Paul Erlich's 'Middle Path' now online

This excellent paper by Paul Erlich catalogues decades of
collaboration on this list in search of the best non-equal
temperaments and explains Paul's own optimisation method involving
Tempered Octaves Please (TOP). It presents the information in several
stunning visualisations as well as convenient tables.

At last, it is available online. Thanks Paul.

http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-MiddlePath.pdf

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> This excellent paper by Paul Erlich catalogues decades of
> collaboration on this list in search of the best non-equal
> temperaments and explains Paul's own optimisation method involving
> Tempered Octaves Please (TOP). It presents the information in several
> stunning visualisations as well as convenient tables.
>
> At last, it is available online. Thanks Paul.
>
> http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-
>MiddlePath.pdf
>
> -- Dave Keenan
>

Thanks to you and Paul Ehrlich for posting these papers. "The
Middle Path" paper is well-written and clear, although
I feel that the whole basic idea of basing tunings on
approximating Just intervals is of dubious artistic integrity.
To each their own of course.

-Cameron Bobro

-Cameron Bobro wrote

I feel that the whole basic idea of basing tunings on
approximating Just intervals is of dubious artistic integrity.
To each their own of course.

What would be of artistic integrity?

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> -Cameron Bobro wrote
>
> I feel that the whole basic idea of basing tunings on
> approximating Just intervals is of dubious artistic integrity.
> To each their own of course.
>
> What would be of artistic integrity?

Using the interval you want, not an approximation of it. Accepting
a thing for what it is, not what it's "supposed" to be- a taco is
not a badly made hamburger.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> >
> > -Cameron Bobro wrote
> >
> > I feel that the whole basic idea of basing tunings on
> > approximating Just intervals is of dubious artistic integrity.
> > To each their own of course.
> >
> > What would be of artistic integrity?
>
> Using the interval you want, not an approximation of it.

Sometimes constructing a musical scale with the exact intervals one
wants produces other intervals one doesn't want.

> Accepting
> a thing for what it is, not what it's "supposed" to be- a taco is
> not a badly made hamburger.

An interval might be an approximation of a just interval while still
having its own identity, for instance the 1/4-comma meantone fifth.

Kalle Aho

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>> -Cameron Bobro wrote
>>
>> I feel that the whole basic idea of basing tunings on
>> approximating Just intervals is of dubious artistic integrity.
>> To each their own of course.
>>
>> What would be of artistic integrity?
> > Using the interval you want, not an approximation of it. Accepting
> a thing for what it is, not what it's "supposed" to be- a taco is
> not a badly made hamburger. I'm definitely in favor of using the interval that I want. It just so happens that most of the time I want intervals that aren't exact integer ratios. And that includes octaves. :-)

I also like the challenge of taking a tuning considered "bad" (such as bug or father temperament) and trying to make something out of it that sounds good, or at least having an interesting flavor.

i am siding with Cameron on this one. The idea of making something out of something defective sounds like more work than necessary. Kinda like making a good painting out of inferior paints. Outside a piano timbre have never seen any advantage to messing up octaves. Harrison work with unstretched octaves seem to be fine on the piano. Despite all the approval of the method, i have heard little of it being put into practice.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
> >
> > --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> > >
> > > -Cameron Bobro wrote
> > >
> > > I feel that the whole basic idea of basing tunings on
> > > approximating Just intervals is of dubious artistic integrity.
> > > To each their own of course.
> > >
> > > What would be of artistic integrity?
> >
> > Using the interval you want, not an approximation of it.
>
> Sometimes constructing a musical scale with the exact intervals one
> wants produces other intervals one doesn't want.

Obviously. But unless you're a hardcore serialist, where is it
written that you must use all intervals in a tuning? If you're not
going to use all intervals in a tuning, why compromise the
qualities of those you are going to use in order to improve the
ones you aren't going to use? Is all things to everyone
and not really anything to anyone a worthwhile artistic goal?

>
> > Accepting
> > a thing for what it is, not what it's "supposed" to be- a taco is
> > not a badly made hamburger.
>
> An interval might be an approximation of a just interval while
>still
> having its own identity, for instance the 1/4-comma meantone
>fifth.

A 1/4 comma meantone fifth doesn't sound like a 3/2, it sounds
like a 1/4 comma meantone fifth. In name and tonal function
it may replace 3/2, but it's a different interval. As an
"approximation" it's a piece of crap. As an interval, it's
very nice indeed.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i am siding with Cameron on this one. The idea of making something
>out
> of something defective sounds like more work than necessary.
>Kinda >like
> making a good painting out of inferior paints. Outside a piano
>timbre
> have never seen any advantage to messing up octaves. Harrison work
>with
> unstretched octaves seem to be fine on the piano. Despite all the
> approval of the method, i have heard little of it being put into
>practice.

The only reason I can see for changing the octave is that you prefer
the new sound. Tempering 2:1 to get a whole bunch of "almost-
perfect" 5/4s for example seems silly to me, for if a pure 5/4 is so
important, then leave it pure and use adaptable JI. I don't get the
point of making a thousand inferior versions of adaptable JI.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
> > >
> > > --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> > > >
> > > > -Cameron Bobro wrote
> > > >
> > > > I feel that the whole basic idea of basing tunings on
> > > > approximating Just intervals is of dubious artistic integrity.
> > > > To each their own of course.
> > > >
> > > > What would be of artistic integrity?
> > >
> > > Using the interval you want, not an approximation of it.
> >
> > Sometimes constructing a musical scale with the exact intervals one
> > wants produces other intervals one doesn't want.
>
> Obviously. But unless you're a hardcore serialist, where is it
> written that you must use all intervals in a tuning?

This problem may arise even when not using each and every interval in
a tuning.

> If you're not
> going to use all intervals in a tuning, why compromise the
> qualities of those you are going to use in order to improve the
> ones you aren't going to use?

One might want to avoid a comma pump for example in a progression like
I-vi-ii-V-I. For fixed-pitch instruments this requires tempering. But
as soon as one gives up the idea that there must be only one pitch and
not a range of pitches for every note the problem vanishes. That's why
I advocate the use of adaptive intonation whenever it is possible.

> > > Accepting
> > > a thing for what it is, not what it's "supposed" to be- a taco is
> > > not a badly made hamburger.
> >
> > An interval might be an approximation of a just interval while
> >still
> > having its own identity, for instance the 1/4-comma meantone
> >fifth.
>
> A 1/4 comma meantone fifth doesn't sound like a 3/2, it sounds
> like a 1/4 comma meantone fifth. In name and tonal function
> it may replace 3/2, but it's a different interval. As an
> "approximation" it's a piece of crap. As an interval, it's
> very nice indeed.

For me they do sound very similar even when the other one is beatless
and the other one has a nice chorusing sound. I believe the tonal
function of the 1/4-comma meantone fifth is caused by its proximity to
3/2. Trivially they are different intervals but I don't think the
1/4-comma meantone fifth sound special in any way. It doesn't stand
out from the other fifths in its neighborhood like 3/2 does.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
> >
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> > wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@>
wrote:
> > > > >
> > > > > -Cameron Bobro wrote
> > > > >
> > > > > I feel that the whole basic idea of basing tunings on
> > > > > approximating Just intervals is of dubious artistic
integrity.
> > > > > To each their own of course.
> > > > >
> > > > > What would be of artistic integrity?
> > > >
> > > > Using the interval you want, not an approximation of it.
> > >
> > > Sometimes constructing a musical scale with the exact
intervals one
> > > wants produces other intervals one doesn't want.
> >
> > Obviously. But unless you're a hardcore serialist, where is it
> > written that you must use all intervals in a tuning?
>
> This problem may arise even when not using each and every interval
>in
> a tuning.
>
> > If you're not
> > going to use all intervals in a tuning, why compromise the
> > qualities of those you are going to use in order to improve the
> > ones you aren't going to use?
>
> One might want to avoid a comma pump for example in a progression
>like
> I-vi-ii-V-I. For fixed-pitch instruments this requires tempering.

The thing is, the "comma pump" is a feature of JI. I'm just not into
the whole seedless-grapes and nippleless-Barbie thing, different
strokes of course.

The physical experience of the "comma pump" is
a very cool thing- I remember a formative experience. Before I knew
what the "comma pump" was theoretically, I had a disconcerting
experience of finding that our choral group always wound up
a semitone (!) flat of the starting pitch when running through
a certain round ("the hoot-owl is sitting"). Being the first bass
and ultimately anchoring the whole intonation, at first I thought
I was screwing up the whole thing when the harmonies hit seconds,
but I found that the more carefully I sang and the more more in tune
we were, the more concrete the effect was of the whole tune
dropping. I was able to "correct", almost exactly, by slowing
sharping every time through the round, at which point it lost, to
my ears, "the real sound". So I just let it drop like it was born to
do, and started looking deeper into what was going on.

The thing is- if you don't want comma pumps, you don't really want
JI.

>But
> as soon as one gives up the idea that there must be only one pitch
>and
> not a range of pitches for every note the problem vanishes. That's
>why
> I advocate the use of adaptive intonation whenever it is
>possible.

That's above-board, in my book.

> > A 1/4 comma meantone fifth doesn't sound like a 3/2, it sounds
> > like a 1/4 comma meantone fifth. In name and tonal function
> > it may replace 3/2, but it's a different interval. As an
> > "approximation" it's a piece of crap. As an interval, it's
> > very nice indeed.
>
> For me they do sound very similar even when the other one is
>beatless
> and the other one has a nice chorusing sound. I believe the tonal
> function of the 1/4-comma meantone fifth is caused by its
>proximity to
> 3/2.

I think that this tonal function happens when it's "sol", but it
still doesn't make it a 3/2. "Sol" can be an eighth-tone off of 3/2
and still function as sol. When it appears as a harmonic
interval and not literally as sol, it's a certain harmonic
color- not a 3/2.

>Trivially they are different intervals but I don't think the
> 1/4-comma meantone fifth sound special in any way. It doesn't stand
> out from the other fifths in its neighborhood like 3/2 does.

I find all the meantone fifths in that area to sound "soft", while
3/2 doesn't. And while I like high fifths, I think that most will
agree with me that high fifths get radical and hard more quickly
than low fifths. Maybe in isolation the difference between a
meantone fifth and a 3/2 is trivial (I don't think so but whatever),
but the total effect is completely different. The literal appearance
of 3/2 isn't incessant except in block-chord tunes anyway.

-Cameron Bobro.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote
> I feel that the whole basic idea of basing tunings on
> approximating Just intervals is of dubious artistic
> integrity.
> To each their own of course.

Look at it this way. Linear temperaments are not pretending to _be_ JI
(except perhaps those few we call microtemperaments or
nanotemperaments). They are of musical interest in and of themselves.

However, many people find they prefer the sound of linear temperaments
that are in some sense _closer_ to JI. But this has to be weighed
against the preference to also minimise the number of different
pitches required on fixed-pitch instruments.

Comma pumps are just fine for a cappella and variable pitch
instruments, but cause problems for those of us whose thing might be
guitar or keyboards or indeed any ensemble containing at least one
fixed-pitch instrument. Surely we can still be allowed "artistic
integrity" despite wanting to modulate widely _and_ use fixed pitch
instruments. (Incidentally, the only thing I could be remotely said to
have ever _composed_ is in strict JI. And I am now building microtonal
guitars for which strict JI is difficult).

One point of Paul's paper is that this does not limit us to a choice
between JI and ETs as the debate often seems to be cast. There is a
whole world of middle paths to explore. However to save a lot of time,
he has catalogued for us the few dozen most promising areas for
exploration, based on them being good tradeoffs between closeness to
JI and number of pitches required.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i am siding with Cameron on this one. The idea of making something out
> of something defective sounds like more work than necessary. Kinda
like
> making a good painting out of inferior paints. Outside a piano timbre
> have never seen any advantage to messing up octaves. Harrison work with
> unstretched octaves seem to be fine on the piano. Despite all the
> approval of the method, i have heard little of it being put into
practice.

Hi Kraig,

I'm not sure you would have known if you _had_ heard it put into
practice. I expect some of Hermann Miller's pieces use tempered
octaves. The meantone choob I'm working on is based on TOP meantone.

But what you have to realise is that tempering of octaves is really a
very minor tweak on top of tempering in general. If you look at the
tables in Paul's paper
http://eceserv0.ece.wisc.edu/~sethares/paperspdf/Erlich-MiddlePath.pdf
you'll see that the typical defects in the octave are less than 3
cents. I doubt you'll find better octaves, except by accident, in most
non-electronic JI instruments or a cappella singing.

The point is, if you're willing to temper intervals at all, you might
as well throw the octave into the fray, as yet another place to try to
hide a little piece of whatever comma it is that you are tempering
out. The only reason it wasn't done much in the past was the lack of
convenient mathematical methods. We now have those.

-- Dave Keenan

Kraig Grady wrote:
> i am siding with Cameron on this one. The idea of making something out > of something defective sounds like more work than necessary. Kinda like > making a good painting out of inferior paints. Outside a piano timbre > have never seen any advantage to messing up octaves. Harrison work with > unstretched octaves seem to be fine on the piano. Despite all the > approval of the method, i have heard little of it being put into practice.

Untempered octaves sound great with acoustic instruments, but my taste for tempered octaves really took off when I tried a 1/7-comma meantone tuning with octaves tempered wide by 1/7 of a comma on my DX7II. With electronic instruments, sounds are mixed inside the instrument and played through a single speaker instead of emanating from separate sound sources and mixing in the complex acoustical environment of a room. Tempering the octaves even slightly helps to make the individual notes more distinct.

Obviously people have used untempered octaves with electronic instruments for decades and there's nothing wrong with that. I still use untempered octaves from time to time. But dismissing tempered intervals as "inferior", and temperament as a lack of "artistic integrity", is a point of view that I can't understand. Not that it's totally unexpected, of course; these kinds of disagreements come up far too often. But my point of view is that each of the tuning systems that have their advocates, from JI to ET and everything in between, has its own kind of integrity and usefulness for musical purposes. Some are better than others for a particular purpose, of course, but that's up to the composer or performer to decide for themselves.

Obviously Gamelan scales can stretch octaves and many of the recurrent sequences can be used in a similar fashion. i was not so siding with the 'integrity' notion, maybe the 'obsession' with tempering in general. On the other hand I don't know if picking the exact interval one wants every time would work. It is like the experience of editing a tape of music down using only the parts that one finds best and finding it falls flat. (Teo Marcero working with Miles played off energy of sections that worked so much better)
Personally i will play through scales first looking for ones i like though. Some i find i can keep playing others i want to move on. I see it as a symbiotic relationship of a scale feeding me as much as i feed it. Like how one chooses one friends based on such mutual interactions. Scales though are more than its parts in the same way all those myspace profiles never really tell you much about the people. Which i am wary of too much categorizing of scales. But one does learn what one likes or dislikes at a certain point, but isn't life always filled with surprises.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Dave Keenan wrote:

> The point is, if you're willing to temper intervals at all, you might
> as well throw the octave into the fray, as yet another place to try to
> hide a little piece of whatever comma it is that you are tempering
> out. The only reason it wasn't done much in the past was the lack of
> convenient mathematical methods. We now have those.

I didn't think there ever was a problem, mathematically speaking. It looked more like an idea whose time had come (within a small community). Even without a quantitative method you can always tune your octaves by ear. While it's topical, though, here are some better reasons for keeping pure octaves:

- some keyboards only allow octave-repeating tunings

- even without such keyboards it's convenient mathematically to have things repeating at a 2:1

- if you refret a guitar there's at least one fret you don't have to move

- octaves are a pure interval most of our ears are used to

- you can check that a keyboard is tuned correctly by listening to the intervals that should be pure octaves and verifying that they really are pure

- it makes it easier to set instruments in different registers in tune with each other

- it simplifies implementations involving lookup tables

- it's one less parameter to think about

and, specifically with regard to TOP-like tunings:

- typical psychoacoustic scale stretches appear to be much larger than typical TOP stretches, and vary considerably with both listeners and timbres

Graham

Graham,

Nice list! Practical!

Mark Rankin

--- Graham Breed <gbreed@gmail.com> wrote:

> Dave Keenan wrote:
>
> > The point is, if you're willing to temper
> intervals at all, you might
> > as well throw the octave into the fray, as yet
> another place to try to
> > hide a little piece of whatever comma it is that
> you are tempering
> > out. The only reason it wasn't done much in the
> past was the lack of
> > convenient mathematical methods. We now have
> those.
>
> I didn't think there ever was a problem,
> mathematically
> speaking. It looked more like an idea whose time
> had come
> (within a small community). Even without a
> quantitative
> method you can always tune your octaves by ear.
> While it's
> topical, though, here are some better reasons for
> keeping
> pure octaves:
>
> - some keyboards only allow octave-repeating tunings
>
> - even without such keyboards it's convenient
> mathematically
> to have things repeating at a 2:1
>
> - if you refret a guitar there's at least one fret
> you don't
> have to move
>
> - octaves are a pure interval most of our ears are
> used to
>
> - you can check that a keyboard is tuned correctly
> by
> listening to the intervals that should be pure
> octaves and
> verifying that they really are pure
>
> - it makes it easier to set instruments in different
>
> registers in tune with each other
>
> - it simplifies implementations involving lookup
> tables
>
> - it's one less parameter to think about
>
> and, specifically with regard to TOP-like tunings:
>
> - typical psychoacoustic scale stretches appear to
> be much
> larger than typical TOP stretches, and vary
> considerably
> with both listeners and timbres
>
>
> Graham
>

____________________________________________________________________________________
Shape Yahoo! in your own image. Join our Network Research Panel today! http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7

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

> I'm definitely in favor of using the interval that I want. It just so
> happens that most of the time I want intervals that aren't exact
integer
> ratios. And that includes octaves. :-)

I like intervals detuned from rationals by about a cent. That maks a
certain range of regular temperaments quite interesting to me.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:

> The thing is, the "comma pump" is a feature of JI. I'm just not
into
> the whole seedless-grapes and nippleless-Barbie thing, different
> strokes of course.

I don't understand your apparent support of JI, nor Kraig's support
of you. You've been advoctating Q(pi) tunings; that is not JI and
it's not anything which makes sense psychoacoustically either--it's
numerology. So what's your beef? You aren't making a consistent case
for anything.

> I find all the meantone fifths in that area to sound "soft", while
> 3/2 doesn't.

Absolutely--the gentle meantone fifth is a characteristic feature of
meantone tunings in the best region of it. Sometimes you want
something a little sharper, such as 1/6 comma.

Hi Cameron, Kraig, et al,

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> >
> > i am siding with Cameron on this one. The idea of making
> > something out of something defective sounds like more
> > work than necessary.

You know the old saying: "one man's meat is another man's
poison". What is "defective" about a scale is entirely
in the ears/mind of the beholder. Temperaments can do
things that non-temperaments cannot do -- perfect example
is a comma-pump chord progression which cycles back to
its original pitches each time is starts over again.

> The only reason I can see for changing the octave is
> that you prefer the new sound. Tempering 2:1 to get a
> whole bunch of "almost-perfect" 5/4s for example seems
> silly to me, for if a pure 5/4 is so important, then
> leave it pure and use adaptable JI. I don't get the
> point of making a thousand inferior versions of
> adaptable JI.

The whole point of TOP tunings is that the approximation
is distributed over *all* of the prime-factors instead
of all-except-the-identity. It makes the tuning a little
bit closer to JI by not insisting that the identity-interval
has to remain untempered, which is how all non-TOP
temperaments work.

I think by "adaptable JI" you really mean "adaptive-JI".
Sure, that's one solution to tuning. But TOP is certainly
a viable alternative. As i pointed out above, there are
things that you can do in a temperament that you can't
do otherwise.

For one thing, the entire corpus of music in the standard
repertoire (i.e., Bach, Mozart, Beethoven, etc.) was
composed with some form of meantone in mind, or for
a well-temperament which also ignores the difference
of the syntonic-comma. There are ways to retune some
of that music into JI, but for the most part, only a
tuning which tempers out the syntonic-comma will work.

A couple of months ago i was involved in a project to
create versions of Erlich's TOP temperaments for
Tonescape. I got about halfway thru the 5-limit versions,
and took a hiatus. But if more folks could get Tonescape
running, they'd be able to try these out.

-monz
http://tonalsoft.com
Tonescape microtonal music software

*There is something to be said about very slow beating ( maybe
phasing might be more appropriate term) that such intervals cause.
*

*P**osted by: "Gene Ward Smith" *
I like intervals detuned from rationals by about a cent. That maks a
certain range of regular temperaments quite interesting to me.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
>
> > The thing is, the "comma pump" is a feature of JI. I'm just not
> into
> > the whole seedless-grapes and nippleless-Barbie thing, different
> > strokes of course.
>
> I don't understand your apparent support of JI,

I'm supporting integrity, purpose, consistency (and quite likely
the Noumenon, LOL), not any specific tuning scheme.

>nor Kraig's support
> of you.

I think Kraig is only agreeing (as he has before some time
ago, IIRC) that it's about saying what you mean musically
without watering your words (the intervals) in order to make
them more "universal" or more one-size-fits-all.

>You've been advoctating Q(pi) tunings; that is not JI and
> it's not anything which makes sense psychoacoustically either--
>it's
> numerology.

The harmonic means of "JI" intervals don't make sense
psychoacoustically? I guess we'll have to disagree on
that one. And how do you get "advocating" out of an observation
that a speculative "inharmonic series" (surely you're familiar with
Sethares' work as well as programming direct synthesis and can see
how any altered harmonic series with a simple pattern can be
incorporated into electronic music ) happened to instantly churn out
a whole bunch of intervals I've long used?

> So what's your beef?

My beef is that "approximating" JI intervals relegates non-JI
intervals to a kind of inferior status. Despite pious claims to
contrary, the whole (very clever BTW) concept of minimizing
travel distance on a lattice, and talking about "good thirds" for
example, DOES bestow royality upon JI. One problem with this is
a matter of artistic consistency: if JI is so hot why not just
take it as it is?

Another problem is this: JI tunings are interpretations and
applications of the harmonic series; they are not the harmonic
series itself. There are other ways to
interpret and relate to the harmonic series, and the whole
concept of "simple ratios".

>You aren't making a consistent case
> for anything.

I'm consistent to the point of monomania. Actually reading and
understanding what I say, and acknowledging that it's not stupid
or crazy, would be tantamount to conceding that there may be
gaping holes in the foundations of tuning theory as it
manifests itself on this list.

>
> > I find all the meantone fifths in that area to sound "soft",
> while
> > 3/2 doesn't.
>
> Absolutely--the gentle meantone fifth is a characteristic feature
>of
> meantone tunings in the best region of it. Sometimes you want
> something a little sharper, such as 1/6 comma.
>

Yet you have refused to acknowledge my (frequent) statements that
sheer proximity to a JI interval is not the whole story. Given
softness as a criterium (a nice criterium IMO), would you say that a
fifth 4 cents sharp of pure is better than a fifth
6 cents flat? In terms of sheer proximity to the pure interval, the
higher fifth is inarguably "better", yet even I who like high fifths
("brassy" to my ears) would choose the lower fifth without
hesitation if softness were the issue. If this is so, then my
statement that sheer proximity to a JI interval is not the whole
story is a simple and obvious fact.

If you acknowledge this, then you must acknowledge that minimizing
travel on a lattice simply can't be gauged on quantity alone, if
musical character is an issue. If you acknowledge musical character
of an interval, you must surely also acknowledge that different
intervals can be more, or less, similar in terms of general
character. And so on....

-Cameron Bobro

Cameron Bobro wrote:
> if JI is so hot why not just
> take it as it is? > How about this-the desire to sound enough like JI, yet modulate without audible commas! Some people like this. Some people also like a consistant step size.

I find this whole battle an illusion--I've said it before--JI rocks for certain things--I love the sound of non-modulatory music in a small set of pitches for ethnic folk music, rustic music, experimental improvs, Indian music, etc. Even JI modulating, and hearing the commas is nice, and sometimes refreshingly weird.

But why stop there? Why use one (temperament or JI) exclusively? If you do, be happy with your choice, and leave everyone else alone to enjoy what they do....unless you are not convinced enough by your choices, why do you have to convince others?

Temperament exists so that a close to JI sound can be had without the inconvenience of larger and larger pitch sets for modulations. The larger the JI set, the harder it is to track one's musical landscape. So if you are the type to go all over the universe with grand modulation schemes, it comes in handy to have a finite pitch set, end of story. For instance, you would be hard pressed to hear an audible difference between 441-edo and 7-limit JI, yet the former has the advantage of less 'scope creep'. For smaller sets (31-edo, 53-edo), it also takes on a character of it's own, so that you have commas disappearing into unison vectors.

Plus, you have tunings which have nothing to do with JI, and those are great too.

Cheers,
Aaron.

Why do they like something is another question, practicality or poetic?
There are very few cultures that like equal steps and when they do it is the result of theory. Often from the outside. Yet structural possibilities are just as expressive as micro sonic events. It seems the question could be what are you willing to sacrifice or not. Or maybe the question never appears. Some are fine with 12 ET. Some are fine with a 7-limit just regardless or how they move in it.
But the answer to the question i would side on a poetic solution to the problem. whichever direction it leads

Posted by: "Aaron K. Johnson"
How about this-the desire to sound enough like JI, yet modulate without
audible commas! Some people like this. Some people also like a
consistent step size.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

monz wrote:

> For one thing, the entire corpus of music in the standard
> repertoire (i.e., Bach, Mozart, Beethoven, etc.) was > composed with some form of meantone in mind, or for
> a well-temperament which also ignores the difference
> of the syntonic-comma. There are ways to retune some
> of that music into JI, but for the most part, only a
> tuning which tempers out the syntonic-comma will work.

Tunings that reduce the size of the syntonic comma can also work. It might be interesting to try miracle temperament for chord progressions with a syntonic comma pump -- somewhere between 72-ET and 31-ET, the size of the comma shift should be small enough that it starts to become unobjectionable.

Then there are a few tunings that have more than one size of good fifth.

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Herman Miller wrote:
> monz wrote:
>
>> For one thing, the entire corpus of music in the standard
>> repertoire (i.e., Bach, Mozart, Beethoven, etc.) was
>> composed with some form of meantone in mind, or for
>> a well-temperament which also ignores the difference
>> of the syntonic-comma. There are ways to retune some
>> of that music into JI, but for the most part, only a
>> tuning which tempers out the syntonic-comma will work.
>
> Tunings that reduce the size of the syntonic comma can also work. It
> might be interesting to try miracle temperament for chord progressions
> with a syntonic comma pump -- somewhere between 72-ET and 31-ET, the
> size of the comma shift should be small enough that it starts to become
> unobjectionable.
>
> Then there are a few tunings that have more than one size of good fifth.
>
>

Beethoven probably straddled the bridge between meantone and equal
temperament, but I'd really be surprised to hear Brahms, or even
Schumann, Schubert or Mendelssohn as having been "composed with some
form of meantone in mind". And by the time you get to Dvor�k, Bruckner,
Wagner, early Richard Strauss, etc., I don't think anything except
12-tone equal temperament can be made to work.

And let's not forget those two great composers for the piano in the
"standard repertoire", Chopin and Liszt. How could they have
"composed with some form of meantone in mind?" Beethoven might well work
on a meantone fortepiano, but how could Chopin or Liszt?
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--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:

For the nth time- I AM NOT TALKING ABOUT "JI VS TEMPERAMENT".

If this all weren't so funny it would be an Orwellian nightmare.

Your thread title creates smoke to obscure the real issue. However,
it's good that you did write
"JI vs. temperament", for the expression itself reveals a
fundamental misunderstanding I'm bitching about.

Once again, very slowly:

"JI" is NOT the harmonic series. It is an INTERPRETATION and
APPLICATION of the harmonic series.

Intervals that are not "JI" are not necessarily "tempered" at all.

Take the Just Intonation interval 5:4.

As a MAJOR THIRD in relation to the fundamental, it doesn't exist in
the harmonic series. In other words, if we have a tone with a
fundamental of 100 Hz, and the timbre is harmonic, we're not going
to find a partial at 125 Hz, which is where the fundamental of
another tone in a "5:4" relationship with our original 100 Hz tonic
would sit.

"5:4" is found in its natural state at 500 and 400 Hz in the
harmonic series of our 100 Hz tone. It is not found at 125 Hz.

Our pure "5:4" major third is an interpretation and application of
something found in the harmonic series. This is unlike, for example,
the octave above the tonic, 2:1, which is found in literal form
in the harmonic series.

Obviously using a 5:4 major third isn't exactly going far afield or
out on the limb as far as interpreting and applying the
harmonic series; it's a simple matter of dropping something in plain
earshot into the first octave, and the original is sitting on top
of an octave of the tonic anyway.

"Everyone knows that" someone will say, to which I say, oh yeah?

If you truly KNOW this, then it is obvious that an interval that
is simply near to the 5:4 third IS NOT AUTOMATICALLY A TEMPERED 5:4.

Now let's say we say that we want 5:4 as our third. Great,
wonderful. And we're going to have to temper it to avoid
"comma pumps" and all that jazz. Fine, groovy, whatever.
Now, unlike the octave, 5:4 as a major third in relation to the
fundamental simply isn't physically, directly found in the harmonic
series.
This means that a: we can temper it a lot, and b: we can't temper it
too much at all.

We can temper it a lot because it's not likely to be directly
and loudly contrasting with our tempered version, which 2:1 for
example tends to do. But we CAN'T temper 5:4 too much for the same
reason:
as an interpretation, although a strong and good one, of the
harmonic series, it doesn't directly, physically assert itself like
the 2:1 does and therefore, once we tweak our M3 a bit away from the
exact 5:4, IT IS NO LONGER 5:4.

AND, because 5:4 is NOT engraved in stone, there can be many
different M3s that were never intended to have anything to do
with 5:4 in the first place.

AND, even if a "JI" interval is strong enough to assert itself
in its manifestations, not just its original form, for example
3:2 (which is an interpretaion of the partial 3:1) can appear as
2:3, 2:6, 6:2, etc., to the point where it can still be felt
through a good amount of tempering, it DOES matter, audibly
(whether anyone here wants to admit it or not), whether it's
tempered up or down!
DIFFERENT SOUND. DIFFERENT CHARACTER.

"approximating Just intervals" is simply not a firm foundation
without many qualifying factors.

"JI" is not the center, source, or constant point of reference, of
tuning! The harmonic series is.
If "JI" is STATED to be the desired point of reference, that's fine
and dandy. If it's
assumed as some kind of universal truth, that's bullshit. And
if "JI" is stated to
be the desired "sound", which is also just dandy, then a quality
approach to
achieving that goal is NOT just a matter getting near to
specific "JI" intervals:
it matters whether you're high or low, and once you have a set
of "tempered"
intervals, that set has its own demands as far as sounding cohesive.

Now to any replies of yes we know all this, I say: then show me the
vast tomes in
the archives addressing the intervals that are most decidely
NOT "JI". Show me the
evidence that intervals are accepted for what they are, and not
inevitably cartooned into
"tempered JI intervals". Traditional triadic harmony doesn't fly
with the so-called
"neutral" intervals, yet they sound great in harmonies, so, where
are the long
discussions on alternative harmonic theories which are obviously
necessary for
polyphonic music heavy in "neutral" intervals?

Take care.

-Cameron Bobro

--- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@...>
wrote:
> Beethoven probably straddled the bridge between meantone and equal
> temperament, but I'd really be surprised to hear Brahms, or even
> Schumann, Schubert or Mendelssohn as having been "composed with some
> form of meantone in mind".

12-tET *is* a form of meantone. -Carl

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

>
> The whole point of TOP tunings is that the approximation
> is distributed over *all* of the prime-factors instead
> of all-except-the-identity. It makes the tuning a little
> bit closer to JI by not insisting that the identity-interval
> has to remain untempered, which is how all non-TOP
> temperaments work.

That's just fine, very clever, but what, concretely,
does "approximation" and "a little bit closer" actually entail
in real life? Since things sound like what they are, and
not what they're "supposed to be", at least to everyone
who hasn't trained themselves to hear otherwise, what
devices are used to manipulate the actual overall SOUND
of the tuning, other than the (audibly bogus)
shear proximity to a set of Just intervals?

>
> I think by "adaptable JI" you really mean "adaptive-JI".

Yes, thanks.

> For one thing, the entire corpus of music in the standard
> repertoire (i.e., Bach, Mozart, Beethoven, etc.) was
> composed with some form of meantone in mind, or for
> a well-temperament which also ignores the difference
> of the syntonic-comma. There are ways to retune some
> of that music into JI, but for the most part, only a
> tuning which tempers out the syntonic-comma will work.

I don't know who brought up retuning Bach into JI, it would
probably sound just plain wrong. I use hardly any "JI" at all
by the way, and I think that those who do use "JI" often do
so in ways that are radically different (and more dissonant) than
is usually associated with the term.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@>
> wrote:
> > Beethoven probably straddled the bridge between meantone and equal
> > temperament, but I'd really be surprised to hear Brahms, or even
> > Schumann, Schubert or Mendelssohn as having been "composed with
some
> > form of meantone in mind".
>
> 12-tET *is* a form of meantone. -Carl
>

12-tET is a form of Pythagorean tuning, audibly.
The ultimate Pythagorean tuning: a closed circle of damn-near
perfect fifths. Even though it can be technically called meantone,
the egregious violation of meantone's intended "good" thirds
is just too much too bear. Lessee... I hear 12 good 81/64's.
Pythagorean, man.

-Cameron Bobro

Hi Ed, Carl, Cameron,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@>
> wrote:
> > Beethoven probably straddled the bridge between
> > meantone and equal temperament, but I'd really be
> > surprised to hear Brahms, or even Schumann, Schubert
> > or Mendelssohn as having been "composed with some
> > form of meantone in mind".
>
> 12-tET *is* a form of meantone. -Carl

And in the entire "standard repertoire", there's only
one "A" pitch-class, only one "B" pitch-class, etc.
And this is predicated upon the tempering-out -- or at
least, if it's not tempered out, the irrelevance --
of the syntonic-comma ... which means that it's all,
by definition, meantone.

And i've pointed out here many times Mahler's
complaint to Schoenberg around 1904 that "it's too
bad we got rid of meantone". What he meant was that
he missed having the subtlety of the two different-sized
semitones (unless he got things confused and was
actually referring to the loss of well-temperament,
which is a possibility). The fact that all of
Mahler's large works are composed for the orchestra
and not the piano, and also the fact that he spent
every day of his career conducting orchestras made up
entirely of flexible-pitch instruments, leads me to
believe that even up to the first decade of the
20th century, at least part of the time, meantone
may have been the tuning paradigm of choice, in
Mahler's mind,

-monz
http://tonalsoft.com
Tonescape microtonal music software

> > 12-tET *is* a form of meantone. -Carl
>
> 12-tET is a form of Pythagorean tuning, audibly.

Does this mean you consider the 12-tET fifth an
*approximation* of 3/2??

-Carl

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Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>> --- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@>
>> wrote:
>>> Beethoven probably straddled the bridge between meantone and equal
>>> temperament, but I'd really be surprised to hear Brahms, or even
>>> Schumann, Schubert or Mendelssohn as having been "composed with
> some
>>> form of meantone in mind".
>> 12-tET *is* a form of meantone. -Carl

Not the way I define meantone ;).
>>
>
> 12-tET is a form of Pythagorean tuning, audibly.
> The ultimate Pythagorean tuning: a closed circle of damn-near
> perfect fifths. Even though it can be technically called meantone,
> the egregious violation of meantone's intended "good" thirds
> is just too much too bear. Lessee... I hear 12 good 81/64's.
> Pythagorean, man.

12-TET is 12-TET, OK?

Anyone have any Brahms they think could be made to work in a
tuning/temperament other than 12-TET?

