Lumma temperament

On the warped canon page, one of the tunings used is "Lumma
temperament". Searching the tuning-math archives turns up nothing
about it. It uses a fifth of 700 cents, and a major third of 384.4
cents; I can't see this is specially well suited for tempering
something out. Can someone (Carl? Herman?) explain what it is all about?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> On the warped canon page, one of the tunings used is "Lumma
> temperament". Searching the tuning-math archives turns up nothing
> about it. It uses a fifth of 700 cents, and a major third of 384.4
> cents; I can't see this is specially well suited for tempering
> something out. Can someone (Carl? Herman?) explain what it is all about?

One feature that should be noted is that it's a pretty good marvel
tuning, but marvel isn't a 5-limit temperament, of course. Might be
the point anyway, in which case it should be described by adding that
a 7/4 comes to 968.8 cents.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > On the warped canon page, one of the tunings used is "Lumma
> > temperament". Searching the tuning-math archives turns up nothing
> > about it. It uses a fifth of 700 cents, and a major third of 384.4
> > cents; I can't see this is specially well suited for tempering
> > something out. Can someone (Carl? Herman?) explain what it is all
about?
>
> One feature that should be noted is that it's a pretty good marvel
> tuning, but marvel isn't a 5-limit temperament, of course. Might be
> the point anyway, in which case it should be described by adding that
> a 7/4 comes to 968.8 cents.

700 cents could be a waage fifth, and 400-384.4 = 15.6 cents is a good
waage generator, very near the 7-limit poptimal range, and the minimax
tuning in particular. I'm guessing that Carl invented waage tempering
at some point. Carl?

>> On the warped canon page, one of the tunings used is "Lumma
>> temperament". Searching the tuning-math archives turns up nothing
>> about it. It uses a fifth of 700 cents, and a major third of 384.4
>> cents; I can't see this is specially well suited for tempering
>> something out. Can someone (Carl? Herman?) explain what it is all about?
>
>One feature that should be noted is that it's a pretty good marvel
>tuning, but marvel isn't a 5-limit temperament, of course. Might be
>the point anyway, in which case it should be described by adding that
>a 7/4 comes to 968.8 cents.

I didn't name it, but I think it's 225/224 planar. For a while
scales based on this were going by "Lumma/Fokker scales".

-Carl

Weird, I somehow wound up replying to this message, which I
hadn't read. I was replying to your first message. Damn
mail client!

Isn't marvel 225/224 planar?

-Carl

>>> On the warped canon page, one of the tunings used is "Lumma
>>> temperament". Searching the tuning-math archives turns up nothing
>>> about it. It uses a fifth of 700 cents, and a major third of 384.4
>>> cents; I can't see this is specially well suited for tempering
>>> something out. Can someone (Carl? Herman?) explain what it is all about?
>>
>>One feature that should be noted is that it's a pretty good marvel
>>tuning, but marvel isn't a 5-limit temperament, of course. Might be
>>the point anyway, in which case it should be described by adding that
>>a 7/4 comes to 968.8 cents.
>
>I didn't name it, but I think it's 225/224 planar. For a while
>scales based on this were going by "Lumma/Fokker scales".

-Carl

>700 cents could be a waage fifth, and 400-384.4 = 15.6 cents is a good
>waage generator, very near the 7-limit poptimal range, and the minimax
>tuning in particular. I'm guessing that Carl invented waage tempering
>at some point. Carl?

Don't know what waage is. There's no publicly-available list of
names > 5-limit, and the 5-limit one (Paul's database) may very well
be out of date.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I didn't name it, but I think it's 225/224 planar. For a while
> scales based on this were going by "Lumma/Fokker scales".

Are those 5-limit scales tempered by a 225/224 tuning?

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> Weird, I somehow wound up replying to this message, which I
> hadn't read. I was replying to your first message. Damn
> mail client!
>
> Isn't marvel 225/224 planar?

Right, or in the 11-limit {225/224, 385/384}-planar, as the tuning is
pretty much the same.

>> I didn't name it, but I think it's 225/224 planar. For a while
>> scales based on this were going by "Lumma/Fokker scales".
>
>Are those 5-limit scales tempered by a 225/224 tuning?

The ones I was looking at started as 7-limit scales, but since
they're tempered they usually (always?) can be considered
either way.

