar after meantone.
>
> I called it didymus. Will that do? For 49/48, you could call it slendro, but I think a name which expressed the fact the fourth was divided in two would be better. Semaphore was an example of that idea.

I've used "didymic" for 5-limit JI (or 5-limit with the tuning
abstracted). I didn't think I invented that but a Google search
doesn't bring up any other cases.

There's also "syntonic" for 81:80-planar to annoy those who use it as
a near-synonym for "meantone".

I don't find "hyper" anywhere in the names. A hyper-something would
rule the something family.

"Hyper-semaphore" sounds like a synonym for "telegraph". Maybe that's
too cryptic.

Graham

🔗genewardsmith <genewardsmith@...>

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

> > no suffix - the nearest approximations of all primes
> > b - a less accurate approximation of prime 3
> > c - a less accurate approximation of prime 5

I like this idea.

> I'll suggest the no suffix case should refer to an unambiguous mapping
> -- the definition of which I'll leave hanging for now. Where there is
> ambiguity, a "p" can mean the nearest approximation of all primes.
> The "p" is for either "prime" or "patent".

I hate this idea. The point of using patent vals is that anyone can play. It's not only unambiguous, it's dead simple. Now you introduce a concept which you haven't defined, and which will presumably make it more difficult to find what temperament is being referred to if it is defined.

🔗Michael <djtrancendance@...>

>"The point of using patent vals is that anyone can play."

Seriously? Correct me if I'm wrong but I always thought the point of vals and monzos together was to calculate where in an EDO the best estimate of an interval occurs.

The real problem I see with Vals multiplied by Monzos ...is they seem to say nothing about with what accuracy a prime is estimated by. I can easily figure out where a prime ratio is (IE 3/2 is the 7th step of 12EDO), but with no indication of accuracy (IE is my, say 4/3 a good estimate or a lousy one?).
-----------------------------
Perhaps if we can more closely estimate, say, how closely 3/1 and 2/1 occur in a val we can infer how close ratios like 4/3 and 3/2 will be...for example?

I am trying to get a handle on if modifying/extending vals can help us solve such problems.
Personally I wonder how useful a plain and simple val is when I can, say, generate an EDO in seconds via code and look for the ratios by eye (IE if I see 706 cents...obviously it's a 3/2 fifth...why should I bother to prove it via calculation?) Sure, the mathematics work out elegantly...but what's the added value here?

-----------------------
Side question: I haven't messed with vals and linear temperaments...but can't linear
temperaments give two different mappings for the same interval (IE if
the scale is generated by two different vals)?

🔗Graham Breed <gbreed@...>

Me:
>> I'll suggest the no suffix case should refer to an unambiguous mapping
>> -- the definition of which I'll leave hanging for now. Where there is
>> ambiguity, a "p" can mean the nearest approximation of all primes.
>> The "p" is for either "prime" or "patent".

Gene:
> I hate this idea. The point of using patent vals is that anyone can play. It's not only unambiguous, it's dead simple. Now you introduce a concept which you haven't defined, and which will presumably make it more difficult to find what temperament is being referred to if it is defined.

Yes, patent vals are simple and unambiguous once you define them. But
if you give an octave division and don't say how you chose the
mapping, there may be ambiguity. I suggested adding a "p" to remove
the ambiguity.

I'm not introducing the concept of ambiguity now. I introduced it
years ago when I argued with you against standardizing on patent vals
(or whatever you were calling them at the time).

I don't know how the "p" would make it more difficult to find
anything. This looks like your old habit of raging against anything
you disagree with.

Graham

🔗Carl Lumma <carl@...>

Herman Miller <hmiller@...> wrote:

> I use a method for labeling
> these temperaments that adds letter suffixes to the basic ET
> numbers:
>
> no suffix - the nearest approximations of all primes
> b - a less accurate approximation of prime 3
> c - a less accurate approximation of prime 5

Have you considered using caps to indicate direction?
Like B for prime 3 up a step; b for down a step?