As an aside, perhaps that's why I don't like listening to Brahms, Dvor�k
, Chopin and Liszt as much as I like earlier and later composers. :)
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--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > 12-tET *is* a form of meantone. -Carl
> >
> > 12-tET is a form of Pythagorean tuning, audibly.
>
> Does this mean you consider the 12-tET fifth an
> *approximation* of 3/2??

Certainly. And 400 cents, in this context, being part of the circle
of fifths, an "approximation" of 81/64. As I've said before, I find
the idea that 400 cents represents 5/4, rather than 81/64,
ridiculous.

In the case of 700 cents, we're talking less than 2 cents from 3/2,
and in the "soft" direction. 704 cents would be iffy, I think.

I'm not saying these "approximations" are good or bad things, but
700 cents is clearly a tempered 3/2.

Chopin tuned his own piano with pure thirds, look where his melodies often start. Lou Harrison had a good resource on this, but i don't remember. There is often assumption than , well any of the older tunings ( even JI ) would not be used chromatically . composer though often grow accustom to other intervals and like the sound for what they provide and the whole set of tones becomes a dynamic structure. .
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@>
> wrote:
> > Beethoven probably straddled the bridge between meantone and equal
> > temperament, but I'd really be surprised to hear Brahms, or even
> > Schumann, Schubert or Mendelssohn as having been "composed with
some
> > form of meantone in mind".
>
> 12-tET *is* a form of meantone. -Carl
>

Carl,

There is far from a consensus about this. I, for one, reserve the
name "meantone" for the quarter-common tuning, in which the whole
tone divides the 5:4 major third equally, distributing the syntonic
comma over four fifths. I would then characterize meantone as being
part of the family of tunings with distributed commas: 1/3 comma, 1/5
(my favorite -- my opera is in 1/5 comma tuning), 2/7, 1/6 etc., and
of which 12tet is also located as 1/11 comma tuning.

djw

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@...> > wrote:
> >> Beethoven probably straddled the bridge between meantone and equal
>> temperament, but I'd really be surprised to hear Brahms, or even
>> Schumann, Schubert or Mendelssohn as having been "composed with some
>> form of meantone in mind".
>> >
> 12-tET *is* a form of meantone. -Carl
>
> More accurately---12 is on the outer limits of meantone, a special case where there is no difference between the chromatic and and diatonic semitone.

One could argue that in common usage of the term 'meantone', 12 wouldn't fit the bill b/c of this special quality, even though technically it is a 'meantone'.

--- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@...> wrote:
>
>
> 12-TET is 12-TET, OK?
>
> Anyone have any Brahms they think could be made to work in a
> tuning/temperament other than 12-TET?
>
>

Brahms wrote a lot of choral and orchestral works that have nothing
necessarily to do with temperament.

The canonical example of JI in Brahms is the final few seconds of the
Second Symphony, where the three trombones have a D major root
position chord. I think good brass players will get a pretty much pure
4:5:6 there.
~~~T~~~

Certainly when Chopin was in Majorca with the little upright he would
need to do the tuning himself.

What he did with it? ... I'm highly doubtful that either you or Lou
Harrison - or anyone else - knows!

Where d o his melodies often start ?

He did compose an awful lot of pieces in Ab and Db - how awful should
they sound?

~~~T~~~

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Chopin tuned his own piano with pure thirds, look where his melodies
> often start. Lou Harrison had a good resource on this, but i don't
> remember. There is often assumption than , well any of the older
tunings
> ( even JI ) would not be used chromatically . composer though often
grow
> accustom to other intervals and like the sound for what they provide
and
> the whole set of tones becomes a dynamic structure. .
> --
> Kraig Grady
>

> Anyone have any Brahms they think could be made to work in a
> tuning/temperament other than 12-TET?

I think Gene will probably have something to say here.

-Carl

> I'm not saying these "approximations" are good or bad things, but
> 700 cents is clearly a tempered 3/2.

Who are you and what have you done with Cameron?!

-Carl

> > 12-tET *is* a form of meantone. -Carl
>
> Carl,
>
> There is far from a consensus about this. I, for one, reserve the
> name "meantone" for the quarter-common tuning, in which the whole
> tone divides the 5:4 major third equally, distributing the syntonic
> comma over four fifths. I would then characterize meantone as being
> part of the family of tunings with distributed commas: 1/3 comma,
> 1/5 (my favorite -- my opera is in 1/5 comma tuning), 2/7, 1/6 etc.,
> and of which 12tet is also located as 1/11 comma tuning.

Historically 1/3-comma meantone was called just that: meantone.
Many, many modern authors have followed suit. And these lists
now make the largest body of literature and discourse, and throw
in a nice model to boot, which says that temperaments in
which 81/80 vanish are meantones.

-Carl

Hey Cameron-

No need to start 'yelling' in all capital letters.

Everything you say is true about the harmonic series, etc.

However, 5/4 derives it's special consonance from the coincident harmonics of the overtones of 2 harmonic series in conjunction. In this sense---I have to disagree---JI *is* in the harmonic series. It's not simply an 'interpretation' as you insist, when the brain is simply perceiving co-incident tones among pairs (or groups) of series. So, what we really have is you talking at cross-purposes by insisting that we should not say "6" but "a half dozen".

Another thing to consider---you brought up how it would be 'ridiculous' to think of 400 cents as a sharp 5/4 instead of thinking of it as 81/64. On one level, yes, what you say is true, in that 12-equal is both a Pythagorean and an extreme meantone simultaneously, however, the ear hears 400 cents, nonetheless, as a sharp 5/4, not a flat 81/64.

The proof is simple---no dyad as complex 81/64 will be perceived as beatless. 5/4 can be perceived as beatless, 81/64 cannot, because the brain interprets it as a member of the 5/4 family. This is perfectly in line with what Harmonic Entropy predicts.

All this of course, says nothing about the aesthetic issues and choices about whether or not to use 81/64 in music. I'm just simply stating basic facts about human auditory perception---81/64 is not a beatless dyad.

As for temperament, it's simply the desire to distribute the fruits of JI among all the 'tonics' equally---communism/socialism of a sort. JI is arch-monarchy, equal-temperament is idealistic communism or socialism, and unequal temperament might be considered a brand of democratic capitalism (haves, have-nots, and have-nothings) or even a type of capitalistic constitutional monarchy in some cases (C major is golden, F# major lives in dire poverty in the ghetto). Non-JI, non-octave temperament is perhaps anarchy (looters are everywhere, no one has anything, people are eating people for lunch)?

Ok, now let's get serious...

Let's make this conversation a bit more polite and civil, shall we?

Best,
Aaron.

Cameron Bobro wrote:
> For the nth time- I AM NOT TALKING ABOUT "JI VS TEMPERAMENT".
>
> If this all weren't so funny it would be an Orwellian nightmare.
>
> Your thread title creates smoke to obscure the real issue. However, > it's good that you did write > "JI vs. temperament", for the expression itself reveals a > fundamental misunderstanding I'm bitching about.
>
> Once again, very slowly:
>
> "JI" is NOT the harmonic series. It is an INTERPRETATION and > APPLICATION of the harmonic series. >
> Intervals that are not "JI" are not necessarily "tempered" at all.
>
> Take the Just Intonation interval 5:4. >
> As a MAJOR THIRD in relation to the fundamental, it doesn't exist in
> the harmonic series. In other words, if we have a tone with a > fundamental of 100 Hz, and the timbre is harmonic, we're not going
> to find a partial at 125 Hz, which is where the fundamental of > another tone in a "5:4" relationship with our original 100 Hz tonic > would sit.
>
> "5:4" is found in its natural state at 500 and 400 Hz in the > harmonic series of our 100 Hz tone. It is not found at 125 Hz. >
> Our pure "5:4" major third is an interpretation and application of
> something found in the harmonic series. This is unlike, for example, > the octave above the tonic, 2:1, which is found in literal form > in the harmonic series. >
> Obviously using a 5:4 major third isn't exactly going far afield or > out on the limb as far as interpreting and applying the > harmonic series; it's a simple matter of dropping something in plain > earshot into the first octave, and the original is sitting on top > of an octave of the tonic anyway. >
> "Everyone knows that" someone will say, to which I say, oh yeah?
>
> If you truly KNOW this, then it is obvious that an interval that
> is simply near to the 5:4 third IS NOT AUTOMATICALLY A TEMPERED 5:4.
>
> Now let's say we say that we want 5:4 as our third. Great, > wonderful. And we're going to have to temper it to avoid
> "comma pumps" and all that jazz. Fine, groovy, whatever. > Now, unlike the octave, 5:4 as a major third in relation to the > fundamental simply isn't physically, directly found in the harmonic > series. > This means that a: we can temper it a lot, and b: we can't temper it > too much at all. >
> We can temper it a lot because it's not likely to be directly
> and loudly contrasting with our tempered version, which 2:1 for > example tends to do. But we CAN'T temper 5:4 too much for the same > reason: > as an interpretation, although a strong and good one, of the > harmonic series, it doesn't directly, physically assert itself like > the 2:1 does and therefore, once we tweak our M3 a bit away from the > exact 5:4, IT IS NO LONGER 5:4.
>
> AND, because 5:4 is NOT engraved in stone, there can be many > different M3s that were never intended to have anything to do
> with 5:4 in the first place.
>
> AND, even if a "JI" interval is strong enough to assert itself
> in its manifestations, not just its original form, for example
> 3:2 (which is an interpretaion of the partial 3:1) can appear as > 2:3, 2:6, 6:2, etc., to the point where it can still be felt
> through a good amount of tempering, it DOES matter, audibly > (whether anyone here wants to admit it or not), whether it's > tempered up or down!
> DIFFERENT SOUND. DIFFERENT CHARACTER.
>
> "approximating Just intervals" is simply not a firm foundation
> without many qualifying factors. >
> "JI" is not the center, source, or constant point of reference, of > tuning! The harmonic series is. > If "JI" is STATED to be the desired point of reference, that's fine > and dandy. If it's
> assumed as some kind of universal truth, that's bullshit. And > if "JI" is stated to
> be the desired "sound", which is also just dandy, then a quality > approach to
> achieving that goal is NOT just a matter getting near to > specific "JI" intervals:
> it matters whether you're high or low, and once you have a set > of "tempered" > intervals, that set has its own demands as far as sounding cohesive. >
> Now to any replies of yes we know all this, I say: then show me the > vast tomes in
> the archives addressing the intervals that are most decidely > NOT "JI". Show me the
> evidence that intervals are accepted for what they are, and not > inevitably cartooned into
> "tempered JI intervals". Traditional triadic harmony doesn't fly > with the so-called > "neutral" intervals, yet they sound great in harmonies, so, where > are the long > discussions on alternative harmonic theories which are obviously > necessary for > polyphonic music heavy in "neutral" intervals? >
> Take care. >
>
> -Cameron Bobro
>
>
>
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--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Historically 1/3-comma meantone was called just that: meantone.
> Many, many modern authors have followed suit. And these lists
> now make the largest body of literature and discourse, and throw
> in a nice model to boot, which says that temperaments in
> which 81/80 vanish are meantones.
>
> -Carl
>

Carl,

Read the sources a bit more closely. Zarlino's 2/7-comma temperament
was not called meantone, and he later referred to it as "inferior to
meantone". Salinas did not call the 1/3 comma tuning meantone, and
explicitly described it as an alternative to meantone.

Theorists, especially in the post-meantone era, have been somewhat
sloppy abouy this. Barbour puts it most clearly: "Strictly, there is
only one meantone temperament. But theorists have been inclined to
lump together under that head all sorts of systems intended for
keyboard instruments."

It is simply more accurate terminologically AND historically to
identify the family of temperaments with the vanishing or distributed
syntonic comma than with the term meantone which is simply one member
of the family.

Please let me know when this list is supposed to have come to some
consensus on this point; I certainly would have protested if such
lumping together under the name meantone had been proposed.

djw

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Hey Cameron-
>
> No need to start 'yelling' in all capital letters.

Haha! Okay.
>
> Everything you say is true about the harmonic series, etc.
>
> However, 5/4 derives it's special consonance from the coincident
> harmonics of the overtones of 2 harmonic series in conjunction.

Consonance, yes, that's what I mean when I say "literal" consonance-
there are lower partials literally as one. But consonance is a
thing, not the only thing.

>In this
> sense---I have to disagree---JI *is* in the harmonic series.

Do you find 9/8 beatless? In terms of literal consonance
and "stillness", I find 7/5 for example more concordant than 9/8.
Just an observation. Anyway, are we going to equate beatless
intervals with the harmonic series? That won't work because any
integer ratio can be derived from the harmonic series and we can
have all kinds of wildly beating ratios. Beatless intervals are
a certain class of integer ratios- an interpretation and
application of the harmonic series, not the harmonic series
and all its potentials itself. Just like I said before. :-)

>It's >not
> simply an 'interpretation' as you insist, when the brain is simply
> perceiving co-incident tones among pairs (or groups) of series.

As soon as you establish any kind of limit- prime, n*d complexity,
whatever, you are dealing with an interpretation. And I did not
say that an interpretation is simply the brain perceiving coincident
tones, for the things that make JI what it is are "real" (ie its
not just some conditioned thing). The same inborn perceptions
also make other interpretations of the harmonic series as "real" as
JI.

>So, what
> we really have is you talking at cross-purposes by insisting that
>we
> should not say "6" but "a half dozen".

I am saying that "some of the eggs" shouldn't be referred to
as "all the eggs". Anyway sometimes it is very important
to distinguish between "six" and "half a dozen", for example
when what you're talking about some kind of process like
counting by dozens.
>
> Another thing to consider---you brought up how it would
>be 'ridiculous'
> to think of 400 cents as a sharp 5/4 instead of thinking of it as
81/64.
> On one level, yes, what you say is true, in that 12-equal is both
>a
> Pythagorean and an extreme meantone simultaneously, however, the
ear
> hears 400 cents, nonetheless, as a sharp 5/4, not a flat 81/64.

My ear does not, what can I say? I just tuned up a dozen 3/2s and
sure enough, the triads with 81/64 (in isolation) sound just like
12-tET "only better", the triads with the dim4 version of the M3
also sound pretty good but nothing at all like 12-tET. Actually
this straight and dry Pythagorean tuning sounds pretty good IMO.
>
> The proof is simple---no dyad as complex 81/64 will be perceived
>as
> beatless.

But beatlessness is a thing, not the thing. Beatlessness equals
beatlessness, not the harmonic series. Beating doesn't bother
me in the slightest. Come to think of it, my wife tends to be
highly irked by beatless intervals.

>5/4 can be perceived as beatless, 81/64 cannot, because the
> brain interprets it as a member of the 5/4 family.

This is a theory, and it simply does not agree with my experience.
81/64 cannot be percieved as beatless for the simple reason that
it beats, and it beats because it beats, not because it is not
a 5/4.

"Dang that girl is ugly- she doesn't look like Sharon Stone at
all!"

>This is perfectly in
> line with what Harmonic Entropy predicts.

Does harmonic Entropy predict that I (and everyone I know out
in the physical world, afaik) that 60/49 is a soft and
consonant interval?
>
> All this of course, says nothing about the aesthetic issues and
>choices
> about whether or not to use 81/64 in music. I'm just simply
>stating
> basic facts about human auditory perception---81/64 is not a
>beatless dyad.

Yes 81/64 beats, and it beats in the same place that 5/4 doesn't,
but that does not make it a detuned 5/4. In fact, that's what
makes it NOT a detuned 5/4, for the identity of 5/4 includes
the softness of conincident partials- an interval a couple of
cents above 5/4 still has softness, a slow beat or creaming
effect, in the same place 5/4 does, so it can be legitimately
viewed as a tempered or detuned 5/4. (An interval just below
5/4 doesn't have as much potential to be percieved of as a
detuned 5/4 because as you go down, the first couple of partials
start getting into harsh zones and the 5/4 character gets lost
more quickly but this is definitely more subjective).

>
> As for temperament, it's simply the desire to distribute the
>fruits of
> JI among all the 'tonics' equally---communism/socialism of a sort.
>JI is
> arch-monarchy, equal-temperament is idealistic communism or
socialism,
> and unequal temperament might be considered a brand of democratic
> capitalism (haves, have-nots, and have-nothings) or even a type of
> capitalistic constitutional monarchy in some cases (C major is
>golden,
> F# major lives in dire poverty in the ghetto). Non-JI, non-octave
> temperament is perhaps anarchy (looters are everywhere, no one has
> anything, people are eating people for lunch)?
>
> Ok, now let's get serious...

Actually I take those kinds of comparisons most seriously. :-)
>
> Let's make this conversation a bit more polite and civil, shall we?

Okay, no sweat, take care.
-Cameron Bobro

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > I'm not saying these "approximations" are good or bad things, but
> > 700 cents is clearly a tempered 3/2.
>
> Who are you and what have you done with Cameron?!

In plain view, about a centimeter above what you quoted:

"In the case of 700 cents, we're talking less than 2 cents from 3/2,
and in the "soft" direction. 704 cents would be iffy, I think."

Haha! Yes, to me 700 cents sounds like a tempered 3/2, and so does
699 cents for that matter. 705 cents however is already in a place
where the straightness or stillness or whatever it is of the 3/2
is getting overshadowed by brassiness and I have a hard time
feeling it as a 3/2. A "fifth", yes, but a 3/2, no.

Don't you agree that it makes a difference whether you temper up or
down (or whether an interval you got by some other means other than
tempering, osteomancy or whatever, which happens to live very close
to a powerful manifestation of the harmonic series, lives above or
below that manifestion)?

-Cameron Bobro

I have no idea why one would claim that 1/3 comma was 'historically
called meantone'. For a start, most people using meantone historically
didn't speak English. In the 16th/17th century, such systems were
often called something like 'sistema participata' or 'allgemeine
Temperatur' (this last was more likely to refer to 1/4 comma).

The term 'meantone' in English comes, I think, from the 18th or even
19th centuries. By the time it was coined, the tuning system itself
was extremely old.

One could very well argue that the 'mean tone' referred to was the
mean of the 9/8 and 10/9 tones, which restricts you to 1/4 comma. For
any other regular tuning with flattened fifths, one can say '1/x comma
meantone' or however you like.

~~~T~~~

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > 12-tET *is* a form of meantone. -Carl
> >
> > Carl,
> >
> > There is far from a consensus about this. I, for one, reserve the
> > name "meantone" for the quarter-common tuning, in which the whole
> > tone divides the 5:4 major third equally, distributing the syntonic
> > comma over four fifths. I would then characterize meantone as being
> > part of the family of tunings with distributed commas: 1/3 comma,
> > 1/5 (my favorite -- my opera is in 1/5 comma tuning), 2/7, 1/6 etc.,
> > and of which 12tet is also located as 1/11 comma tuning.
>
> Historically 1/3-comma meantone was called just that: meantone.
> Many, many modern authors have followed suit. And these lists
> now make the largest body of literature and discourse, and throw
> in a nice model to boot, which says that temperaments in
> which 81/80 vanish are meantones.
>
> -Carl
>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote
> > I feel that the whole basic idea of basing tunings on
> > approximating Just intervals is of dubious artistic
> > integrity.
> > To each their own of course.
>
> Look at it this way. Linear temperaments are not pretending to
>_be_ JI
> (except perhaps those few we call microtemperaments or>
>nanotemperaments).

One of these temperaments, Gene's ennealimmal, does seem to be
claiming to sound like "JI", and if we consider "7-limit JI" in the
way it should be considered, ie "simple ratios" including the
ones where literal consonance at the seventh partial is
happening, I think it is successful harmonically. It's an
interesting effect- close to stillness harmonically but much
more even-sounding as far as step sizes. From what I have
heard done in this temperament, it succeeds very well in doing
what the "middle path" paper is addressing.

My gripe- and to me this is a very important thing- is about
the fundamental position of "JI" as a kind of center of the
tuning universe. In a way or to a degree, it must be (even in a
negative sense, ie deliberately avoiding it), for it
is such a direct application of the harmonic series. But I
violently disagree that "JI" "IS" the harmonic series, for it
is simply not.

A "middle path" between JI and ET is just fine- the
implication that "JI and ET" are the mountains between which
paths lie is just plain wrong.

>They are of musical interest in and of >themselves.

That's great- but when this is true, then it is inevitable
that either by tempering JI intervals or using other means
to create tunings, you will create tunings which simply
cannot be understood in terms of JI approximates. Unless of
course you extend what you mean by "JI".

>
> However, many people find they prefer the sound of linear
>temperaments
> that are in some sense _closer_ to JI. But this has to be weighed
> against the preference to also minimise the number of different
> pitches required on fixed-pitch instruments.
>
> Comma pumps are just fine for a cappella and variable pitch
> instruments, but cause problems for those of us whose thing might
be
> guitar or keyboards or indeed any ensemble containing at least one
> fixed-pitch instrument. Surely we can still be allowed "artistic
> integrity" despite wanting to modulate widely _and_ use fixed pitch
> instruments. (Incidentally, the only thing I could be remotely
said to
> have ever _composed_ is in strict JI. And I am now building
>microtonal
> guitars for which strict JI is difficult).
>
> One point of Paul's paper is that this does not limit us to a
>choice
> between JI and ETs as the debate often seems to be cast. There is a
> whole world of middle paths to explore. However to save a lot of
time,
> he has catalogued for us the few dozen most promising areas for
> exploration, based on them being good tradeoffs between closeness
>to
> JI and number of pitches required.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

>
> >In this
> > sense---I have to disagree---JI *is* in the harmonic series.

Yes, "In" the harmonic series, but not "Is" the harmonic series.
There's a fundamental difference.

Hi Cameron--

Just a quick question before we dismiss what I brought up about beating---if 81/64 does not beat because it is a mistuned 5/4, why *does* it beat, then?

Best,
Aaron.

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> Hey Cameron-
>>
>> No need to start 'yelling' in all capital letters.
>> >
> Haha! Okay.
> >> Everything you say is true about the harmonic series, etc.
>>
>> However, 5/4 derives it's special consonance from the coincident >> harmonics of the overtones of 2 harmonic series in conjunction. >> >
> Consonance, yes, that's what I mean when I say "literal" consonance-
> there are lower partials literally as one. But consonance is a > thing, not the only thing. >
> >> In this >> sense---I have to disagree---JI *is* in the harmonic series. >> >
> Do you find 9/8 beatless? In terms of literal consonance > and "stillness", I find 7/5 for example more concordant than 9/8. > Just an observation. Anyway, are we going to equate beatless > intervals with the harmonic series? That won't work because any > integer ratio can be derived from the harmonic series and we can
> have all kinds of wildly beating ratios. Beatless intervals are
> a certain class of integer ratios- an interpretation and > application of the harmonic series, not the harmonic series
> and all its potentials itself. Just like I said before. :-)
>
>
> >> It's >not >> simply an 'interpretation' as you insist, when the brain is simply >> perceiving co-incident tones among pairs (or groups) of series. >> >
> As soon as you establish any kind of limit- prime, n*d complexity,
> whatever, you are dealing with an interpretation. And I did not
> say that an interpretation is simply the brain perceiving coincident
> tones, for the things that make JI what it is are "real" (ie its
> not just some conditioned thing). The same inborn perceptions
> also make other interpretations of the harmonic series as "real" as > JI. >
>
> >> So, what >> we really have is you talking at cross-purposes by insisting that >> we >> should not say "6" but "a half dozen".
>> >
> I am saying that "some of the eggs" shouldn't be referred to
> as "all the eggs". Anyway sometimes it is very important > to distinguish between "six" and "half a dozen", for example
> when what you're talking about some kind of process like > counting by dozens. > >> Another thing to consider---you brought up how it would >> be 'ridiculous' >> to think of 400 cents as a sharp 5/4 instead of thinking of it as >> > 81/64. > >> On one level, yes, what you say is true, in that 12-equal is both >> a >> Pythagorean and an extreme meantone simultaneously, however, the >> > ear > >> hears 400 cents, nonetheless, as a sharp 5/4, not a flat 81/64.
>> >
> My ear does not, what can I say? I just tuned up a dozen 3/2s and > sure enough, the triads with 81/64 (in isolation) sound just like
> 12-tET "only better", the triads with the dim4 version of the M3 > also sound pretty good but nothing at all like 12-tET. Actually
> this straight and dry Pythagorean tuning sounds pretty good IMO.
> >> The proof is simple---no dyad as complex 81/64 will be perceived >> as >> beatless. >> >
> But beatlessness is a thing, not the thing. Beatlessness equals > beatlessness, not the harmonic series. Beating doesn't bother
> me in the slightest. Come to think of it, my wife tends to be
> highly irked by beatless intervals.
>
> >> 5/4 can be perceived as beatless, 81/64 cannot, because the >> brain interprets it as a member of the 5/4 family. >> >
> This is a theory, and it simply does not agree with my experience.
> 81/64 cannot be percieved as beatless for the simple reason that
> it beats, and it beats because it beats, not because it is not
> a 5/4.
>
> "Dang that girl is ugly- she doesn't look like Sharon Stone at > all!"
>
> >> This is perfectly in >> line with what Harmonic Entropy predicts.
>> >
> Does harmonic Entropy predict that I (and everyone I know out
> in the physical world, afaik) that 60/49 is a soft and
> consonant interval?
> >> All this of course, says nothing about the aesthetic issues and >> choices >> about whether or not to use 81/64 in music. I'm just simply >> stating >> basic facts about human auditory perception---81/64 is not a >> beatless dyad.
>> >
> Yes 81/64 beats, and it beats in the same place that 5/4 doesn't, > but that does not make it a detuned 5/4. In fact, that's what
> makes it NOT a detuned 5/4, for the identity of 5/4 includes
> the softness of conincident partials- an interval a couple of
> cents above 5/4 still has softness, a slow beat or creaming > effect, in the same place 5/4 does, so it can be legitimately
> viewed as a tempered or detuned 5/4. (An interval just below
> 5/4 doesn't have as much potential to be percieved of as a
> detuned 5/4 because as you go down, the first couple of partials > start getting into harsh zones and the 5/4 character gets lost > more quickly but this is definitely more subjective). >
> >> As for temperament, it's simply the desire to distribute the >> fruits of >> JI among all the 'tonics' equally---communism/socialism of a sort. >> JI is >> arch-monarchy, equal-temperament is idealistic communism or >> > socialism, > >> and unequal temperament might be considered a brand of democratic >> capitalism (haves, have-nots, and have-nothings) or even a type of >> capitalistic constitutional monarchy in some cases (C major is >> golden, >> F# major lives in dire poverty in the ghetto). Non-JI, non-octave >> temperament is perhaps anarchy (looters are everywhere, no one has >> anything, people are eating people for lunch)?
>>
>> Ok, now let's get serious...
>> >
> Actually I take those kinds of comparisons most seriously. :-) > >> Let's make this conversation a bit more polite and civil, shall we?
>> >
> Okay, no sweat, take care. > -Cameron Bobro
>
>
>
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>

Unless we had Chopin on the list, it is true. Harrison referenced
someone who wrote on it, i apologize for not having the reference. I usually avoid discussions about historical tunings by particular
composers for just these reasons.

Like JI one always assumes that you can only do certain things or
only certain things sound good. People complain about 40/27 or 27/20
in a Just major scale. It can be exactly what one wants at times and
having a pure fifth or fourth would not work for what it says. It is
an added resource not necessary something one must always avoid by
everyone. Especially when we move away from church music and
institutional musical circles.

While we do not know exactly what Chopin tuned to and likewise if
/when he did we can not be sure that he didn't like things we assume
are not musically significant. Look at the intervals used in Eastern
Europe folk music and it is even hard to guess what people were
doing in Poland at the time.
What can be 'proven' can only be proved in places and musical situations of a certain class.

But one has only to listen still to this day to the folk music all throughout Europe and we have to question some implied notions. We will find neutral thirds for example or in Norwegian fiddle music different intonation used in the upper octave. Listen to French traditional music and one is confronted with intervals the theory avoids dealing with. Can we tell where the line between them being (albeit highly gifted) folk artist or products of institutions of the early Romantic composers. Many of them were lower class loaded up with Syphilis. Sometimes they were able to do more when others noticed their abilities.

One has only to listen to early recordings of orchestras and one can be appalled by the intonation. I see no reason not to assume that such "tolerances" or varied interpretations have not been apart of the fabric for quite some time or at least present to varied degrees. Artist have never been conformist to what others tell them. they are the ones that tell others, and when they hit on something the lesser then use it to build a wall against the next developments. Yet another group comes along and pays no attention to ideas or right and wrong and in the process and the sometimes stumbling into many dead ends music as a whole finds it way and it progresses.

Posted by: "Tom Dent" <http://profiles.yahoo.com/sphaerenklang>

Mon Sep 10, 2007 10:11 am (PST)

Certainly when Chopin was in Majorca with the little upright he would
need to do the tuning himself.

What he did with it? ... I'm highly doubtful that either you or Lou
Harrison - or anyone else - knows!

Where d o his melodies often start ?

He did compose an awful lot of pieces in Ab and Db - how awful should
they sound?

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Tom Dent wrote:
> I have no idea why one would claim that 1/3 comma was 'historically
> called meantone'. For a start, most people using meantone historically
> didn't speak English. In the 16th/17th century, such systems were
> often called something like 'sistema participata' or 'allgemeine
> Temperatur' (this last was more likely to refer to 1/4 comma).
>
> The term 'meantone' in English comes, I think, from the 18th or even
> 19th centuries. By the time it was coined, the tuning system itself
> was extremely old. >
> One could very well argue that the 'mean tone' referred to was the
> mean of the 9/8 and 10/9 tones, which restricts you to 1/4 comma. For
> any other regular tuning with flattened fifths, one can say '1/x comma
> meantone' or however you like.
>
> I think this is what Carl was trying to say.

-A.

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
>
> >>> In this >>> sense---I have to disagree---JI *is* in the harmonic series. >>> >
> Yes, "In" the harmonic series, but not "Is" the harmonic series. > There's a fundamental difference. > Ok, I can handle that.

I personally restrict 'JI' to audibly sets of audibly beatless intervals, and the full-of-beats combinations that comes as a side effect (e.g. 40/27 in 5-limit duodene, etc., 81/64 in 3-limit Pyth.)

The higher up stuff, (e.g. 29/23) I call 'rational intonation'.

So, more correctly, I would say "JI is a subset of the harmonic series". Does that fly with you?

I still contend that 81/64 beats because the ear 'wants/tries' to hear it as a 5/4....until you come up with a better theory about why it beats, I'm sticking with that.

Best,
Aaron.

> Please let me know when this list is supposed to have come to some
> consensus on this point;

It was already in consensus when I first asked for a definition of
meatone in 1997 or early '98. It's really not up for debate. The
best you could hope for is a "regular temperaments" sense and a
"historical" sense.

-Carl

> Don't you agree that it makes a difference whether you temper
> up or down

Yes.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Please let me know when this list is supposed to have come to
some
> > consensus on this point;
>
> It was already in consensus when I first asked for a definition of
> meatone in 1997 or early '98. It's really not up for debate. The
> best you could hope for is a "regular temperaments" sense and a
> "historical" sense.
>
> -Carl
>

Defintely not; about that point in time I wrote a FAQ item on
meantone which I abandoned because of the vociferous lack of
consensus.

djw

> > It was already in consensus when I first asked for a definition
> > of meatone in 1997 or early '98. It's really not up for debate.
> > The best you could hope for is a "regular temperaments" sense
> > and a "historical" sense.
> >
> > -Carl
>
> Defintely not; about that point in time I wrote a FAQ item on
> meantone which I abandoned because of the vociferous lack of
> consensus.
>
> djw

The only FAQ effort I know of occurred in 2001. At any rate, as
one of the most frequent contributors and main archivers of these
lists it is my carefully considered opinion that there was a
strong consensus on the syntonic comma definition of the term
"meantone temperament".

-Carl

> I still contend that 81/64 beats because the ear 'wants/tries' to
> hear it as a 5/4....until you come up with a better theory about
> why it beats, I'm sticking with that.

Hi Aaron,

It's somewhat of an abuse to say intervals beat because they are
mistunings of JI intervals. Intervals beat when they place
partials inside the critical band. Plenty of extended JI
intervals fit this bill, and all JI intervals < an octave will
if rooted at a low enough pitch.

-Carl

Carl Lumma wrote:
>> I still contend that 81/64 beats because the ear 'wants/tries' to
>> hear it as a 5/4....until you come up with a better theory about
>> why it beats, I'm sticking with that.
>> >
> Hi Aaron,
>
> It's somewhat of an abuse to say intervals beat because they are
> mistunings of JI intervals. Intervals beat when they place
> partials inside the critical band. Plenty of extended JI
> intervals fit this bill, and all JI intervals < an octave will
> if rooted at a low enough pitch.
>
> True; duly noted.

In fairness to what I was trying to say, I still think what I say stands re: the typical use of 81/64 as a maj. 3rd

I also define JI as those interval that are beatless in common usage, not super-low labratory frequencies.

Yes, extended JI (I would put this at the 9 limit or higher e.g an 9/7 or 11/8 interval) has beating dyads, and some intervals are more dissonant when they don't have a harmonic series context with which to be interpreted.

Hermmph, surely beating is an objective phenomenon, meaning periodic
variations in power over a timescale much longer than the fundamental
vibrations. In order to be perceived, such variations have to have a
certain size (which comes from harmonic content) and lie within a
certain range of frequency (which depends on both interval and
absolute pitch).

It is true for *some* 81:64's that they beat by virtue of being
mistuned 5:4's - but not others. For example, say, just below tenor C
on a piano you will get fairly slow beat rates and the character of
the interval is not so far from 5:4. But if you go up to the treble
octave (ie between one and two octaves above middle C), first the
variation in power is much more rapid and probably beyond the range
where the listener can hear it as a beat; second, the 5th partial is
getting weaker; third, the sensitivity of the ear to changes in
interval is greater in this octave. In this case the ear will probably
not hear definite beats (but will certainly hear something different
from a 5:4).

There are possibly situations where 81:64 beats because it is a
mistuned 19:15 - that is, perceptible variations in power arise from
the 19th partial of the lowest fundamental. As I described some time
ago, once when searching for a pure third just below middle C on an
Italian harpsichord I hit a 19:15 instead - and was able to tune it,
out of curiosity.

There is a small class of 'beatless' intervals which (given harmonic
timbres) never produce perceptible beats when sounded in an audible
range. 7/6 may be more or less the boundary of this class, I'm not
sure, one would have to experiment a bit. All the rest are then more
or less beating, depending on timbre and pitch...

The question may really be unresolvable if we believe (as Helmholtz
more or less said) that sufficiently low single notes with a
sufficiently strong high harmonic content are perceived as dissonant
and rough in themselves. Does anyone have audio examples of such things?

~~~T~~~

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
>
> I still contend that 81/64 beats because the ear 'wants/tries' to hear
> it as a 5/4....until you come up with a better theory about why it
> beats, I'm sticking with that.
>
> Best,
> Aaron.
>

Aaron K. Johnson wrote:
>
> I also define JI as those interval that are beatless in common usage, > not super-low labratory frequencies.
That is to say: we all know even an octave sounds dissonant if placed low enough, but that wasn't the context of the discussion.

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Carl Lumma wrote:
> >> I still contend that 81/64 beats because the ear 'wants/tries' to
> >> hear it as a 5/4....until you come up with a better theory about
> >> why it beats, I'm sticking with that.
> >>
> >
> > Hi Aaron,
> >
> > It's somewhat of an abuse to say intervals beat because they are
> > mistunings of JI intervals. Intervals beat when they place
> > partials inside the critical band. Plenty of extended JI
> > intervals fit this bill, and all JI intervals < an octave will
> > if rooted at a low enough pitch.
> >
> >
> True; duly noted.
>
> In fairness to what I was trying to say, I still think what
> I say stands re: the typical use of 81/64 as a maj. 3rd
>
> I also define JI as those interval that are beatless in common
> usage, not super-low labratory frequencies.

