Calling all Partch fans

I've been asked to do a talk on Partch at the school where I teach, and I'm wondering if anybody knows if the various videos which can be found on YouTube are available anywhere in higher quality. I'd really love a fair copy of that absolutely wonderful production of Daphne of the Dunes by Alice Farley Dance Theater, and/or a copy of Delusions of the Fury. Anybody know any sources?

Thanks in advance.

Ciao,

P

--- In tuning@yahoogroups.com, "Paul" <paul@...> wrote:
>
> I've been asked to do a talk on Partch at the school where I
> teach, and I'm wondering if anybody knows if the various videos
> which can be found on YouTube are available anywhere in higher
> quality. I'd really love a fair copy of that absolutely
> wonderful production of Daphne of the Dunes by Alice Farley Dance
> Theater, and/or a copy of Delusions of the Fury. Anybody know
> any sources?
>
> Thanks in advance.
>
> Ciao,
>
> P

Hi Paul (Rubenstein?)

Enclosures VII and VIII from Innova are the DVD sources for
Partch that I know of:
http://www.innova.mu/artist1.asp?skuID=263
http://www.innova.mu/artist1.asp?skuID=312

They have Delusion but I don't see Daphne.

-Carl

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

> Hi Paul (Rubenstein?)

Hi Carl, nope, it's Paul Poletti, been absent for quite a spell, too busy with lots of things, among others going over Arnaut von Zwolle's manuscript with a fine-toothed comb, found some inner-wresting stuff.

>
> Enclosures VII and VIII from Innova are the DVD sources for
> Partch that I know of:
> http://www.innova.mu/artist1.asp?skuID=263
> http://www.innova.mu/artist1.asp?skuID=312

Thanks much, that should be great!!
>
> They have Delusion but I don't see Daphne.

Maybe I'll have to ring-up Alice Farley Dance Theater. They don't seem to have much web presence.

Thanks again!

Ciao,

P

PS BTW, Mark Lindley has given me the task of the care and feeding of the Grove's Dictionary article on Temperament, so if anybody out there has written or knows of new interesting articles that should be included in the bibliography, let me know, I'll see to it.

Also, Mark's webpage on Bach temperaments at the Staatliches Institut Berlin is about to go public, I'll let the list know when it happens.

PPS Here's a little something I whipped up back in the summer for a talk I gave here in Spain for an audience that knew nothing about alternative tuning. It's an animated tour of all of the intervals within an octave, show on what I call "the Christmas Tree of Consonance", which shows the relative amounts of aural consonance/dissonance based on Critical Band distance between harmonics of two tones. Now all I need to do is add a soundtrack. Comments welcome...

http://www.youtube.com/watch?v=qPyfjoVu0mU

> > Hi Paul (Rubenstein?)
>
> Hi Carl, nope, it's Paul Poletti, been absent for quite a spell,

Oh, hi Paul! Good to hear from you.

> PS BTW, Mark Lindley has given me the task of the care and
> feeding of the Grove's Dictionary article on Temperament, so if
> anybody out there has written or knows of new interesting
> articles that should be included in the bibliography, let me
> know, I'll see to it.

Would it be within your powers to add a paragraph on regular
mapping?

> Also, Mark's webpage on Bach temperaments at the Staatliches
> Institut Berlin is about to go public, I'll let the list know
> when it happens.

Cool, please do.

> PPS Here's a little something I whipped up back in the summer
> for a talk I gave here in Spain for an audience that knew
> nothing about alternative tuning. It's an animated tour of all
> of the intervals within an octave, show on what I call "the
> Christmas Tree of Consonance", which shows the relative amounts
> of aural consonance/dissonance based on Critical Band distance
> between harmonics of two tones. Now all I need to do is add a
> soundtrack. Comments welcome...
>
> http://www.youtube.com/watch?v=qPyfjoVu0mU

Looks reasonable.

-Carl

On Sat, Feb 12, 2011 at 5:06 PM, Carl Lumma <carl@...> wrote:
>
> > PS BTW, Mark Lindley has given me the task of the care and
> > feeding of the Grove's Dictionary article on Temperament, so if
> > anybody out there has written or knows of new interesting
> > articles that should be included in the bibliography, let me
> > know, I'll see to it.
>
> Would it be within your powers to add a paragraph on regular
> mapping?

Seconded this.

-Mike

On 13 February 2011 00:49, Paul <paul@...> wrote:

> PS BTW, Mark Lindley has given me the task of the care and feeding of the Grove's Dictionary article on Temperament, so if anybody out there has written or knows of new interesting articles that should be included in the bibliography, let me know, I'll see to it.