-Carl

>> Weird, I somehow wound up replying to this message, which I
>> hadn't read. I was replying to your first message. Damn
>> mail client!
>>
>> Isn't marvel 225/224 planar?
>
>Right, or in the 11-limit {225/224, 385/384}-planar, as the tuning is
>pretty much the same.

This might be a good time to ask what you currently favor for
families. Do you have a blurb on your current proposal anywhere?

-Carl

>>> I didn't name it, but I think it's 225/224 planar. For a while
>>> scales based on this were going by "Lumma/Fokker scales".
>>
>>Are those 5-limit scales tempered by a 225/224 tuning?
>
>The ones I was looking at started as 7-limit scales, but since
>they're tempered they usually (always?) can be considered
>either way.

This may help

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

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> This might be a good time to ask what you currently favor for
> families. Do you have a blurb on your current proposal anywhere?

I don't think I ever got Paul to agree with the idea that two
temperaments with the same TOP tuning should keep the same name. In
general, I like calling things by the same name if the commas are
compatible and the tunings are close, but how to formalize that or
whether it should be formalized at all remains an issue.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> On the warped canon page, one of the tunings used is "Lumma
> >> temperament". Searching the tuning-math archives turns up nothing
> >> about it. It uses a fifth of 700 cents, and a major third of 384.4
> >> cents; I can't see this is specially well suited for tempering
> >> something out. Can someone (Carl? Herman?) explain what it is all
about?
> >
> >One feature that should be noted is that it's a pretty good marvel
> >tuning, but marvel isn't a 5-limit temperament, of course. Might be
> >the point anyway, in which case it should be described by adding that
> >a 7/4 comes to 968.8 cents.
>
> I didn't name it, but I think it's 225/224 planar. For a while
> scales based on this were going by "Lumma/Fokker scales".

At least, the 12-note periodicity blocks, where 225:224 is a unison
vector and is either tempered out or untempered, were so referred to.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >700 cents could be a waage fifth, and 400-384.4 = 15.6 cents is a
good
> >waage generator, very near the 7-limit poptimal range, and the
minimax
> >tuning in particular. I'm guessing that Carl invented waage tempering
> >at some point. Carl?
>
> Don't know what waage is. There's no publicly-available list of
> names > 5-limit, and the 5-limit one (Paul's database) may very well
> be out of date.

It's not, though it still has the Woolhouse tunings.

You'll note that one of them is called "compton, waage, aristoxenean."

The 7-limit version of Waage uses 2 generators to get an approximate
7:4: if the octaves are pure, then the period alone gets you 1000
cents; subtract 2 generators from that, and you should be near 7:4.

Waage wrote articles on this in 1/1, even though it's not quite JI. ;)

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > This might be a good time to ask what you currently favor for
> > families. Do you have a blurb on your current proposal anywhere?
>
> I don't think I ever got Paul to agree with the idea that two
> temperaments with the same TOP tuning should keep the same name.

I basically followed this idea in my paper, Gene! There, the relevant
horagrams do get the same name, and I don't provide any other names
which might be interpreted as those belonging to the temperament maps
or wedgies.

But what if someone is using, say, minimax Kees instead of TOP?

> In
> general, I like calling things by the same name if the commas are
> compatible and the tunings are close, but how to formalize that or
> whether it should be formalized at all remains an issue.

In general, I dislike any formalizations that are based on arbitrary
or judgmental cutoffs and their resulting categorizations, including
definitions of 'close', etc. It's a human tendency to make these
categorizations, but I prefer to keep them out of most theory.
Particularly any theory that some other theory might end up depending
on.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> But what if someone is using, say, minimax Kees instead of TOP?

Most of the time they correspond.

> In general, I dislike any formalizations that are based on arbitrary
> or judgmental cutoffs and their resulting categorizations, including
> definitions of 'close', etc.

Do we want to multiply names unduly, for things which are in some
sense more or less the same?

Gene Ward Smith wrote:
> On the warped canon page, one of the tunings used is "Lumma
> temperament". Searching the tuning-math archives turns up nothing
> about it. It uses a fifth of 700 cents, and a major third of 384.4
> cents; I can't see this is specially well suited for tempering
> something out. Can someone (Carl? Herman?) explain what it is all about?

I believe that was lumma.scl from the Scala archive.