7/5 has beating partials throughout the musical range. Is
it JI?

3/2 beats in much of the piano's left hand, which is why it's
almost always voiced as a 12th there.

Musical instruments go down very near (and in some organs,
below) the limit of human hearing. They do not get close
to the upper limit.

> Yes, extended JI (I would put this at the 9 limit or higher

Classically, JI included only the 5-limit intervals. I
still see this usage all over. Anything 7 or above is
extended JI.

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> Hermmph, surely beating is an objective phenomenon, meaning
> periodic variations in power over a timescale much longer than
> the fundamental vibrations.

Beating is a psychoacoustic phenomenon that results from the
design of the basilar membrane and the rest of the hearing
apparatus. It's also distinctly different from sound waves
(longitudinal waves in air) -- it's A.M. of sound waves.

> It is true for *some* 81:64's that they beat by virtue of being
> mistuned 5:4's - but not others.

No.

> For example, say, just below tenor C
> on a piano you will get fairly slow beat rates and the character of
> the interval is not so far from 5:4. But if you go up to the treble
> octave (ie between one and two octaves above middle C), first the
> variation in power is much more rapid and probably beyond the range
> where the listener can hear it as a beat;

What's really happening is the resolution of the basilar
membrane is expressed in constant frequency units, so it
improves in terms of log scale as you go up the piano.

> There is a small class of 'beatless' intervals which (given
> harmonic timbres) never produce perceptible beats when sounded
> in an audible range. 7/6 may be more ...

7/6 partials have clearly audible beats throughout most
of the musical range -- the so-call "periodicity buzz" of
the interval.

-Carl

Hey,

Instead of getting into a little match with you about what constitutes JI (I've got other things to do right now) I'll say this--you win, ok?.
Now that you agree with Cameron, one wonder why you two are going at it.

perhaps my best definition is this---I know JI when I hear it. 7/5 has a beatless 'quality' enough to me that yes, it does count.

When is a heap a pile?

-A.

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> Carl Lumma wrote:
>> >>>> I still contend that 81/64 beats because the ear 'wants/tries' to
>>>> hear it as a 5/4....until you come up with a better theory about
>>>> why it beats, I'm sticking with that.
>>>> >>>> >>> Hi Aaron,
>>>
>>> It's somewhat of an abuse to say intervals beat because they are
>>> mistunings of JI intervals. Intervals beat when they place
>>> partials inside the critical band. Plenty of extended JI
>>> intervals fit this bill, and all JI intervals < an octave will
>>> if rooted at a low enough pitch.
>>>
>>> >>> >> True; duly noted.
>>
>> In fairness to what I was trying to say, I still think what
>> I say stands re: the typical use of 81/64 as a maj. 3rd
>>
>> I also define JI as those interval that are beatless in common
>> usage, not super-low labratory frequencies.
>> >
> 7/5 has beating partials throughout the musical range. Is
> it JI?
>
> 3/2 beats in much of the piano's left hand, which is why it's
> almost always voiced as a 12th there.
>
> Musical instruments go down very near (and in some organs,
> below) the limit of human hearing. They do not get close
> to the upper limit.
>
> >> Yes, extended JI (I would put this at the 9 limit or higher
>> >
> Classically, JI included only the 5-limit intervals. I
> still see this usage all over. Anything 7 or above is
> extended JI.
>
> -Carl
>
>
>
> You can configure your subscription by sending an empty email to one
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>
>
>
>
>

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

> The only FAQ effort I know of occurred in 2001. At any rate, as
> one of the most frequent contributors and main archivers of these
> lists it is my carefully considered opinion that there was a
> strong consensus on the syntonic comma definition of the term
> "meantone temperament".

For our purposes it's the best choice, and one wonders what else we are
going to call "2/7-comma meantone" if we can't call it meantone. The
abstract temperament is more important than the precise tuning, and
hence by a natural evolution of language will tend to glom the name.

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

> The only FAQ effort I know of occurred in 2001. At any rate, as
> one of the most frequent contributors and main archivers of these
> lists it is my carefully considered opinion that there was a
> strong consensus on the syntonic comma definition of the term
> "meantone temperament".
>
> -Carl
>

I recall the FAQ from before my Budapest years, i.e. before 2000.
Prior to writing the FAQ I was very loose myself in the use of the
term meantone, but research showed clearly that the use on the list
of the term to include other comma-fraction tunings was historically
unprecedented and misleading. As noted in my previous post, there
was some abuse of the term by theorists, especially in the 19th
century, but this abuse was not to describe the family of distributed
comma temperaments, but rather to describe all manner of non-12tet
keyboard tunings. Gradually, I adopted the term "meantone-like", for
the specific purpose of describing tunings used in historical musical
practice that did not go beyond the tonal resources of meantone, for
example the widespread 1/6 comma temperament.

In any case, let me now officially register my dissent from any such
supposed consensus; my FAQ experience demonstrates amply that there
are further dissidents. Put simply: what is to be gained by using the
meantone label for the entire family, including tunings which do not
have an interval of a tone at the mean of a just major third when the
perfectly good alternative of identifying the family simply by the
comma is question is adequate and sufficient?

djw

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> One could very well argue that the 'mean tone' referred to was the
> mean of the 9/8 and 10/9 tones, which restricts you to 1/4 comma.

Unless you perversly decide it means a tone of 161/144, which would
mean a ffith of sqrt(322)/12, which is actually 1/4.01246 -comma
meantone. Then there's the harmonic mean, the mediant, and an infinite
number of other possibilities.

Of course, this is silly, but for the purposes of this list, so is
restricting meantone to 1/4 comma. It's not going to happen, however
historically well-supported, since it's an attempt to get the tail to
wag the dog. Having allowed "q-comma meantone" as acceptable, you've in
effect conceded the issue yourself.

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

>
> > It is true for *some* 81:64's that they beat by virtue of being
> > mistuned 5:4's - but not others.
>
> No.

What is that 'No' referring to? Is my statement 100% wrong, partially
wrong, or what?

If on a normal 'equal-tempered' piano I play C two octaves above
middle C and the E above that, I can't hear anything that I could
describe as beating. Why not?

Since AM is an objective physical property of waves, so is beating...
however, the question of what we hear as a 'beating' interval is one
of human perception of that physical property. Which differs widely
between musical situations.
Is there any point trying to classify abstract intervals into
'beating' or 'non-beating' based on some vague assumption of 'normal'
timbre and pitch range?
~~~T~~~

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Anyone have any Brahms they think could be made to work in a
> > tuning/temperament other than 12-TET?
>
> I think Gene will probably have something to say here.

You could download my Brahms string quartet rendering in 31-et from
Classical Archives and take a listen! I think Brahms is easier in
general to tune to 31 than Wagner.

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:

> More accurately---12 is on the outer limits of meantone, a special
case
> where there is no difference between the chromatic and and diatonic
> semitone.

You could certainly argue that 12 and 19 form the natural boundriues of
meantone.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
>
> >
> > > It is true for *some* 81:64's that they beat by virtue of being
> > > mistuned 5:4's - but not others.
> >
> > No.
>
> What is that 'No' referring to? Is my statement 100% wrong,
> partially wrong, or what?

The majority of intervals beat. 81/64 is one of them,
but it doesn't beat *because* it's a mistuning of any
particular JI interval.

> If on a normal 'equal-tempered' piano I play C two octaves above
> middle C and the E above that, I can't hear anything that I could
> describe as beating. Why not?

There aren't any partials of sufficient amplitude within a
critical band.

Sorry I don't have more time for a better response. And
I'm a poor proxy for Paul Erlich anyway.

-Carl

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

> Put simply: what is to be gained by using the
> meantone label for the entire family, including tunings which do not
> have an interval of a tone at the mean of a just major third when the
> perfectly good alternative of identifying the family simply by the
> comma is question is adequate and sufficient?

The "81/80 comma temperament" or "Didymus temperament" or what have you
is not a recognized name, that's the problem. As you not yourself, the
usage you object to is over 100 years old. You are ttying to shut the
door after the horse has already left the barn, and since "81/80
temperament" is about 100 times more important than "1/4 comma
meantone", why fight it?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> Of course, this is silly, but for the purposes of this list, so is
> restricting meantone to 1/4 comma. It's not going to happen, however
> historically well-supported, since it's an attempt to get the tail to
> wag the dog. Having allowed "q-comma meantone" as acceptable, you've in
> effect conceded the issue yourself.
>

Not quite. For example: how many legs has a three-legged dog? But how
many legs has a dog? Still four.

What a lot of people have used is for 'meantone' to be 1/4 comma as
default; anything else is to be specified or deduced from context. For
example 'family of meantone tunings'.

The problem with formally allowing 'meantone' to cover all regular
tunings with narrowed fifths is that you can't make statements like
'chromatic semitones are narrow in meantone'. (But if your fifths are
narrowed by 1/12 or 1/15 or 1/18 comma...) Nor could you talk
meaningfully of a historical clash between meantone and 12-ET.

Usages that make the most mathematical sense rarely make much musical
or historical sense - and vice versa.

~~~T~~~

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

> The "81/80 comma temperament" or "Didymus temperament" or what have
you
> is not a recognized name, that's the problem. As you not yourself,
the
> usage you object to is over 100 years old. You are ttying to shut
the
> door after the horse has already left the barn, and since "81/80
> temperament" is about 100 times more important than "1/4 comma
> meantone", why fight it?
>

Gene,

No. The usage here of meantone for this family of tunings is new. You
will find no hisotrical precedent for it. Even Barbour, who includes
a group of regular temperaments in his chapter on meantone identifies
them (a) as not being meantone, and (b) as "2/7-comma temperament","1/
3 comma temperament" etc..

In the past, especially in the post-meantone era, the name was
sometimes used -- and I believe we will all agree, misused -- to
describe _all_ non-equal 12-tone keyboard temperaments, not just
regular fraction-of-a-comma temperaments.

As musicians, I would expect that there would be a consensus that the
name "1/4 comma meantone", or just plain "meantone" remains
immeasurably more important (and not 100 times less important) than
"81/80 temperament" simply because it is associated with an
extrardinary repertoire of real, existing music.

Finally, if the purpose here is to come up with a clear and efficient
system of classifying tunings, I have to frankly wonder why you would
wish to also identify tunings that do not have tones that are mean
divisions of a just major third with that particular label. This
would seem to contradict your own impulse in asserting that

> '81/80
> temperament' is about 100 times more important than '1/4 comma
> meantone'

The salient characteristic shared by this particular family of
tunings is the regular distribution of the 81/80 comma, not the
interval of a mean tone, which is present only in 1/4 comma.

djw

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> Usages that make the most mathematical sense rarely make much
musical
> or historical sense - and vice versa.
>
> ~~~T~~~
>

Tom,

But if we reserve the word "meantone" for the 1/4 comma tuning within
the family of regular tunings with distributed 81/80 commas then we
make sense both mathematically and music-historically.

Zarlino and Salinas both offered their alternatives to meantone as
related temperaments (in that they distributed the 81/80 comma over 7/
2 and 3 fifths, respectively). They did not discribe their tunings as
meantones, understanding, that they were variations on, but not
varieties of, meantone.

djw

I was first introduced to the term "meantone" to describe LucyTuning
by Johnny Rheinhard, yet I have never been entirely happy with the
term "meantone",

as it suggests the common average of integer ratios; as though JI is
some holy grail.

LucyTuning, although it cuts between all the integer ratios except
2/1, is not the "common average" however you may chose to "bake" it.

We really do need some more descriptive term; after all Lucytuning
derived from pi can, at present, be described as:

1) a meantone-type tuning,

2) an edo, (approx. 88edo or more accurately 1420edo); or

3) as a 5L+2s tuning with octave ratio of 2,

4) an "irrational" tuning

5) a "transcendental" tuning

6) a pi-derived tuning

yet originally it was derived from the irrational, transcendental
number π.

I welcome suggestions for replacements/limitations/revised
definitions for the "loose/muddy" term "meantone".

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 11 Sep 2007, at 23:17, djwolf_frankfurt wrote:

> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> > Usages that make the most mathematical sense rarely make much
> musical
> > or historical sense - and vice versa.
> >
> > ~~~T~~~
> >
>
> Tom,
>
> But if we reserve the word "meantone" for the 1/4 comma tuning within
> the family of regular tunings with distributed 81/80 commas then we
> make sense both mathematically and music-historically.
>
> Zarlino and Salinas both offered their alternatives to meantone as
> related temperaments (in that they distributed the 81/80 comma over 7/
> 2 and 3 fifths, respectively). They did not discribe their tunings as
> meantones, understanding, that they were variations on, but not
> varieties of, meantone.
>
> djw
>
>
>

Cameron Bobro wrote:

> A "middle path" between JI and ET is just fine- the > implication that "JI and ET" are the mountains between which > paths lie is just plain wrong.

It does seem to be the case, though, that JI and ET are the tuning systems that get the most attention. Then there are the historical 12-note keyboard tunings. Other systems such as the varied gamelan scales of Indonesia get some attention from time to time. Occasionally something wildly different like Erv Wilson's golden horograms or Gary Morrison's 88-CET comes up. Still, JI and ET (specifically EDO) are among the most popular systems, for whatever reasons, and it's in that context that Paul's paper and the related work by various contributors in the tuning-math group make the most sense.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
>> Put simply: what is to be gained by using the
>> meantone label for the entire family, including tunings which do not
>> have an interval of a tone at the mean of a just major third when the
>> perfectly good alternative of identifying the family simply by the
>> comma is question is adequate and sufficient?
>
> The "81/80 comma temperament" or "Didymus temperament" or what have you
> is not a recognized name, that's the problem. As you not yourself, the
> usage you object to is over 100 years old. You are ttying to shut the
> door after the horse has already left the barn, and since "81/80
> temperament" is about 100 times more important than "1/4 comma
> meantone", why fight it?
>
>
Am I imagining it, or did the name "meantone" arise from the *tone*
being defined by some kind of mean?

Meantone means an averaging of potentially different size whole tones so
that that they both bisect a major third of any variant. Meantone's real
competition was irregular tuning, wherein each key is intentionally distinguishable
from each other.

I see no reason to insist that meantone is 5/4 exclusive, and it certainly
hasn't been taken that way. This is especially true in that meantone is an
English language term, and the term has come to mean more.

Johnny

************************************** See what's new at http://www.aol.com

djwolf_frankfurt wrote:

> No. The usage here of meantone for this family of tunings is new. You > will find no hisotrical precedent for it. Even Barbour, who includes > a group of regular temperaments in his chapter on meantone identifies > them (a) as not being meantone, and (b) as "2/7-comma temperament","1/
> 3 comma temperament" etc.. The usage may be "new" in a relative sense (compared with the historical periods when meantone was prevalent), but I'm sure that I've seen "meantone" used in a more general sense before subscribing to this list. I don't recall where I first read the term, but I know that I didn't think anything unusual about calling a tuning that I was using "1/6-comma meantone" back around 1990. It must have been in use in a book that was published no later than the 1980's, but I don't recall the author or title.

I think I've suggested "syntonic" before for 81/80 temperament -- that was at a time when we were using names like "kleismic" for a temperament that tempers out the 15625/15552 kleisma. I generally don't have much of a problem with "meantone", but using it for a tuning with fifths sharper than just does seem a bit of a stretch.

Carl Lumma wrote:
> Musical instruments go down very near (and in some organs,
> below) the limit of human hearing. They do not get close
> to the upper limit.

That depends on how you define the upper limit. High-frequency
sensitivity decays rapidly with age. And what's the fundamental
frequency of the highest note on the piccolo? 8K?

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> The problem with formally allowing 'meantone' to cover all
> regular tunings with narrowed fifths is that you can't
> make statements like 'chromatic semitones are narrow in
> meantone'. (But if your fifths are narrowed by 1/12 or
> 1/15 or 1/18 comma...) Nor could you talk meaningfully
> of a historical clash between meantone and 12-ET.

But the usage we've had here on this list for about the
last 14 years is not that meantone = "all regular tunings
with narrowed fifths", but rather that meantone = all
tunings which temper out the 81:80 syntonic-comma.

12-edo is the special case where both the chromatic
and diatonic semitones happen to be the same size.
In all other meantones, the diatonic-semitone is always
larger than the chromatic.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> Carl Lumma wrote:
> > Musical instruments go down very near (and in some organs,
> > below) the limit of human hearing. They do not get close
> > to the upper limit.
>
> That depends on how you define the upper limit. High-frequency
> sensitivity decays rapidly with age. And what's the fundamental
> frequency of the highest note on the piccolo? 8K?

4K.

What it is close to, is the upper limit of interspike timing
on the auditory nerve. . .

-Carl

--- In tuning@yahoogroups.com, "M. Edward (Ed) Borasky" <znmeb@...>
wrote:

> Am I imagining it, or did the name "meantone" arise from the *tone*
> being defined by some kind of mean?

1/4-comma meantone, the bog standard meantone, has a tone which is
exactly the geometric mean of 9/8 and 10/9. As I pointed out, you could
just as well assume it meant some other mean, eg arithmetic, going only
by the name.

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
> As musicians, I would expect that there would be a consensus that
the
> name "1/4 comma meantone", or just plain "meantone" remains
> immeasurably more important (and not 100 times less important) than
> "81/80 temperament" simply because it is associated with an
> extrardinary repertoire of real, existing music.

Oh, please. 1/4-comma meantone is not of any great importance except
historically. It has the characteristic that major thirds are just,
and it does show up on some theoretical radars, but it's just one
tuning out of (in theory) an uncountable number. It is much, much,
much, MUCH less important than the general concept of a mrantone
tempoerament.

Any FYI, the same real exciting music can be played in those other
tunings, which is the point, and makes your argument nonsense.

> Finally, if the purpose here is to come up with a clear and
efficient
> system of classifying tunings, I have to frankly wonder why you
would
> wish to also identify tunings that do not have tones that are mean
> divisions of a just major third with that particular label.

What gives you the idea people want to classify tunings? Tinings are
NOT as important as the temperaments they instantiate.

> The salient characteristic shared by this particular family of
> tunings is the regular distribution of the 81/80 comma, not the
> interval of a mean tone, which is present only in 1/4 comma.

A fact of almost no importance. Big deal.

Herman Miller wrote:
> Cameron Bobro wrote:
> > >>A "middle path" between JI and ET is just fine- the >>implication that "JI and ET" are the mountains between which >>paths lie is just plain wrong.
> > It does seem to be the case, though, that JI and ET are the tuning > systems that get the most attention. Then there are the historical > 12-note keyboard tunings. Other systems such as the varied gamelan > scales of Indonesia get some attention from time to time. Occasionally > something wildly different like Erv Wilson's golden horograms or Gary > Morrison's 88-CET comes up. Still, JI and ET (specifically EDO) are > among the most popular systems, for whatever reasons, and it's in that > context that Paul's paper and the related work by various contributors > in the tuning-math group make the most sense.

I don't agree with Cameron's implication anyway. A middle path is the path between two other paths, maybe a high and low path. I've never heard this idea of mountains before. More specifically it's a compromise (Dread Word!) between two extremes. I don't think Paul intended anything more specific than that.

Wikipedia has an entry on "Middle way" you know. The only quote that mentions the metaphorical meaning in any way is

"Monks, these two extremes ought not to be practiced by one who has gone forth from the household life. (What are the two?) There is addiction to indulgence of sense-pleasures, which is low, coarse, the way of ordinary people, unworthy, and unprofitable; and there is addiction to self-mortification, which is painful, unworthy, and unprofitable.

"Avoiding both these extremes, the Tathagata (the Perfect One) has realized the Middle Path..."

How can a mountain be low?

Graham

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> > As musicians, I would expect that there would be a consensus that
> the
> > name "1/4 comma meantone", or just plain "meantone" remains
> > immeasurably more important (and not 100 times less important)
than
> > "81/80 temperament" simply because it is associated with an
> > extrardinary repertoire of real, existing music.
>
> Oh, please. 1/4-comma meantone is not of any great importance
except
> historically. It has the characteristic that major thirds are just,
> and it does show up on some theoretical radars, but it's just one
> tuning out of (in theory) an uncountable number. It is much, much,
> much, MUCH less important than the general concept of a mrantone
> tempoerament.
>

I agree completely that it is one of a theoretically uncountable
number of tunings, but the name of this tuning describes its unique
features, and they are not found in the other tunings in the family.

> Any FYI, the same real exciting music can be played in those other
> tunings, which is the point, and makes your argument nonsense.
>

The fact that the music _could_ be played in a theortically
uncountable number of tunings is not relevant to the fact that real,
existing music _was_ composed and played specifically in 1/4-comma
meantone.

> > Finally, if the purpose here is to come up with a clear and
> efficient
> > system of classifying tunings, I have to frankly wonder why you
> would
> > wish to also identify tunings that do not have tones that are
mean
> > divisions of a just major third with that particular label.
>
> What gives you the idea people want to classify tunings? Tinings
are
> NOT as important as the temperaments they instantiate.
>
> > The salient characteristic shared by this particular family of
> > tunings is the regular distribution of the 81/80 comma, not the
> > interval of a mean tone, which is present only in 1/4 comma.
>
> A fact of almost no importance. Big deal.
>

It's a fact of substantial importance -- when I play sackbut in or
sing early music, knowing that the major thirds are just and that the
tones are means to those thirds is extremely important.

And there is also contemporary repertoire -- for example Leedy's _The
Leaves Be Green_ or Ligeti's _Passacaglia Ungarese_, in which the
just thirds and mean tones are specific features of the music.

Again, I simply have to wonder: Why you are so attached to applying
the term meantone to all of these tunings that are plainly lacking in
mean tones? The use of the word meantone to describe the family is
misleading on the one hand, in that it is no longer descriptive, and
refers to historical conditions which you clearly consider of no
importance or irrelevant, on the other.

"Meantone-like" would be a compromise label for the family, but it
does not specify which features of meantone are shared within the
family. It's far better to identify the family simply with the
regular distribution of the comma.

djw

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> I see no reason to insist that meantone is 5/4 exclusive, and it
certainly
> hasn't been taken that way. This is especially true in that
meantone is an
> English language term, and the term has come to mean more.
>

But by taking the term to "mean more", that is to describe a larger
number of tuning, it actually means less, in that several of the
salient qualities of meantone have to be given up to accomodate
tunings which (a) do not have mean tones, (b) do not have just major
thirds, and possibly, depending upon what tunings you include in the
family: (c) are not regular, or (d) do not have larger diatonic
semitones than chromatic semitones, etc..

The English language term meantone is precisely analogous to terms in
other languages (German Mittelton, French ton moyen etc.) and the
fact that it has been misused in the past -- some 19th century
theorists used it to describe _all_ non-equal 12-tone keyboard
tunings and Ll.S. Lloyd used it as a synonym for just intonation --
is simply not an argument for misusing it further.

The comparison of meatone with other tunings is very important, but
we have adequate vocabulary to do that correctly: "meantone-like" is
often useful, and in an active theoretical and practical enviroment
like ours, in which such a large number of possible and practical
tunings are under consideration, what's the harm in simply being
explicit about the most salient feature, which, in the family
presently under discussion, is the regular distribution of the
syntonic comma, and not many of the other salient charcateristics of
meantone.

djw

Cameron Bobro wrote:

> My gripe- and to me this is a very important thing- is about
> the fundamental position of "JI" as a kind of center of the
> tuning universe. In a way or to a degree, it must be (even in a > negative sense, ie deliberately avoiding it), for it
> is such a direct application of the harmonic series. But I
> violently disagree that "JI" "IS" the harmonic series, for it
> is simply not. So you have a gripe but not really?

I can't see the point of this "JI is not the harmonic series" argument. But I'll note that if all you're interested in is the harmonic series as a set of intervals relative to the fundamental, TOP-max tuning (as Paul used) will give exactly the same results as if you included all the intervals between harmonics. Why you'd only be interested in the harmonics I don't know. But replacing "JI" with "the harmonic series" (the way you seem to understand it) makes no quantitative difference.

Graham

Cameron Bobro wrote:

> Now to any replies of yes we know all this, I say: then show me the > vast tomes in
> the archives addressing the intervals that are most decidely > NOT "JI". Show me the
> evidence that intervals are accepted for what they are, and not > inevitably cartooned into
> "tempered JI intervals". Traditional triadic harmony doesn't fly > with the so-called > "neutral" intervals, yet they sound great in harmonies, so, where > are the long > discussions on alternative harmonic theories which are obviously > necessary for > polyphonic music heavy in "neutral" intervals? It's an unavoidable law of the tuning list that people talk about what they want to talk about, not the burning issues that you think they should be talking about. If you don't like this you can either accept it and contribute to whatever threads do interest you, post the things you want to read, sit back and become a lurker, quietly unsubscribe, or unsubscribe in a public way with paranoid complaints about persecution.

To your question, then. Actual threads about alternative theories of harmony are quite thin on the ground. There are good reasons for this. It takes a long time to produce a body of music from which you can deduce valuable harmonic rules. Most of us are working in different areas so it's difficult to find common ground. A lot of artists aren't good at explaining what they actually do. So, no, there aren't long threads about alternative harmonic theories.

But to neutral intervals! There have been threads about neutral thirds. I can think of...

- Vicentino's enhmarmonic. (Search for "neutral" or something along with "vicentino" so you don't get hits for his adaptive 5-limit JI scheme.)

- The neutral third MOS (in the Middle Path paper as dicot, with a dubious 5-limit mapping). Also has neutral seconds. Also known as mohajira.

- Arabic/Persian/whatever scales, and various other ethnic/historical tunings.

- Miracle temperament (great in the 7-limit and with simple neutral thirds).

Of course some of these threads will involve messages that disagree with you about neutral intervals not being JI. They're going to associate neutral thirds with 11:9 and neutral seconds with 12:11 or 11:10. That really comes down to other people not being you. If you can come to terms with this you could also try searching for threads on 11-limit harmony.

Graham

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
> Why you are so attached to applying
> the term meantone to all of these tunings that are plainly
> lacking in mean tones?

They all have a single whole tone (instead of two) between
10/9 and 9/8. That's not good enough for you?

-Carl

Hi Gene and Daniel,

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

> Again, I simply have to wonder: Why you are so attached
> to applying the term meantone to all of these tunings
> that are plainly lacking in mean tones? The use of the
> word meantone to describe the family is misleading on
> the one hand, in that it is no longer descriptive, and
> refers to historical conditions which you clearly consider
> of no importance or irrelevant, on the other.
>
> "Meantone-like" would be a compromise label for the family,
> but it does not specify which features of meantone are
> shared within the family. It's far better to identify the
> family simply with the regular distribution of the comma.

Knowing that my Encyclopedia is a frequently-cited
reference for folks who care about this stuff, i've
always been careful in those webpages to note that
the name "meantone" refers specifically to 1/4-comma
meantone and only by extension to other temperaments
which temper out the syntonic-comma.

So if there's substantial disagreement on this usage,
then perhaps we shall call this class of temperaments
"syntonic" or "didymic" or some such, and reserve
"meantone" for only the 1/4-comma case.

I'd appreciate an attempt to reach a consensus on this,
because in the Tonalsoft Encyclopedia i *very* frequently
use "meantone" to refer to the whole class of temperaments,
and want to change all of those references if this usage
is deemed inappropriate.

-monz
http://tonalsoft.com
Tonescape microtonal music software

"regular distribution of the comma"

Sorry, but this is not how musicians think about music, only theorists. The
term meantone, based on everyone's usage, requires a ratio preceding it.
There is no "family" of meantone unless we take the words as they appear, as an
averaging (or mean) of whole tone size. Hallelujah, I agree with Carl on
this, and even about the squiggles.

Perhaps the bias towards a just intonation major third is similar to any
other type of bias. And one becomes invested in a lifetime of belief, often set
off by a critical peak first experience. It simply serves no purpose to
distinguish sixth-comma "temperament" as being in a different family than
meantone (or even quarter-comma meantone). Ultimatley, we seem to emulate
religious beliefs as to tuning. Best once we state our views we retreat to neutral
corners and switch topics.

I truly don't want to be mean, nor, I believe, does anyone else on this List.

Johnny

************************************** See what's new at http://www.aol.com

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> "regular distribution of the comma"
>
> Sorry, but this is not how musicians think about music, only
theorists. The
> term meantone, based on everyone's usage, requires a ratio
preceding it.

Perhaps you misunderstand: "regular" is simply Bosanquet's term for a
tuning in which all the fifths are the same size. That's certainly
something musicians understand as well as theorists. And sorry,
mentioning the distribution of the comma is unavoidable -- that tells
you how much -- in fractions of a comma -- each and every fifth is
going to be tempered. In meantone, the Major thirds are just, and in
order to make four perfect fifths come out to an octave multiple of a
just major third above the initial tone, each of the fifths have to be
tempered by 1/4 of the comma. Again, something that musicians, or at
leats the musicians I know and work with, have no problem understanding.

djw

> So if there's substantial disagreement on this usage,

There isn't. It's only Daniel at this point. And now that
I've said this, whoever else comes out of the woodwork.

-Carl

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=9p-NmJQlbHofsuIJtzHvYQlNaYdPb7GjYxfYj6kHmd829C0YEeE-36m5bJTx188KixS
L-2lnyZ86Xs2rJWVEGA) , Afmmjr@... wrote:
>
> "regular distribution of the comma"
>
> Sorry, but this is not how musicians think about music, only
theorists. The
> term meantone, based on everyone's usage, requires a ratio
preceding it.

DW: Perhaps you misunderstand: "regular" is simply Bosanquet's term for a
tuning in which all the fifths are the same size.

JR: Yes, we are speaking two different languages. Nothing Bosanquet is
"simply" anything to a musician. When the musicians, or student, sees "quarter
comma meantone" its meaning is derived more as a title of a tuning than as a
resultant of technical machinations of the splitting of musical atoms.

DW: That's certainly something musicians understand as well as theorists.
And sorry,
mentioning the distribution of the comma is unavoidable -- that tells
you how much -- in fractions of a comma -- each and every fifth is
going to be tempered.

JR: Some musicians, yes. Only, by your perspective there is only one
single meantone tuning. It doesn't even need a ratio preceding it, as a result.
There is no longer a generic meantone family, only a single species.

DW: In meantone, the Major thirds are just,

JR: Sorry to interrupt, but could you point me to where it says that the
generic word meantone, without any ratio, requires a just major third?

DW: and in
order to make four perfect fifths come out to an octave multiple of a
just major third above the initial tone, each of the fifths have to be
tempered by 1/4 of the comma. Again, something that musicians, or at
leats the musicians I know and work with, have no problem understanding.

JR: Yes, we live in the same world, only different countries, and perhaps
different spheres. That's healthy for all. Only, by substituting 1/6, or
2/7, etc. we have a case of "which of these things is more like the other" and a
family of temperament is recognizable. You may be thinking too hard about
this. I certainly don't want to misrepresent meantone to my students. But I
certainly don't want to be too anal about something that is already
intellectually far removed from most musicians.

best, Johnny

************************************** See what's new at http://www.aol.com

> Perhaps you misunderstand: "regular" is simply Bosanquet's term
> for a tuning in which all the fifths are the same size.

That's not quite the same as the modern definition of
"regular temperament".

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > So if there's substantial disagreement on this usage,
>
> There isn't. It's only Daniel at this point. And now that
> I've said this, whoever else comes out of the woodwork.
>
> -Carl
>

It's not just me -- I was prompted on my own sloppy usage by Douglas
Leedy, author of the AmeriGrove article on Tuning and Temperament,

--- In tuning@yahoogroups.com, Afmmjr@... wrote:

> JR: Some musicians, yes. Only, by your perspective there is only one
> single meantone tuning. It doesn't even need a ratio preceding it,
as a result.
> There is no longer a generic meantone family, only a single species.
>
>

The "1/4" here is not a ratio but a fraction of a comma; the relevant
ratios here are the 5:4 Major third and the 2:1 octave.

It is not my perspective, but rather the perspective of Zarlino and
Salinas, the most important early musicians to propose alternatives to
meantone.

djw

Afmmjr@aol.com wrote:
> "regular distribution of the comma"
> > Sorry, but this is not how musicians think about music, only > theorists. The term meantone, based on everyone's usage, requires a > ratio preceding it. There is no "family" of meantone unless we take > the words as they appear, as an averaging (or mean) of whole tone > size. Hallelujah, I agree with Carl on this, and even about the > squiggles. > I agree with you and Carl (and Gene) about this---all these temperaments are based, like it or not, on a third of given size being split into two whole tones.

I disagree with both of you about squiggles (probability, probability, probability).

Isn't life rich? :)

-A.

> Perhaps the bias towards a just intonation major third is similar to > any other type of bias. And one becomes invested in a lifetime of > belief, often set off by a critical peak first experience. It simply > serves no purpose to distinguish sixth-comma "temperament" as being in > a different family than meantone (or even quarter-comma meantone). > Ultimatley, we seem to emulate religious beliefs as to tuning. Best > once we state our views we retreat to neutral corners and switch topics.
> > I truly don't want to be mean, nor, I believe, does anyone else on > this List.
>

Mahler said that western music made a big mistake when it abandoned meantone, this would leave out 12 ET
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:

> >
>
> I agree with you and Carl (and Gene) about this---all these
temperaments
> are based, like it or not, on a third of given size being split into
two
> whole tones.
>

That is not what these "temperaments are based upon" at all, but a
consequence; the mean tone is located at the geometric mean between
major (9:8) and minor (10:9) whole tones, and only in the tuning in
which the tempered fifths land after four iterations on an octave of
the 5:4 is is this the case. Moreover, there are theoretically
uncountable number of tunings in which your defintion would be true
but which do not belong to this family, 11tet or 13tet, for example,
in which the best "major third" do indeed divide into two equal "whole
tones".

Daniel Wolf

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> >
> > I see no reason to insist that meantone is 5/4 exclusive, and it
certainly
> > hasn't been taken that way. This is especially true in that
meantone is an
> > English language term, and the term has come to mean more.
>
> But by taking the term to "mean more", that is to describe a larger
> number of tuning, it actually means less, in that several of the
> salient qualities of meantone have to be given up to accomodate
> tunings which (a) do not have mean tones, (b) do not have just
major
> thirds, and possibly, depending upon what tunings you include in
the
> family: (c) are not regular, or (d) do not have larger diatonic
> semitones than chromatic semitones, etc..
>
> The English language term meantone is precisely analogous to terms
in
> other languages (German Mittelton, French ton moyen etc.) and the
> fact that it has been misused in the past -- some 19th century
> theorists used it to describe _all_ non-equal 12-tone keyboard
> tunings and Ll.S. Lloyd used it as a synonym for just intonation --
> is simply not an argument for misusing it further.
>
> The comparison of meatone with other tunings is very important, but
> we have adequate vocabulary to do that correctly: "meantone-like"
is
> often useful, and in an active theoretical and practical enviroment
> like ours, in which such a large number of possible and practical
> tunings are under consideration, what's the harm in simply being
> explicit about the most salient feature, which, in the family
> presently under discussion, is the regular distribution of the
> syntonic comma, and not many of the other salient charcateristics
of
> meantone.
>
> djw

I've tried to pick & choose carefully those threads in which to
participate, lest I become obligated to commit much more time &
effort than I had expected in their resolution. In particular, I've
made it a point to steer clear of debates in which I have no
significant personal or special interest. In this case I feel I need
to make an exception, because there's too much at stake here
regarding how the outside world perceives us.

I believe it's in our best interest to make our terminology as useful
and meaningful as possible, and as such, it should be clear and
concise, and not misleading.

Do we all agree with the following statements?