That's a bit like taking a child to a house made entirely of jelly
beans and saying "Is there anything you'd like to eat?" isn't it?

Graham

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 12, 2011 at 5:06 PM, Carl Lumma <carl@...> wrote:
> >
> > > PS BTW, Mark Lindley has given me the task of the care and
> > > feeding of the Grove's Dictionary article on Temperament, so if
> > > anybody out there has written or knows of new interesting
> > > articles that should be included in the bibliography, let me
> > > know, I'll see to it.
> >
> > Would it be within your powers to add a paragraph on regular
> > mapping?
>
> Seconded this.
>
Sorry to take so long to get back to you on this, I'm wearing too many hats, doesn't leave me much time.

Let me begin by saying that I would be the first to first to admit that Grove's sorely needs an article on microtonality or xenharmony or whatever it ought to be called, including all the various terms and concepts which have been developed and are regularly used by folks who frequent this group. However, I think we would all agree that in order to do the topic justice, even an introductory article would have to be at least as long as the current temperament article, and therefore I think it would be a bad idea to try to include it in an expanded version of the current temperament article, as it would only further muddy waters which are already exceedingly murky for the great unwashed. Should anybody here be seriously interested in attempting such a task, I would be more than happy to suggest it to the editors.

Regarding the temperament article in general, as I take up the torch from Mark Lindley I want to keep the same focus, that is, keep it bound to traditional terminology. In this sense, a temperament by definition is an aberration, a less-than-perfect departure from an idealized situation, a compromise between conflicting requirements. This compromise is required by a deficiency in the instrumentarium, an insufficient number of fixed pitches which must nonetheless be employed to produce, more or less, all desirable harmonic structures. Furthermore, historically the idealized point of departure has always been some form of JI, and as such implies the octave as the interval of repetition. Werckmeister gave a wonderfully succinct definition is his 1698 treatise on continuo playing:

"Die Temperatur aber hat ihren Uhrsprung daher weil man bey dem Gebrauch des Clavier nicht alle Consonantien wenn man von einem Accord zum andern schreitet rein haben kan so muß daher einer Consonantie etwas gegeben einer andern etwas abgenommen werden daß also ein erträgliches und angenehmes temperament daraus enstehet"

"Temperament has its origin in the fact that when a keyboard is used, it is not possible to have all the consonances pure if one moves from one chord to another. Therefore, a little must be given to the one consonance and a little taken away from the other in such a way that a pleasing temperament is formed." [my translation]

Thus, by this definition, neither 11 nor 10 nor 13 EDO nor any XcET system is a temperament, since none of them attempt to approximate any JI distribution (often quite the contrary!), i.e there is absolutely nothing which is intentionally "tempered". Neither are they "tunings", unless of course, a la Sethares, they are applied to an inharmonic spectrum which has consonance maximas precisely at certain intervals which are available in the system. In this sense, if any EDO or cET system is consciously adopted precisely in order to approximate an unobtainable JI system for an instrumentarium which has an inharmonic spectrum, then it would be a temperament.

Up to now, the article has only dealt with temperaments based on 5-limit, and I think at least a mention of expanded JI is appropriate, briefly mentioning that the concept of "temperament" can also exist in larger expanded harmonic universes and is not just a phenomenon of the simplistic confines of traditional 5-limit harmony on traditional dodecdatonic (primarily) keyboard instruments. In fact, one could argue that the larger the JI universe becomes, the more temperament is needed in order to keep the physical process of the production of musical notes from becoming unmanageable due to their sheer number. Additionally, the background assumption has always been harmonic spectra, and I think Sethares' conclusions regarding tuning and tempering in relation to inharmonic spectra should be mentioned, perhaps in a new subsection on the future of temperament.

Naturally, I'm open to at least consider any and all suggestions.

Ciao,

P

On Sun, Mar 6, 2011 at 3:26 AM, Paul <paul@...> wrote:
>
> Let me begin by saying that I would be the first to first to admit that Grove's sorely needs an article on microtonality or xenharmony or whatever it ought to be called, including all the various terms and concepts which have been developed and are regularly used by folks who frequent this group. However, I think we would all agree that in order to do the topic justice, even an introductory article would have to be at least as long as the current temperament article, and therefore I think it would be a bad idea to try to include it in an expanded version of the current temperament article, as it would only further muddy waters which are already exceedingly murky for the great unwashed. Should anybody here be seriously interested in attempting such a task, I would be more than happy to suggest it to the editors.