! lumma.scl
!
Carl Lumma, 7-limit, 6 tetrads + 4 triads within 2c of Just, TL 19-2-99 12
! 5-limit 7-limit
115.5870 ! 16/15 +3.9c, 15/14 -3.9c
200.0542 ! 9/8 -3.9c, 28/25 +3.9c
268.7988 ! 75/64 -5.8c, 7/6 +1.9c
384.3858 ! 5/4 -1.9c, 56/45 +5.8c
499.9729 ! 4/3 +1.9c 75/56 -5.8c
584.4401 ! 45/32 -5.8c 7/5 +1.9c
700.0271 ! 3/2 -1.9c, 112/75 +5.8c
815.6142 ! 8/5 +1.9c, 45/28 -5.8c
5/3 ! 884.3587c, 224/135+7.7c
7/4 !225/128-7.7c, 968.8259c
1084.4130! 15/8 -3.9c, 28/15 +3.9c
2/1

I traced this back to a message from 1999:

/tuning/topicId_1188.html#1188

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

>
> I traced this back to a message from 1999:
>
> /tuning/topicId_1188.html#1188

Would it be correct to attribute the invention of 225/224 tempering to
Dave and Carl?

>> This might be a good time to ask what you currently favor for
>> families. Do you have a blurb on your current proposal anywhere?
>
>I don't think I ever got Paul to agree with the idea that two
>temperaments with the same TOP tuning should keep the same name.
>In general, I like calling things by the same name if the commas
>are compatible and the tunings are close, but how to formalize
>that or whether it should be formalized at all remains an issue.

I wonder how well a pure comma-centric approach could work... any
temperament with 225/224 in the kernel gets a certain name, or root
of a name, regardless of its rank / implied harmonic limit.

I like the idea of comma sequences. One idea that comes to mind
is ordering their commas by least badness. In principle, this
would limit the number of name roots needed.

Thoughts?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I wonder how well a pure comma-centric approach could work... any
> temperament with 225/224 in the kernel gets a certain name, or root
> of a name, regardless of its rank / implied harmonic limit.

I dunno; I think the comma sequence idea may be better.

> I like the idea of comma sequences. One idea that comes to mind
> is ordering their commas by least badness. In principle, this
> would limit the number of name roots needed.

In other words, instead of Tenney reducion you'd use TOP badness
reduction?

> Thoughts?

I think the Hermite comma sequences are a good basis for defining
family relationships.

>> I wonder how well a pure comma-centric approach could work... any
>> temperament with 225/224 in the kernel gets a certain name, or root
>> of a name, regardless of its rank / implied harmonic limit.
>
>I dunno; I think the comma sequence idea may be better.

I don't see this as contrary to the spirit of comma sequences.
It's more exclusive of two-ETs naming, that Graham seemed to use
a lot, at least early on, and size-of-canonical-generator naming,
which Dave has favored.

>> I like the idea of comma sequences. One idea that comes to mind
>> is ordering their commas by least badness. In principle, this
>> would limit the number of name roots needed.
>
>In other words, instead of Tenney reducion you'd use TOP badness
>reduction?

The two are both badness-related. I just mean I wouldn't start
the sequence with the 5-limit and go up. If 225/224 is the 'best'
comma in the sequence, place it first, etc. I'm not familiar
enough with family relationships to know if this would cause
insurmountable problems, but it seems like a natural approach to
me.

>> Thoughts?
>
>I think the Hermite comma sequences are a good basis for defining
>family relationships.

It's nice that they're unique, but their commas are apparently
too complex.

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > But what if someone is using, say, minimax Kees instead of TOP?
>
> Most of the time they correspond.
>
> > In general, I dislike any formalizations that are based on
arbitrary
> > or judgmental cutoffs and their resulting categorizations,
including
> > definitions of 'close', etc.
>
> Do we want to multiply names unduly, for things which are in some
> sense more or less the same?

The problem is coming up with a non-arbitrary definition for "some
sense" and "more or less".