1) Originally the term "meantone" had a clear, unambiguous
definition: a pich or interval defined as a whole step of a certain
size, specifically the geometric mean between the minor tone (10/9)
and major tone (9/8).

2) The term "meantone temperament", without any additional
qualifiers, is thereby understood to refer to a tuning consisting of
a chain of fifths tempered narrow by 1/4 of a syntonic (or didymus)
comma, which results in "meantone" whole steps, as described above.

3) J. Murray Barbour, while acknowledging the foregoing, introduced
qualifiers in the form "m/n-comma meantone" to specify meantone-like
temperaments in which the fifths are tempered narrow by other than
1/4 comma. Over 30 years ago, others in the English-speaking
alternative tunings community began adopting this usage, and it
continues into the present. As long as a qualifier is used, this
does not appear to have caused any serious confusion.

Now here's what seems to be at issue:

Within the past few years the term "meantone" has begun to be used on
this list (and tuning-math), without any qualifiers, as a generic
term encompassing an entire continuum (or family) of narrow-fifth
temperaments, in which the best 5/4 is arrived at by a chain of 4
(tempered) fifths. By this definition, even a 7-tone pythagorean
tuning could be (and, on at least one occasion, has been) included
under the "meantone" label. This can lead (and has in fact led) to
all sorts of confusion (or, on one occasion, a "mean-tempered"
reaction) on the part of those outside our group, so I think it's
fair to say that it's counter-productive to use the term in this way.

Gene wrote:

> The "81/80 comma temperament" or "Didymus temperament" or what have
you
> is not a recognized name, that's the problem. As you not yourself,
the
> usage you object to is over 100 years old. You are ttying to shut
the
> door after the horse has already left the barn, and since "81/80
> temperament" is about 100 times more important than "1/4 comma
> meantone", why fight it?

Well, if the horse is out there running around and trampling other
people's musical gardens, then maybe it's time to put the unruly
horse back in the barn, tie it up permanently, and go get a better-
behaved horse.

So why not adopt a different term? If we can readily understand and
remember what the 1/9-schismic or 1/4-kleismic temperaments are, then
why not use the term "syntonic" or "didymic" in the same manner? (I
prefer "pythagorean" and "didymic" to "ditonic" and "syntonic",
because the latter are too easily confused with one another --
Barbour himself once fell into that trap -- and never corrected his
mistake!) After all, isn't it much more accurate and concise to
say "1/3-syntonic" or "2/7-didymic" than "1/3-comma meantone" or "2/7-
comma meantone" when referring to temperaments? If we stopped
using "m/n-comma meantone", then the term "meantone" could gradually
revert back to its original (more mean-ingful) meaning, whereby it
would become simply a single member of one happy (didymic) family.

An outsider may ask you to clarify what you mean by a "didymic"
or "syntonic" temperament, but I doubt anyone is going to argue about
the proper definition of the term.

While we're at it, why not use the term "archytan" (instead
of "superpythagorean", Archytas' comma being 63:64) for temperaments
that have the best 7/4 as a chain of two 3:4's? You could then say
that 22-ET and 27-ET approximate 1/4-archytan and 1/3-archytan
temperament. (Regarding the name of the 63:64 comma,
wouldn't "archytan" be a much better name than "septimal" for a
family of temperaments?)

The bottom line is that our terminology should be clear, concise, and
free from conflict with established usage, so that others would have
no problem adopting it.

Take heart, Daniel! You're no longer alone in the den of lions. ;-)

--George

I am almost tempted to side with you, George. But what about Prof. Ayhan
Zeren claiming that there are three Didymus commas: Syntonic (81:80), Magna
(128:125), and Diesis (2048:2025)?

Oz.

----- Original Message -----
From: "George D. Secor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 12 Eyl�l 2007 �ar�amba 22:08
Subject: [tuning] Re: "Meantone" - better term/definitions needed?

> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> > >
> > > I see no reason to insist that meantone is 5/4 exclusive, and it
> certainly
> > > hasn't been taken that way. This is especially true in that
> meantone is an
> > > English language term, and the term has come to mean more.
> >
> > But by taking the term to "mean more", that is to describe a larger
> > number of tuning, it actually means less, in that several of the
> > salient qualities of meantone have to be given up to accomodate
> > tunings which (a) do not have mean tones, (b) do not have just
> major
> > thirds, and possibly, depending upon what tunings you include in
> the
> > family: (c) are not regular, or (d) do not have larger diatonic
> > semitones than chromatic semitones, etc..
> >
> > The English language term meantone is precisely analogous to terms
> in
> > other languages (German Mittelton, French ton moyen etc.) and the
> > fact that it has been misused in the past -- some 19th century
> > theorists used it to describe _all_ non-equal 12-tone keyboard
> > tunings and Ll.S. Lloyd used it as a synonym for just intonation --
> > is simply not an argument for misusing it further.
> >
> > The comparison of meatone with other tunings is very important, but
> > we have adequate vocabulary to do that correctly: "meantone-like"
> is
> > often useful, and in an active theoretical and practical enviroment
> > like ours, in which such a large number of possible and practical
> > tunings are under consideration, what's the harm in simply being
> > explicit about the most salient feature, which, in the family
> > presently under discussion, is the regular distribution of the
> > syntonic comma, and not many of the other salient charcateristics
> of
> > meantone.
> >
> > djw
>
> I've tried to pick & choose carefully those threads in which to
> participate, lest I become obligated to commit much more time &
> effort than I had expected in their resolution. In particular, I've
> made it a point to steer clear of debates in which I have no
> significant personal or special interest. In this case I feel I need
> to make an exception, because there's too much at stake here
> regarding how the outside world perceives us.
>
> I believe it's in our best interest to make our terminology as useful
> and meaningful as possible, and as such, it should be clear and
> concise, and not misleading.
>
> Do we all agree with the following statements?
>
> 1) Originally the term "meantone" had a clear, unambiguous
> definition: a pich or interval defined as a whole step of a certain
> size, specifically the geometric mean between the minor tone (10/9)
> and major tone (9/8).
>
> 2) The term "meantone temperament", without any additional
> qualifiers, is thereby understood to refer to a tuning consisting of
> a chain of fifths tempered narrow by 1/4 of a syntonic (or didymus)
> comma, which results in "meantone" whole steps, as described above.
>
> 3) J. Murray Barbour, while acknowledging the foregoing, introduced
> qualifiers in the form "m/n-comma meantone" to specify meantone-like
> temperaments in which the fifths are tempered narrow by other than
> 1/4 comma. Over 30 years ago, others in the English-speaking
> alternative tunings community began adopting this usage, and it
> continues into the present. As long as a qualifier is used, this
> does not appear to have caused any serious confusion.
>
> Now here's what seems to be at issue:
>
> Within the past few years the term "meantone" has begun to be used on
> this list (and tuning-math), without any qualifiers, as a generic
> term encompassing an entire continuum (or family) of narrow-fifth
> temperaments, in which the best 5/4 is arrived at by a chain of 4
> (tempered) fifths. By this definition, even a 7-tone pythagorean
> tuning could be (and, on at least one occasion, has been) included
> under the "meantone" label. This can lead (and has in fact led) to
> all sorts of confusion (or, on one occasion, a "mean-tempered"
> reaction) on the part of those outside our group, so I think it's
> fair to say that it's counter-productive to use the term in this way.
>
> Gene wrote:
>
> > The "81/80 comma temperament" or "Didymus temperament" or what have
> you
> > is not a recognized name, that's the problem. As you not yourself,
> the
> > usage you object to is over 100 years old. You are ttying to shut
> the
> > door after the horse has already left the barn, and since "81/80
> > temperament" is about 100 times more important than "1/4 comma
> > meantone", why fight it?
>
> Well, if the horse is out there running around and trampling other
> people's musical gardens, then maybe it's time to put the unruly
> horse back in the barn, tie it up permanently, and go get a better-
> behaved horse.
>
> So why not adopt a different term? If we can readily understand and
> remember what the 1/9-schismic or 1/4-kleismic temperaments are, then
> why not use the term "syntonic" or "didymic" in the same manner? (I
> prefer "pythagorean" and "didymic" to "ditonic" and "syntonic",
> because the latter are too easily confused with one another --
> Barbour himself once fell into that trap -- and never corrected his
> mistake!) After all, isn't it much more accurate and concise to
> say "1/3-syntonic" or "2/7-didymic" than "1/3-comma meantone" or "2/7-
> comma meantone" when referring to temperaments? If we stopped
> using "m/n-comma meantone", then the term "meantone" could gradually
> revert back to its original (more mean-ingful) meaning, whereby it
> would become simply a single member of one happy (didymic) family.
>
> An outsider may ask you to clarify what you mean by a "didymic"
> or "syntonic" temperament, but I doubt anyone is going to argue about
> the proper definition of the term.
>
> While we're at it, why not use the term "archytan" (instead
> of "superpythagorean", Archytas' comma being 63:64) for temperaments
> that have the best 7/4 as a chain of two 3:4's? You could then say
> that 22-ET and 27-ET approximate 1/4-archytan and 1/3-archytan
> temperament. (Regarding the name of the 63:64 comma,
> wouldn't "archytan" be a much better name than "septimal" for a
> family of temperaments?)
>
> The bottom line is that our terminology should be clear, concise, and
> free from conflict with established usage, so that others would have
> no problem adopting it.
>
> Take heart, Daniel! You're no longer alone in the den of lions. ;-)
>
> --George
>
>
>
>
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djwolf_frankfurt wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> I agree with you and Carl (and Gene) about this---all these temperaments are based, like it or not, on a third of given size being split into two whole tones.
>> > That is not what these "temperaments are based upon" at all, but a
> consequence; the mean tone is located at the geometric mean between
> major (9:8) and minor (10:9) whole tones, and only in the tuning in
> which the tempered fifths land after four iterations on an octave of
> the 5:4 is is this the case. Moreover, there are theoretically
> uncountable number of tunings in which your defintion would be true
> but which do not belong to this family, 11tet or 13tet, for example,
> in which the best "major third" do indeed divide into two equal "whole
> tones".
Yes, this is true---however the practical existence of 11- or 13-edo is not to make the 81/80 comma vanish.

In all the tunings declared to be 'meantone' in common usage around here, people know what is meant by 'comma'--it stands for syntonic comma.

However, I'm comfortable with not saying 'meantone' if that's consensus--'1/3-comma temperament' says it all anyway, and much shorter, too. I guess the whole purpose is clear communication, so I wouldn't fuss about it either way.

-A.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I am almost tempted to side with you, George. But what about Prof.
Ayhan
> Zeren claiming that there are three Didymus commas: Syntonic (81:80),
Magna
> (128:125), and Diesis (2048:2025)?

The first of these comes directly from Didymus' diatonic scale, as the
difference between the two sizes of whole tone in that scale. How are
the other two linked to Didymus?

--George

Hi George and Daniel (pro) and all the others (contra),

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

> So why not adopt a different term? If we can readily
> understand and remember what the 1/9-schismic or 1/4-kleismic
> temperaments are, then why not use the term "syntonic"
> or "didymic" in the same manner? (I prefer "pythagorean"
> and "didymic" to "ditonic" and "syntonic", because the
> latter are too easily confused with one another -- Barbour
> himself once fell into that trap -- and never corrected his
> mistake!) After all, isn't it much more accurate and
> concise to say "1/3-syntonic" or "2/7-didymic" than
> "1/3-comma meantone" or "2/7-comma meantone" when referring
> to temperaments? If we stopped using "m/n-comma meantone",
> then the term "meantone" could gradually revert back to
> its original (more mean-ingful) meaning, whereby it would
> become simply a single member of one happy (didymic) family.
>
> An outsider may ask you to clarify what you mean by a
> "didymic" or "syntonic" temperament, but I doubt anyone
> is going to argue about the proper definition of the term.
>
> <snip>
>
> The bottom line is that our terminology should be
> clear, concise, and free from conflict with established
> usage, so that others would have no problem adopting it.

I totally agree with this. For that matter, i heartily
deplore the use of "comma" in its loose sense, since
there are already several intervals known as "comma"
which have a qualifier specifying *which* comma.
It's much better to say "1/3-didymic" etc.

As i said, my Encyclopedia is full of references to
the "meantone family" of temperaments, and it will be
a huge job to change all of these. But i agree that it
should be changed, and i will do it pending resolution
of objections from Gene and those who agree with him.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> In all the tunings declared to be 'meantone' in common usage around
> here, people know what is meant by 'comma'--it stands for syntonic
> comma.

Hardly. Comma is a much more generic term here than "meantone".

-Carl

> As i said, my Encyclopedia is full of references to
> the "meantone family" of temperaments, and it will be
> a huge job to change all of these. But i agree that it
> should be changed, and i will do it pending resolution
> of objections from Gene and those who agree with him.

What convinced you?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > In all the tunings declared to be 'meantone' in common usage around
> > here, people know what is meant by 'comma'--it stands for syntonic
> > comma.
>
> Hardly. Comma is a much more generic term here than "meantone".

In fact, while "q-comma meantone" normally means a qth fraction of a
syntonic comma, sometimes it's a fraction of a Pythagorean
comma. "Comma" used without a clear context is far more generic.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

> 2) The term "meantone temperament", without any additional
> qualifiers, is thereby understood to refer to a tuning consisting
of
> a chain of fifths tempered narrow by 1/4 of a syntonic (or didymus)
> comma, which results in "meantone" whole steps, as described above.

Depends on context. In some contexts, including nearly all you will
find in the tuning-math archives, no. It does not mean this.

> This can lead (and has in fact led) to
> all sorts of confusion (or, on one occasion, a "mean-tempered"
> reaction) on the part of those outside our group, so I think it's
> fair to say that it's counter-productive to use the term in this
way.

Perhaps, but the abstract temperament is far, far more important than
the particular tuning. Asking for the tail to wag the dog doesn't
stike me as all that productive.

> While we're at it, why not use the term "archytan" (instead
> of "superpythagorean", Archytas' comma being 63:64) for
temperaments
> that have the best 7/4 as a chain of two 3:4's?

We could, I suppose, but I'm reaching name-change burnout. You should
dig up Paul and get him to nag about it.

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@> wrote:
>
> > >
> >
> > I agree with you and Carl (and Gene) about this---all these
> temperaments
> > are based, like it or not, on a third of given size being split
into
> two
> > whole tones.
> >
>
> That is not what these "temperaments are based upon" at all, but a
> consequence; the mean tone is located at the geometric mean between
> major (9:8) and minor (10:9) whole tones, and only in the tuning in
> which the tempered fifths land after four iterations on an octave of
> the 5:4 is is this the case. Moreover, there are theoretically
> uncountable number of tunings in which your defintion would be true
> but which do not belong to this family, 11tet or 13tet, for example,
> in which the best "major third" do indeed divide into two
equal "whole
> tones".
>
> Daniel Wolf
>

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

> That is not what these "temperaments are based upon" at all, but a
> consequence; the mean tone is located at the geometric mean between
> major (9:8) and minor (10:9) whole tones, and only in the tuning in
> which the tempered fifths land after four iterations on an octave of
> the 5:4 is is this the case.

What would you say to the suggwstion that this could be
called "meantone tuning" rather than "meantone temperament"?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> > Why you are so attached to applying
> > the term meantone to all of these tunings that are plainly
> > lacking in mean tones?
>
> They all have a single whole tone (instead of two) between
> 10/9 and 9/8. That's not good enough for you?

And in all cases, two tones of exactly the same size comprise a major
third.

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

> The comparison of meatone with other tunings is very important, but
> we have adequate vocabulary to do that correctly: "meantone-like" is
> often useful, and in an active theoretical and practical enviroment
> like ours, in which such a large number of possible and practical
> tunings are under consideration, what's the harm in simply being
> explicit about the most salient feature, which, in the family
> presently under discussion, is the regular distribution of the
> syntonic comma, and not many of the other salient charcateristics of
> meantone.

The biggest problem with our vocabular is probably a failure to clearly
distinguish between tunings and (abstract) temperaments. The latter are
more important.

> > That is not what these "temperaments are based upon" at all, but a
> > consequence; the mean tone is located at the geometric mean between
> > major (9:8) and minor (10:9) whole tones, and only in the tuning in
> > which the tempered fifths land after four iterations on an octave of
> > the 5:4 is is this the case.
>
> What would you say to the suggwstion that this could be
> called "meantone tuning" rather than "meantone temperament"?

Hey, that seems like a good way out.

The only drawback to this kind of thing is, if one keeps
tiddling terminology around to keep everyone happy like
this, newcomers run into a potential minefield of these
special cases. The terminology of the raw theory is hard
enough...

-Carl

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

> It's a fact of substantial importance -- when I play sackbut in or
> sing early music, knowing that the major thirds are just and that
the
> tones are means to those thirds is extremely important.

OK, I agree that particularly in the case of two-part harmony, the
fact that you have just thirds and tenths is important if you are
using very precise tuning--there's quite a distinction involved in
moving from a major sixth to a major third interval. But I don't
think in general claiming the tuning is the really important thing
makes sense. If you use fixed tunings, you aren't going to notice a
hell of a lot of difference between 1/4-comma and 31-equal, and when
you do you might prefer 31-equal, as the mixture of pure and impure
intervals, especially with two parts, can get kind of goofy.

> Again, I simply have to wonder: Why you are so attached to applying
> the term meantone to all of these tunings that are plainly lacking
in
> mean tones?

They all have mean tones; there's just one size of tone.

> "Meantone-like" would be a compromise label for the family, but it
> does not specify which features of meantone are shared within the
> family. It's far better to identify the family simply with the
> regular distribution of the comma.

Then you start wanting to distibute 126/125 as well. Mathematically,
{81/80, 126/125}-temperament is a fine name. I don't see it as one
many people would warm to.

Gene Ward Smith wrote:

> What would you say to the suggwstion that this could be > called "meantone tuning" rather than "meantone temperament"?

Unfortunately you can't stop the rest of the world using the phrase "meantone temperament" to mean the specific tuning of quarter-comma meantone. A better way is "meantone temperaments" for the class (isn't that the term we agreed?) and "the meantone temperament" for a specific tuning. To remove all ambuguity you have to say "quarter comma meantone" and you can't blame the tuning list for that one.

In a discussion about 12 note keyboard tunings, the phrase "12-tet and meantone" should be unremarkable. We can assume in this case that "meantone" refers to some tuning with a noticeable wolf. The phrase "Werckmeister and meantone" is more likely to specifically refer to the 1/4-comma variety. The phrase "1/6-comma meantone and meantone" is plain bizzare.

In a discussion about temperament classes, you can assume "meantone" refers to the class and that 12-equal is a valid tuning of meantone.

Graham

Gene Ward Smith wrote:

> The biggest problem with our vocabular is probably a failure to clearly > distinguish between tunings and (abstract) temperaments. The latter are > more important.

There seems to be a problem with *your* vocabulary because *you* persist in thinking that a temperament does not have a specific tuning and expecting the rest of the world to agree with you. Strictly speaking this is not correct. The word "temperament" has always been used historically to refer to tunings. This is a case where we really should keep the existing meaning.

The only problem is that "temperament" can also mean "the process of tempering". So "meantone temperament" can be "the process of tempering within the meantone class". That's something you have to be careful about.

Graham

monz wrote:

> As i said, my Encyclopedia is full of references to
> the "meantone family" of temperaments, and it will be
> a huge job to change all of these. But i agree that it
> should be changed, and i will do it pending resolution
> of objections from Gene and those who agree with him.

At least, I thought that should have been "meantone class" because "temperament family" had some other meaning. Although if we want to change to "family" I'd be quite happy because I favored that in the first place. Are there any terms we can agree on?

Graham

> Gene Ward Smith wrote:
>
> > What would you say to the suggwstion that this could be
> > called "meantone tuning" rather than "meantone temperament"?
>
> Unfortunately you can't stop the rest of the world using the
> phrase "meantone temperament" to mean the specific tuning of
> quarter-comma meantone.

And we don't have to, and probably shouldn't want to.

> The phrase "1/6-comma meantone and meantone" is plain bizzare.

You got that right.

-Carl

To repeat myself; the real problems that I have with the widest definition and use of the "meantone" term are:

a) It assumes all these tunings, temperaments, or whatever are derived from integer ratios. i.e. it has such a JI bias
b) "mean" is an ugly word - i.e. I have a poetic/aesthetic objection to the word. It even sounds "mean" (as in stingy).
c) "mean" has so many possible mean-ings; as has been illustrated by examples already appearing in this thread.
d) I would suggest something on the lines of "5L+2s per octave"; and reserve meantone for those tunings/temperaments which truly are common averages of various commas or other JI intervals.

There also seems to be a few problems about circular and non-circular phrases used in the existing definitions.

To my "irrational" mind I would expect 99% of the tunings/temperaments called "meantone" to actually be circular if you are prepared to counts steps approaching infinity as permissible for as those derived from integer constructions I suspect would eventually arrive back at the 1/1 or starting point at some (possibly in some cases, vast) number of iterations.

Charles Lucy lucy@lucytune.com

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On 13 Sep 2007, at 03:26, Graham Breed wrote:

> Gene Ward Smith wrote:
>
> > The biggest problem with our vocabular is probably a failure to > clearly
> > distinguish between tunings and (abstract) temperaments. The > latter are
> > more important.
>
> There seems to be a problem with *your* vocabulary because
> *you* persist in thinking that a temperament does not have a
> specific tuning and expecting the rest of the world to agree
> with you. Strictly speaking this is not correct. The word
> "temperament" has always been used historically to refer to
> tunings. This is a case where we really should keep the
> existing meaning.
>
> The only problem is that "temperament" can also mean "the
> process of tempering". So "meantone temperament" can be
> "the process of tempering within the meantone class".
> That's something you have to be careful about.
>
> Graham
>
>
>

djwolf_frankfurt wrote:

> But by taking the term to "mean more", that is to describe a larger > number of tuning, it actually means less, in that several of the > salient qualities of meantone have to be given up to accomodate > tunings which (a) do not have mean tones, (b) do not have just major > thirds, and possibly, depending upon what tunings you include in the > family: (c) are not regular, or (d) do not have larger diatonic > semitones than chromatic semitones, etc.. By the middle path definition they're always regular and (d) is only for very exceptional examples. Yes, they may not have just major thirds which you may take as meaning they don't have mean tones. It's strange for a meantone not to have mean tones but we didn't invent the term "1/4-comma meantone" which implies this possibility.

> The English language term meantone is precisely analogous to terms in > other languages (German Mittelton, French ton moyen etc.) and the > fact that it has been misused in the past -- some 19th century > theorists used it to describe _all_ non-equal 12-tone keyboard > tunings and Ll.S. Lloyd used it as a synonym for just intonation -- > is simply not an argument for misusing it further.

It's unfortunate to disagree with other languages, but do French or German have a significant body of work about alternative temperament classes? What do they call the meantone class?

Saying the term is historically confused is a strange argument for imposing a strict definition now.

> The comparison of meatone with other tunings is very important, but > we have adequate vocabulary to do that correctly: "meantone-like" is > often useful, and in an active theoretical and practical enviroment > like ours, in which such a large number of possible and practical > tunings are under consideration, what's the harm in simply being > explicit about the most salient feature, which, in the family > presently under discussion, is the regular distribution of the > syntonic comma, and not many of the other salient charcateristics of > meantone.

Throughout it's history in the English language, I think we can say that the word "cat" has referred to small, furry animals that make good pets and catch mice. To compare cats with other animals we could say "cat-like" but who ever does? When the need came to talk about other members of the cat family we generalized the word "cat". So if somebody says "a tiger is a cat" we know exactly what they mean, and don't expect tigers to make good pets or be interested in catching mice. But if somebody says "I like cats" we wouldn't expect, without any other context, that they're keen on tigers, ocelots, etc.

If we want to be specific, of course we can say "domestic cats" or "felis catus" on the one hand and "the cat family" or "family Felidae" on the other. Most of the time the context makes it clear.

Really, why should "meantone" be any different? There hasn't been a great need to distinguish meantone from other regular temperament classes before so there isn't an established name. Why not name the class after it's most famous representative member?

Graham

As far as I can tell, he defines the "Magna comma" as the difference between
two diatonic minor semitones and a minor whole tone, or between 16:15 and
256:243. The "Diesis comma", according to him, is the difference between two
16:15 and one 9:8. The first he approximates with 43:42, the latter with
89:88.

Oz.

----- Original Message -----
From: "George D. Secor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 12 Eyl�l 2007 �ar�amba 23:54
Subject: [tuning] Re: "Meantone" - better term/definitions needed?

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I am almost tempted to side with you, George. But what about Prof.
> Ayhan
> > Zeren claiming that there are three Didymus commas: Syntonic (81:80),
> Magna
> > (128:125), and Diesis (2048:2025)?
>
> The first of these comes directly from Didymus' diatonic scale, as the
> difference between the two sizes of whole tone in that scale. How are
> the other two linked to Didymus?
>
> --George
>

Charles Lucy wrote:
> To repeat myself; the real problems that I have with the widest > definition and use of the "meantone" term are:
> > a) It assumes all these tunings, temperaments, or whatever are derived > from integer ratios. i.e. it has such a JI bias

The word "temperament" has always referred to tunings that approximate integer ratios. Calling that a "JI bias" is rather strange as "JI" has always very specifically referred to tunings that are not tempered.

If you persist in believing that LucyTuning has no relationship to integer ratios, it naturally follows that it is not a temperament and so not a member of the meantone temperament class.

You could possibly call it a "meantone tuning" but unfortunately that contradicts the precise phrase that Gene chose to have a different, unambiguous meaning.

> b) "mean" is an ugly word - i.e. I have a poetic/aesthetic objection to > the word. It even sounds "mean" (as in stingy).

Well, sure, and "temper" sounds like "angry" and "just" has a too positive connotation. But we get over these things.

> c) "mean" has so many possible mean-ings; as has been illustrated by > examples already appearing in this thread.

The "mean" in "meantone" means nothing as it's been distorted by centuries of lax usage.

> d) I would suggest something on the lines of "5L+2s per octave"; and > reserve meantone for those tunings/temperaments which truly are common > averages of various commas or other JI intervals.

Yes, call it "5L 2s" if that's what you mean. But it's nice to have friendly names for the most common classes.

> There also seems to be a few problems about circular and non-circular > phrases used in the existing definitions.
> > To my "irrational" mind I would expect 99% of the tunings/ temperaments > called "meantone" to actually be circular if you are prepared to counts > steps approaching infinity as permissible for as those derived from > integer constructions I suspect would eventually arrive back at the 1/1 > or starting point at some (possibly in some cases, vast) number of > iterations.

All tunings will get arbitrarily close to some arbitrarily large EDO and all tunings will get arbitrarily close to some arbitrarily large integer ratios. What's the point?

Graham

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > As i said, my Encyclopedia is full of references to
> > the "meantone family" of temperaments, and it will be
> > a huge job to change all of these. But i agree that it
> > should be changed, and i will do it pending resolution
> > of objections from Gene and those who agree with him.
>
> What convinced you?

Well, it's not exactly a case of me becoming "convinced".
As i wrote in an earlier post, i've always been careful to
note that the term "meantone" refers historically and
specifically to 1/4-[syntonic-]comma meantone, as Daniel
argues.

But at the same time, i *have* accepted the usage
of "meantone" to represent the whole family of tunings
which temper out this comma, along with nearly everyone
else on the tuning lists who care about this.

So i'm somewhat on the fence. But as the creator and
editor of the Encyclopedia which i hope is or becomes
the standard reference on the subject, it's important
to me that terminology which has been around for awhile
reflects historical usage as well as more recent
accepted usage.

It seems that what i'll have to do is create another
numbered webpage of meantone definitions, #1 for the
restricted usage to refer to 1/4-comma meantone, and
#2 for the wider usage which refers to the whole family
of temperaments which make the syntonic-comma vanish.

This is really no big deal to me: look at my definition
of "diesis", which has 7 different definitions of the
term, all of them referring to a small musical interval,
which can range in size from the ~90 cents of Philolaus
down to the ~22 cents of my interpretation of Marchetto
of Padua's tuning description.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Gene, Daniel, and Carl,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> > > Why you are so attached to applying
> > > the term meantone to all of these tunings that are plainly
> > > lacking in mean tones?
> >
> > They all have a single whole tone (instead of two) between
> > 10/9 and 9/8. That's not good enough for you?
>
> And in all cases, two tones of exactly the same size
> comprise a major third.

Note especially to Carl and Daniel: this is exactly why i'm
still somewhat on the fence about this issue.

I was hesitant to argue about it with Daniel, but that
was my first inclination, precisely because of what Gene
writes here.

Even tho 1/4-syntonic-comma meantone is the only one
which provides a "whole-tone" which is exactly the geometric
mean between the two standard JI whole-tones, there are
lots of other ways of calculating means, and in any case,
even if the size of the whole-tone is not exactly calculated
by one of those methods, any tuning in which there is only
one size of whole-tone, 2 of which compose the major-3rd,
falls into the so-called "meantone" family.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Graham (and Carl, Daniel, and Gene),

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

> Throughout it's history in the English language, I think we
> can say that the word "cat" has referred to small, furry
> animals that make good pets and catch mice. To compare cats
> with other animals we could say "cat-like" but who ever
> does? When the need came to talk about other members of the
> cat family we generalized the word "cat". So if somebody
> says "a tiger is a cat" we know exactly what they mean, and
> don't expect tigers to make good pets or be interested in
> catching mice. But if somebody says "I like cats" we
> wouldn't expect, without any other context, that they're
> keen on tigers, ocelots, etc.
>
> If we want to be specific, of course we can say "domestic
> cats" or "felis catus" on the one hand and "the cat family"
> or "family Felidae" on the other. Most of the time the
> context makes it clear.
>
> Really, why should "meantone" be any different? There
> hasn't been a great need to distinguish meantone from other
> regular temperament classes before so there isn't an
> established name. Why not name the class after it's most
> famous representative member?

For the record, i can go along with what Graham says here.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> There seems to be a problem with *your* vocabulary because
> *you* persist in thinking that a temperament does not have a
> specific tuning and expecting the rest of the world to agree
> with you. Strictly speaking this is not correct. The word
> "temperament" has always been used historically to refer to
> tunings. This is a case where we really should keep the
> existing meaning.

But this isn't how we've been using the terms! I'm fairly
certain even you have been using them Gene's way.

-Carl

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Carl,
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > > As i said, my Encyclopedia is full of references to
> > > the "meantone family" of temperaments, and it will be
> > > a huge job to change all of these. But i agree that it
> > > should be changed, and i will do it pending resolution
> > > of objections from Gene and those who agree with him.
> >
> > What convinced you?
>
> Well, it's not exactly a case of me becoming "convinced".
> As i wrote in an earlier post, i've always been careful to
> note that the term "meantone" refers historically and
> specifically to 1/4-[syntonic-]comma meantone, as Daniel
> argues.

That's not the impression I got from reading your definition
of meantone.

> So i'm somewhat on the fence. But as the creator and
> editor of the Encyclopedia which i hope is or becomes
> the standard reference on the subject, it's important
> to me that terminology which has been around for awhile
> reflects historical usage as well as more recent
> accepted usage.

Absolutely. I think it's totally appropriate to note
historical or secondary usage, as the Wikipedia entry does.

-Carl

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

>
> It's unfortunate to disagree with other languages, but do
> French or German have a significant body of work about
> alternative temperament classes? What do they call the
> meantone class?

Salinas is defintely exploring this class, as a class (independent
from pythagorean, for example), and Werckmeister's temperaments can
defintely be construed as classes.

>
> Saying the term is historically confused is a strange
> argument for imposing a strict definition now.
>

I specifically indicated that incidents of historical confusion arose
in the late 19th century, well after the meantone era, in conflating
all non-12tet keyboard tunings (a mistake not made by the better
tuning theorists: Bosanquet, Riemann, Tanaka etc.) and in the 20th
century, with Lloyd who used it synonymously with just, and with this
group. Even the oft-confused Barbour has it right, and his book
usefully is organized into what may be construed as classes.

> Throughout it's history in the English language, I think we
> can say that the word "cat" has referred to small, furry
> animals that make good pets and catch mice. To compare cats
> with other animals we could say "cat-like" but who ever
> does? --- Why not name the class after it's most
> famous representative member?
>

Try reading some taxonomy texts -- "cat-like" is frequently
encountered. In fact, descriptions of unfamiliar animals are
inevitably in these terms. The marsupial family is full of them.

I just returned from a country where the favorite sandwich is a
cheeseburger. What is proposed here is precisely like using
"cheeseburger" to described all sandwiches, whether hot, cold, with
or withour meat, open or closed faced, with or without cheese, on a
bun or sliced bread. Careful -- you order a cheeseburger and you
might just end up with a slice of toast smeared with Schmalz and red
onion.

djw

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

>
> Then you start wanting to distibute 126/125 as well. Mathematically,
> {81/80, 126/125}-temperament is a fine name. I don't see it as one
> many people would warm to.
>

I have absolutely no problem with that name.

djw

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

> > The phrase "1/6-comma meantone and meantone" is plain bizzare.
>
> You got that right.

But "1/6 comma temperament and meantone" is perfectly clear, and
would have been a phrase understood throughout the centuries in which
the two were common alternatives, indeed competitors for organ
tuning. Indeed, any of the major organ builders today would
understand immediately.

djw

djwolf_frankfurt wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>It's unfortunate to disagree with other languages, but do >>French or German have a significant body of work about >>alternative temperament classes? What do they call the >>meantone class?
> > Salinas is defintely exploring this class, as a class (independent > from pythagorean, for example), and Werckmeister's temperaments can > defintely be construed as classes. Then what does Salinas call it? (I take it you're using "French" to denote the Romance language branch.)

Maybe I should have said "regular temperament classes". But still, if temperament class means "a set of temperaments with the same mapping from ratios to interval classes" I can happily accept different irregular temperament classes. They'd each have same number of notes to the octave. Did Werckmeister look at many such or did he only consider 12?

>>Saying the term is historically confused is a strange >>argument for imposing a strict definition now.
> > I specifically indicated that incidents of historical confusion arose > in the late 19th century, well after the meantone era, in conflating > all non-12tet keyboard tunings (a mistake not made by the better > tuning theorists: Bosanquet, Riemann, Tanaka etc.) and in the 20th > century, with Lloyd who used it synonymously with just, and with this > group. Even the oft-confused Barbour has it right, and his book > usefully is organized into what may be construed as classes.

But George said it was Barbour who invented the "fractional comma meantone" terminology. So did he or did he not use "meantone" for tunings other than 1/4-comma?

"Temperament class" is a technical term. It means a set of temperaments with the same mapping. It isn't the same as an organization into what "may be construed as classes". Did Barbour give names to a number of temperament classes? If so, what were they?

>>Throughout it's history in the English language, I think we >>can say that the word "cat" has referred to small, furry >>animals that make good pets and catch mice. To compare cats >>with other animals we could say "cat-like" but who ever >>does? --- Why not name the class after it's most >>famous representative member?
> > Try reading some taxonomy texts -- "cat-like" is frequently > encountered. In fact, descriptions of unfamiliar animals are > inevitably in these terms. The marsupial family is full of them.

Okay, you've got me on a superior knowledge of taxonomy (it's news to me that marsupials are a family). You can call Werckmeister III "meantone-like" if you want.

> I just returned from a country where the favorite sandwich is a > cheeseburger. What is proposed here is precisely like using > "cheeseburger" to described all sandwiches, whether hot, cold, with > or withour meat, open or closed faced, with or without cheese, on a > bun or sliced bread. Careful -- you order a cheeseburger and you > might just end up with a slice of toast smeared with Schmalz and red > onion.

Ah, you're baiting me with the "burgers are sandwiches" line. Well, sure, if you want a word for anything between two lumps of bread, why not "sandwich"? In the country I live they're more likely to be called "burgers" in English. But anyway, whatever your analogy's supposed to prove it's flawed. The words "burger" and "sandwich" are already in common use in most of the English speaking world. What's the existing word for the meantone temperament class?