I'm seriously interested in Carl Lumma attempting such a task. In fact
I think that if we have this opportunity to finally get this in the
Grove Dictionary, then we will finally have a way for academia to
catch on to what we're doing, which would be nice.

> Regarding the temperament article in general, as I take up the torch from Mark Lindley I want to keep the same focus, that is, keep it bound to traditional terminology. In this sense, a temperament by definition is an aberration, a less-than-perfect departure from an idealized situation, a compromise between conflicting requirements. This compromise is required by a deficiency in the instrumentarium, an insufficient number of fixed pitches which must nonetheless be employed to produce, more or less, all desirable harmonic structures.

Argh! No! That is absolutely not all that temperament is about. The
elimination of comma pumps creates an entirely new musical effect, and
it's been central to the music we've enjoyed for hundreds of years
now. Temperament creates puns, and those are important. And, frankly,
they're so important that I'd say they're almost fundamental to our
perception of music

> Thus, by this definition, neither 11 nor 10 nor 13 EDO nor any XcET system is a temperament, since none of them attempt to approximate any JI distribution (often quite the contrary!), i.e there is absolutely nothing which is intentionally "tempered".

11 approximates 4:7:9:11 very well and works well if you think of it
as being in the 2.7.9.11 subgroup. 13-EDO is a father temperament and
hence supports father tempered 5-limit harmony. It can perhaps be
thought of as being in the 2.3.5.11 subgroup.

> Neither are they "tunings", unless of course, a la Sethares, they are applied to an inharmonic spectrum which has consonance maximas precisely at certain intervals which are available in the system. In this sense, if any EDO or cET system is consciously adopted precisely in order to approximate an unobtainable JI system for an instrumentarium which has an inharmonic spectrum, then it would be a temperament.

Every EDO or cET system is consciously adopted precisely in order to
approximate just harmonies, that's the entire point of regular
mapping. To say that 13-tet doesn't approximate just harmony is
misleading at best and wrong at worst. Some approximate them better
than others and how much error a composer is willing to tolerate is
best left up to the composer, not written into the Grove dictionary.

This community is very split on how much error is tolerable. On the
one hand, you have Gene, who prefers microtemperament, and on the
other you have Igs, who uses stuff like 13-tet all the time by finding
what JI subgroups he can within it. To stick in the Grove article some
notion that 13-tet is so far out that it's not even a temperament is I
think going to sent a lot of people on the wrong track.

There are those who claim that 12-equal doesn't approximate 5-limit
harmony because the major third is so sharp - shall we entertain those
as well? Some quick listening tests can confirm that a virtual 1/1
pops out for 0-400 cents as though it were a 5/4, and likewise with
the sharp 3/2's of 13-equal.

Frankly, the issue of mistuning tolerance is one of psychoacoustics
and not really relevant. We already have the regular mapping paradigm
as a way to manipulate temperaments in the abstract sense without
having to deal with it, and that's the angle I think we should work.

> Up to now, the article has only dealt with temperaments based on 5-limit, and I think at least a mention of expanded JI is appropriate, briefly mentioning that the concept of "temperament" can also exist in larger expanded harmonic universes and is not just a phenomenon of the simplistic confines of traditional 5-limit harmony on traditional dodecdatonic (primarily) keyboard instruments. In fact, one could argue that the larger the JI universe becomes, the more temperament is needed in order to keep the physical process of the production of musical notes from becoming unmanageable due to their sheer number. Additionally, the background assumption has always been harmonic spectra, and I think Sethares' conclusions regarding tuning and tempering in relation to inharmonic spectra should be mentioned, perhaps in a new subsection on the future of temperament.

I don't mind a mention of Sethares' work as long as it's not framed in
such a way that it sounds like partials beating is all that matters. I
don't think it does. I do think that it's very important.

-Mike

--- In tuning@yahoogroups.com, "Paul" <paul@...> wrote:
>
> "Die Temperatur aber hat ihren Uhrsprung daher weil man bey dem Gebrauch des Clavier nicht alle Consonantien wenn man von einem Accord zum andern schreitet rein haben kan so muß daher einer Consonantie etwas gegeben einer andern etwas abgenommen werden daß also ein erträgliches und angenehmes temperament daraus enstehet"
>
> "Temperament has its origin in the fact that when a keyboard is used, it is not possible to have all the consonances pure if one moves from one chord to another. Therefore, a little must be given to the one consonance and a little taken away from the other in such a way that a pleasing temperament is formed." [my translation]

Good translation- it might be of importance, or interest, to translate "ertraegliches" as well. A bearable and pleasing temperament. This, I feel, is important because it suggests that too much deviance from pure would be "unertaeglich", emphasizing the import of pure intervals in Werkmeister's time and place.
>
> Thus, by this definition, neither 11 nor 10 nor 13 EDO nor any XcET >system is a temperament, since none of them attempt to approximate >any JI distribution (often quite the contrary!), i.e there is >absolutely nothing which is intentionally "tempered".