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> I wonder how well a pure comma-centric approach could work... any
> >> temperament with 225/224 in the kernel gets a certain name, or
root
> >> of a name, regardless of its rank / implied harmonic limit.
> >
> >I dunno; I think the comma sequence idea may be better.
>
> I don't see this as contrary to the spirit of comma sequences.
> It's more exclusive of two-ETs naming, that Graham seemed to use
> a lot, at least early on, and size-of-canonical-generator naming,
> which Dave has favored.
>
> >> I like the idea of comma sequences. One idea that comes to mind
> >> is ordering their commas by least badness. In principle, this
> >> would limit the number of name roots needed.
> >
> >In other words, instead of Tenney reducion you'd use TOP badness
> >reduction?
>
> The two are both badness-related. I just mean I wouldn't start
> the sequence with the 5-limit and go up. If 225/224 is the 'best'
> comma in the sequence, place it first, etc.

Using badness (defined for the one comma as if there were no others
vanishing) seems silly because there might be much simpler commas
than 225/224, and the vanishing of 225/224 may in fact have little
impact on the tuning in question, so associating the tuning primarily
with 225/224 would seem inappropriate. August and Pajara are pretty
good examples of this, I think.

>> I just mean I wouldn't start
>> the sequence with the 5-limit and go up. If 225/224 is the 'best'
>> comma in the sequence, place it first, etc.
>
>Using badness (defined for the one comma as if there were no others
>vanishing) seems silly because there might be much simpler commas
>than 225/224, and the vanishing of 225/224 may in fact have little
>impact on the tuning in question, so associating the tuning primarily
>with 225/224 would seem inappropriate. August and Pajara are pretty
>good examples of this, I think.

This seems to argue for a error-based naming, which would be
one possibility. Another would be complexity-based naming,
and this might better reflect how one things in the temperament
musically (than if the tuning is similar).

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> I just mean I wouldn't start
> >> the sequence with the 5-limit and go up. If 225/224 is
the 'best'
> >> comma in the sequence, place it first, etc.
> >
> >Using badness (defined for the one comma as if there were no
others
> >vanishing) seems silly because there might be much simpler commas
> >than 225/224, and the vanishing of 225/224 may in fact have little
> >impact on the tuning in question, so associating the tuning
primarily
> >with 225/224 would seem inappropriate. August and Pajara are
pretty
> >good examples of this, I think.
>
> This seems to argue for a error-based naming, which would be
> one possibility.

I don't get it. Can you elaborate?

> Another would be complexity-based naming,
> and this might better reflect how one things in the temperament
> musically (than if the tuning is similar).

What do you have in mind when you say "complexity-based naming"?

>> >Using badness (defined for the one comma as if there were no
>> >others vanishing) seems silly because there might be much
>> >simpler commas than 225/224, and the vanishing of 225/224
>> >may in fact have little impact on the tuning in question, so
>> >associating the tuning primarily with 225/224 would seem
>> >inappropriate. August and Pajara are pretty good examples of
>> >this, I think.
>>
>> This seems to argue for a error-based naming, which would be
>> one possibility.
>
>I don't get it. Can you elaborate?

If you're wanting the first comma in the sequence and/or the
one used as the root for the name to be the one dominating
the tuning of the temperament, wouldn't commas with high
heuristic error qualify?

>> Another would be complexity-based naming,
>> and this might better reflect how one things in the temperament
>> musically (than if the tuning is similar).
>
>What do you have in mind when you say "complexity-based naming"?

Instead of badness, lattice distance.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> >Using badness (defined for the one comma as if there were no
> >> >others vanishing) seems silly because there might be much
> >> >simpler commas than 225/224, and the vanishing of 225/224
> >> >may in fact have little impact on the tuning in question, so
> >> >associating the tuning primarily with 225/224 would seem
> >> >inappropriate. August and Pajara are pretty good examples of
> >> >this, I think.
> >>
> >> This seems to argue for a error-based naming, which would be
> >> one possibility.
> >
> >I don't get it. Can you elaborate?
>
> If you're wanting the first comma in the sequence and/or the
> one used as the root for the name to be the one dominating
> the tuning of the temperament, wouldn't commas with high
> heuristic error qualify?

Yes, this bears more consideration.

> >> Another would be complexity-based naming,
> >> and this might better reflect how one things in the temperament
> >> musically (than if the tuning is similar).
> >
> >What do you have in mind when you say "complexity-based naming"?
>
> Instead of badness, lattice distance.

So choose the simplest comma to base the naming on. Perhaps.