Graham

djwolf_frankfurt wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >>> The phrase "1/6-comma meantone and meantone" is plain bizzare.
>>
>>You got that right.
> > But "1/6 comma temperament and meantone" is perfectly clear, and > would have been a phrase understood throughout the centuries in which > the two were common alternatives, indeed competitors for organ > tuning. Indeed, any of the major organ builders today would > understand immediately.

Sure. And if you go to an English speaking pet shop and ask for a cat you won't walk away with a baby leopard, will you?

Graham

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

> Okay, you've got me on a superior knowledge of taxonomy
> (it's news to me that marsupials are a family).

My knowledge of taxonomy is seriously limited -- actually marsupials
are an infraclass.

> common use in most of the English speaking world. What's
> the existing word for the meantone temperament class?
>

It's a synecdoche, using the part to describe the whole; but in this
case salient features of the part which are not shared with other
members of the class are lost.

djw

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

> Sure. And if you go to an English speaking pet shop and ask
> for a cat you won't walk away with a baby leopard, will you?
>

No, but if you wish your body of work to be approachable to others,
among them organ builders who are enormously well informed about
tuning, then you have to be more clear rather than less.

djw

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Cameron Bobro wrote:
>
> > Now to any replies of yes we know all this, I say: then show me
the
> > vast tomes in
> > the archives addressing the intervals that are most decidely
> > NOT "JI". Show me the
> > evidence that intervals are accepted for what they are, and not
> > inevitably cartooned into
> > "tempered JI intervals". Traditional triadic harmony doesn't >
fly
> > with the so-called
> > "neutral" intervals, yet they sound great in harmonies, so,
where
> > are the long
> > discussions on alternative harmonic theories which are obviously
> > necessary for
> > polyphonic music heavy in "neutral" intervals?
>
> It's an unavoidable law of the tuning list that people talk
> about what they want to talk about,

Obviously- is my writing really so poor that you're under
the impression that I'm a complete idiot?

>not the burning issues
> that you think they should be talking about.

Where do you get this crazy stuff from? I am saying: there
must be certain assumptions about what is "central" (a subset/
interpretation of "JI" to be specific) to tuning, otherwise
the worlds of tuning that are not bound to that presumed center
would be far more in evidence.

The work here (I continually read the archives) on
the possibities of : 1/1,(6/5),5/4,3/2 (7/4) : is staggering in
quantity and excellent in quality. I would doubt the
honesty or musicality of someone who would claim otherwise.
I would also doubt the honesty or musicality of someone
who would deny the massive presence on the tuning list of
this particular subset of "JI".

Now this is just fine, to each their own, as I said
in the generative post of this particular sprawling
discussion, if it really is a matter of musical
preference. But if it's a matter of assuming the
divine right or manifest destiny of this particular
subset of JI, that's a different story.

By the way I am fully aware of the "natural" force of
the aforesaid subset of JI, and I bet I could come
up with more explanations and descriptions of its
inborn weight than you could, for if you were truly
aware of the myriad of things that give it weight
you'd anticipate the muscle of other interpretations
of the harmonic series and not be trying to bicker with me.

Hahaha! :-)

> If you don't
> like this

You can save these kinds of lines for teenagers- like and
dislike are pretty silly concepts in a life of duty
and responsibility.

> you can either accept it and contribute to
> whatever threads do interest you, post the things you want
> to read, sit back and become a lurker, quietly unsubscribe,
> or unsubscribe in a public way with paranoid complaints
> about persecution.
>
> To your question, then. Actual threads about alternative
> theories of harmony are quite thin on the ground.

Yes, and I am also share the blame for this of course.

> There are
> good reasons for this.
>It takes a long time to produce a
> body of music from which you can deduce valuable harmonic
> rules. Most of us are working in different areas so it's
> difficult to find common ground. A lot of artists aren't
> good at explaining what they actually do. So, no, there
> aren't long threads about alternative harmonic theories.

It's not just this tuning list. Although some might claim
otherwise, this tuning list is not an
ivory tower or self-contained system. I perform in public
and physically promote "alternative" tuning- we're right in
the middle of a mini-festival I have organized, of non-standard
music and performance (great shadow-theatre to-nite, we had an
Indian raga, sarod and tabla, last week). I guess everybody
here has musical stuff going on in the physical world. So,
when I bitch about something I feel to a fundamental problem,
don't take it personally because I think bogosities
are evident everywhere in tuning theory. Nor am I innocent of
perpetuating of the same bogosities, for they are part and
parcel of the theatrical sound-languages that most of the
Western world mistakenly considers to be "music".

>
> But to neutral intervals! There have been threads about
> neutral thirds. I can think of...
>
> - Vicentino's enhmarmonic. (Search for "neutral" or
> something along with "vicentino" so you don't get hits for
> his adaptive 5-limit JI scheme.)

Yes I am familiar with this...
>
> - The neutral third MOS (in the Middle Path paper as dicot,
> with a dubious 5-limit mapping). Also has neutral seconds.
> Also known as mohajira.

...but not this, thanks.
>
> - Arabic/Persian/whatever scales, and various other
> ethnic/historical tunings.

Obviously (I live in the former Yugoslavia, so I can just
turn on the radio- HRT1 had a fantastic show of village
singers singing all kinds of bitchin diads yesterday for
example).
>
> - Miracle temperament (great in the 7-limit and with simple
> neutral thirds).

Have to check this out as well.

>
> Of course some of these threads will involve messages that
> disagree with you about neutral intervals not being JI.

Where do you get this from? I have several definitions of
JI, one ultra-conservative historical, one realistic and
positive rather than negative (ie, audible coincident lower
partials rather than "beatlessness"), and my own personal
and private definition based on other concepts of what is
a "simple ratio". All three include "neutral" intervals.

> They're going to associate neutral thirds with 11:9 and
> neutral seconds with 12:11 or 11:10.

That's fine as long as it doesn't imply that for example 27/22
is a detuned 11/9, an audibly bogus idea as I physically
experienced the other week, singing with a couple of
musicians who performed in the festival.

>That really comes down
> to other people not being you.

This is something you should really take to heart. There are
many intervals I, and the musicians I work with afaik, simply
do not hear as detuned JI intervals, and "dissonances" that
simply do not sound dissonant. On the evening I mentioned before
had a singer hold a tone and I sang a "neutral" third, whereupon
the contrabass player immediately said "middle third...soft!...350
cents" (his ears are frightening).

>If you can come to terms
> with this

Do you have any idea how ridiculous that sounds, in light
of the fact that one of the fundamental things I've been
bitching about since I came here is an apparent failure to
accept the idea that "other people aren't you", as evidenced
by assumptions that certained intervals are heard as temperings
of JI intervals, when they heard otherwise by people "who are
not you".

Too much "the ear..." and not enough "my ear..."

>you could also try searching for threads on
> 11-limit harmony.

I think I'll search first for a non-ludicrous and non-numerological
definition of "11-limit", hahaha!

Take care,

-Cameron Bobro

Cameron --

if I may interrupt, the question of the (if any) relationship between
voice leading and tuning is a subtle and deep one, but one in which
we have very few useful tools for discussing it, and little certainty
that the tools we have are the right ones. Furthermore, the problem
in a community as musically diverse as this one is that it is
unltimately very difficult to separate questions about voice leading
from those of musical style, and the ranges of styles and aesthetics
is here so diverse that I generally avoid discussing my own
composition practice here, so as to stick to the salient practical
matter of tuning and not to get sucked into a unresolveable flame war
over aesthetic dimensions. So from time to time, I'll toss out a
little neoclassical etude or a bit of juvenalia, but keep my more
experimental work out of this forum.

That said, the recent thread of discussions between the
Mathemusicality blog

(start here: http://mathemusicality.wordpress.com/2007/08/31/harmony-
still-undefended/ )

and Scott Spiegelberg's Musical Perceptions Blog

(see: http://musicalperceptions.blogspot.com/2007/08/chopin-
redux.html )

is as good a place as any to see how far voice leading theory is from
intonational theory. James Cook, of Mathemusicality makes what might
be called a strong (and, imo, cranky) voice leading argument for the
ultimate irrelevance of harmonic theory. Theorists working in neo-
Riemannian theory have a closer point of contact, in that the neo-
Riemannian operations tend to translate themselves well to moves on
tone lattices. In my work -- still in progress -- about Javanese
gender playing, I try to show that the two-voice gender style uses
the maximal contrapuntal complexity in a pentatonic enviroment,
drawing a parallel with modal counterpoint in a seven-tone
environment.

From your messages here, I take it that your interest is in creating
a polyphonic voice leading enviroment which is pitch- and interval-
richer than traditional western diatonic or chromatic enviroments. I
am not certain how much I can help you, but the harmonic use of
intervals suggesting, if not actually corresponding to,
configurations higher up in the harmonic series (especially "mid-
tone" intervals like 11:10, 12:11, 13:12, but also neutral and wider
thirds 11:9, 9:7, 14:11) found in Bulgarian or Georgian choral music,
especially in higher (female) tessituras is definitely worth
exploring. I would really like to have some in-depth analysis to see
if these interval do, indeed, "lock" over consonant difference tones.

Paul Erlich, who was very active on this list in the past, correctly
pointed out that the dominant 9th chord (c-e-g-bb-d) represented a
particular limit in 12tet harmonic practice, in that, within 12tet,
this chord and its inversion, the subharmonic 9th chord, were
intonationally indistinguishable. I have a suspicion that these
choral practices with harmonies in the 9:10:11:12:13:14 neighborhood
(lots of major seconds and midtones) are touching a similar level of
ambiguity or limit of clearly-defined intervals, and that singers are
simply aiming for interval that lock over good difference tones
rather than consistantly aiming for particular pitches and intervals.
If so, this could indicate a path to a very flexible -- if somewhat
chaotic in functional harmonic terms -- form of voice leading. But
this is no more than a suspicion on my part.

djw

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Don't you agree that it makes a difference whether you temper
> > up or down
>
> Yes.
>
> -Carl
>

:-) And this is why I keep saying, ad nauseum, that "sheer proximity
to a JI interval is not enough". If we associate softness with
JI (a subjective choice of course), we can't say that a 706 cent
fifth is "better" than a 696 cent fifth merely because it is closer
to 3/2, can we? To my ears, and to many others I believe, it
is a noticably worse fifth in terms of softness. So the idea of
approximating JI intervals requires a lot of qualifying, doesn't it?
The actual manner in which we minimize travel on a lattice
(a very clever idea as I said before), where we swerve left and
right, makes a difference in the musical character of the
resulting intervals and ultimately the whole tuning.

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

>The majority of intervals beat. 81/64 is one of them,
>but it doesn't beat *because* it's a mistuning of any
>particular JI interval.

I maintain that it is not nutty or numerological, quite the
opposite, to claim that a tuning can have an overall "timbre",
and I believe one of the sources of this "timbre" is where
tempered or otherwise divined intervals lie in relationship,
above or below as well as how far from, to strong partials
and their heavyweight interpretations. This is not defining
81/64 in terms of 5/4, I most certainly agree with Carl here,
but it is also not going into fairyland by claiming that say 384
cents won't be heard in terms of 5/4.

I also believe that the actual region around even the strongest
simple interpretations of the harmonic series is not only lopsided
but very narrow, and that other factors defining character kick in
quite quickly.

One reason for this, I believe, is difference tones. Take a listen
to the difference tones of 5/4, 400 cents, and 81/64. Heavy duty
differences in the differences.

Aaron wrote:

>I personally restrict 'JI' to audibly sets of audibly beatless
>intervals, and the full-of-beats combinations that comes as a side
>effect (e.g. 40/27 in 5-limit duodene, etc., 81/64 in 3-limit Pyth.)

And I personally restrict the idea of limits to actual audible
partials- for example 11/10 would be the limit of the 11-limit
in my personal view, which I'm not asking anyone to adopt of
course.

>So, more correctly, I would say "JI is a subset of the harmonic
>series".
>Does that fly with you?

Yes that sounds good- even though I consider JI to be a matter of
interpretation/application of the harmonic series, not the harmonic
series itself, I agree that the practical effect of "classic" JI is
that of being a subset. I don't argue with 5/4 as a "reality", I
just don't consider it a god, or agree with the idea that someone
who does consider it a god (to each their own) should monkey with it
without serious contemplation and consideration of the musical
impact of the monkeying. Just getting near a god without concern
whether you're sitting at her right or left hand doesn't fly in my
book.

>I still contend that 81/64 beats because the ear 'wants/tries' to
>hear
>it as a 5/4....until you come up with a better theory about why it
>beats, I'm sticking with that.

Carl answered this better than I can- my actual argument is first
and foremost, but it simply doesn't sound that way to me, at all!

A couple of observations. Going
as far below 5/4 as the 12-tET third is above harvests the most
rotten-lemon and un-5/4y third I've heard yet, try it.

And, there's a very interesting ultra-soft third about 8 cents
BELOW 5/4, 56/45, which to my ears DOES fall into a 5/4 feeling
while being something different at the same time. I found it by
applying my own interpretation of "simple ratios" to one specific
low partial, and humorously enough, upon hitting "compare scale" in
Scala, found that I had come up with a tuning practically identical
(2.5 cents difference overall) to one of Gene's, "171-ET Hahn-
reduced meantone".

I wonder if Gene is conscious of the delightful "numerological"
(actually, remarkably audibly pleasant, raising doubts about how
numberological the numerology really is) nature of his fifth in that
tuning?

-Cameron Bobro

> From your messages here, I take it that your interest is in
>creating
> a polyphonic voice leading enviroment which is pitch- and interval-
> richer than traditional western diatonic or chromatic enviroments.
>

Yes- your reply is so long and interesting, awesome, that I must
say, have to run to take care of my son but I'll be back this
evening to read it and answer as soon as possible!

-Cameron Bobro

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> Cameron --
>
> if I may interrupt, the question of the (if any) relationship
between
> voice leading and tuning is a subtle and deep one, but one in
which
> we have very few useful tools for discussing it, and little
certainty
> that the tools we have are the right ones. Furthermore, the
problem
> in a community as musically diverse as this one is that it is
> unltimately very difficult to separate questions about voice
leading
> from those of musical style, and the ranges of styles and
aesthetics
> is here so diverse that I generally avoid discussing my own
> composition practice here, so as to stick to the salient practical
> matter of tuning and not to get sucked into a unresolveable flame
war
> over aesthetic dimensions. So from time to time, I'll toss out a
> little neoclassical etude or a bit of juvenalia, but keep my more
> experimental work out of this forum.
>
> That said, the recent thread of discussions between the
> Mathemusicality blog
>
> (start here:
http://mathemusicality.wordpress.com/2007/08/31/harmony-
> still-undefended/ )
>
> and Scott Spiegelberg's Musical Perceptions Blog
>
> (see: http://musicalperceptions.blogspot.com/2007/08/chopin-
> redux.html )
>
> is as good a place as any to see how far voice leading theory is
from
> intonational theory. James Cook, of Mathemusicality makes what
might
> be called a strong (and, imo, cranky) voice leading argument for
the
> ultimate irrelevance of harmonic theory. Theorists working in neo-
> Riemannian theory have a closer point of contact, in that the neo-
> Riemannian operations tend to translate themselves well to moves
on
> tone lattices. In my work -- still in progress -- about Javanese
> gender playing, I try to show that the two-voice gender style uses
> the maximal contrapuntal complexity in a pentatonic enviroment,
> drawing a parallel with modal counterpoint in a seven-tone
> environment.
>
> From your messages here, I take it that your interest is in
creating
> a polyphonic voice leading enviroment which is pitch- and interval-

> richer than traditional western diatonic or chromatic
enviroments. I
> am not certain how much I can help you, but the harmonic use of
> intervals suggesting, if not actually corresponding to,
> configurations higher up in the harmonic series (especially "mid-
> tone" intervals like 11:10, 12:11, 13:12, but also neutral and
wider
> thirds 11:9, 9:7, 14:11) found in Bulgarian or Georgian choral
music,
> especially in higher (female) tessituras is definitely worth
> exploring. I would really like to have some in-depth analysis to
see
> if these interval do, indeed, "lock" over consonant difference
tones.
>
> Paul Erlich, who was very active on this list in the past,
correctly
> pointed out that the dominant 9th chord (c-e-g-bb-d) represented a
> particular limit in 12tet harmonic practice, in that, within
12tet,
> this chord and its inversion, the subharmonic 9th chord, were
> intonationally indistinguishable. I have a suspicion that these
> choral practices with harmonies in the 9:10:11:12:13:14
neighborhood
> (lots of major seconds and midtones) are touching a similar level
of
> ambiguity or limit of clearly-defined intervals, and that singers
are
> simply aiming for interval that lock over good difference tones
> rather than consistantly aiming for particular pitches and
intervals.
> If so, this could indicate a path to a very flexible -- if
somewhat
> chaotic in functional harmonic terms -- form of voice leading. But
> this is no more than a suspicion on my part.
>
> djw
>

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>Cameron Bobro wrote:
>>
>>
>>>Now to any replies of yes we know all this, I say: then show me > the >>>vast tomes in
>>>the archives addressing the intervals that are most decidely >>>NOT "JI". Show me the
>>>evidence that intervals are accepted for what they are, and not >>>inevitably cartooned into
>>>"tempered JI intervals". Traditional triadic harmony doesn't > > fly >>>with the so-called >>>"neutral" intervals, yet they sound great in harmonies, so, > where >>>are the long >>>discussions on alternative harmonic theories which are obviously >>>necessary for >>>polyphonic music heavy in "neutral" intervals? >>
>>It's an unavoidable law of the tuning list that people talk >>about what they want to talk about, > > Obviously- is my writing really so poor that you're under
> the impression that I'm a complete idiot? I've seen lots of people get angry (as far as I can tell via ASCII) about the tuning list not being what they want it to be. You look like one of the gang.

>>not the burning issues >>that you think they should be talking about. > > Where do you get this crazy stuff from? I am saying: there
> must be certain assumptions about what is "central" (a subset/
> interpretation of "JI" to be specific) to tuning, otherwise
> the worlds of tuning that are not bound to that presumed center
> would be far more in evidence. Your original argument seemed to be that if we understood certain obvious things to be obvious (that there's more to life than getting close to JI, and high and low make a difference) then we'd be talking about the one particular subject that's still in the quotes above.

Have you considered that some subjects are inherently easier to talk about than others? Or that different list subscribers have different assumptions and presumptions to the generalization you're painting?

> The work here (I continually read the archives) on > the possibities of : 1/1,(6/5),5/4,3/2 (7/4) : is staggering in > quantity and excellent in quality. I would doubt the
> honesty or musicality of someone who would claim otherwise.
> I would also doubt the honesty or musicality of someone
> who would deny the massive presence on the tuning list of > this particular subset of "JI".

Have you got back to the last round of arguments, about there not being enough JI on the list, and the "balance" being wrong? Of course that was also about there being too much temperament. You seem to be equating temperament with JI. If you carry this logic any further you should be careful on zebra crossings.

> Now this is just fine, to each their own, as I said
> in the generative post of this particular sprawling > discussion, if it really is a matter of musical
> preference. But if it's a matter of assuming the > divine right or manifest destiny of this particular > subset of JI, that's a different story. What you said was "I feel that the whole basic idea of basing tunings on approximating Just intervals is of dubious artistic integrity." Hardly an inclusive sentiment.

> By the way I am fully aware of the "natural" force of
> the aforesaid subset of JI, and I bet I could come
> up with more explanations and descriptions of its
> inborn weight than you could, for if you were truly
> aware of the myriad of things that give it weight
> you'd anticipate the muscle of other interpretations
> of the harmonic series and not be trying to bicker with me. > > Hahaha! :-)

So where's the beef? You're saying you object to treating (an incomplete) 7-limit JI as special, although of course it is?

Incidentally, you seem to be hung up on the 7-limit. Well, that is as far as Paul got in the Middle Path paper. And he says why. Don't you believe him?

>>There are >>good reasons for this. >>It takes a long time to produce a >>body of music from which you can deduce valuable harmonic >>rules. Most of us are working in different areas so it's >>difficult to find common ground. A lot of artists aren't >>good at explaining what they actually do. So, no, there >>aren't long threads about alternative harmonic theories.
> > It's not just this tuning list. Although some might claim > otherwise, this tuning list is not an > ivory tower or self-contained system. I perform in public
> and physically promote "alternative" tuning- we're right in
> the middle of a mini-festival I have organized, of non-standard
> music and performance (great shadow-theatre to-nite, we had an
> Indian raga, sarod and tabla, last week). I guess everybody
> here has musical stuff going on in the physical world. So,
> when I bitch about something I feel to a fundamental problem,
> don't take it personally because I think bogosities
> are evident everywhere in tuning theory. Nor am I innocent of > perpetuating of the same bogosities, for they are part and
> parcel of the theatrical sound-languages that most of the > Western world mistakenly considers to be "music". Good for you on the performances! But you are bitching. And only the Western world -- am I out of it?

>>- The neutral third MOS (in the Middle Path paper as dicot, >>with a dubious 5-limit mapping). Also has neutral seconds. >> Also known as mohajira.
> > ...but not this, thanks.

I used to like that. Got as far as writing a song in it.

>>- Arabic/Persian/whatever scales, and various other >>ethnic/historical tunings.
> > > Obviously (I live in the former Yugoslavia, so I can just > turn on the radio- HRT1 had a fantastic show of village
> singers singing all kinds of bitchin diads yesterday for
> example).

That's nice. I live in a musical desert, unfortunately. I got up and switched on the radio before writing this paragraph, actually, and ... no music.

>>- Miracle temperament (great in the 7-limit and with simple >>neutral thirds).
> > Have to check this out as well.

There was so much about it back in 2001 that it caused huge ructions on the list. And it was the spark that led to the Middle Path paper (and it's listed).

>>Of course some of these threads will involve messages that >>disagree with you about neutral intervals not being JI.
> > > Where do you get this from? I have several definitions of
> JI, one ultra-conservative historical, one realistic and
> positive rather than negative (ie, audible coincident lower > partials rather than "beatlessness"), and my own personal
> and private definition based on other concepts of what is > a "simple ratio". All three include "neutral" intervals.

From the original message I was quoting. `Show me the
evidence that intervals are accepted for what they are, and not inevitably cartooned into "tempered JI intervals".'

>>They're going to associate neutral thirds with 11:9 and >>neutral seconds with 12:11 or 11:10. > > That's fine as long as it doesn't imply that for example 27/22
> is a detuned 11/9, an audibly bogus idea as I physically > experienced the other week, singing with a couple of > musicians who performed in the festival.

I usually work with systems where 11/9 and 27/22 approximate to the same interval. It simplifies matters.

>>That really comes down >>to other people not being you. > > This is something you should really take to heart. There are
> many intervals I, and the musicians I work with afaik, simply
> do not hear as detuned JI intervals, and "dissonances" that
> simply do not sound dissonant. On the evening I mentioned before
> had a singer hold a tone and I sang a "neutral" third, whereupon
> the contrabass player immediately said "middle third...soft!...350 > cents" (his ears are frightening). This is the must f*****g annoying thing I've heard all week. Congratulations, you've riled me. What do you mean "take to heart"? Like do you believe in the pits of your ignorant soul that I believe everybody hears as I do? And because I happen to treat 350 as an approximation to 11:9 (whatever that means) then I have no artistic integrty? Well, f**k you! I've heard enough of the 11-limit that it convinces *me* and I'm not answerable to you, or the musicians you work with.

>>If you can come to terms >>with this > > Do you have any idea how ridiculous that sounds, in light
> of the fact that one of the fundamental things I've been
> bitching about since I came here is an apparent failure to > accept the idea that "other people aren't you", as evidenced > by assumptions that certained intervals are heard as temperings > of JI intervals, when they heard otherwise by people "who are
> not you".

What you're bitching about is that a large section of the microtonal community does use temperaments. You doubt our integrety, our honesty, and our musicality. Because -- why else? -- we're not you.

> Too much "the ear..." and not enough "my ear..."
>>you could also try searching for threads on >>11-limit harmony.
> > I think I'll search first for a non-ludicrous and non-numerological
> definition of "11-limit", hahaha!

Ludicrous and numerological as well?

> Take care,

Churz 'en!

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> djwolf_frankfurt wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> >>It's unfortunate to disagree with other languages, but do
> >>French or German have a significant body of work about
> >>alternative temperament classes? What do they call the
> >>meantone class?
> >
> > Salinas is defintely exploring this class, as a class
(independent
> > from pythagorean, for example), and Werckmeister's temperaments
can
> > defintely be construed as classes.
>
> Then what does Salinas call it? (I take it you're using
> "French" to denote the Romance language branch.)
>
> Maybe I should have said "regular temperament classes". But
> still, if temperament class means "a set of temperaments
> with the same mapping from ratios to interval classes" I can
> happily accept different irregular temperament classes.
> They'd each have same number of notes to the octave. Did
> Werckmeister look at many such or did he only consider 12?
>
> >>Saying the term is historically confused is a strange
> >>argument for imposing a strict definition now.
> >
> > I specifically indicated that incidents of historical confusion
arose
> > in the late 19th century, well after the meantone era, in
conflating
> > all non-12tet keyboard tunings (a mistake not made by the better
> > tuning theorists: Bosanquet, Riemann, Tanaka etc.) and in the
20th
> > century, with Lloyd who used it synonymously with just, and with
this
> > group. Even the oft-confused Barbour has it right, and his book
> > usefully is organized into what may be construed as classes.
>
> But George said it was Barbour who invented the "fractional
> comma meantone" terminology. So did he or did he not use
> "meantone" for tunings other than 1/4-comma?

To the best of my recollection he did, because I specifically
remember reading his caveat that, strictly speaking, the
label "meantone" designates the regular temperament (i.e., what we
call a regular tuning) having fifths narrow by 1/4 (syntonic) comma.
(Had he not used the "m/n-meantone" terminology, there would have
been no reason for the caveat.) I have the book (but not handy at
the moment), so I'll have to look for something to quote. (I'll be
away from the internet till Monday, so I won't be able to report back
till then.)

It's important to observe that he considered these other tunings
*variants* of the meantone temperament, so that without any m/n
qualifier the term "meantone" would default to the tuning with 1/4-
comma fifths. To use the term "meantone", without any qualifier, to
represent an entire class of tunings (named after its pre-eminent
member) would deprive the term of the context required for the proper
interpretation of its meaning.

There's another thing I should point out about Barbour's
terminology. The title of his book is _Tuning and Temperament_, and
he treats the terms "tuning" and "temperament" as mutually
exclusive! For Barbour a tuning is what we would call a *rational
tuning*, while a temperament is what we would call a *tempered
tuning*. (I'll report back with a quote confirming this.) To the
best of my knowledge, everyone back then understood the
term "temperament" to mean either a tempered tuning or the process of
altering intervals to produce a tempered tuning (and that has always
been my understanding of the term).

This is very different from the distinction Gene makes between those
two terms, if I'm interpreting him correctly.

> "Temperament class" is a technical term. It means a set of
> temperaments with the same mapping.

As I understand it, Gene is now using the word "temperament" to refer
to a whole class of temperaments (having the same mapping) and the
word "meantone" to refer to the temperament (class) that arrives at
its best 5/4 by a chain of fifths. This is in distinction to the
term "tuning", which refers to a set of tones with specific interval
sizes (either rational or irrational). Is this correct, Gene?

If so, then I'm afraid that the rest of the musical world is going to
take exception to the way these terms have been redefined. It's
going to alienate others, something we can ill afford to do.

As far as I'm concerned, it's okay to use "tuning" to apply to either
rational or irrational tunings (since I'm not sure that anyone is
currently using it the way Barbour defined it), but the use
of "temperament" (in the singular) for an entire class of tunings,
and "meantone" or "meantone temperament" for a particular class of
tunings, is guaranteed to lead to confusion, because mainstream
authorities don't use those terms that way. The term "meantone
temperament" (without any qualifiers) invariably indicates the 1/4-
comma tuning (and "comma" in that context is understood to mean
80:81). That's the way Barbour understood it, and that's the way the
rest of the musical world understands it. To use the term otherwise
is to invite confusion.

> It isn't the same as an
> organization into what "may be construed as classes". Did
> Barbour give names to a number of temperament classes? If
> so, what were they?

He did classify temperaments (i.e., tempered tunings) in various
ways, e.g., regular vs. irregular and open vs. closed. Apart from
that, I don't remember any formal classes.

--George

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> As far as I can tell, he defines the "Magna comma" as the
difference between
> two diatonic minor semitones and a minor whole tone, or between
16:15 and
> 256:243. The "Diesis comma", according to him, is the difference
between two
> 16:15 and one 9:8. The first he approximates with 43:42, the latter
with
> 89:88.
>
> Oz.

So if "he" and "him" refers to Prof. Ayhan Zeren, then what is the
justification for linking these other intervals to Didymus?

I've never heard of the comma of Didymus being anything other than
80:81, so I see no problem with naming the temperament class in which
this comma vanishes as "Didymic".

--George

> ----- Original Message -----
> From: "George D. Secor" <gdsecor@...>
> To: <tuning@yahoogroups.com>
> Sent: 12 Eylül 2007 Çarþamba 23:54
> Subject: [tuning] Re: "Meantone" - better term/definitions needed?
>
>
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > I am almost tempted to side with you, George. But what about
Prof.
> > Ayhan
> > > Zeren claiming that there are three Didymus commas: Syntonic
(81:80),
> > Magna
> > > (128:125), and Diesis (2048:2025)?
> >
> > The first of these comes directly from Didymus' diatonic scale,
as the
> > difference between the two sizes of whole tone in that scale.
How are
> > the other two linked to Didymus?
> >
> > --George
> >
>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

> To the best of my recollection he did, because I specifically
> remember reading his caveat that, strictly speaking, the
> label "meantone" designates the regular temperament (i.e., what we
> call a regular tuning) having fifths narrow by 1/4 (syntonic)
comma.
> (Had he not used the "m/n-meantone" terminology, there would have
> been no reason for the caveat.) I have the book (but not handy at
> the moment), so I'll have to look for something to quote. (I'll be
> away from the internet till Monday, so I won't be able to report
back
> till then.)
>

Barbour's nomenclature is:

X's Meantone Temperament (1/4 comma)

and

Y's A/B - Comma Temperament

Just in passing, I noticed that my Brockhaus-Riemann Musiklexikon
uses exactly the same construction. 1/4-Comma Mittelton-Temperatur
is contrasted with 1/3-Comma-Temperatur.

djw

Hi Graham and Daniel,

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

> I just returned from a country where the favorite sandwich
> is a cheeseburger. What is proposed here is precisely
> like using "cheeseburger" to described all sandwiches,
> whether hot, cold, with or withour meat, open or closed
> faced, with or without cheese, on a bun or sliced bread.
> Careful -- you order a cheeseburger and you might just
> end up with a slice of toast smeared with Schmalz and red
> onion.

But those things *are* all called "sandwich".

The whole thing here is that we want to force language
to be neat, and to carefully follow rules that seem
logical to us ... but unfortunately, language simply
doesn't work that way. It's a living thing which develops
and changes just like everything else concerning lifeforms.

Apparently "meantone" will be one of those words
which has multiple meanings, and there are thousands
in the English language which do that, so no big deal.

I'm pretty sure that context will indicate whether the
writer is referring to 1/4-comma meantone or to the
abstract family.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > Hi Carl,
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> > >
> > > > As i said, my Encyclopedia is full of references to
> > > > the "meantone family" of temperaments, and it will be
> > > > a huge job to change all of these. But i agree that it
> > > > should be changed, and i will do it pending resolution
> > > > of objections from Gene and those who agree with him.
> > >
> > > What convinced you?
> >
> > Well, it's not exactly a case of me becoming "convinced".
> > As i wrote in an earlier post, i've always been careful to
> > note that the term "meantone" refers historically and
> > specifically to 1/4-[syntonic-]comma meantone, as Daniel
> > argues.
>
> That's not the impression I got from reading your definition
> of meantone.

Um ... you're right. I guess along with moving and
having a baby, i lost track of some of the more recent
versions of this page that i have on a hard-drive somewhere.

Anyway, now i've updated the beginning of the page (exactly
the part you quoted in a recent post) to reflect the
dissent expressed here over the two different definitions
of "meantone":

http://tonalsoft.com/enc/m/meantone.aspx

PS -- I've also begun slipping the internal Encyclopedia
links back into my pages manually, so this one is updated
in that respect too.

-monz
http://tonalsoft.com
Tonescape microtonal music software

He links them to Didymus, not me. I see that there is no basis to such an
approach.

Oz.

----- Original Message -----
From: "George D. Secor" <gdsecor@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 13 Eyl�l 2007 Per�embe 21:57
Subject: [tuning] Re: "Meantone" - better term/definitions needed?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> As far as I can tell, he defines the "Magna comma" as the
difference between
> two diatonic minor semitones and a minor whole tone, or between
16:15 and
> 256:243. The "Diesis comma", according to him, is the difference
between two
> 16:15 and one 9:8. The first he approximates with 43:42, the latter
with
> 89:88.
>
> Oz.

So if "he" and "him" refers to Prof. Ayhan Zeren, then what is the
justification for linking these other intervals to Didymus?

I've never heard of the comma of Didymus being anything other than
80:81, so I see no problem with naming the temperament class in which
this comma vanishes as "Didymic".

--George

> ----- Original Message -----
> From: "George D. Secor" <gdsecor@...>
> To: <tuning@yahoogroups.com>
> Sent: 12 Eyl�l 2007 �ar�amba 23:54
> Subject: [tuning] Re: "Meantone" - better term/definitions needed?
>
>
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > I am almost tempted to side with you, George. But what about
Prof.
> > Ayhan
> > > Zeren claiming that there are three Didymus commas: Syntonic
(81:80),
> > Magna
> > > (128:125), and Diesis (2048:2025)?
> >
> > The first of these comes directly from Didymus' diatonic scale,
as the
> > difference between the two sizes of whole tone in that scale.
How are
> > the other two linked to Didymus?
> >
> > --George
> >
>

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> What's
> the existing word for the meantone temperament class?

Oo, oo! I know this one! "Meantone". -Carl

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
> > Sure. And if you go to an English speaking pet shop and ask
> > for a cat you won't walk away with a baby leopard, will you?
>
> No, but if you wish your body of work to be approachable to others,
> among them organ builders who are enormously well informed about
> tuning, then you have to be more clear rather than less.
>
> djw

Organ builders are not enormously well-informed about tuning
theory, nor do they need to be. They're well-informed about
how to tune organs, and maybe in common organ scales and history
of their use on organs.

Tuning theory is a technical field, with a need for precise
terminology. One doesn't join a string theory list and accuse
them of misappropriating the word "string". When Gene arrived
here and solved many of the problems we'd be unsure how to
approach for years, the first thing he said was that we needed
definitions. And after years of a pretty generous process of
consensus building, we now have some. Let's let the future of
those terms be decided by history, not some political process.

-Carl

> > > Don't you agree that it makes a difference whether you temper
> > > up or down
> >
> > Yes.
>
> :-) And this is why I keep saying, ad nauseum, that "sheer
> proximity to a JI interval is not enough".

It matters, but it doesn't matter so much that it isn't
appropriate to ignore it as an expedient way to do
calculations. In general, the harmonic entropy function
is very symmetrical with respect to detuning. Though see
a recent post of mine to MMM re. 7:4 in 19.

Whoops, the number 19 isn't the same thing as 19-tone
equal temperament. I meant 19-tone equal temperament.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
>
> Organ builders are not enormously well-informed about tuning
> theory, nor do they need to be.