This is correct. One thing that the crew here, excepting to my knowledge Gene Ward Smith, has not acknowledged (or made clear, or even understood, perhaps) is that regular temperaments do not ever "equate" to equal divisions of the octave (or any other specific array of intervals for that matter).

Standing alone, 11, 10, 13, any XcET, etc. are not temperaments. A modality is required to yield a temperament from an array of intervals.

For example, the statement that 19 equal divisions of an octave is a meantone temperament (as seen on Wikipedia) is false. There are other modalities of 19 equal which are not meantone temperaments. "Magic" temperament can be implemented as a modality of 19-edo. A better tuning of "Magic" is found using 41-edo, not 31-edo as you might expect were 19 a "meantone"; perhaps this best points out how fundamentally different these modalities are.

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

> 11 approximates 4:7:9:11 very well and works well if you think of it
> as being in the 2.7.9.11 subgroup. 13-EDO is a father temperament and
> hence supports father tempered 5-limit harmony. It can perhaps be
> thought of as being in the 2.3.5.11 subgroup.

I wouldn't say it's "in" a subgroup, but it can be considered as a tempering of various subgroups--for example, it does quite a good job on the 2.21/5.11.13/5.17/5.19/5 subgroup, if you like 10-13-17-19-21 chords.

> This community is very split on how much error is tolerable. On the
> one hand, you have Gene, who prefers microtemperament, and on the
> other you have Igs, who uses stuff like 13-tet all the time by finding
> what JI subgroups he can within it.

Actually, I prefer accurate but non-micro temperaments such as miracle or rodan.

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

> This is correct. One thing that the crew here, excepting to my knowledge Gene Ward Smith, has not acknowledged (or made clear, or even understood, perhaps) is that regular temperaments do not ever "equate" to equal divisions of the octave (or any other specific array of intervals for that matter).

My preferred way of phrasing the relationship is that N-edo "supports" a given regular temperament. If I were to make that precise, obviously not a good thing to attempt in a Grove article, I would say N-edo supports p-limit temperament T if its p-limit patent val belongs to the val group of T (with the definition extended appropriately for subgroups.) If you object to what Carl considers my obsession with patent vals you can fix it accordingly.

> For example, the statement that 19 equal divisions of an octave is a meantone temperament (as seen on Wikipedia) is false.

Isn't all that is meant is that 19edo supports meantone? If the article does not mention other temperaments, however, it should.

I find "supports" clear. It's the "is", the equating of an edo with a temperament, that is wrong. "12-tET" actually suffers from this confusion, has since the days of the first 12-tone serialists. The distinction between 12-edo and 12-tET might have been a good thing from the get-go.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > This is correct. One thing that the crew here, excepting to my knowledge Gene Ward Smith, has not acknowledged (or made clear, or even understood, perhaps) is that regular temperaments do not ever "equate" to equal divisions of the octave (or any other specific array of intervals for that matter).
>
> My preferred way of phrasing the relationship is that N-edo "supports" a given regular temperament. If I were to make that precise, obviously not a good thing to attempt in a Grove article, I would say N-edo supports p-limit temperament T if its p-limit patent val belongs to the val group of T (with the definition extended appropriately for subgroups.) If you object to what Carl considers my obsession with patent vals you can fix it accordingly.
>
> > For example, the statement that 19 equal divisions of an octave is a meantone temperament (as seen on Wikipedia) is false.
>
> Isn't all that is meant is that 19edo supports meantone? If the article does not mention other temperaments, however, it should.
>

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

> My preferred way of phrasing the relationship is that N-edo
> "supports" a given regular temperament. If I were to make that
> precise, obviously not a good thing to attempt in a Grove article,
> I would say N-edo supports p-limit temperament T if its p-limit
> patent val belongs to the val group of T (with the definition
> extended appropriately for subgroups.) If you object to what Carl
> considers my obsession with patent vals you can fix it accordingly.

I'm not the only one critical of it. Why not use the best val?

-Carl

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

> This is correct. One thing that the crew here, excepting to my
> knowledge Gene Ward Smith, has not acknowledged (or made clear,
> or even understood, perhaps) is that regular temperaments do not
> ever "equate" to equal divisions of the octave

The relationship between rank 1 and rank 2 temperaments is well
understood by the acolytes here (both are regular temperaments
by the way).