Graham wrote:

> I'll suggest the no suffix case should refer to an unambiguous
> mapping -- the definition of which I'll leave hanging for now.

It ought to be the patent val.

-Carl

🔗Herman Miller <hmiller@...>

🔗Graham Breed <gbreed@...>

On 13 April 2011 05:26, Herman Miller <hmiller@...> wrote:

> I can't think of a case where the distinction would be useful (i.e.,
> where you'd ever want to use the third most accurate approximation). If
> it does become useful for some temperament that I'm not aware of, how
> about b+ vs. b- ?

I updated my scripts a long time ago to work with all possible
approximations for a given prime, rather than the best two. It's so
long ago that I can't remember how much difference it made. There are
surely cases where the third best approximation of a prime leads to
the best approximation for the temperament overall. But they aren't
very important.

I thought, if a case like this came up, you'd obviously double the
letter. So b indicates the second most accurate approximation of 5
and bb indicates the third most accurate.

Graham

🔗Graham Breed <gbreed@...>

On 12 April 2011 21:26, Carl Lumma <carl@...> wrote:

> Graham wrote:
>
>> I'll suggest the no suffix case should refer to an unambiguous
>> mapping -- the definition of which I'll leave hanging for now.
>
> It ought to be the patent val.

It's certainly a good rule to say that anything that isn't a patent
val is ambiguous. You also have to say that a mapping that doesn't
give the lowest possible optimal error is ambiguous. The result is
that there seem to be a lot of ambiguous mappings. In practice, what
counts as ambiguous has to depend on the reader's expectations. If
you give a list of mappings and there's only one <12 ...] on it, then
that's the mapping for 12-equal you'll subsequently be talking about.
In that context, there isn't enough ambiguity to require the wart.

Another rule for ambiguity would be how close the optimal errors of
the two best mappings are.

Graham

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> > Have you considered using caps to indicate direction?
> > Like B for prime 3 up a step; b for down a step?
>
> I can't think of a case where the distinction would be
> useful (i.e., where you'd ever want to use the third most
> accurate approximation). If it does become useful for some
> temperament that I'm not aware of, how about b+ vs. b- ?

Regardless of whether 3rd-best approximations are needed,
wouldn't it be nice if the notation told us which direction
the 2nd-best one is in, so we don't have to compute it?

+/- could work, but would make the string longer.

As it happens, I did find that for 12-ET in the 7.11.13
subgroup, the patent val is <34 42 44| while the Tenney-
weighted-RMS-best val is <35 43 46|.

-Carl

🔗Herman Miller <hmiller@...>

On 4/13/2011 3:40 AM, Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Herman Miller<hmiller@...> wrote:
>
>>> Have you considered using caps to indicate direction?
>>> Like B for prime 3 up a step; b for down a step?
>>
>> I can't think of a case where the distinction would be
>> useful (i.e., where you'd ever want to use the third most
>> accurate approximation). If it does become useful for some
>> temperament that I'm not aware of, how about b+ vs. b- ?
>
> Regardless of whether 3rd-best approximations are needed,
> wouldn't it be nice if the notation told us which direction
> the 2nd-best one is in, so we don't have to compute it?
>
> +/- could work, but would make the string longer.

It seems to me you're going to have to compute it regardless. If all you know is that 12e has the second closest approximation of prime 11, you need to calculate log(2) of 11 and multiply by 12, giving 41.513. So instead of rounding up to get the closest approximation, you just round down. Knowing that it's "12e-" doesn't save any significant amount of work to justify the added notation complexity, since you'll still need to do the calculation.

🔗clumma <carl@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> >>> Have you considered using caps to indicate direction?
> >>> Like B for prime 3 up a step; b for down a step?
> >>
> >> I can't think of a case where the distinction would be
> >> useful (i.e., where you'd ever want to use the third most
> >> accurate approximation). If it does become useful for some
> >> temperament that I'm not aware of, how about b+ vs. b- ?
> >
> > Regardless of whether 3rd-best approximations are needed,
> > wouldn't it be nice if the notation told us which direction
> > the 2nd-best one is in, so we don't have to compute it?
> >
> > +/- could work, but would make the string longer.
>
> It seems to me you're going to have to compute it regardless.
> If all you know is that 12e has the second closest approximation
> of prime 11, you need to calculate log(2) of 11 and multiply
> by 12, giving 41.513. So instead of rounding up to get the
> closest approximation, you just round down. Knowing that it's
> "12e-" doesn't save any significant amount of work to justify
> the added notation complexity, since you'll still need
> to do the calculation.