I'm sorry, but this is simply not confirmed from my experience with a
number of organ builder both in the US and in Germany. I have found
them, with only one exception (a builder of romantic organs), to be
both well informed and to have had imaginative ideas of their own.
They do move a it more slowly than we do -- building an organ is a
bit like contracting for a major building, after all -- but theydo
understand and pay attention to tuning theory in a non-trivial way.

>
> Tuning theory is a technical field, with a need for precise
> terminology.

I agree, and I agree with Gene's proposal to me in in this thread. It
would make the work more clear for others.

One doesn't join a string theory list and accuse
> them of misappropriating the word "string".

There is no parallel here. The word string already had a large
number of meanings, and in string theory, the word was not selected
casually.

When Gene arrived
> here and solved many of the problems we'd be unsure how to
> approach for years, the first thing he said was that we needed
> definitions. And after years of a pretty generous process of
> consensus building, we now have some. Let's let the future of
> those terms be decided by history, not some political process.

You were the one who described the decision to use meantone in this
way as a "consensus" decision; that's politics, and your decision to
ignore dissent to that position and still claim a consensus is worse
politics. Moreover, you want to leave these matters to history, but
you approach is first to simply ignore history. No wonder a lot of
work around here get looks upon as unnecessarily obscure or even
cranky. This is especially disappointing because I recognize a group
of people around here who are totally capable of taking this work out
of the cranky category.

You're being very parochial about the tuning list. The work here is
interesting and important (and I praise it specifically in my
Contemporary Music Review article), but if you get out into the world
a bit you will soon discovery that there are huge numbers of people
out there doing sophisticated work in tuning, both practice and
theory, and doing it just fine without the list. I have taken part
in a number of projects, conferences or festivals with a tuning focus
in which the only connection to the Tuning List is my own (ironic as
that may be): the Ratio conference in Den Haag, the post-Partch
centered festival in Berlin, the Young/Amacher/Tenney event in Krems,
the MusikKonzepte microtone issue, the CMR issue. These are big
events, and they don't get noticed here. Almost everywhere I go
these days, I encounter exciting work and am constantly disappointed
when I report it here to get no response at all. And likewise, people
at these even often indicate that they have looked into the tuning
list and have then quickly departed because of the clubishness.

For example, for years around here, I recommended reading Clarence
Barlow's "Bus Road To Parametron" before making conclusions about one
formular or another that Clarence uses. Among other things, it's the
most entertaining (genuinely funny at times) AND frustrating text in
all the tuning theory I've read, and tuning theory certainly could
use a bit of humor and literary ambition. To the best of my
knowledge, not one other member of this list has ever followed up on
it, although a number of parties here were happy to critique the
formulas in the absence of their original context, which was the
production of a piece of music.

This is my last post on meantone, ever. I promise.

djw

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> Organ builders are not enormously well-informed about tuning
> theory, nor do they need to be. They're well-informed about
> how to tune organs, and maybe in common organ scales and history
> of their use on organs.

So you are an authority on what organbuilders do and do not know?
Come on. This is totally absurd. I worked for an organ
builder and became familiar with that world (and IMO it is a rich and
diverse subculture all its own). Some are passionate about tuning
theory and some don't care much. Anyway, you would do well to stop
making pronouncements on things you obviously know nothing about.

Yours,
Aaron Hunt
H-Pi Instruments

> > Organ builders are not enormously well-informed about tuning
> > theory, nor do they need to be. They're well-informed about
> > how to tune organs, and maybe in common organ scales and history
> > of their use on organs.
>
> So you are an authority on what organbuilders do and do not know?
> Come on. This is totally absurd. I worked for an organ
> builder and became familiar with that world (and IMO it is a rich and
> diverse subculture all its own). Some are passionate about tuning
> theory and some don't care much. Anyway, you would do well to stop
> making pronouncements on things you obviously know nothing about.

I lived down the hall from an organ builder for a year, and
I lived down the street from a guy with an organ in his house
for three years, and helped him tune it on a few occasions.

Cite one thing written by an organ builder that has to do
with tuning theory of the regular temperaments variety. I
would suggest it is *you* who don't know anything about the
latter, to even qualify if someone else knows about it or not.

-Carl

Daniel wrote...
> You were the one who described the decision to use meantone in
> this way as a "consensus" decision; that's politics, and your
> decision to ignore dissent to that position and still claim a
> consensus is worse politics.

I'll just paste what I wrote to you off-list:

If terms are defined by precedent, the body of work I've
pointed to should be more than enough. If they're defined
by logic, then the reasoning Gene's outlined should be
more than enough. The age of precedents and literal
interpretations of the prefix "mean" (in a contraction,
no less), respectively, do not cut the mustard in my
opinion.

If terms should be defined by anyone with a complaint,
and those who roll over in the face of complaints (i.e.
politics), I think that's stupid.

> Moreover, you want to leave these
> matters to history, but you approach is first to simply ignore
> history.

The progress of knowledge is exponential. More history
has occurred in tuning theory in the last 20 years than
in the 200 years before that.

> You're being very parochial about the tuning list.
//
> These are big events, and they don't get noticed here. Almost
> everywhere I go these days, I encounter exciting work and am
> constantly disappointed when I report it here to get no response
> at all.

Sounds like another case of complaining that discussion
here isn't about what it 'should be'.

I agree I've been a bit of a crank, though, and I regret that.

I quite like the vibe on some of the other lists, especially
your SpecMus list. I would still like to see discussion crop
up there again. Maybe I'll share something there to test the
waters . . .

-Carl

Thanks, Carl. I'll get back to the civilized world now if
you don't mind. I believe the readers of TL are smart
enough to recognize complete BS when they read it, so
I promise to resist pointing it out, though it's sure to come
up again, and again, and again...

Yours,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Organ builders are not enormously well-informed about tuning
> > > theory, nor do they need to be. They're well-informed about
> > > how to tune organs, and maybe in common organ scales and history
> > > of their use on organs.
> >
> > So you are an authority on what organbuilders do and do not know?
> > Come on. This is totally absurd. I worked for an organ
> > builder and became familiar with that world (and IMO it is a rich and
> > diverse subculture all its own). Some are passionate about tuning
> > theory and some don't care much. Anyway, you would do well to stop
> > making pronouncements on things you obviously know nothing about.
>
> I lived down the hall from an organ builder for a year, and
> I lived down the street from a guy with an organ in his house
> for three years, and helped him tune it on a few occasions.
>
> Cite one thing written by an organ builder that has to do
> with tuning theory of the regular temperaments variety. I
> would suggest it is *you* who don't know anything about the
> latter, to even qualify if someone else knows about it or not.
>
> -Carl
>

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

> Anyway, now i've updated the beginning of the page (exactly
> the part you quoted in a recent post) to reflect the
> dissent expressed here over the two different definitions
> of "meantone":
>
> http://tonalsoft.com/enc/m/meantone.aspx
>
>
> PS -- I've also begun slipping the internal Encyclopedia
> links back into my pages manually, so this one is updated
> in that respect too.

I've completely rewritten the first section of the
"meantone" page, and added some new graphics of
Tonescape Lattice diagrams.

Criticisms, additions, etc., greatly appreciated.

-monz
http://tonalsoft.com
Tonescape microtonal music software

djwolf_frankfurt wrote:

> You're being very parochial about the tuning list. The work here is > interesting and important (and I praise it specifically in my > Contemporary Music Review article), but if you get out into the world > a bit you will soon discovery that there are huge numbers of people > out there doing sophisticated work in tuning, both practice and > theory, and doing it just fine without the list. I have taken part > in a number of projects, conferences or festivals with a tuning focus > in which the only connection to the Tuning List is my own (ironic as > that may be): the Ratio conference in Den Haag, the post-Partch > centered festival in Berlin, the Young/Amacher/Tenney event in Krems, > the MusikKonzepte microtone issue, the CMR issue. These are big > events, and they don't get noticed here. Almost everywhere I go > these days, I encounter exciting work and am constantly disappointed > when I report it here to get no response at all. And likewise, people > at these even often indicate that they have looked into the tuning > list and have then quickly departed because of the clubishness. I looked up the Contemporary Music Review issue. It did in fact get noticed here (despite no official announcements of either a call for articles or publication that I could see). None of us said anything about reading it because of course it isn't freely available. So I'm looking at a page here which tells me I can read the full text of an article for $36.95. That's 37 dollars for *one* article! If they want the same for the other 7, then it's nearly $300 for the whole issue! (If they charge by number of pages, it's even more shocking. The site's down for maintenance so I can't check it now.)

So why was its publication a big event? You'll have to tell us because from the outside it doesn't look special to me. And it's not going to cause a stir on the list as long as we know so little about it.

If the tuning list's a club, at least it's one with open membership and no fee. Naturally some people won't like it for that very reason.

Now, as our honored ambassador from the academic world, perhaps you can give us a run-down of this exciting theory we're missing out on. Maybe you did mention something before but it's easy for it to get lost in the noise.

> For example, for years around here, I recommended reading Clarence > Barlow's "Bus Road To Parametron" before making conclusions about one > formular or another that Clarence uses. Among other things, it's the > most entertaining (genuinely funny at times) AND frustrating text in > all the tuning theory I've read, and tuning theory certainly could > use a bit of humor and literary ambition. To the best of my > knowledge, not one other member of this list has ever followed up on > it, although a number of parties here were happy to critique the > formulas in the absence of their original context, which was the > production of a piece of music.

There are a load of articles I would like to read, but it isn't worth the time it takes to procure them to get any kind of comprehensive survey. If you point at one specific article, it may indeed have been neglected. I know I don't have it or much idea what it contains (formulae, you say). (And do you mean "Bus journey to Parametron"?)

> This is my last post on meantone, ever. I promise.

That's not going to help either. If you have something worth saying you should say it. You should have been more forceful a long time ago.

Graham

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

> There seems to be a problem with *your* vocabulary because
> *you* persist in thinking that a temperament does not have a
> specific tuning and expecting the rest of the world to agree
> with you.

I'm a mathematician, We like to define things precisely. This is a move
in that direction.

Strictly speaking this is not correct. The word
> "temperament" has always been used historically to refer to
> tunings. This is a case where we really should keep the
> existing meaning.

Except that we--including you--have already abandoned that meaning.

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

> To
> remove all ambuguity you have to say "quarter comma
> meantone" and you can't blame the tuning list for that one.

I *always* say 1/4-comma. I'd recommend that to anyone who aims at
clarity.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:

>
> But one has only to listen still to this day to the folk music all
> throughout Europe and we have to question some implied notions.

It seems to me that learning by rote in the village may be
the most rigorous musical education of all.

>We will
> find neutral thirds for example or in Norwegian fiddle music
>different
> intonation used in the upper octave. Listen to French traditional
>music
> and one is confronted with intervals the theory avoids dealing
>with. Can
> we tell where the line between them being (albeit highly gifted)
folk
> artist or products of institutions of the early Romantic
composers. Many
> of them were lower class loaded up with Syphilis. Sometimes they
>were
> able to do more when others noticed their abilities.

I have yet to hear one professional recording of a male octet
that approaches what I heard eight drunk guys in a bar in
Ljubljana do. They were "pros" but their TV and radio
appearances don't even come close. Drinking wine in a bar is
true concert hall for a lot of music. And so it is with all
folk music- the gypsy boy who trains on a bench outside
my studio, with his friends as coaches, and the old guy with
the zither and Franz Josef mustaches in the neighboring alley,
wouldn't come across in a studio recordings, or even appear to
be "good" to a lot of people I bet, but it doesn't matter, they're
as much a part of the city and cultural as the stone monuments.

>
> One has only to listen to early recordings of orchestras and one
>can be
> appalled by the intonation.

Personally I'm thrilled by the various intonations and basically
am uninterested in post-war recordings for that very reason. Not
to mention rubato, LOL.

>I see no reason not to assume that such
> "tolerances" or varied interpretations have not been apart of the
>fabric
> for quite some time or at least present to varied degrees. Artist
>have
> never been conformist to what others tell them. they are the ones
>that
> tell others, and when they hit on something the lesser then use it
to
> build a wall against the next developments. Yet another group
comes
> along and pays no attention to ideas or right and wrong and in the
> process and the sometimes stumbling into many dead ends music as a
whole
> finds it way and it progresses.
>
>

djw, my long reply (I thought about it on and off all weekend while
beating rugs and such for our autumn cleaning) seems to have
disappeared. (I posted it several hours ago). If you PM me I'll
float you my "real" email address.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> > From your messages here, I take it that your interest is in
> >creating
> > a polyphonic voice leading enviroment which is pitch- and
interval-
> > richer than traditional western diatonic or chromatic
enviroments.
> >
>
> Yes- your reply is so long and interesting, awesome, that I must
> say, have to run to take care of my son but I'll be back this
> evening to read it and answer as soon as possible!
>
> -Cameron Bobro
>
> --- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@> wrote:
> >
> > Cameron --
> >
> > if I may interrupt, the question of the (if any) relationship
> between
> > voice leading and tuning is a subtle and deep one, but one in
> which
> > we have very few useful tools for discussing it, and little
> certainty
> > that the tools we have are the right ones. Furthermore, the
> problem
> > in a community as musically diverse as this one is that it is
> > unltimately very difficult to separate questions about voice
> leading
> > from those of musical style, and the ranges of styles and
> aesthetics
> > is here so diverse that I generally avoid discussing my own
> > composition practice here, so as to stick to the salient
practical
> > matter of tuning and not to get sucked into a unresolveable
flame
> war
> > over aesthetic dimensions. So from time to time, I'll toss out a
> > little neoclassical etude or a bit of juvenalia, but keep my
more
> > experimental work out of this forum.
> >
> > That said, the recent thread of discussions between the
> > Mathemusicality blog
> >
> > (start here:
> http://mathemusicality.wordpress.com/2007/08/31/harmony-
> > still-undefended/ )
> >
> > and Scott Spiegelberg's Musical Perceptions Blog
> >
> > (see: http://musicalperceptions.blogspot.com/2007/08/chopin-
> > redux.html )
> >
> > is as good a place as any to see how far voice leading theory is
> from
> > intonational theory. James Cook, of Mathemusicality makes what
> might
> > be called a strong (and, imo, cranky) voice leading argument for
> the
> > ultimate irrelevance of harmonic theory. Theorists working in
neo-
> > Riemannian theory have a closer point of contact, in that the
neo-
> > Riemannian operations tend to translate themselves well to moves
> on
> > tone lattices. In my work -- still in progress -- about
Javanese
> > gender playing, I try to show that the two-voice gender style
uses
> > the maximal contrapuntal complexity in a pentatonic enviroment,
> > drawing a parallel with modal counterpoint in a seven-tone
> > environment.
> >
> > From your messages here, I take it that your interest is in
> creating
> > a polyphonic voice leading enviroment which is pitch- and
interval-
>
> > richer than traditional western diatonic or chromatic
> enviroments. I
> > am not certain how much I can help you, but the harmonic use of
> > intervals suggesting, if not actually corresponding to,
> > configurations higher up in the harmonic series (especially "mid-
> > tone" intervals like 11:10, 12:11, 13:12, but also neutral and
> wider
> > thirds 11:9, 9:7, 14:11) found in Bulgarian or Georgian choral
> music,
> > especially in higher (female) tessituras is definitely worth
> > exploring. I would really like to have some in-depth analysis
to
> see
> > if these interval do, indeed, "lock" over consonant difference
> tones.
> >
> > Paul Erlich, who was very active on this list in the past,
> correctly
> > pointed out that the dominant 9th chord (c-e-g-bb-d) represented
a
> > particular limit in 12tet harmonic practice, in that, within
> 12tet,
> > this chord and its inversion, the subharmonic 9th chord, were
> > intonationally indistinguishable. I have a suspicion that these
> > choral practices with harmonies in the 9:10:11:12:13:14
> neighborhood
> > (lots of major seconds and midtones) are touching a similar
level
> of
> > ambiguity or limit of clearly-defined intervals, and that
singers
> are
> > simply aiming for interval that lock over good difference tones
> > rather than consistantly aiming for particular pitches and
> intervals.
> > If so, this could indicate a path to a very flexible -- if
> somewhat
> > chaotic in functional harmonic terms -- form of voice leading.
But
> > this is no more than a suspicion on my part.
> >
> > djw
> >
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Don't you agree that it makes a difference whether you temper
> > > > up or down
> > >
> > > Yes.
> >
> > :-) And this is why I keep saying, ad nauseum, that "sheer
> > proximity to a JI interval is not enough".
>
> It matters, but it doesn't matter so much that it isn't
> appropriate to ignore it as an expedient way to do
> calculations. In general, the harmonic entropy function
> is very symmetrical with respect to detuning. Though see
> a recent post of mine to MMM re. 7:4 in 19.

I see what you're saying. The way I use equal divisions of
octave is as a frame of reference for irregular tunings,
kin of the opposite of approximating JI. If you approximate
an EDO, you can get a great deal of modulatory and transposing
possibilities without sacrificing specific intervals.

So I'd have to say that approximating an EDO interval IS "enough"
within limits, but even there it seems pretty tight to me- you can
work (in a well or ill temperaments) slightly low and pure fifths
into an approximate EDO, where the EDO by nature has a high fifth,
but only so far, for example.

The symmetry of harmonic entropy in relation to detuning
is something I just don't agree with, either by ear or theory,
for harmonic spectra are usually weighted toward the bottom and
critical band interactions in the first couple of partials
must surely carry a lot of weight.

I believe that most would agree that there's more tempering room
below a 3/2 and more above a 5/4, for example. There's
a curious amount silence on this issue, LOL. A simple agree or
disagree would do, guys.

So, if HE gives me a "good" rating for something that sounds
"bad" to me, in a specific context, how would it be useful?

If HE were expressed in terms
of a specific set of "ideal" timbres, it would be more
attractive, and probably more accurate, it seems to me. Triangle,
saw, and two pulses (50 and 33 percent duty cycle) would be cool,
and familiar. Obviously that
doesn't cover the infinity of timbres, but it's an
amazing versatile and informative little set of cartoon timbres,
I think.

-Cameron Bobro

> > > :-) And this is why I keep saying, ad nauseum, that "sheer
> > > proximity to a JI interval is not enough".
> >
> > It matters, but it doesn't matter so much that it isn't
> > appropriate to ignore it as an expedient way to do
> > calculations. In general, the harmonic entropy function
> > is very symmetrical with respect to detuning. Though see
> > a recent post of mine to MMM re. 7:4 in 19.
>
> I see what you're saying. The way I use equal divisions of
> octave is as a frame of reference for irregular tunings,
> kin of the opposite of approximating JI. If you approximate
> an EDO, you can get a great deal of modulatory and transposing
> possibilities without sacrificing specific intervals.

I have also done some experiments with JI scales that
approximate ETs.

> The symmetry of harmonic entropy in relation to detuning
> is something I just don't agree with, either by ear or theory,
> for harmonic spectra are usually weighted toward the bottom and
> critical band interactions in the first couple of partials
> must surely carry a lot of weight.

Critical band interactions with the louder/lower partials
do carry a lot of weight. How does this lead to assymetry
of dissonance with positive or negative detuning of a dyad?

> I believe that most would agree that there's more tempering room
> below a 3/2 and more above a 5/4, for example.

More above 5/4, yes. I dunno about 3/2.

> So, if HE gives me a "good" rating for something that sounds
> "bad" to me, in a specific context, how would it be useful?

I guess it wouldn't be. But have you actually tried doing
listening tests and then comparing to HE, and importantly,
some other model that you may have? Or are you just picking
over what I say and selectively finding disagreements?

> If HE were expressed in terms
> of a specific set of "ideal" timbres, it would be more
> attractive, and probably more accurate, it seems to me.

That's one possibility. But it's meant to be the simplest
model of consonance, and as such, it ignores such details.

-Carl

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> > >>There seems to be a problem with *your* vocabulary because >>*you* persist in thinking that a temperament does not have a >>specific tuning and expecting the rest of the world to agree >>with you.
> > I'm a mathematician, We like to define things precisely. This is a move > in that direction.

I'm an English teacher. I like to use words with their existing meanings. Precise but wrong definitions don't really help.

> Strictly speaking this is not correct. The word >>"temperament" has always been used historically to refer to >>tunings. This is a case where we really should keep the >>existing meaning.
> > Except that we--including you--have already abandoned that meaning.

I've been strict about this for years now and I don't know why Carl and your good self think that I haven't. Of course, it can be difficult to infer from context what definition somebody's using, which is why there's so much scope for confusion.

Even if all three of us did change the definition, is that at all significant, compared to the huge body of literature on temperament? Can you find any other examples of your definition?

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > > :-) And this is why I keep saying, ad nauseum, that "sheer
> > > > proximity to a JI interval is not enough".
> > >
> > > It matters, but it doesn't matter so much that it isn't
> > > appropriate to ignore it as an expedient way to do
> > > calculations. In general, the harmonic entropy function
> > > is very symmetrical with respect to detuning. Though see
> > > a recent post of mine to MMM re. 7:4 in 19.
> >
> > I see what you're saying. The way I use equal divisions of
> > octave is as a frame of reference for irregular tunings,
> > kin of the opposite of approximating JI. If you approximate
> > an EDO, you can get a great deal of modulatory and transposing
> > possibilities without sacrificing specific intervals.
>
> I have also done some experiments with JI scales that
> approximate ETs.

Judging from a couple of scales in the Scala archive, Margo
Schulter has also done the same. Maybe (maybe) it could be
argued that the approach is as old as the hills, because you
could also view extending JI or "pythagorean" tunings, and
continuing divisions of the tetrachord, as a drive toward the
same, which was then fulfilled, or sidetracked, by ETs themselves.
It's not something we can ever really know I guess.
>
> > The symmetry of harmonic entropy in relation to detuning
> > is something I just don't agree with, either by ear or theory,
> > for harmonic spectra are usually weighted toward the bottom and
> > critical band interactions in the first couple of partials
> > must surely carry a lot of weight.
>
> Critical band interactions with the louder/lower partials
> do carry a lot of weight. How does this lead to assymetry
> of dissonance with positive or negative detuning of a dyad?

Well, if you bring say the second or third partial either down
or up into a combat zone, I think it's a big deal. My listening
tests with the little Csound program I made for this seemed to
confirm this. I think the version I posted here had a band-limited
1/n "saw" and was in mono, if not I can hunt it down and post it
again. I tried L/R stereo tones with headphones and it's either
extremely misleading or far more reflective of "real life", LOL.
Very different.
>
> > I believe that most would agree that there's more tempering room
> > below a 3/2 and more above a 5/4, for example.
>
> More above 5/4, yes. I dunno about 3/2.

I really like "high fives" but I think they completely suck as far
softnesss (on their own). IIRC, tempering 3/2 upward brings
one of the lower partials into a strident zone quickly, whereas
tempering down doesn't, but I'll have to check again. Of course
the whole business is tempered by the nature
of critical band interaction zones, which is somewhat subjective
as far as I can tell.

>
> > So, if HE gives me a "good" rating for something that sounds
> > "bad" to me, in a specific context, how would it be useful?
>
> I guess it wouldn't be. But have you actually tried doing
> listening tests and then comparing to HE, and importantly,
> some other model that you may have?

I think I was pretty diligent about listening through the 22 paper,
finding myself in strong general disagreement, and I do listen
to everything that pops up here, at least a little. I can't explain
many things of course, like why does 46-EDO sound like shit to
me but 41-EDO very good?

The models I use are based on character/character-similarities,
not dissonance/consonance per se, and since I deduced them from
listening I guess its not surprising that they seem to work
very well.

>Or are you just picking
> over what I say and selectively finding disagreements?

You and everyone you doesn't have their head rammed rigorously
up their behind know very well that that's completely
incompatible with everything I say and do, so I'll take the
question as a good-natured joke, hahaha! Actually
pretty funny.

>
> > If HE were expressed in terms
> > of a specific set of "ideal" timbres, it would be more
> > attractive, and probably more accurate, it seems to me.
>
> That's one possibility. But it's meant to be the simplest
> model of consonance, and as such, it ignores such details.

I browse at the HE list. As a measure of brute consonance,
questions of musical character aside, the log version seems
to be very good. How do 60/49 and 24/17 fare, I wonder? Namely,
I find that harmonic means between lower partials, and between
simple JI intervals, tend to be far more "simple" sounding than
they "should" be and I wonder if HE reflects that.

Because I believe that the big gates to xenharmony are
opened by various cohesions among intervals, with little
regard to brute consonance and dissonance, HE probably
won't ever interest me much. What would be its uses?

-Cameron Bobro

> > I have also done some experiments with JI scales that
> > approximate ETs.
>
> Judging from a couple of scales in the Scala archive, Margo
> Schulter has also done the same. Maybe (maybe) it could be
> argued that the approach is as old as the hills, because you
> could also view extending JI or "pythagorean" tunings, and
> continuing divisions of the tetrachord, as a drive toward the
> same, which was then fulfilled, or sidetracked, by ETs
> themselves.

Yes, that's true. But in my case I was very directly
starting with the ET, and then finding successive better
rational approximations to each pitch.

> > > So, if HE gives me a "good" rating for something that sounds
> > > "bad" to me, in a specific context, how would it be useful?
> >
> > I guess it wouldn't be. But have you actually tried doing
> > listening tests and then comparing to HE, and importantly,
> > some other model that you may have?
>
> I think I was pretty diligent about listening through the 22 paper,
> finding myself in strong general disagreement, and I do listen
> to everything that pops up here, at least a little. I can't explain
> many things of course, like why does 46-EDO sound like shit to
> me but 41-EDO very good?

I would be curious to hear why if you ever figure it out.

-Carl

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >...
> > But George said it was Barbour who invented the "fractional
> > comma meantone" terminology. So did he or did he not use
> > "meantone" for tunings other than 1/4-comma?
>
> To the best of my recollection he did, because I specifically
> remember reading his caveat that, strictly speaking, the
> label "meantone" designates the regular temperament (i.e., what we
> call a regular tuning) having fifths narrow by 1/4 (syntonic)
comma.
> (Had he not used the "m/n-meantone" terminology, there would have
> been no reason for the caveat.) I have the book (but not handy at
> the moment), so I'll have to look for something to quote. (I'll be
> away from the internet till Monday, so I won't be able to report
back
> till then.)

Well, I'm back, and it took a couple of days to catch up on my
reading of this thread (that just won't die!).

I was wrong -- Barbour didn't invent the m/n-meantone terminology,
nor did he use it.

The following is quoted from from J. Murray Barbour, _Tuning and
Temperament_, beginning on page 31:

<< Other Varieties of Meantone Temperament

Strictly, there is only one meantone temperament. But theorists have
been inclined to lump together under that head all sorts of systems
intended for keyboard instruments. ... >>

At this point Barbour speculates that irregular temperaments may have
been included by some writers under the "meantone" label, which
would, of course, have been misleading. There's no point in quoting
any of this, since I think we're all in agreement that irregular
tunings should not be classified as "meantone". Continuing the quote
several paragraphs later:

<< Bosanquet called "regular" a temperament constructed with one
size of fifth. The Pythagorean tuning, equal temperament, meantone
temperament -- all are regular systems. The systems that follow are
also regular, with values for the fifth smaller than that of equal
temperament and (usually) larger than that of the meantone
temperament. Since their construction is similar, it is easy to
describe them as varieities of the meantone temperament. In all of
them, the tone is precisely half of the major third. No harm will be
done by such a nomenclature if we realize that these are regular
temperaments which the earlier theorists themselves considered of the
same type as the 1/4-comma temperament and some of which they
preferred to it.

The first regular temperament to be advocated after the description
of the ordinary meantone temperament was that described by Zarlino in
which "each fifth remains diminished and imperfect by 2/7 comma." ...

In Table 26, we see the 2/7-comma temperament applied to a keyboard
with 12 notes to the octave. ...

The next variety of meantone temperament is also highly
unsatisfactory when applied to an octave of twelve semitones. This
is the 1/3-comma temperament, the invention of Francisco
Salinas, ... >>

The following is quoted from the Glossary:

<< A Tuning -- A system all of whose intervals can be expressed in
rational numbers.

Temperament -- A system, some or all of whose intervals cannot be
expressed in rational numbers.

Positive System -- A regular system whose fifth has a ratio larger
than 3:2.

Negative System -- A regular system whose fifth has a ratio smaller
than 3:2.

Varities of Meantone Temperament -- Regular temperaments formed on
the same principle as themeantone temperament, with flattened fifths
and (usually) sharp thirds. >>

From the above, we see that:

1) Barbour's definition of "a tuning" is what we would call a
rational tuning, whereas we've defined "a tuning" to mean a set of
tones related by intervals of specific sizes, or (if a particular
starting pitch is specified) a specific set of pitches to which one
may tune an instrument. This particular difference in terminology is
not at issue in this discussion.

2) Barbour's definition of "temperament" is such that, if we compare
it with his definition of "a tuning, we must conclude that he
intended the term to apply to what we call a (single) "tempered
tuning", not to multiple tempered tunings in the same classification.

3) Barbour avoided using the word "meantone" in identifying specific
temperaments, except in the case of the 1/4-comma (meantone)
temperament. Instead he called them individually "m/n-comma
temperament" and collectively as "varities of meantone temperament",
going so far as to put the latter term into his glossary.

I'd say that Barbour went out of his way *not* to use the
term "meantone" for any individual temperament (other than strict 1/4-
comma), and when he used the term collectively he was careful to use
the qualifier "varieties of" with it.

At this point I'd like to respond to a few comments:

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> [#73137]
> Anyway, now i've updated the beginning of the page (exactly
> the part you quoted in a recent post) to reflect the
> dissent expressed here over the two different definitions
> of "meantone":
>
> http://tonalsoft.com/enc/m/meantone.aspx

Hmmm, the article "Meantone" says,

<< The term "meantone" refers to both
1. a specific tuning, and
2. an abstract family of temperaments, of which that tuning is a
member. >>

It then begins to elaborate on item 2 without defining the "specific
tuning" mentioned in item 1 --until some 6 screens later, where it's
stated that "some theorists prefer to restrict the meaning to only
the former definition". If "former definition" is intended to refer
back to item 1 at the very beginning of the article, then I would
imagine that many readers would have forgotten that by this time.
The original (strict) definition needs to be stated explicitly at the
very top.

Also, the statement attributing the expression "2/7-comma meantone",
etc., to J. Murray Barbour is not correct and needs to be changed. I
thought that Barbour was the source of this terminology, but I was
wrong; I apologize.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> [#71302]
> If we want to be specific, of course we can say "domestic
> cats" or "felis catus" on the one hand and "the cat family"
> or "family Felidae" on the other. Most of the time the
> context makes it clear.
>
> Really, why should "meantone" be any different? There
> hasn't been a great need to distinguish meantone from other
> regular temperament classes before so there isn't an
> established name. Why not name the class after it's most
> famous representative member?

Its most famous member? Think about this for a moment. In articles
on the history of tuning, the terms "meantone temperament" and "equal
temperament" are frequently used to identify two *distinctly
different* tunings, i.e., the (1/4-comma didymic) meantone
temperament and 12-tone equal temperament, respectively. We all
agree that both of these tunings are (and ought to be) in the same
temperament class (which some individuals on this list have been
calling "meantone"). However, I'd say that the most famous
representative member of the class is the latter (12-equal) rather
than the former (1/4-comma), so if we're naming the temperament class
that way, perhaps we should call it "equal" rather
than "meantone". "No way!" you say? I submit that, to theorists
outside this group, it's just as confusing (should I say outrageous?)
to call meantone temperament "equal" as to call equal
temperament "meantone". When you have terms that have long been
thought of (and frequently written about) as *mutually exclusive* by
many authorities, you're asking for trouble if you insist on using
one of these as a name for a category that includes the other.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> [#73302]
> I agree with Monz, we can live with both a 'narrow' and a 'broad'
> definition, the difference is determined (hopefully) by context.

Hopefully by context? How, specifically? Will everyone be so
meticulous as to refer collectively to the members of the temperament
class as "meantone (temperament) class"? I think not! (You need
look no further than Monz's "Meantone" encyclopedia entry, where one
word is indicated to define an entire "family of temperaments".)
Instead, this will usually be shortened (for the sake of convenience)
to "meantone temperament" or simply "meantone", just as we now
customarily rattle off one-word names such as schismic, miracle,
magic, etc., to designate other temperament classes. One would then
have to use the qualifier "1/4-comma" to specify the traditional
meantone temperament. "Clear enough!" you say? Not if it's in
direct opposition to traditional usage, where "meantone" (*without
any qualifiers*) is understood to refer *specifically to 1/4-comma
temperament* and qualifiers (such as "m/n-comma") are required for
variations on the original. It's the same thing with the term "equal
temperament" without any qualifiers (meaning 12-equal, not n-equal
divisions in general). (The term "comma" has also acquired multiple
levels of meaning, but fortunately context seems to work for that
term.)

Before I came to this list I was working on a book about alternative
tunings, and I hope to finish it sometime in the foreseeable future.
In case I do, I'd like to see it published and used by others, but I
suspect that others outside this group (particularly theory class
instructors) wouldn't use it if it used terms in ways that conflict
with established usage.

Some recent messages have reminded us that certain remarks made from
time to time on this tuning list have already made a less-than-
stellar impression on others, so we can ill afford to offend others
further by redefining terminology for our own convenience.

I hope you'll all take the time to give this some careful
consideration.

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> Hopefully by context? How, specifically? Will everyone be so
> meticulous as to refer collectively to the members of the temperament
> class as "meantone (temperament) class"? I think not! (You need

I'm not wild about the terminology "temperament class". For one thing,
it conceptualizes the abstract temperament as a set of tunings, which I
think is most of the time going to be a bad way to think about it. For
another, it perpetuates the notion that it is the precise tunings which
are important, which I've been finding is apparently a serious problem
in connection with this business.

George wrote...

> I was wrong -- Barbour didn't invent the m/n-meantone terminology,
> nor did he use it.

But it looks like he did -- twice in what you quote!

> << ... No harm will be
> done by such a nomenclature if we realize that these are regular
> temperaments which the earlier theorists themselves considered of
> the same type as the 1/4-comma temperament ...
> The next variety of meantone temperament is also highly
> unsatisfactory when applied to an octave of twelve semitones.
> This is the 1/3-comma temperament, the invention of Francisco
> ... >>

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > I have also done some experiments with JI scales that
> > > approximate ETs.
> >
> > Judging from a couple of scales in the Scala archive, Margo
> > Schulter has also done the same. Maybe (maybe) it could be
> > argued that the approach is as old as the hills, because you
> > could also view extending JI or "pythagorean" tunings, and
> > continuing divisions of the tetrachord, as a drive toward the
> > same, which was then fulfilled, or sidetracked, by ETs
> > themselves.
>
> Yes, that's true. But in my case I was very directly
> starting with the ET, and then finding successive better
> rational approximations to each pitch.

I wonder how far you have to go before it's indistinguishable?
Probably not far on the one hand and at the same time amazingly
far, judging by my experiences- ie, it "works" as equal fairly
quickly but the actual overall sound of the EDO takes very
complex intervals. For example I don't actually like 34-EDO in
it's pure state very much (unlike 41 which I do), but it
becomes very beautiful when even mildly irregular (a matter
of taste of course).
>
> > > > So, if HE gives me a "good" rating for something that sounds
> > > > "bad" to me, in a specific context, how would it be useful?
> > >
> > > I guess it wouldn't be. But have you actually tried doing
> > > listening tests and then comparing to HE, and importantly,
> > > some other model that you may have?
> >
> > I think I was pretty diligent about listening through the 22
paper,
> > finding myself in strong general disagreement, and I do listen
> > to everything that pops up here, at least a little. I can't
explain
> > many things of course, like why does 46-EDO sound like shit to
> > me but 41-EDO very good?
>
> I would be curious to hear why if you ever figure it out.