> For example, the statement that 19 equal divisions of an octave
> is a meantone temperament (as seen on Wikipedia) is false. There
> are other modalities of 19 equal which are not meantone
> temperaments.

That does not mean it isn't a meantone temperament.
Both "is" and "supports" are perfectly OK in my opinion but
I won't be arguing about it further because it's not important.

-Carl

On Sun, Mar 6, 2011 at 3:53 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > My preferred way of phrasing the relationship is that N-edo
> > "supports" a given regular temperament. If I were to make that
> > precise, obviously not a good thing to attempt in a Grove article,
> > I would say N-edo supports p-limit temperament T if its p-limit
> > patent val belongs to the val group of T (with the definition
> > extended appropriately for subgroups.) If you object to what Carl
> > considers my obsession with patent vals you can fix it accordingly.
>
> I'm not the only one critical of it. Why not use the best val?

What is the best val?

-Mike

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

> I'm not the only one critical of it. Why not use the best val?

Because that characterization is completely meaningless.

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

> > I'm not the only one critical of it. Why not use the best val?
>
> What is the best val?

For a rank 1 temperament, the one with the least error.
All my code works from the best val, per Paul Erlich's vehement
objections to Gene's use of the patent val.

-Carl

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

> > I'm not the only one critical of it. Why not use the best val?
>
> Because that characterization is completely meaningless.

Nonsense. -Carl

On Sun, Mar 6, 2011 at 4:48 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > I'm not the only one critical of it. Why not use the best val?
> >
> > What is the best val?
>
> For a rank 1 temperament, the one with the least error.
> All my code works from the best val, per Paul Erlich's vehement
> objections to Gene's use of the patent val.

What are some ETs where the best val differs from the patent val? For
example, is the best 5-limit val for 17 the meantone one or the dicot
one?

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > > I'm not the only one critical of it. Why not use the best val?
> >
> > What is the best val?
>
> For a rank 1 temperament, the one with the least error.

I don't believe any such val exists, and in any case you haven't defined "least error".

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > > I'm not the only one critical of it. Why not use the best val?
> >
> > Because that characterization is completely meaningless.
>
> Nonsense. -Carl

What is the best meantone val, and why is it best?

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

> What are some ETs where the best val differs from the patent val?
> For example, is the best 5-limit val for 17 the meantone one or
> the dicot one?

There is no dicot val for an ET. Recall that you need two vals
to specify a rank 2 temperament.

What val is best depends on what error you use. Until now I've
used TOP error but I'm thinking of switching to TE error to
harmonize with Gene and Graham, but they should give very similar
results. It also depends on whether you allow stretched octaves.
I don't have a list of examples to hand but 64-ET is a favorite.

-Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > For a rank 1 temperament, the one with the least error.
>
> I don't believe any such val exists, and in any case you haven't
> defined "least error".

I have, in numerous posts. Graham and I have discussed it at
length. Maybe you weren't here then, but you were here when
Paul and I discussed it at length, and when Paul and you discussed
it at some length. So I'm not sure what you're objection is, but
I wish you'd come out with it already.

-Carl

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

> It also depends on whether you allow stretched octaves.
> I don't have a list of examples to hand but 64-ET is a favorite.

So you mean the least error val for an edo in a particular prime limit. Should have said so. But this seems to have nothing to do with the original question, which was to find vals supporting a temperament.

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

> So I'm not sure what you're objection is, but
> I wish you'd come out with it already.

My objection is that the discussion was about choice of val for a temperament, so this is a complete red herring.

On Sun, Mar 6, 2011 at 5:21 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > What are some ETs where the best val differs from the patent val?
> > For example, is the best 5-limit val for 17 the meantone one or
> > the dicot one?
>
> There is no dicot val for an ET. Recall that you need two vals
> to specify a rank 2 temperament.

I meant if you get the val that supports dicot or the val that
supports meantone. As in, does 5/4 get mapped to 5\17 or 6\17?

> What val is best depends on what error you use. Until now I've
> used TOP error but I'm thinking of switching to TE error to
> harmonize with Gene and Graham, but they should give very similar
> results. It also depends on whether you allow stretched octaves.
> I don't have a list of examples to hand but 64-ET is a favorite.

I'd be interested in seeing how things work out with some kind of
woolhouse-error as well.

-Mike

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

> So you mean the least error val for an edo in a particular
> prime limit. Should have said so. But this seems to have nothing
> to do with the original question, which was to find vals
> supporting a temperament.