>> >> Another would be complexity-based naming,
>> >> and this might better reflect how one things in the temperament
>> >> musically (than if the tuning is similar).
>> >
>> >What do you have in mind when you say "complexity-based naming"?
>>
>> Instead of badness, lattice distance.
>
>So choose the simplest comma to base the naming on. Perhaps.

Yes.

-Carl

Carl Lumma wrote:
>>>I wonder how well a pure comma-centric approach could work... any
>>>temperament with 225/224 in the kernel gets a certain name, or root
>>>of a name, regardless of its rank / implied harmonic limit.
>>
>>I dunno; I think the comma sequence idea may be better.
> > I don't see this as contrary to the spirit of comma sequences.
> It's more exclusive of two-ETs naming, that Graham seemed to use
> a lot, at least early on, and size-of-canonical-generator naming,
> which Dave has favored.

It's not far off the two-ETs. If you're using commas to differentiate two temperaments with similar shapes, you can also use the ET with the two commas equal. 225/224 implies a three-ET definition of planar temperaments. You can always filter ETs by the commas they temper out, or filter commas by the ETs that temper them out. You can also calculate the same wedgie both ways.

Really, 225/224 isn't a good example because it works with so many shapes.

The size-of-generator approach is different, because the two ETs come with mappings but the generator size leaves this ambiguous. Note that you need the size of the period as well.

> The two are both badness-related. I just mean I wouldn't start
> the sequence with the 5-limit and go up. If 225/224 is the 'best'
> comma in the sequence, place it first, etc. I'm not familiar
> enough with family relationships to know if this would cause
> insurmountable problems, but it seems like a natural approach to
> me.

I'd go by the equal temperaments (or commas) that best represent a particular shape. That needn't be 5-limit because 243:242 defines neutral thirds. But you also have to be careful about conserving the shape, which means considering the period and generator sizes. If there's ambiguity in higher limits, it can often be removed by adding "micro" type prefixes to indicate the accuracy you're going for. I suggest nano->micro->meso->macro->exo for increasing error. If there's still ambiguity, that tells you that you need more names. Meantone in the 11-limit is an example of where there's ambiguity.

Graham

>>>>I wonder how well a pure comma-centric approach could work... any
>>>>temperament with 225/224 in the kernel gets a certain name, or root
>>>>of a name, regardless of its rank / implied harmonic limit.
>>>
>>>I dunno; I think the comma sequence idea may be better.
>>
>> I don't see this as contrary to the spirit of comma sequences.
>> It's more exclusive of two-ETs naming, that Graham seemed to use
>> a lot, at least early on, and size-of-canonical-generator naming,
>> which Dave has favored.
>
>It's not far off the two-ETs. // You can always filter ETs by the
>commas they temper out, or filter commas by the ETs that temper
>them out. You can also calculate the same wedgie both ways.

Yes. But this doesn't mean they're on equal footing
on a family-relationship-forming or a naming basis.

>Really, 225/224 isn't a good example because it works with so many
>shapes.

What's a shape?

Since 225/224 is one of the most important commas out there, it'd
better be a good example for whatever system is being proposed.

>The size-of-generator approach is different, because the two ETs come
>with mappings but the generator size leaves this ambiguous. Note that
>you need the size of the period as well.

Yes, this criticism was brought up when Dave proposed his scheme.
He may have come up with ways of dealing with it; I forget.

>> The two are both badness-related. I just mean I wouldn't start
>> the sequence with the 5-limit and go up. If 225/224 is the 'best'
>> comma in the sequence, place it first, etc. I'm not familiar
>> enough with family relationships to know if this would cause
>> insurmountable problems, but it seems like a natural approach to
>> me.
>
>I'd go by the equal temperaments (or commas) that best represent a
>particular shape. That needn't be 5-limit because 243:242 defines
>neutral thirds. But you also have to be careful about conserving the
>shape, which means considering the period and generator sizes. If
>there's ambiguity in higher limits, it can often be removed by adding
>"micro" type prefixes to indicate the accuracy you're going for. I
>suggest nano->micro->meso->macro->exo for increasing error. If there's
>still ambiguity, that tells you that you need more names. Meantone in
>the 11-limit is an example of where there's ambiguity.

I don't follow this but maybe you can make a page like this
one for it:

http://66.98.148.43/~xenharmo/commaseq.htm

-Carl