It's easier to find the closest approximation and add or
subtract 1, than to find the closest, 2nd-closest, and
3rd-closest approximations.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Apr 13, 2011 at 10:44 PM, clumma <carl@...> wrote:
>
> It's easier to find the closest approximation and add or
> subtract 1, than to find the closest, 2nd-closest, and
> 3rd-closest approximations.
>
> -Carl

I agree with this, but why not just take it all the way? Why deal with
letters like a, b, and c at all, which are supposed to be placeholders
that index primes? Why not just do something like 17(+5) to signify
the patent val for 17, with prime 5 raised by 1, or something like
that? Being as the "best" val may change depending on which error
metric you use, at least this is clear to specify the one you want and
is unambiguous regardless.

-Mike

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> I agree with this, but why not just take it all the way?
> Why deal with letters like a, b, and c at all, which are
> supposed to be placeholders that index primes? Why not
> just do something like 17(+5) to signify the patent val
> for 17, with prime 5 raised by 1, or something like that?
> Being as the "best" val may change depending on which
> error metric you use, at least this is clear to specify
> the one you want and is unambiguous regardless.

Because letters are shorter, easier to say, and easier to
recognize with a regular expression. A single letter for
each prime also optimizes the common case where you want
the nearest or next-nearest and leaves the very uncommon
cases where you want more remote approximations more
difficult to deal with. That's the right way round.

Graham

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Dave's solution was to use the size of the generator (e.g.
> "hemithirds"). The problem is that the same generator can be
> used with different mappings. Also, "half a major third" is
> not very precise.

Hi Carl,

I don't want to reopen the discussion, merely to correct the misconceptions above.

I did not propose "hemithirds". I did however propose "semithirds", as you can see in Figure 1 of this article.
http://dkeenan.com/Music/MicroGuitar.pdf

"Semithirds" does not merely tell you the approximate size of the generator, but tells you something important about the mapping as well. It tells you that two generators give the temperament's best approximation to a 4:5 ratio. Otherwise the temperament might have been called the "major tones" temperament or some such.

It also tells you, by omission, that the period is an approximate octave. Otherwise it would have been called "twin semithirds" or "triple semithirds" etc.

It also tells you, by omission, that it is the least complex of the usable temperaments having such a generator and period. Otherwise it would have been called "complex semithirds" or "supercomplex semithirds" etc.

Such names can of course also be qualified by the prime limit of their mapping, e.g. "7-limit semithirds" versus "11-limit semithirds".

You can see other examples, followed by question marks, in the abovementioned article. Again, I'm not arguing for this system, just correcting the history.

I was interested to see that I wrote back then:
"My purpose in proposing systematic naming methods for both linear
temperaments and commas is to avoid drowning in lots of meaningless
names where, if you haven't been following the tuning-math list
religiously for the past x years the only way you have of figuring out
what someone's talking about is to look the names up in a database
somewhere."

-- Dave

🔗Carl Lumma <carl@...>

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > I did not propose "hemithirds".
>
> That was just an example, but as it happens, it seems
> you did
> /tuning-math/message/3682

Sorry Carl, but you are still mistaken. Near the end of that post I attribute that name to Gene. You may have been misled by my use of the plural form. If you search for the first occurrence of the root form "hemithird" you will find this earliest post by Gene.
/tuning-math/message/3481

But thanks for finding that post, because it shows me as finding reasons to agree with as many of Gene's proposed names as possible. And it shows that any suggestions of simliarity between my proposals and CAS or IUPAC are spurious, given my proposed limit on the number of syllables.

-- Dave Keenan