Sorry if I misunderstood. Here's the original:

> My preferred way of phrasing the relationship is that N-edo
> "supports" a given regular temperament. If I were to make that
> precise, obviously not a good thing to attempt in a Grove article,
> I would say N-edo supports p-limit temperament T if its p-limit
> patent val belongs to the val group of T (with the definition
> extended appropriately for subgroups.) If you object to what Carl
> considers my obsession with patent vals you can fix it accordingly.

It seems you already suggested the modification I'm advocating.

-Carl

Mike Battaglia <battaglia01@...> wrote:

> I meant if you get the val that supports dicot or the val that
> supports meantone. As in, does 5/4 get mapped to 5\17 or 6\17?

The TOP-best 5-limit val for 17 is <17 27 40|, so the latter.
(As it happens, this is not the patent val.)

> I'd be interested in seeing how things work out with some kind of
> woolhouse-error as well.

You can certainly do that. However most everyone agrees
that weighted error is better.

-Carl

On Sun, Mar 6, 2011 at 5:55 PM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > I meant if you get the val that supports dicot or the val that
> > supports meantone. As in, does 5/4 get mapped to 5\17 or 6\17?
>
> The TOP-best 5-limit val for 17 is <17 27 40|, so the latter.
> (As it happens, this is not the patent val.)

OK. Then I support doing things this way then.

-Mike

"genewardsmith" <genewardsmith@...> wrote:

> My objection is that the discussion was about choice of val
> for a temperament,

In that case, why not use this approach

/tuning-math/message/15572

and

/tuning-math/message/15573

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> "genewardsmith" <genewardsmith@> wrote:
>
> > My objection is that the discussion was about choice of val
> > for a temperament,
>
> In that case, why not use this approach
>
> /tuning-math/message/15572
>
> and
>
> /tuning-math/message/15573

Well, it's OK if you want to define "best" in that manner but it seems to be going in the opposite direction from what I thought you were originally suggesting, which was why not go to even higher numbers than the optimal patent val? Why not use, instead of 81edo, 970edo, which can get you marginally closer to the POTE tuning and is interesting in other ways? But there's no cutoff if you take that line.

I think it is of the greatest importance to make the fundamentals clear. Especially in a dictionary.

A dictionary definition should not be completely opaque to all but acolytes. For example, do guys really think that the Grove's article on temperament should even contain the term "val" at all?

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > This is correct. One thing that the crew here, excepting to my
> > knowledge Gene Ward Smith, has not acknowledged (or made clear,
> > or even understood, perhaps) is that regular temperaments do not
> > ever "equate" to equal divisions of the octave
>
> The relationship between rank 1 and rank 2 temperaments is well
> understood by the acolytes here (both are regular temperaments
> by the way).
>
> > For example, the statement that 19 equal divisions of an octave
> > is a meantone temperament (as seen on Wikipedia) is false. There
> > are other modalities of 19 equal which are not meantone
> > temperaments.
>
> That does not mean it isn't a meantone temperament.
> Both "is" and "supports" are perfectly OK in my opinion but
> I won't be arguing about it further because it's not important.
>
> -Carl
>

On Mon, Mar 7, 2011 at 1:24 AM, lobawad <lobawad@...> wrote:
>
> I think it is of the greatest importance to make the fundamentals clear. Especially in a dictionary.

One way to make them not clear is to say that 13-equal isn't a
temperament. Or that it isn't a tuning.

> A dictionary definition should not be completely opaque to all but acolytes. For example, do guys really think that the Grove's article on temperament should even contain the term "val" at all?

No.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Mar 7, 2011 at 1:24 AM, lobawad <lobawad@...> wrote:
> >
> > I think it is of the greatest importance to make the fundamentals clear. Especially in a dictionary.
>
> One way to make them not clear is to say that 13-equal isn't a
> temperament. Or that it isn't a tuning.

Saying "13 equal divisions of the octave is not a temperament" is completely different from avoiding statements like "13-edo is such-and-such a temperament".

>
> > A dictionary definition should not be completely opaque to all but acolytes. For example, do guys really think that the Grove's article on temperament should even contain the term "val" at all?
>
> No.

Should you not then retitle posts discussing vals to something other than "Grove's article on temperament"?

(I am also guilty of forgetting to retitle posts, but would thank anyone catching my error).

On Mon, Mar 7, 2011 at 1:35 AM, lobawad <lobawad@...> wrote:
> > One way to make them not clear is to say that 13-equal isn't a
> > temperament. Or that it isn't a tuning.
>
> Saying "13 equal divisions of the octave is not a temperament" is completely different from avoiding statements like "13-edo is such-and-such a temperament".