Yeah, me too. :-)

George D. Secor wrote:

<snip>
> I'd say that Barbour went out of his way *not* to use the > term "meantone" for any individual temperament (other than strict 1/4-
> comma), and when he used the term collectively he was careful to use > the qualifier "varieties of" with it.

Which suggests the term was already in doubt when he was writing, and he had to be extra-careful to be clear without falling into a trap.

> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>[#71302]
>>If we want to be specific, of course we can say "domestic >>cats" or "felis catus" on the one hand and "the cat family" >>or "family Felidae" on the other. Most of the time the >>context makes it clear.
>>
>>Really, why should "meantone" be any different? There >>hasn't been a great need to distinguish meantone from other >>regular temperament classes before so there isn't an >>established name. Why not name the class after it's most >>famous representative member?
> > Its most famous member? Think about this for a moment. In articles > on the history of tuning, the terms "meantone temperament" and "equal > temperament" are frequently used to identify two *distinctly > different* tunings, i.e., the (1/4-comma didymic) meantone > temperament and 12-tone equal temperament, respectively. We all > agree that both of these tunings are (and ought to be) in the same > temperament class (which some individuals on this list have been > calling "meantone"). However, I'd say that the most famous > representative member of the class is the latter (12-equal) rather > than the former (1/4-comma), so if we're naming the temperament class > that way, perhaps we should call it "equal" rather > than "meantone". "No way!" you say? I submit that, to theorists > outside this group, it's just as confusing (should I say outrageous?) > to call meantone temperament "equal" as to call equal > temperament "meantone". When you have terms that have long been > thought of (and frequently written about) as *mutually exclusive* by > many authorities, you're asking for trouble if you insist on using > one of these as a name for a category that includes the other.

I did think about that before writing, which is why I added the word "representative". 12-equal may or may not be in the meantone temperament class, but it certainly isn't representative. It has a much better fifth and worse thirds than the more optimal temperaments.

Leaving aside such verbal gymnastics, there are better reasons for not calling meantone temperaments "equal". There are plenty of temperaments (and by implication temperament classes) that are equal. So the term would be ambiguous. Similiarly, we couldn't borrow "regular" from Barbour or whoever because there are other regular temperaments (by any reasonable definitions). And I hope I don't have to argue against "the temperament temperament class" following "1/6-comma temperament". OTOH there is, by the old, strict definition of "meantone", only possible temperament class that could contain it (at least in the 5-limit). So that's the meantone temperament class.

> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> >>[#73302]
>>I agree with Monz, we can live with both a 'narrow' and a 'broad'
>>definition, the difference is determined (hopefully) by context.
> > > Hopefully by context? How, specifically? Will everyone be so > meticulous as to refer collectively to the members of the temperament > class as "meantone (temperament) class"? I think not! (You need > look no further than Monz's "Meantone" encyclopedia entry, where one > word is indicated to define an entire "family of temperaments".) > Instead, this will usually be shortened (for the sake of convenience) > to "meantone temperament" or simply "meantone", just as we now > customarily rattle off one-word names such as schismic, miracle, > magic, etc., to designate other temperament classes. One would then > have to use the qualifier "1/4-comma" to specify the traditional > meantone temperament. "Clear enough!" you say? Not if it's in > direct opposition to traditional usage, where "meantone" (*without > any qualifiers*) is understood to refer *specifically to 1/4-comma > temperament* and qualifiers (such as "m/n-comma") are required for > variations on the original. It's the same thing with the term "equal > temperament" without any qualifiers (meaning 12-equal, not n-equal > divisions in general). (The term "comma" has also acquired multiple > levels of meaning, but fortunately context seems to work for that > term.)

You say "would then have to" as if this weren't already the case! If it isn't obvious that you're talking about a specific 12 note tuning, then of course you have to clarify it. The language evolves, and in this case has evolved. The same way you have to specify "domestic cats" in some contexts. The traditional usage *is not* current.

> Before I came to this list I was working on a book about alternative > tunings, and I hope to finish it sometime in the foreseeable future. > In case I do, I'd like to see it published and used by others, but I > suspect that others outside this group (particularly theory class > instructors) wouldn't use it if it used terms in ways that conflict > with established usage.

And if they don't like it, it's tough titty. The New Grove agrees with us. Established usage has changed and had changed before this list started up.

> Some recent messages have reminded us that certain remarks made from > time to time on this tuning list have already made a less-than-
> stellar impression on others, so we can ill afford to offend others > further by redefining terminology for our own convenience.

We didn't redefine this. Okay, we may have extended it a little, like allowing for more notes and a wider range of fifths. But we picked up the nearest term that suited our purposes, which had already been established as "meantone".

I wish you'd join in on Gene's definition of "temperament" which plainly is a redefinition.

> I hope you'll all take the time to give this some careful > consideration.

Certainly we can consider it, and keep the existing definition we're happy with. Any more dissenters?

Graham

Hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

> At this point I'd like to respond to a few comments:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > [#73137]
> > Anyway, now i've updated the beginning of the page (exactly
> > the part you quoted in a recent post) to reflect the
> > dissent expressed here over the two different definitions
> > of "meantone":
> >
> > http://tonalsoft.com/enc/m/meantone.aspx
>
> Hmmm, the article "Meantone" says,
>
> << The term "meantone" refers to both
> 1. a specific tuning, and
> 2. an abstract family of temperaments, of which that tuning is a
> member. >>
>
> It then begins to elaborate on item 2 without defining
> the "specific tuning" mentioned in item 1 --until some
> 6 screens later, where it's stated that "some theorists
> prefer to restrict the meaning to only the former definition".
> If "former definition" is intended to refer back to item 1
> at the very beginning of the article, then I would
> imagine that many readers would have forgotten that
> by this time.
> The original (strict) definition needs to be stated
> explicitly at the very top.

That's another thing over which i hesitated, so i've
changed it now to follow your ideas. Indeed, in all
other Encyclopedia entries where a single terms has
more than one definition, i've always put the numbered
definitions in separate sections with separate headers,
so now this page is consistent with those.

> Also, the statement attributing the expression
> "2/7-comma meantone", etc., to J. Murray Barbour is
> not correct and needs to be changed. I thought that
> Barbour was the source of this terminology, but I was
> wrong; I apologize.

OK, i've changed that too. Thanks for the detailed
explanation of Barbour's usage ... i don't have access
to my copy right now.

-monz
http://tonalsoft.com
Tonescape microtonal music software

I missed the part where anyone beyond GWS agreed that a temperament
should be an abstract mapping from rational numbers to a 'group of
smaller rank' - ie a mathematical construction. (What are temperament
ordinaire and irregular circulating temperament, then? Must they be
rechristened 'tuning ordinaire' etc.)

If I ask how this or that piece sounds in '2/7 comma meantone
(temperament)', none of the words means a mathematical construct. They
mean that someone tuned an (unspecified) instrument with some
(unspecified) pitch standard by narrowing each fifth, or widening
fourths, etc., by some particular amount ... or someone programmed a
tone-producing computer! ... in order to render certain harmonic
progressions tolerable. Some features of the audible result will be
very well approximated by mathematical entities (and hopefully we can
see beyond the ends of our noses that inaudible inaccuracies in tuning
are ignorable) but what I mean is the audible result.

If one wants to be more precise, a temperament is a way to tune
musical intervals where at least some intervals are adjusted away from
purity by an irrational amount. Even without a very accurate
mathematical description of what this amount is (eg temperament
ordinaire!) one can have a temperament.