But it should be okay to say that 13-edo is -A- father temperament, as
well as all of the other things that it is. 12-tet is -A- meantone
temperament, and it's also -A- diminished temperament, and -AN-
augmented temperament, and so on. That's the terminology everyone
seems to have been using around here since before I joined and it's
fine with me.

> > > A dictionary definition should not be completely opaque to all but acolytes. For example, do guys really think that the Grove's article on temperament should even contain the term "val" at all?
> >
> > No.
>
> Should you not then retitle posts discussing vals to something other than "Grove's article on temperament"?
>
> (I am also guilty of forgetting to retitle posts, but would thank anyone catching my error).

If it causes confusion.

-Mike

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

> > > One thing that the crew here, excepting to my
> > > knowledge Gene Ward Smith, has not acknowledged (or made
> > > clear, or even understood, perhaps) is that regular
> > > temperaments do not ever "equate" to equal divisions
> > > of the octave
> >
> > The relationship between rank 1 and rank 2 temperaments is
> > well understood by the acolytes here (both are regular
> > temperaments by the way).
>
> A dictionary definition should not be completely opaque to all
> but acolytes. For example, do guys really think that the
> Grove's article on temperament should even contain the term
> "val" at all?

I certainly don't. My issue was with the statement that of
those here, only Gene has acknowledged or understood the
relationship between rank 1 and rank 2 temperaments. That's
not true by any stretch of the imagination.

-Carl

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

> But it should be okay to say that 13-edo is -A- father temperament, as
> well as all of the other things that it is. 12-tet is -A- meantone
> temperament, and it's also -A- diminished temperament, and -AN-
> augmented temperament, and so on. That's the terminology everyone
> seems to have been using around here since before I joined and it's
> fine with me.

I don't use it. I say it "supports" or is "a tuning" of some particular temperament.

On Mon, Mar 7, 2011 at 1:50 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > But it should be okay to say that 13-edo is -A- father temperament, as
> > well as all of the other things that it is. 12-tet is -A- meantone
> > temperament, and it's also -A- diminished temperament, and -AN-
> > augmented temperament, and so on. That's the terminology everyone
> > seems to have been using around here since before I joined and it's
> > fine with me.
>
> I don't use it. I say it "supports" or is "a tuning" of some particular temperament.

I swear I've heard you say things like "19's a meantone temperament"
before. And I've been saying that kind of thing since I learned all
this stuff and nobody stopped me. But alright, I won't argue this
anymore. This is one of those bike shed color things.

My comment was actually addressed to this:

> Thus, by this definition, neither 11 nor 10 nor 13 EDO nor any XcET system is a temperament, since none of them attempt to approximate any JI distribution (often quite the contrary!), i.e there is absolutely nothing which is intentionally "tempered". Neither are they "tunings", unless of course, a la Sethares, they are applied to an inharmonic spectrum which has consonance maximas precisely at certain intervals which are available in the system. In this sense, if any EDO or cET system is consciously adopted precisely in order to approximate an unobtainable JI system for an instrumentarium which has an inharmonic spectrum, then it would be a temperament.

To say that 13-EDO simply "doesn't approximate 5-limit harmony"
because it supports father temperament is absurd and a disservice to
folks like Igs who are hell bent on making musical use of stuff like
that. Rather, it's more that it's just not everyone's cup of tea,
because the error is so high. Saying that 11-equal isn't a temperament
is even worse, because it covers half of what 22-equal covers, and
22-equal is one of the Best ETs Ever.

-Mike

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

> I swear I've heard you say things like "19's a meantone temperament"
> before.

I don't say 19edo is a meantone temperament. To say 19et is a meantone temperament is is an acceptable shorthand, because it's a temperament which belongs to the meantone val group.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > > > One thing that the crew here, excepting to my
> > > > knowledge Gene Ward Smith, has not acknowledged (or made
> > > > clear, or even understood, perhaps) is that regular
> > > > temperaments do not ever "equate" to equal divisions
> > > > of the octave
> > >
> > > The relationship between rank 1 and rank 2 temperaments is
> > > well understood by the acolytes here (both are regular
> > > temperaments by the way).
> >
> > A dictionary definition should not be completely opaque to all
> > but acolytes. For example, do guys really think that the
> > Grove's article on temperament should even contain the term
> > "val" at all?
>
> I certainly don't. My issue was with the statement that of
> those here, only Gene has acknowledged or understood the
> relationship between rank 1 and rank 2 temperaments. That's
> not true by any stretch of the imagination.
>
> -Carl
>

That statement was never made. What is to be distinguished, clarified, understood is not the difference between rank 1 and rank 2 temperaments, but the fundamental difference between a process and a thing. Temperament is a process, has been since the beginning, see the Werckmeister quote. Any specific tuning is a thing.

Of course you understand this- it is an understanding essential to the "regular temperament paradigm". But, this main ingredient is hidden from comprehension by language fog.

"Is" will often be misunderstood as an equal sign, unfortunately.

Perhaps you will say the fog is only in my head. That would be silly- I have understood in spite of the fog; it is not I but others who have obviously not had the whole business clearly presented.

Take a look at this, from Kyle Gann:

" Some hot-shot who's figured out that 137 pitches per octave is the perfect equal division will harangue me that my music could be redone in a 137-equal scale and I'd never be able to tell the difference, and maybe he's right - but I would never have written the piece the way I did thinking in 137 equal steps. (I do, however, enjoy being told that by adding lots more pitches, I could approximate what I've already got exactly.)"

I'm not knocking Kyle Gann, who may be one of xenharmony's most valuable soldiers. Just, how is it that someone so bright and knowledgable obviously does not understand, QED this quote, the "regular temperament paradigm"?

Because it is not here writ large and clear that temperament is a process and tuning merely a thing.

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

> Naturally, I'm open to at least consider any and all suggestions.

Thanks for writing back, Paul. My suggestion is to add a
paragraph on regular mapping. Something along the lines of

"Modern efforts have revisited the fundamental question of
temperament. Such efforts were foreshadowed in the Italian
musica reservata by Nicola Vicentino, who built a microtonal
harpsichord ("archicembalo") and wrote several pieces of
"enharmonic music". But other than passing mention in
notebooks of Huygens and Newton, such inquiry remained
remarkably rare until the late 19th century, when Helmholtz
and Bosanquet independently suggested that better intonation
could be achieved by tempering out the schisma instead of the
syntonic comma, as all canon temperaments until that time had
done. The latter realized his ideas in a 53-tone harmonium.
By 1952, Norwegian composer Eivind Groven had implemented a
similar system on an electronic organ. One year earlier,
physicist Adriaan Fokker had completed a 31-tone organ in the
Netherlands. Fokker realized that while schisma-based systems
enjoyed more accurate intonation they would be incompatible
with common-practice repertoire, which assumes that the
syntonic comma vanishes. His organ improved intonation while
maintaining this feature. By the 1970s, musicians in
California and elsewhere, following the work of Wyshnegradsky,
Fokker and others, were building novel instruments to play in
a wide variety of temperaments, some quite foreign to the
Western canon. By the late 1990s, internet mailing lists
supported international collaboration on temperament theory,
which attempts to explain and generalize the diatonic scale
and other features of common-practice music. By the mid 2000s,
inexpensive and flexible software synthesizers permitted
widespread experimentation in these radically different
temperament systems."

Important caveats: 1. I haven't read the existing entry, so
I have no idea if this meshes with what's there, 2. this is
off the top of my head at 1am.

-Carl

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

>>>>> One thing that the crew here, excepting to my
>>>>> knowledge Gene Ward Smith, has not acknowledged (or made
>>>>> clear, or even understood, perhaps) is that regular
>>>>> temperaments do not ever "equate" to equal divisions
>>>>> of the octave
>>>>
>>>> The relationship between rank 1 and rank 2 temperaments is
>>>> well understood by the acolytes here (both are regular
>>>> temperaments by the way).
>>>
>>> A dictionary definition should not be completely opaque to
>>> all but acolytes. For example, do guys really think that the
>>> Grove's article on temperament should even contain the term
>>> "val" at all?
>>
>> I certainly don't. My issue was with the statement that of
>> those here, only Gene has acknowledged or understood the
>> relationship between rank 1 and rank 2 temperaments. That's
>> not true by any stretch of the imagination.
>
> That statement was never made.

Not only was it made, it remains at the top of this message.
As I already explained, it contains an error that necessitates
the minor rewording.

-Carl

Gene wrote:

>>> My objection is that the discussion was about choice of val
>>> for a temperament,
>>
>> In that case, why not use this approach
>> /tuning-math/message/15572
>> and
>> /tuning-math/message/15573
>
> Well, it's OK if you want to define "best" in that manner but
> it seems to be going in the opposite direction from what I
> thought you were originally suggesting, which was why not go
> to even higher numbers than the optimal patent val?

I see you have a whole page on this!

http://xenharmonic.wikispaces.com/Optimal+patent+val

Well, those are most accurate not best, but still, cool page.

-Carl