This group is 'tuning' not 'tuning-math'. If someone wants to talk
about relevant mathematics they are welcome, but it does no good to
complain that other people are using words in the traditional and
practical sense of audible procedures and results in tuning.
~~~T~~~

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
> > Hopefully by context? How, specifically? Will everyone be so
> > meticulous as to refer collectively to the members of the temperament
> > class as "meantone (temperament) class"? I think not! (You need
>
> I'm not wild about the terminology "temperament class". For one thing,
> it conceptualizes the abstract temperament as a set of tunings, which I
> think is most of the time going to be a bad way to think about it. For
> another, it perpetuates the notion that it is the precise tunings which
> are important, which I've been finding is apparently a serious problem
> in connection with this business.

Hmmm...something funny is happening 'round here...I always thought there was wide agreement that 'tuning' was rational, and 'temperament' involved irrationals designed to cancel a comma.

I see Gene *not* using it that way, and ditto Monz the other day.

I just read George's post regarding 'meantone', which I wholeheartedly agree with: not only is 'm/n-comma temperament' more precise, it aligned with historical usage and avoids confusion. Anyway, he also notes Barbour used 'tuning' for rational sets of pitches, and temperament for the others..I like that standard, and wish we would stick to it.

Anyone?

-A.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> >> Hopefully by context? How, specifically? Will everyone be so >> meticulous as to refer collectively to the members of the temperament >> class as "meantone (temperament) class"? I think not! (You need >> >
> I'm not wild about the terminology "temperament class". For one thing, > it conceptualizes the abstract temperament as a set of tunings, which I > think is most of the time going to be a bad way to think about it. For
> another, it perpetuates the notion that it is the precise tunings which > are important, which I've been finding is apparently a serious problem > in connection with this business.
>

Carl Lumma wrote:
> George wrote...
> > >> I was wrong -- Barbour didn't invent the m/n-meantone terminology, >> nor did he use it.
>> >
> But it looks like he did -- twice in what you quote!
>
> '1/3-comma temperament' != '1/3-comma meantone'

Thank, Tom. My recent post is about this same problem.

I call it 'terminology hijacking'.

-A.

Tom Dent wrote:
> I missed the part where anyone beyond GWS agreed that a temperament
> should be an abstract mapping from rational numbers to a 'group of
> smaller rank' - ie a mathematical construction. (What are temperament
> ordinaire and irregular circulating temperament, then? Must they be
> rechristened 'tuning ordinaire' etc.)
>
> If I ask how this or that piece sounds in '2/7 comma meantone
> (temperament)', none of the words means a mathematical construct. They
> mean that someone tuned an (unspecified) instrument with some
> (unspecified) pitch standard by narrowing each fifth, or widening
> fourths, etc., by some particular amount ... or someone programmed a
> tone-producing computer! ... in order to render certain harmonic
> progressions tolerable. Some features of the audible result will be
> very well approximated by mathematical entities (and hopefully we can
> see beyond the ends of our noses that inaudible inaccuracies in tuning
> are ignorable) but what I mean is the audible result.
>
> If one wants to be more precise, a temperament is a way to tune
> musical intervals where at least some intervals are adjusted away from
> purity by an irrational amount. Even without a very accurate
> mathematical description of what this amount is (eg temperament
> ordinaire!) one can have a temperament.
>
> This group is 'tuning' not 'tuning-math'. If someone wants to talk
> about relevant mathematics they are welcome, but it does no good to
> complain that other people are using words in the traditional and
> practical sense of audible procedures and results in tuning. > ~~~T~~~
>
> >

Hi Aaron,

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Hmmm...something funny is happening 'round here...
> I always thought there was wide agreement that 'tuning'
> was rational, and 'temperament' involved irrationals
> designed to cancel a comma.
>
> I see Gene *not* using it that way, and ditto Monz
> the other day.

I've never held this view. To me, temperaments and scales
have always been abstract musical entities, and tunings
are specific instances of either of them.

> I just read George's post regarding 'meantone',
> which I wholeheartedly agree with: not only is
> 'm/n-comma temperament' more precise, it aligned
> with historical usage and avoids confusion.

I don't like it, because today it's not specific enough.

It worked OK for Barbour, because when he was writing (1951),
the only unison-vector any Western theorist cared about
tempering out was the syntonic-comma ... indeed, Barbour's
book is one of the seminal works on temperament theory
of the 20th century.

But today, we're interested in tempering out all sorts
of unison-vectors, so (to me) it makes sense to think
of things Gene's way: a "temperament" is an abstract
entity in which a certain unison-vector is tempered out,
and then we need names for all the various temperaments
which may be found: thus we have meantone, magic, miracle,
orwell, hanson, helmholtz, etc. etc.

Each of these temperaments, in turn, supports an infinte
variety of tunings, which is to say simply that there
are an infinite number of different ways to tune up
each temperament.

> Anyway, he also notes Barbour used 'tuning' for
> rational sets of pitches, and temperament for the
> others..I like that standard, and wish we would
> stick to it.
>
> Anyone?

To my way of thinking, a rational tuning will pretty
much always be a periodicity-block, which carries
along with it the important concept of in which type
of tonespace the tuning or periodicity-block is
embedded (i.e., what are the period and generators?).

It's quite obvious that 2/7-comma meantone, for example,
*is* a specific tuning. So it doesn't make sense to me
to restrict the meaning of "tuning" to rational tunings.

If only i had all the time i'd like to have ... i would
like to rewrite Barbour's entire book from the perspective
we have today. I think it would be really illuminating.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> Carl Lumma wrote:
> > George wrote...
> >
> >
> >> I was wrong -- Barbour didn't invent the m/n-meantone
terminology,
> >> nor did he use it.
>

Does anyone actually read my posts? I have twice posted citing
chapter and verse from Barbour and his terminology, and George has
now posted the same: Barbour uses the form "1/4-comma
meantone" _only_ for plain-vanilla-5/2-divided-into-four-equal-parts-
geometric-mean-of-10/9-and-9/8-whole-tone-regular-distributed-
syntonic/didymus/81:81-comma-meantone, and "p/q-comma
temperament" (without the word meantone) for all the other fractions-
of-a-comma temperaments.

djw

monz wrote:
>
>> I just read George's post regarding 'meantone',
>> which I wholeheartedly agree with: not only is
>> 'm/n-comma temperament' more precise, it aligned >> with historical usage and avoids confusion. >> >
> I don't like it, because today it's not specific enough.
> Well, there is usage in the outside world to contend with. BUT----

For what it's worth, I think this whole conversation is pointless (and frankly, pedantic)---I don't see how anyone would be confused by any usage proposed so far.

-A.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> I missed the part where anyone beyond GWS agreed that a temperament
> should be an abstract mapping from rational numbers to a 'group of
> smaller rank' - ie a mathematical construction.

You must not be reading my posts, and I think Paul Erlich and
Herman Miller agree too. Graham has used the term that way
for years, but now it seems he doesn't agree (or something).

> (What are temperament
> ordinaire and irregular circulating temperament, then? Must they be
> rechristened 'tuning ordinaire' etc.)

Strictly speaking, "temperament" in the above sense is short
for "regular temperament". But anyway, words to not have
one and only one meaning for all time. They evolve, and take
on specialized meanings in specialize contexts.

> If I ask how this or that piece sounds in '2/7 comma meantone
> (temperament)', none of the words means a mathematical
> construct.

The 2/7-comma part is a tuning. The meantone temperament
part is a regular temperament.

> If one wants to be more precise, a temperament is a way to tune
> musical intervals where at least some intervals are adjusted
> away from purity by an irrational amount. Even without a very
> accurate mathematical description of what this amount is
> (eg temperament ordinaire!) one can have a temperament.

If you say so. Please, why don't you declare definitions for
all the terms used in the theory of regular temperaments, or
for that matter, in the English language?

> This group is 'tuning' not 'tuning-math'. If someone wants to talk
> about relevant mathematics they are welcome, but it does no good to
> complain that other people are using words in the traditional and
> practical sense of audible procedures and results in tuning.

A nice reversal of the situation. It is "other people" who are
complaining. Sometimes they just complain (starting this thread),
other times they first ask what the terms mean in the theory of
regular temperaments, and then complain at the answer (current
message I'm replying to).

-Carl

> > But it looks like he did -- twice in what you quote!
> >
> >
> '1/3-comma temperament' != '1/3-comma meantone'

thanks, sorry. I just figured it out from Aaron's reply. -C.

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Hmmm...something funny is happening 'round here...I always
> thought there was wide agreement that 'tuning' was rational,

All tunings are rational? Where'd you get that idea?

> and 'temperament' involved irrationals designed to cancel
> a comma.

Cancel one or more commas, and actually cancel an infinite
number of equivalent commas, yes.

> I just read George's post regarding 'meantone', which I
> wholeheartedly agree with: not only is 'm/n-comma temperament'
> more precise, it aligned with historical usage and avoids
> confusion.

Oh, is that what Barbour was saying? Well, that's a terrible
idea, because it doesn't say which comma(s) is/are being
tempered, or how.

-Carl

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Thank, Tom. My recent post is about this same problem.
>
> I call it 'terminology hijacking'.
>
> -A.

You guys are completely off base on this one.

-Carl

> Does anyone actually read my posts?

Traffic here is very high at the moment. I've been saying
the same things for a while now, but nobody seems to reply
to them. And lo, probably everyone is having this feeling.
Welcome to mailing lists.

-Carl

> For what it's worth, I think this whole conversation is
> pointless (and frankly, pedantic)---I don't see how anyone
> would be confused by any usage proposed so far.

You mean Barbour's proposal? I just gave you a very good
reason why it's useless to anyone interested in talking
about regular temperaments.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
> > Hopefully by context? How, specifically? Will everyone be so
> > meticulous as to refer collectively to the members of the
temperament
> > class as "meantone (temperament) class"? I think not! (You need
>
> I'm not wild about the terminology "temperament class". For one
thing,
> it conceptualizes the abstract temperament as a set of tunings,
which I
> think is most of the time going to be a bad way to think about it.
For
> another, it perpetuates the notion that it is the precise tunings
which
> are important, which I've been finding is apparently a serious
problem
> in connection with this business.

Gene, you're going to have to find something other than "temperament"
for this concept, because (as Tom pointed out) the term has long been
used to apply to *irregular* tempered tunings (such as well-
temperaments and modified meantone temperaments) that are clearly
*not* members of any temperament classes (or whatever) to which
you're seeking to apply the label "temperament".

How about "temperament family"? The term, although singular, clearly
indicates that it's *not* referring to a single tuning, and it also
(correctly) implies that there are common characteristics shared by
its members. This could easily be shortened to "family" when used
repeatedly in a theoretical discussion.

My main concern is that the term "meantone temperament" (without any
qualifiers) *not be used* (ever!) to refer to anything other than a
specific (1/4-comma) tempered tuning. Since it appears that "m/n-
comma meantone" has been used too often in the recent past to
backtrack and redo the terminology, I'm willing to go along with a
term such as "meantone family" to designate the related group of
(regular) tempered tunings of which the meantone temperament is a
member. In a discussion of temperament families "meantone
temperament" could thereby be shortened to "meantone", as long as the
qualifier "family" was clearly indicated by the context.

This usage could carry over to other temperament families, as well.
For example, I could make a case that the "miracle temperament" is,
in a strict sense (on historical grounds), the one with the minimax
generator originally described by me (in 1975, without a name), and
that the miracle family could be described (but probably not formally
defined) as consisting of an entire spectrum of temperaments with
generators ranging anywhere from 3deg31 to 4deg41. Likewise,
strict "schismic temperament" would probably be regarded as the 1/8-
schisma temperament that Helmholtz described, whereas the temperament
family "schismic" would be more general than that.

But if not "family", then what?

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

> How about "temperament family"?

Bad for four reasons:

(1) It encourages you to think of it as a family, and not a singular
entity.

(2) It suggests the tuning is more important, which is wrong.

(3) We are already using the term to mean something else.

(4) It's two words. Since the idea is important, that's one too many.

However, I suppose a new term would give me license to define things
algebraically in a way I would prefer.

> My main concern is that the term "meantone temperament" (without
any
> qualifiers) *not be used* (ever!) to refer to anything other than a
> specific (1/4-comma) tempered tuning.

Why? Should miracle temperament only refer to the offical size of
secor?

The tail wags the dog.

Since it appears that "m/n-
> comma meantone" has been used too often in the recent past to
> backtrack and redo the terminology, I'm willing to go along with a
> term such as "meantone family" to designate the related group of
> (regular) tempered tunings of which the meantone temperament is a
> member.

"m/n-comma meantone" suggests, by its form, that "meantone" is
generic for all tunings.

In a discussion of temperament families "meantone
> temperament" could thereby be shortened to "meantone", as long as
the
> qualifier "family" was clearly indicated by the context.

I'm not using "family". You may. Of course maybe what I think won't
much matter in the future if I can't get myself together, but I think
it's a bad usage.

> This usage could carry over to other temperament families, as
well.
> For example, I could make a case that the "miracle temperament" is,
> in a strict sense (on historical grounds), the one with the minimax
> generator originally described by me (in 1975, without a name), and
> that the miracle family could be described (but probably not
formally
> defined) as consisting of an entire spectrum of temperaments with
> generators ranging anywhere from 3deg31 to 4deg41.

I dislike the idea of assuming the octave must be a generator, and
then defining things in terms of the other generators. I hope people
will learn to think on the right level of abstraction.

If you want to use "family", I suggest just that word, and leave
off "temperament". Then it becomes "meantone" or "meantone
family", "miracle" or "miracle family", and so forth, but
never "meantone temperament family" (UGH!) But better would be a
different coinage--call it a "regulum", say. "Meantone
regulum", "miracle regulum", with "meantone" or "miracle" for short.

> Gene, you're going to have to find something other than
> "temperament" for this concept, because (as Tom pointed out)
> the term has long been used to apply to *irregular* tempered
> tunings

That's not how language works.

-Carl

The diamond , the lamdoma, any of the CPS for example are tunings yet hardly any of them are constant structures or periodicity blocks. I don't see any advantage of the latter term over the other. It seems to me constant structures if anything are more than the latter as they do not have to be harmonically based. One can generate them by filling in the gaps say on a generalized keyboard which is illustrated in the early volumes of Xenharmonikon.

Scale i think should be reserved or imply the melodic properties over the harmonic. We refer to scales around the world, many where the ideas of harmonic relations are foriegn to their construction.

Posted by: "monz"

To my way of thinking, a rational tuning will pretty
much always be a periodicity-
block, which carries
along with it the important concept of in which type
of tonespace the tuning or periodicity-block is
embedded (i.e., what are the period and generators?).
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

It seems all you need to know is how many steps in the scale
as in 19 tone 'm/n-comma temperament'

Posted by: "Carl Lumma" > I just read George's post regarding 'meantone', which I
> wholeheartedly agree with: not only is 'm/n-comma temperament'
> more precise, it aligned with historical usage and avoids
> confusion.

Oh, is that what Barbour was saying? Well, that's a terrible
idea, because it doesn't say which comma(s) is/are being
tempered, or how.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Hi Gene and George,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
>
> > How about "temperament family"?
>
> Bad for four reasons:
>
> <snip>

At this point now, i'm totally confused about how
people are or are not using "family" and "class"
in regard to temperaments and/or tunings.

> I'm not using "family". You may. Of course maybe what
> I think won't much matter in the future if I can't get
> myself together, but I think it's a bad usage.

Gene, i have a definition of "family"

http://tonalsoft.com/enc/f/family.aspx

which stems from the hierarchical descriptions which
*you* gave of "offspring" temperaments which inherit
characteristics (by way of tempering out the same
unison-vector) from their "parent" temperaments.

But you don't use this?

I realize that "class" as used in computer programming
(specifically, object-oriented programming) carries
the same connotations of inheritance and hierarchy.

So are "class" and "family" synonymous as they are
being used by tuning theorists? Or if they are different,
then how so? I need an Encyclopedia entry for "class".

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> The diamond, the lamdoma, any of the CPS for example are
> tunings

They are scales, in the tuning of just intonation. At least,
in the vocabulary of the "regular temperament paradigm".
In colloquial speech, you can call them tunings, certainly.

By the way, I reject that these definitions are "Gene's".
He may have suggested them, but they are far more important
than Gene because:

* They survived a debate/consensus process on tuning-math.

* They have been used and explained here and on MMM many
times over a period of years, with no arguments that I've
seen until now.

And most importantly:

* They make sense.

> Scale i think should be reserved or imply the melodic
> properties over the harmonic.

Noted that this is your proposal.

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> It seems all you need to know is how many steps in the scale
> as in 19 tone 'm/n-comma temperament'

Hardly. You need to know which commas. And you need to know
more than one of them in most cases.

-Carl

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

> Gene, i have a definition of "family"
>
> http://tonalsoft.com/enc/f/family.aspx
>
> which stems from the hierarchical descriptions which
> *you* gave of "offspring" temperaments which inherit
> characteristics (by way of tempering out the same
> unison-vector) from their "parent" temperaments.
>
> But you don't use this?

I do use it, but now people want to take the phrase and have it mean
something else.

> So are "class" and "family" synonymous as they are
> being used by tuning theorists? Or if they are different,
> then how so? I need an Encyclopedia entry for "class".

I don't know. In mathematics, "class", "family" and "set" are more or
less synomymous. "Proper class" in some kinds of set theory means
collections so large they cannot be quantified even by infinite
quantities. "Family" suggests that it might be indexed.

Tom Dent wrote:
> I missed the part where anyone beyond GWS agreed that a temperament
> should be an abstract mapping from rational numbers to a 'group of
> smaller rank' - ie a mathematical construction. (What are temperament
> ordinaire and irregular circulating temperament, then? Must they be
> rechristened 'tuning ordinaire' etc.)

Temperament is still a generic word for these things; what Gene is describing is more specifically a "regular temperament". I noticed that Gene used the word "abstract" to describe these things, whatever we want to call them. Actually, "abstract temperament" might be a good name for these "mathematical" things after all (if we want to reserve "temperament" for a particular implementation with specific intervals). In which case we might call this an "abstract regular temperament" or a "regular abstract temperament". Then we can still go about calling them "temperaments" with the understanding that this is a convenient abridgement of these longer terms.

> If I ask how this or that piece sounds in '2/7 comma meantone
> (temperament)', none of the words means a mathematical construct. They
> mean that someone tuned an (unspecified) instrument with some
> (unspecified) pitch standard by narrowing each fifth, or widening
> fourths, etc., by some particular amount ... or someone programmed a
> tone-producing computer! ... in order to render certain harmonic
> progressions tolerable. Some features of the audible result will be
> very well approximated by mathematical entities (and hopefully we can
> see beyond the ends of our noses that inaudible inaccuracies in tuning
> are ignorable) but what I mean is the audible result.

Certainly the sounds are what counts; it doesn't make sense to ask what something sounds like in 12&19 regular temperament (12&19-RT), since there are many possible implementations of this abstract system. 12-ET and 19-ET are only two convenient reference points. You can even tune 12&19-RT with fifths wider than 12-ET or narrower than 19-ET. But it does make sense to investigate what chord progressions are possible in 12&19-RT, since the 81/80 comma vanishes in this system. And you can crunch the numbers and come up with an optimal tuning of this thing, either using TOP or TOP-RMS, or some other method (the results are similar but not identical). In this case it ends up sounding much like a typical meantone tuning. But there are so many of these things that you get lost if you don't name some of them. 12&19-RT is a meantone-like system, so it's only natural to call it "meantone" for convenience. But in a more general context, where "meantone" already has an understood meaning, maybe we could call it something like "abstract meantone".

> If one wants to be more precise, a temperament is a way to tune
> musical intervals where at least some intervals are adjusted away from
> purity by an irrational amount. Even without a very accurate
> mathematical description of what this amount is (eg temperament
> ordinaire!) one can have a temperament.

I agree with the exception that the adjustment isn't necessarily irrational. It tends to be so, but Hammond organs for instance are tuned to a rational scale.

> This group is 'tuning' not 'tuning-math'. If someone wants to talk
> about relevant mathematics they are welcome, but it does no good to
> complain that other people are using words in the traditional and
> practical sense of audible procedures and results in tuning. > ~~~T~~~

There have been numerous changes in the terminology used to describe these "middle path" sorts of constructs, so many that I can understand the reluctance to change yet again. The problem is you need *some* words to talk about the things to begin with, but those don't always turn out to be the best words in the long run. Unless you have a good memory for numbers (then you can just use wedgies to identify these things).

Herman wrote...
> I agree with the exception that the adjustment isn't necessarily
> irrational.

I was hoping someone would say this.

-Carl

George D. Secor wrote:

> My main concern is that the term "meantone temperament" (without any > qualifiers) *not be used* (ever!) to refer to anything other than a > specific (1/4-comma) tempered tuning. Since it appears that "m/n-
> comma meantone" has been used too often in the recent past to > backtrack and redo the terminology, I'm willing to go along with a > term such as "meantone family" to designate the related group of > (regular) tempered tunings of which the meantone temperament is a > member. In a discussion of temperament families "meantone > temperament" could thereby be shortened to "meantone", as long as the > qualifier "family" was clearly indicated by the context.
> > But if not "family", then what?

I really think "family" would be better as a term for a group of related "abstract regular temperaments" or whatever we're going to call these, which share one or more commas. E.g. the starling family includes related (abstract regular) temperaments such as myna and grackle, which temper out 126/125. I don't think there's anything family-like about what we've been calling "regular temperaments". E.g. myna can be thought of as any tuning system in which 126/125, 1728/1715, 2401/2400, etc. are all tempered out. This is like a slice through the space of possible tunings, a continuous region. Another way to describe myna would be using ET's as reference points, e.g. 27&31. Or you could just use the wedgie <<10, 9, 7, -9, -17, -9]], but no one remembers that. The point is that it's not a collection of separate but related tunings; it's an abstract property shared by a whole range of possible tunings.

I don't personally see any problem with using "meantone temperament" as a name for the 12&19 regular temperament, as the context is always clear. It doesn't bother me that bankers use the word "default" with a meaning different from what I'm familiar with from computer science. But I can see the potential for confusion in a forum like this one where historical and new tuning systems are both frequent topics of discussion. So I'm willing to consider something along the lines of "abstract meantone". But I wouldn't go so far as to abandon any connection with meantone. This is the one system that anyone has much chance of already being familiar with, and it's a good point of reference when starting off on a trip into "middle path" space; it should have a familiar name.

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> Thank, Tom. My recent post is about this same problem.
>>
>> I call it 'terminology hijacking'.
>>
>> -A.
>> >
> You guys are completely off base on this one.
>
> Yeah, well, that's like, your opinion, dude.....

sorry, I couldn't resist a 'Big Lebowski' reference.

Aaron K. Johnson wrote:
> Carl Lumma wrote:
>> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>> >>> Hmmm...something funny is happening 'round here...I always
>>> thought there was wide agreement that 'tuning' was rational,
>>> >>
>> All tunings are rational? Where'd you get that idea?
>>
>> > Look at Johnny's recent post...he had the same idea. Are you saying > we're smoking the same crack?
>
> I'll dig it up, I swear I read this somewhere. Johnny must have, too.
>
>
>
Ok, for starters:
http://en.wikipedia.org/wiki/Musical_tuning
"Tuning systems that are not produced with exclusively just intervals are usually referred to as temperaments."

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> Hmmm...something funny is happening 'round here...I always
>> thought there was wide agreement that 'tuning' was rational,
>> >
> All tunings are rational? Where'd you get that idea?
>
> Look at Johnny's recent post...he had the same idea. Are you saying we're smoking the same crack?

I'll dig it up, I swear I read this somewhere. Johnny must have, too.

Hi Aaron,

> > All tunings are rational? Where'd you get that idea?
>
> Look at Johnny's recent post...he had the same idea. Are you saying
> we're smoking the same crack?
>
> I'll dig it up, I swear I read this somewhere. Johnny must have, too.

I hear people referring to scales as "tunings" all the time.
I'm still using the tuning-math scale definition above just
because I have to use something -- it's not necessarily valid
in the context of, say, piano tuning, which is one vocation
where scales are sometimes referred to as "temperaments", but
even more frequently as "tunings".

As for your apparent agreement with Johnny... I'm sure if
you two got down to the nitty gritty... you know, like
colloboratively writing code to search rank-2 temperament
space for good 13-limit temperaments or something, that you'd
realize maybe you didn't start with the same idea of what
"tuning" meant, after all. Once you'd been through that,
and came back and said, "Hey, Johnny and I like to use the
word "mxyzptlk" to describe torsional periodicity blocks with
unusually high Hahn radius", I *wouldn't* tell you that you
were smoking crack and insist that a paragraph from 1876
proves you wrong. Think about it.

-Carl

Aaron K. Johnson wrote:
> Hmmm...something funny is happening 'round here...I always thought there > was wide agreement that 'tuning' was rational, and 'temperament' > involved irrationals designed to cancel a comma.

Well, no wonder the just intonation folks have been complaining about too much temperament talk on the list. All this time they thought tuning and temperament were mutually exclusive concepts! It naturally follows that temperament is off topic on a "tuning" list!

And to think of all that time we were investigating regular temperaments on a "tuning-math" list!

Graham

Aaron K. Johnson wrote:
> Aaron K. Johnson wrote:
> >>Carl Lumma wrote:
>>
>>>--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>>>
>>>>Hmmm...something funny is happening 'round here...I always
>>>>thought there was wide agreement that 'tuning' was rational,
>>>
>>>All tunings are rational? Where'd you get that idea?
>>
>>Look at Johnny's recent post...he had the same idea. Are you saying >>we're smoking the same crack?
>>
>>I'll dig it up, I swear I read this somewhere. Johnny must have, too.
> > Ok, for starters:
> http://en.wikipedia.org/wiki/Musical_tuning
> "Tuning systems that are not produced with exclusively just intervals > are usually referred to as temperaments."

So temperaments are tunings. How do you read that as saying all tunings are rational?

Graham

</tuning/topicId_72835.html#73390;_ylc=X3oDMTJwcm1wMWJhBF9TAzk3MzU5NzE1BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRtc2dJZAM3MzM5MARzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMTkwMjUzNzcx>

Posted by: "Carl Lumma" <http://profiles.yahoo.com/clumma>

> Scale i think should be reserved or imply the melodic
> properties over the harmonic.

Noted that this is your proposal.

This is Erv Wilson's proposal. Partch also referred to his Diamond as a tuning and the 43 tones as a scale. Novaro started with a 7 limit diamond and made a scale with more notes ( (btw in 1927 mhich puts him in the same year as Meyer doing a Diamond) )

The others i mentioned you could also call harmonic constructs. Otherwise we might as well call the elements of a chord a scale including the triad.

Without the distinction between scales and harmonic constructs, one does not have the language to deal with say MOS's. MOS is not so much an original idea of Erv as much as naming what many before him were doing. maybe for millenias instinctively.

-Carl
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

> > Scale i think should be reserved or imply the melodic
> > properties over the harmonic.
>
> Noted that this is your proposal.
>
> This is Erv Wilson's proposal.

I know, actually. But the problem is, you have to make a
judgemet about what constitutes melody, or melodic worthiness,
or whatever. Sticky business.

-Carl

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

> <snip ... > But there are so many of these things
> that you get lost if you don't name some of them.
> 12&19-RT is a meantone-like system, so it's only
> natural to call it "meantone" for convenience.
>
> <snip>
>
> There have been numerous changes in the terminology
> used to describe these "middle path" sorts of constructs,
> so many that I can understand the reluctance to change
> yet again. The problem is you need *some* words to talk
> about the things to begin with, but those don't always
> turn out to be the best words in the long run. Unless
> you have a good memory for numbers (then you can just
> use wedgies to identify these things).

Our discussions and hardware are all so vastly more
sophisticated now than they were before the 1990s
that there is a ton of new stuff to talk about, so
it's only natural that there will be a painful
sieving phase for the terminology. Terms will come
and go, and the good ones will stick.

I generally love the names that Gene comes up with for
temperaments, because most of the time he tries to
pin some numerical aspect of the tuning to some specific
thing that's easy to remember. For example, orwell is
so named because it has one generator which is 19deg84.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:

> sorry, I couldn't resist a 'Big Lebowski' reference.

No apology needed, a welcome reference! When the Power Puff
Girls references start popping up we'll know that the
tuning list is celebrating a true Golden Dawn. BTW has
anyone seen the PPG episode done entirely in Beatles quotes,
where the bad guys unite into an invincible "fab four" and
are only brought down by the PPGs introducing Mojo Yoko
into their midst? I almost had an asthma attack laughing,
better stop thinking about it.

-Cameron Bobro

George D. Secor wrote:

> Gene, you're going to have to find something other than "temperament" > for this concept, because (as Tom pointed out) the term has long been > used to apply to *irregular* tempered tunings (such as well-
> temperaments and modified meantone temperaments) that are clearly > *not* members of any temperament classes (or whatever) to which > you're seeking to apply the label "temperament".

I don't see why an irregular temperament can't belong to a temperament class. It would belong with other regular or irregular temperaments that share the same mapping from just intonation.

Graham

Okay, let's wade into this one.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
> >>How about "temperament family"? > > Bad for four reasons:
> > (1) It encourages you to think of it as a family, and not a singular > entity.

A family is a singular entity.

> (2) It suggests the tuning is more important, which is wrong.

It suggests nothing of the sort. It does suggest that we'll explain the term "temperament" first, which makes sense to me. Go from tuning to temperament to temperament family/class with increasing abstraction.

> (3) We are already using the term to mean something else.

Bingo!

> (4) It's two words. Since the idea is important, that's one too many.

For now two words will have to do. I bet you won't use them as often as you think you will.

I'll add one:

(5) Last time round, we settled on "temperament class".

> However, I suppose a new term would give me license to define things > algebraically in a way I would prefer.

Think a nice one and make use of it in a significant publication.

>>My main concern is that the term "meantone temperament" (without > any >>qualifiers) *not be used* (ever!) to refer to anything other than a >>specific (1/4-comma) tempered tuning.
> > Why? Should miracle temperament only refer to the offical size of > secor?

Ah, but "miracle temperament" can't refer to a singular entity! That'd be "the miracle temperament" or "Miracle Temperament". Without the article, "miracle temperament" is an uncountable noun, and can easily refer to a set of temperaments. At a stretch, it can also refer to a single temperament, if you think of it as an abstract concept that only takes on a real form when set on a musical instrument.

Otherwise, what temperament is Barbour referring to in "Tuning and Temperament"?

I can see an argument for saying "miracle temperaments" instead for disambiguation. Of course you won't like that because it really does put tunings first.

> The tail wags the dog.

In this case, I don't think the world in general wants to remember what tuning "the miracle temperament" has. But "the meantone temperament" is relatively clear.

> If you want to use "family", I suggest just that word, and leave > off "temperament". Then it becomes "meantone" or "meantone > family", "miracle" or "miracle family", and so forth, but > never "meantone temperament family" (UGH!) But better would be a > different coinage--call it a "regulum", say. "Meantone > regulum", "miracle regulum", with "meantone" or "miracle" for short.

That works as an abbreviation. But you'd need some way to specify what kind of family you're referring to.

Graham

Tom Dent wrote:
> I missed the part where anyone beyond GWS agreed that a temperament
> should be an abstract mapping from rational numbers to a 'group of
> smaller rank' - ie a mathematical construction. (What are temperament
> ordinaire and irregular circulating temperament, then? Must they be
> rechristened 'tuning ordinaire' etc.)

Whether you think of them as mappings is neither here nor there. They are mappings and whatever properties you think temperaments should have are consistent with these mappings. Irregular temperaments included.

> If I ask how this or that piece sounds in '2/7 comma meantone
> (temperament)', none of the words means a mathematical construct. They
> mean that someone tuned an (unspecified) instrument with some
> (unspecified) pitch standard by narrowing each fifth, or widening
> fourths, etc., by some particular amount ... or someone programmed a
> tone-producing computer! ... in order to render certain harmonic
> progressions tolerable. Some features of the audible result will be
> very well approximated by mathematical entities (and hopefully we can
> see beyond the ends of our noses that inaudible inaccuracies in tuning
> are ignorable) but what I mean is the audible result.

How do you interpret "2/7" as not being a mathematical construct?

> If one wants to be more precise, a temperament is a way to tune
> musical intervals where at least some intervals are adjusted away from
> purity by an irrational amount. Even without a very accurate
> mathematical description of what this amount is (eg temperament
> ordinaire!) one can have a temperament.

Why does it have to be irrational and, without a very accurate mathematical description, how do you know that it's irrational?

> This group is 'tuning' not 'tuning-math'. If someone wants to talk
> about relevant mathematics they are welcome, but it does no good to
> complain that other people are using words in the traditional and
> practical sense of audible procedures and results in tuning. Oh, come off it.

Graham

I missed this message the first time round. It brings up a possibly
interesting question. According to the group-theoretical definition of
meantone, it can equally well be tuned with fifths (say) 1/18 comma
narrower than pure, as with (say) 1/9 comma.

Also according to what Monz says below, about 'tempering out the
syntonic comma', 1/18-comma should equally well be a member in good
standing of the meantone class. Making the fifths narrow by 1/18-comma
is, logically, a way of tempering out 81/80.

So can a regular tuning with 1/18-comma narrowed fifths possibly be
meantone, or not, and then why not? (I would argue yes, but only under
the widest possible meaning of the term.)

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Tom,
>
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
>
> > The problem with formally allowing 'meantone' to cover all
> > regular tunings with narrowed fifths is that you can't
> > make statements like 'chromatic semitones are narrow in
> > meantone'. (But if your fifths are narrowed by 1/12 or
> > 1/15 or 1/18 comma...) Nor could you talk meaningfully
> > of a historical clash between meantone and 12-ET.
>
>
> But the usage we've had here on this list for about the
> last 14 years is not that meantone = "all regular tunings
> with narrowed fifths", but rather that meantone = all
> tunings which temper out the 81:80 syntonic-comma.
>
> 12-edo is the special case where both the chromatic
> and diatonic semitones happen to be the same size.
> In all other meantones, the diatonic-semitone is always
> larger than the chromatic.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> >>I missed the part where anyone beyond GWS agreed that a temperament
>>should be an abstract mapping from rational numbers to a 'group of
>>smaller rank' - ie a mathematical construction.
> > > You must not be reading my posts, and I think Paul Erlich and
> Herman Miller agree too. Graham has used the term that way
> for years, but now it seems he doesn't agree (or something).

I've always objected to Gene's definitions, in so far as I've understood them. That's the price you pay for trying to be precise. In this case I don't agree that the mapping should be from rational numbers. For example, you may remember Tony said that we were looking at a tuning which approximated the intervals in the timbre of his bellophone. I'd be happy to call that a temperament. (As it happens, he's using the equivalent of Pythagorean intonation for the timbre.) For now I call the things we map from "just intonation". That'd cause all kinds of trouble if people understood what I meant by it. <wink>

One thing you left out is the distinction between "into" and "onto" which is the same as "homomorphism" or "epimorphism". But let's leave that for tuning-math, eh?

>>(What are temperament
>>ordinaire and irregular circulating temperament, then? Must they be
>>rechristened 'tuning ordinaire' etc.)
> > Strictly speaking, "temperament" in the above sense is short
> for "regular temperament". But anyway, words to not have
> one and only one meaning for all time. They evolve, and take
> on specialized meanings in specialize contexts.

Well, that depends. If the group being mapped to is a set of intervals, measured in cents, then it has to be a regular temperament. And it really is a temperament in the sense of having a tuning. (But not in the sense of A440 being a tuning.)

Alternatively, you can interpret the group being mapped to as a set of, let's say, "abstract intervals". By that I mean a set of intervals measured between notes. For example, 5:4 maps to 4 steps on a 12 note scale. You then have a separate mapping (not a homomorophism) from notes to pitches which allows for steps being of different sizes. This definition is fine for irregular temperaments. But to define a temperament you need that mapping from notes to pitches (a tuning). Otherwise it's a temperament class (neither regular nor irregular).

My objection to Gene's definition as I remember it is that he doesn't specify what this group you map to consists of.

Graham

Tom Dent wrote:
> I missed this message the first time round. It brings up a possibly
> interesting question. According to the group-theoretical definition of
> meantone, it can equally well be tuned with fifths (say) 1/18 comma
> narrower than pure, as with (say) 1/9 comma.
> > Also according to what Monz says below, about 'tempering out the
> syntonic comma', 1/18-comma should equally well be a member in good
> standing of the meantone class. Making the fifths narrow by 1/18-comma
> is, logically, a way of tempering out 81/80. > > So can a regular tuning with 1/18-comma narrowed fifths possibly be
> meantone, or not, and then why not? (I would argue yes, but only under
> the widest possible meaning of the term.)

You mean because 1/18-comma tempering would mean wider fifths than 12-equal? Yes, that's allowed by some definitions. As would be Pythagorean intonation itself, or negative tempering: fifths sharper than Pythagorean. After all, schismatic temperaments work like this.

So you have to be careful with your definitions.

Graham

Carl Lumma schrieb:
>> > Scale i think should be reserved or imply the melodic
>> > properties over the harmonic.
>>
>> Noted that this is your proposal.
>>
>> This is Erv Wilson's proposal.
> > I know, actually. But the problem is, you have to make a
> judgemet about what constitutes melody, or melodic worthiness,
> or whatever. Sticky business.
> > -Carl

I don't think worthiness is an issue. I think scales shouldn't be burderned with melodic properties at all.

Remember the old fracas about scales, mode and gamut?*) Only the modes are concerned with melody.

I'm at a loss about which needs to be octave equivalent. Modes obviously don't have to, the mediaeval gamut (a branching structure of hexachords) wasn't, so if anything is octave equivalent, it's the scales, no?

klaus

*) Minor is a gamut of 9 notes, two scales of 7 notes and modal definitons that tell you where the tonic is and that you shouldn't go up again when you've reached the lowered viith degree by stepwise motion form above.

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

> I've always objected to Gene's definitions, in so far as
> I've understood them. That's the price you pay for trying
> to be precise. In this case I don't agree that the mapping
> should be from rational numbers.

So far most of the proposed alternatives look like numerology to me.

> For example, you may
> remember Tony said that we were looking at a tuning which
> approximated the intervals in the timbre of his bellophone.

Do the intervals form a group? How is it defined?

> My objection to Gene's definition as I remember it is that
> he doesn't specify what this group you map to consists of.

It doesn't really matter. However, starting from a wedgie, you can
construct an appropriate group and mapping directly using the
interior product.

> I'm at a loss about which needs to be octave equivalent. Modes
> obviously don't have to, the mediaeval gamut (a branching
> structure of hexachords) wasn't, so if anything is octave
> equivalent, it's the scales, no?
>
> klaus

Anything does not have to be octave equivalent. First, it
could be a "tritave" (3:1) or other interval. And secondly,
an entire instrument could be covered with random pitches.
If it were a MIDI keyboard, it might have a .tun file, and
the thing encoded in that file would be a scale.

-Carl

> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>
> I've always objected to Gene's definitions, in so far as
> I've understood them.

I assume Gene got the right quote here -- I must have missed
your post, Graham. At any rate, can you cite your objections?
Because I don't remember them, either.

> > That's the price you pay for trying
> > to be precise. In this case I don't agree that the mapping
> > should be from rational numbers.

That sounds like a matter of degrees disagreement, not a
fundamental disagreement.

-Carl

Carl Lumma wrote:
>>--- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>>
>>I've always objected to Gene's definitions, in so far as >>I've understood them.
> > I assume Gene got the right quote here -- I must have missed
> your post, Graham. At any rate, can you cite your objections?
> Because I don't remember them, either.

I mentioned them in this thread. A detailed discussion should be on tuning-math but I'm not much interested in that anyway.

>>>That's the price you pay for trying >>>to be precise. In this case I don't agree that the mapping >>>should be from rational numbers. > > That sounds like a matter of degrees disagreement, not a
> fundamental disagreement.

A precise definition should be accurate.

Graham

Gene Ward Smith wrote:

>>For example, you may >>remember Tony said that we were looking at a tuning which >>approximated the intervals in the timbre of his bellophone. > > Do the intervals form a group? How is it defined?

You can call the ideal tuning a group if you want to for the definition. It isn't really defined, it's assumed a priori before you look for a temperament. The point I'm making is that I don't think we need any properties of the rationals other than them being a group.

>>My objection to Gene's definition as I remember it is that >>he doesn't specify what this group you map to consists of.
> > It doesn't really matter. However, starting from a wedgie, you can > construct an appropriate group and mapping directly using the > interior product.

It does matter what the group is if you want this to be music theory.

Graham

well then we don't even need the term scale at all then or mode either . So melodic integrity of a set of pitches can be consider an impossible subject. there is nothing in music but harmony . I apologize for being heavy handed.

Posted by: "Klaus Schmirler

I don't think worthiness is an issue. I think scales shouldn't be
burderned with melodic properties at all.

Remember the old fracas about scales, mode and gamut?*) Only the modes
are concerned with melody.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Carl Lumma schrieb:
>> I'm at a loss about which needs to be octave equivalent. Modes >> obviously don't have to, the mediaeval gamut (a branching
>> structure of hexachords) wasn't, so if anything is octave
>> equivalent, it's the scales, no?
>>
>> klaus
> > Anything does not have to be octave equivalent. First, it
> could be a "tritave" (3:1) or other interval. And secondly,
> an entire instrument could be covered with random pitches.
> If it were a MIDI keyboard, it might have a .tun file, and
> the thing encoded in that file would be a scale.
> > -Carl

So octave equivalence is an optional ingredient. I'm happy with that.

Klaus

Kraig Grady schrieb:
> well then we don't even need the term scale at all then or mode either . > So melodic integrity of a set of pitches can be consider an impossible > subject. there is nothing in music but harmony . I apologize for being > heavy handed.

No need for sarcasm (I hope). But it's true I think that "scale" is a not-so-important concept unless you are practicing an instrument. Viewed from one angle, it is a subset of the gamut (like the heptatonic white-note scale can be a subset of a chain of fifths, or a periodicity block); the method of construction mostly leads to something larger than a scale. From the melodic side, a scale loses all the information about the roles of notes that a mode entails.

Harmony informs the actual tuning, or rather temperament, since the consensus seems to be that it doesn't like commas.

klaus

> > Posted by: "Klaus Schmirler
> > I don't think worthiness is an issue. I think scales shouldn't be
> burderned with melodic properties at all.
> > Remember the old fracas about scales, mode and gamut?*) Only the modes
> are concerned with melody.

> >>I've always objected to Gene's definitions, in so far as
> >>I've understood them.
> >
> > I assume Gene got the right quote here -- I must have missed
> > your post, Graham. At any rate, can you cite your objections?
> > Because I don't remember them, either.
>
> I mentioned them in this thread. A detailed discussion
> should be on tuning-math but I'm not much interested in that
> anyway.

I mean, if you've always objected, where are the posts in
which you did so?

> >>>That's the price you pay for trying
> >>>to be precise. In this case I don't agree that the mapping
> >>>should be from rational numbers.
> >
> > That sounds like a matter of degrees disagreement, not a
> > fundamental disagreement.
>
> A precise definition should be accurate.

Yes, you perhaps disagree, but not to the same extent as
others in this thread.

-Carl

> So melodic integrityis of a set of pitches can be consider
> an impossible subject.

There are some good ideas about how to tackle it, but it's
much less researched than harmony, and even harmony is
ultimately subjective.

I was listening to a Smithsonian Folkways archive recording
of Kentucky bluegrass. I'd be hard-pressed to tell you what
scales they were singing (and bowing), but they sound almost
Arabic.

So yes, we simply use "set of pitches" as the meaning.

-Carl

> Harmony informs the actual tuning, or rather temperament, since the
> consensus seems to be that it doesn't like commas.
>
> klaus

Melody may also inform tuning, to be sure. Even in polyphonic
music, and let alone in homophonic.

-Carl

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

> > It doesn't really matter. However, starting from a wedgie, you
can
> > construct an appropriate group and mapping directly using the
> > interior product.
>
> It does matter what the group is if you want this to be
> music theory.

A strange pronouncement. What we are mapping from is the group of p-
limit positive rationals (or perhaps some other finite rank subgroup
of the positive reals if we generalize as you want to.) If we assign
a base frequency, say 440 Hz, to the identity, then these are
associated to pitches.

What we are mapping to, the image, can be assciated to quite
different things. For instance, for meantone we could have chains of
fifths separated by octaves. Or, we could have a Bosanquet lattice.
Or, we could use the interior product--in the case of rank two
temperaments, that leads to a subgroup of the vals. These isomophic
groups are concretely quite different, but what they are specifically
does not really matter.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>Gene Ward Smith wrote:
> > >>>It doesn't really matter. However, starting from a wedgie, you > can >>>construct an appropriate group and mapping directly using the >>>interior product.
>>
>>It does matter what the group is if you want this to be >>music theory.
> > A strange pronouncement. What we are mapping from is the group of p-
> limit positive rationals (or perhaps some other finite rank subgroup > of the positive reals if we generalize as you want to.) If we assign > a base frequency, say 440 Hz, to the identity, then these are > associated to pitches.

That's what you're mapping from, indeed. Although I think they should be interpreted as pitch differences (intervals), not pitches.

> What we are mapping to, the image, can be assciated to quite > different things. For instance, for meantone we could have chains of > fifths separated by octaves. Or, we could have a Bosanquet lattice. > Or, we could use the interior product--in the case of rank two > temperaments, that leads to a subgroup of the vals. These isomophic > groups are concretely quite different, but what they are specifically > does not really matter.

Right. So you aren't giving an answer to a musician's question "What is a temperament?" And given an entity in the nearest thing we have to a real world, you can't apply the definition to say whether it's a temperament or not. That means the definition's incomplete.

Graham

Carl Lumma wrote:

> I mean, if you've always objected, where are the posts in
> which you did so?

They certainly exist, but I'm no more capable of finding them than you are.

>>>>>That's the price you pay for trying >>>>>to be precise. In this case I don't agree that the mapping >>>>>should be from rational numbers. >>>
>>>That sounds like a matter of degrees disagreement, not a
>>>fundamental disagreement.
>>
>>A precise definition should be accurate.
> > Yes, you perhaps disagree, but not to the same extent as
> others in this thread.

Perhaps. I'm not at all clear about what others' objections are.

Graham

Hi Graham;

I believe that after so many years of thinking about it as a musician who also has a formal engineering background,

we have eventually cracked the problem of "conversion" for musicians who wish to think about tuning and harmony in a meantone-type pattern and come to microtuning

"meantone-type" tunings from a 12edo perspective and indocrination.

5L+2s and a unique scalecoding system covers about all that newbies will need to understand to be able to transfer their 12edo musical skills and knowledge to use with meantone-type tunings.

Your more exotic edo's, (e.g. 46, 88 cents , ... ) Miracle, JI, wedgies, orwell etc. are likely to be more difficult for them to adapt to for harmony, counterpoint, scales, chords etc. until we can

come up with similarly simple thought and classification patterns that they will be able to easily grasp.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 22 Sep 2007, at 05:07, Graham Breed wrote:

> Gene Ward Smith wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >
> >>Gene Ward Smith wrote:
> >
> >
> >>>It doesn't really matter. However, starting from a wedgie, you
> > can
> >>>construct an appropriate group and mapping directly using the
> >>>interior product.
> >>
> >>It does matter what the group is if you want this to be
> >>music theory.
> >
> > A strange pronouncement. What we are mapping from is the group of p-
> > limit positive rationals (or perhaps some other finite rank subgroup
> > of the positive reals if we generalize as you want to.) If we assign
> > a base frequency, say 440 Hz, to the identity, then these are
> > associated to pitches.
>
> That's what you're mapping from, indeed. Although I think
> they should be interpreted as pitch differences (intervals),
> not pitches.
>
> > What we are mapping to, the image, can be assciated to quite
> > different things. For instance, for meantone we could have chains of
> > fifths separated by octaves. Or, we could have a Bosanquet lattice.
> > Or, we could use the interior product--in the case of rank two
> > temperaments, that leads to a subgroup of the vals. These isomophic
> > groups are concretely quite different, but what they are > specifically
> > does not really matter.
>
> Right. So you aren't giving an answer to a musician's
> question "What is a temperament?" And given an entity in
> the nearest thing we have to a real world, you can't apply
> the definition to say whether it's a temperament or not.
> That means the definition's incomplete.
>
> Graham
>
>

Charles Lucy wrote:
> Hi Graham;

Hiya!

> I believe that after so many years of thinking about it as a musician > who also has a formal engineering background,
> > we have eventually cracked the problem of "conversion" for musicians > who wish to think about tuning and harmony in a meantone-type pattern > and come to microtuning
> > "meantone-type" tunings from a 12edo perspective and indocrination.

Well, sure, but that means you're converting them from meantone12 to meantone. Nice, but not that useful if you really want to do something different.

(Incidentally, I see you're calling it "meantone". I did propose an MOS naming scheme, which is on the wiki, and 5L+2s is "diatonic". I don't have any terminology storm troopers to enforce it.)

> 5L+2s and a unique scalecoding system covers about all that newbies > will need to understand to be able to transfer their 12edo musical > skills and knowledge to use with meantone-type tunings.

I don't think their skill and knowledge will be so 12edo as all that, which is the point.

> Your more exotic edo's, (e.g. 46, 88 cents , ... ) Miracle, JI, > wedgies, orwell etc. are likely to be more difficult for them to adapt > to for harmony, counterpoint, scales, chords etc. until we can
> > come up with similarly simple thought and classification patterns that > they will be able to easily grasp.

Miracle, orwell, etc, support very similar thought and classification patterns to meantone. You can learn them with exactly the methods you learned meantone. Some temperament classes, like wonder (or whatever it's called now -- 2.3.7-limit 5&31; every other note of miracle) or neutral-thirds diatonics (I called them "mosh" did I?) are inherently easier. Their virtue is also their vice: they're different.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> Well, sure, but that means you're converting them from
> meantone12 to meantone. Nice, but not that useful if you
> really want to do something different.
>
> (Incidentally, I see you're calling it "meantone". I did
> propose an MOS naming scheme, which is on the wiki, and
> 5L+2s is "diatonic". I don't have any terminology storm
> troopers to enforce it.)

The use of combinations of L and s with integer coefficients, eg
5L+2s as mapped from 2, and 3L+s as mapped from 3/2, is exactly the
despised and dreaded abstract group image in the definition I gave for
temperament, in a particular case.

Hi Cameron,

Sorry I'm a month late in responding. I wonder if this paper by Margo
Schulter and myself from the year 2000 would fit your description
below, although it is not a "vast tome".

http://dkeenan.com/Music/NobleMediant.txt

-- Dave Keenan

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
> Now to any replies of yes we know all this, I say: then show me the
> vast tomes in
> the archives addressing the intervals that are most decidely
> NOT "JI". Show me the
> evidence that intervals are accepted for what they are, and not
> inevitably cartooned into
> "tempered JI intervals". Traditional triadic harmony doesn't fly
> with the so-called
> "neutral" intervals, yet they sound great in harmonies, so, where
> are the long
> discussions on alternative harmonic theories which are obviously
> necessary for
> polyphonic music heavy in "neutral" intervals?

Thanks, Dave Keenan, this is great! And once again eerily similar
to things I use myself- your "noble" high and low thirds are .2 and
.1 cents different than mine, which I got by another means. And
of course the whole paper corresponds precisely to what I wrote
here a couple of months ago, about how the skeleton of my music
seems to be based on the maxima of "harmonic entropy". I find that
these points function both as unstable and as stable, thereby
"floating" the whole music, to my ears.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Hi Cameron,
>
> Sorry I'm a month late in responding. I wonder if this paper by
Margo
> Schulter and myself from the year 2000 would fit your description
> below, although it is not a "vast tome".
>
> http://dkeenan.com/Music/NobleMediant.txt
>
> -- Dave Keenan
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
> > Now to any replies of yes we know all this, I say: then show me
the
> > vast tomes in
> > the archives addressing the intervals that are most decidely
> > NOT "JI". Show me the
> > evidence that intervals are accepted for what they are, and not
> > inevitably cartooned into
> > "tempered JI intervals". Traditional triadic harmony doesn't
fly
> > with the so-called
> > "neutral" intervals, yet they sound great in harmonies, so,
where
> > are the long
> > discussions on alternative harmonic theories which are obviously
> > necessary for
> > polyphonic music heavy in "neutral" intervals?
>

Hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Hi Cameron,
>
> Sorry I'm a month late in responding. I wonder if
> this paper by Margo Schulter and myself from the
> year 2000 would fit your description below,
> although it is not a "vast tome".
>
> http://dkeenan.com/Music/NobleMediant.txt

In Note 5, would you please update the URL to Paul Erlich's
early text on harmonic entropy to this:

http://tonalsoft.com/td/erlich/entropy-erlich.htm

Thanks. (I realize that right now it's still redirecting
to sonic-arts.org, but this page will eventually be at
tonalsoft.)

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> In Note 5,
[of http://dkeenan.com/Music/NobleMediant.txt ]
> would you please update the URL to Paul Erlich's
> early text on harmonic entropy to this:
>
> http://tonalsoft.com/td/erlich/entropy-erlich.htm

Done. Don't forget you may need to hit the reload button to see it.
Thanks very much for that, Monz.

By the way, Monz. I've been trying to email you some encyclopedia
suggestions and twice now have had it bounce after 5 days undelivered.
I tried again yesterday. Do you still not have it?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
hi, Edward & Tom,
> >
"M. Edward (Ed) Borasky" wrote
> > 12-TET is 12-TET, OK?
in deed,
http://de.wikipedia.org/wiki/Martin_Vogel
reports in his book:
"Die Lehre von den Tonbeziehungen"
the stroy:
that J. Brahms abandoned from promoting 12-ET
after
http://en.wikipedia.org/wiki/Shohe_Tanaka
had let Brahms play himself on his famous
JI-organ.
> >
> > Anyone have any Brahms they think could be made to work in a
> > tuning/temperament other than 12-TET?
> >
After that illuminating event Brahms dismissed 12-EDO for ever
even for all his earlier compostions and urged for intonation
as just as possible.
> >
>
> Brahms wrote a lot of choral and orchestral works that have nothing
> necessarily to do with temperament.
His style changed towards JI after his meeting with Tanaka.
>
> The canonical example of JI in Brahms is the final few seconds of the
> Second Symphony, where the three trombones have a D major root
> position chord. I think good brass players will get a pretty much pure
> 4:5:6 there.
Brahms demanded from the brass even sometimes alike Richard Strauss in
http://einfach.jpc.de/jpcng/simple/detail/-/hnum/6083759/rk/simple/rsk/charts
the just pure 11th partial "Alphorn-FA":
http://en.wikipedia.org/wiki/Alphorn
"The song describes the time of bringing the cows to the high country
at cheese making time. Rossini introduced the melody into his opera
William Tell. Brahms was clear that the inspiration for the great
melody that opens the last movement of his First Symphony (played in
the orchestra by the horn) was an alphorn melody he heard in the Rigi
area of Switzerland."
That melody contains in melody:
http://www.music.princeton.edu/~ted/alphorn.html
"Very important: the seventh partial, written Bb, middle line treble
clef, is a lowered 7th -- it sounds flat [as it should]. Also, the
Alphorn FA, the 11th partial, written F#, top line treble clef, is a
raised 4th leading to the G [written]: in the key of F# it sounds
in-between B natural and C natural; it is a very distinct sound. These
notes are obviously not out of tune but part of a natural tuning which
western music has trained musicians to think is out of tune! [just
intonation junkies can come back now. -t.]"

There are only few brahms records with properly executed 7/4 septims
-not to mention 11/8 alphorn-fa's-
sufficinet precisely intonated
in matching the harmonic overtone-series pitches correctly,
as originally desired and demanded by the composer himself.

http://findarticles.com/p/articles/mi_m2822/is_2001_Spring-Summer/ai_100808915/pg_12
"Although Alphorns vary in length and therefore the number of pitches
available, most horns produce pitches through the twelfth overtone.
Certain pitches in the harmonic series sound "out of tune" to western
ears (see Ex. 1). In particular, the 11th partial or overtone, often
used in Swiss music and famously known as the "Alphorn-fa" ("fa" being
the fourth pitch of a scale), contributes to the uniqueness and exotic
appeal of mountain music;..."

Conversely inept 12-EDO intonation shoots down Brahms mind dead.

A.S.

A.S. wrote...
> http://de.wikipedia.org/wiki/Martin_Vogel
> reports in his book:
> "Die Lehre von den Tonbeziehungen"
> the stroy:
> that J. Brahms abandoned from promoting 12-ET
> after
> http://en.wikipedia.org/wiki/Shohe_Tanaka
> had let Brahms play himself on his famous
> JI-organ.

The Tanaka article doesn't mention Brahms. It says
Bruckner saw the "enharmonium". I guess Die Lehre von
den Tonbeziehungen is another text that
1. Isn't available in English.
2. Isn't available on the www.

Sigh.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
Dear Carl,
in deed: you are right in making me aware,
that i was wrong in confusing the names of
Brahms and Bruckner.
Rechecking
> > http://de.wikipedia.org/wiki/Martin_Vogel
's
> > "Die Lehre von den Tonbeziehungen"
# ISBN-10: 3922626092 or
# ISBN-13: 978-3922626091
Bonn 1975, p.318 ff:
again results:
Appearently i had interchanged in memory
that both famous 19th century composers
over the years since the last reading:

http://en.wikipedia.org/wiki/Anton_Bruckner
"At that time there was a feud between those who liked Wagner's music
and those who liked Brahms's music."
http://en.wikipedia.org/wiki/Johannes_Brahms
"With the possible exception of Anton Bruckner, Brahms was arguably
unmatched as a symphonist in the late 19th century."

Vogel's book reports only about that:
> > http://en.wikipedia.org/wiki/Shohe_Tanaka
presentated his JI-reed-organ to Bruckner.
but none reference that he did that also to Brahms.
>
http://www.robertkelleyphd.com/justtonnetz.htm
"Greenberg, Beth. 1976. "Brahms' rhapsody in G minor, Op. 79, No. 2" A
Study of Analyses by Schenker, Schoenberg, and Jonas." In Theory Only
I/9-10: 21-29. "Comment on Greenberg" by Charles J. Smith: 31-32."

http://www.answers.com/topic/joseph-joachim?cat=entertainment
"Joseph Joachim was one of the greatest violin soloists of all time, a
friend of Johannes Brahms,..."
preferred for his own string-quart compositions
performance 53-tone Pythagorean "Reinstimmung"

Martin Vogel p.322
"Joseph Joachim (Berin) ordered an Tanaka JI-organ" in June 1893
produced by Walcker.
p.363, footnote 3
"Joachim was among the few that used the Tanaka-Walcker JI reed-organ
in his [violin] lessons"

http://www.tonalsoft.com/monzo/schoenberg/Vienna1905.htm
"Thru Joachim, Brahms visits Düsseldorf and befriends Robert and Clara
Schumann. Schumann is dazzled by Brahms's three piano sonatas, and
declares him to be the prophet of the musical future, in classically
restrained opposition to the 'New German School' headed by Liszt and
Wagner."

> The Tanaka article doesn't mention Brahms.
Probably they had no contact to each others.
> It says
> Bruckner saw the "enharmonium". I guess Die Lehre von
> den Tonbeziehungen is another text that
> 1. Isn't available in English.
> 2. Isn't available on the www.
but compareable valuable as the precursing Helmholtz's
"Tonempfindungen" 'sensations of tone"
Imho: Vogel's "relations of tones" deserve also an translation.
>
Vogel quotes on p.318/9 two sources about that audio-demo
of the instrument:

1.
F. Eckstein, 'Erinneringen an Anton Bruckner' "Memories on A.B."
Wien(Vienna) and New York 1923, pp39f

..when playing chord-progressions in JI on Tanaka's reed-organ
Bruckner "wallowed in pleasure to hear them really acousictical
sounding without any enharmonics"...

"....Bruckner wollte sich nach all diesem von dem neuen
Harmonium gar nicht mehr trennen..."
'...after all that Bruckner didn't want to
get disassociated from that new reed-organ...'

2.
E. Schwanzara,
'Anton Bruckner und die reine Stimmung' in:
Österreichische Musikzeitschift 4, 1949, 263.

"A. Bruckner and the just intonation" in:
Austrian music-journal 4, 1949, 263.

Bruckner teached his November 9, 1891 lecture
about 'lessons-in-harmonics' at Univ. Vienna:

"...bis mir einmal ein Japaner auf einem sonderbaren Instrument
vorgespielt hat. Ah, das hat wunderbar geklungen!
Aber ich habe mir nicht erklären können, warum.
Bis er gesagt hat:
'Das ist die alte reine Stimmung'.
Seither habe ich nie wieder gesagt,
daß wir die reine Stimmung nicht vertragen..."

tr:
'...until once a japanese played to me on a curious instrument.
Ah, that sounded delightful!
But I wasn't able to explain, why so.
Until he replied: "That's the old JI".
Since then I never said again,
that we would not get along in tolerating JI...'

http://tonalsoft.com/enc/v/vienna.htm
"* The influence Tanaka's pseudo-just-intonation (really 53-edo)
"Enharmonium" may have had on Bruckner's harmonic experiments in his
9th Symphony."

hence my apology:
sorry again for my mistake in muddeling up Brahms and Bruckner
incorrectly. Hope the above citations clarify the error of
my fuzzy memory alike a coarse meshed sieve.

A.S.

Andreas Sparschuh schrieb:
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Dear Carl,
> in deed: you are right in making me aware,
> that i was wrong in confusing the names of
> Brahms and Bruckner.

Touching on this:

Does anyone know who claimed that Bruckner introduced the fifth of ii as a dissonance after his JI conversion? And did anybody ever check if this is true? (Since it would only make sense in, say, piano compositions, less in orchestral works because of the instruments' flexibility or in organ compositions where a retuning can't be expected. It does make sense for the harps in the symphonies, though, as long as their pedals are kept out of play.)

klaus

Andreas wrote...

> > The Tanaka article says
> > Bruckner saw the "enharmonium". I guess Die Lehre von
> > den Tonbeziehungen is another text that
> > 1. Isn't available in English.
> > 2. Isn't available on the www.
>
> but compareable valuable as the precursing Helmholtz's
> "Tonempfindungen" 'sensations of tone"
> Imho: Vogel's "relations of tones" deserve also an translation.
> >
> Vogel quotes on p.318/9 two sources about that audio-demo
> of the instrument:
>
> 1.
> F. Eckstein, 'Erinneringen an Anton Bruckner' "Memories on A.B."
> Wien(Vienna) and New York 1923, pp39f
>
> ..when playing chord-progressions in JI on Tanaka's reed-organ
> Bruckner "wallowed in pleasure to hear them really acousictical
> sounding without any enharmonics"...
>
> "....Bruckner wollte sich nach all diesem von dem neuen
> Harmonium gar nicht mehr trennen..."
> '...after all that Bruckner didn't want to
> get disassociated from that new reed-organ...'
>
> 2.
> E. Schwanzara,
> 'Anton Bruckner und die reine Stimmung' in:
> Österreichische Musikzeitschift 4, 1949, 263.
>
> "A. Bruckner and the just intonation" in:
> Austrian music-journal 4, 1949, 263.
>
> Bruckner teached his November 9, 1891 lecture
> about 'lessons-in-harmonics' at Univ. Vienna:
>
> "...bis mir einmal ein Japaner auf einem sonderbaren Instrument
> vorgespielt hat. Ah, das hat wunderbar geklungen!
> Aber ich habe mir nicht erklären können, warum.
> Bis er gesagt hat:
> 'Das ist die alte reine Stimmung'.
> Seither habe ich nie wieder gesagt,
> daß wir die reine Stimmung nicht vertragen..."
>
> tr:
> '...until once a japanese played to me on a curious instrument.
> Ah, that sounded delightful!
> But I wasn't able to explain, why so.
> Until he replied: "That's the old JI".
> Since then I never said again,
> that we would not get along in tolerating JI...'