Werckmeister III tuning

Anybody know when the identification of Werckmeister III tuning was first
identified in history? Barbour used it, but the use of the copperplate
monochord to distinguish tunings may be only a modern invention. Does anyone know
of any earlier example of the usage of No. 3, or even No. 1 as others had it,
before Barbour?

Otherwise, it can be described as a modified meantone, a rather meaningless
identification. In Werckmeister's day the tuning had no name for
identification.

Johnny

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Anybody know when the identification of Werckmeister III tuning was
> first identified in history? Barbour used it, but the use of the
> copperplate monochord to distinguish tunings may be only a modern
> invention. Does anyone know of any earlier example of the usage
> of No. 3, or even No. 1 as others had it, before Barbour?

Well, certainly both Sorge and Marpurg attributed that same one of
C-G-D-A and B-F# (1/4 PC each) back to Werckmeister.

And according to Barbour's 1947 article "Bach and the Art of
Temperament" (Musical Quarterly 33:1, 1947), there was a 1925 article
"Akustik" by a K. E. Schumann also doing so. This 1947 article by
Barbour gives an appendix that includes "Werckmeister's 'correct'
temperaments" that he himself (Barbour) numbers from 1 to 3, and it's
#1 here.

In Barbour's 1948 article "Irregular systems of temperament" (JAMS
1:3), Barbour again called it "Werckmeister's First 'Correct'
Temperament". (On the same page, incidentally, Barbour offered an
absurd criticism of Marpurg's Temperament G: "In G the comma is
supposed to be divided into five equal parts, but 5 x 5 is 25! To
have come out even, Marpurg should have made the altered fifths 4.8
cents flat, instead of 5 cents." What, Marpurg used cents, years
ahead of his time?!)

Turning to Barbour's 1965-6 article "Temperatur und Stimmung" in MGG,
the article has more technical proofreados than his book did; really a
mess for an article that is barely over seven pages, crammed in.
Tables 11, 12, 13, 20, and 21 (at least) have printing errors, and I
haven't spent so much time checking the earlier pages where there
might be more. The Werckmeister temp given here is table 20, but the
B has a +1/4 superscript instead of a 0. And the text about this has
yet another howler: "In seiner bekanntesten werden die vier Quinten
C-G, G-D, D-A und H-Fis durch 1/3 Komma temperiert, die acht uebrigen
Quinten sind rein. Die beiden besten grossen Terzen erscheinen um 1/4
Komma zu hoch (390 C), und die drei schlechtesten sind pythagoraeisch
(408 C; s. Tab. 20)." Whoever typeset his article didn't exhibit much
care with numerals, giving 1/4 as 1/3. But anyway, that temperament
is not given any name here other than "bekanntesten" (most familiar).

Brad Lehman

Thanks, for getting back, Brad.

But it is not certain at all for Sorge. He described the 4 flat fifths but
he did not identify the prescription for tuning. He didn't say which fifths
were flatted.

What did Marpurg say?

Somehow I though Barbour was at the root of the identification(s). Didn't
expect it to be both ways, as Nos. I and III. Now, this 1925 K.E. Schumann
article in Akustik. Is this the first actual identification of the specific
scale?

This totally disables the Ortgies premise that there was no Werckmeister III
tuning in church organs because there is no evidence in any church records.
It didn't have a name.

Johnny

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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Anybody know when the identification of Werckmeister III tuning was
first
> identified in history? Barbour used it, but the use of the
copperplate
> monochord to distinguish tunings may be only a modern invention.

Well, I suppose if you want to call end of the 16th century "modern"
(Zarlino, Salinas, etc.), then yes, it is a modern invention.

>
> Otherwise, it can be described as a modified meantone, a rather
meaningless
> identification.

I don't see how you can call it a modified meantone, other than W.
himself said it was a fast way to convert a 1/4 meantone organ into a
circulating temperament (not to imply that he used the word
"circulating"). But just because the point of departure is meantone,
the basic structure of the temperamet is so utterly different that
calling it a modified meantone really destroys all useful meaning of
the term.

Which brings us to the second part of the above sentence. Actually,
the term "modified meantone" is quite useful and has a clear meaning,
provided you don't abuse it by applying it to things like Werckmeister
III. It simply means a temperament in which the basis is regular
meantone, but at some point the logic is abandoned by the introduction
of pure or wide fifths in order to smooth out the wolf fifth and wolf
thirds, like Werckmeister's continuo temperament, Rameau, D'Alembert,
and the broad family of French temperaments which Lindley has referred
to as "Ordinaire".

Ciao,

P

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

>
> This totally disables the Ortgies premise that there was no
Werckmeister III
> tuning in church organs because there is no evidence in any church
records.
> It didn't have a name.

I think that is disingenuous to say it "totally disables" Ibo's
assertion that there is no evidence for the application of WIII on
organs. If there is no evidence, there is no evidence. It could have
been referred to in a number of ways, even though it had no specific name.

Ciao,

P

> > This totally disables the Ortgies premise that there was no
> Werckmeister III
> > tuning in church organs because there is no evidence in any church
> records.
> > It didn't have a name.
>
> I think that is disingenuous to say it "totally disables" Ibo's
> assertion that there is no evidence for the application of WIII on
> organs. If there is no evidence, there is no evidence. It could have
> been referred to in a number of ways, even though it had no specific
name.
>

Just as a matter of protocol in reasoning, I have observed it's
awfully easy to confuse or conflate the credibility of several
different statements...all of which are attempts to "prove" a negative:

1. There exists no evidence for X.

2. I am omniscient and I know of no evidence for X, and therefore
there isn't any.

3. If any evidence for X exists, it is not in the format(s) I expect
to find, and therefore since I don't know of any, it doesn't exist.

4. In all the places I have looked, I have not found X, and I consider
myself thorough enough, so therefore X doesn't exist.

5. No evidence for X exists now, so therefore no evidence for X ever
could have existed but have been lost.

6. No compelling evidence for X that sufficiently convinces *me* is at
hand, and my hand is plenty thorough, as is my ability to discern
absolute truth, so therefore X could never have existed.

7. If X ever existed, its users surely would have written it down in
some manner that I would approve and recognize today; but no such
record is known to exist, and therefore X couldn't possibly have existed.

Usw.... Make up ten more, all fallacious along similar lines of
trying to prove a negative about something from another time and place.

Brad Lehman

How nice to hear from you Paul. Thanks to you I have read the Story of "A"
by Bruce Haynes. Our mutual friend Leslie Ross leant me her copy. Thanks
also for your response(s), though it should come as no surprise, we are mostly
in disagreement.

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=hmJG00nHT5FCEwpuDXQI39GW-p3kQFf1KvyFlFILXC9bnpCIgs3kQG6VKzplg7WLOc5
innhS6cmuG8yPsdmjJA) , Afmmjr@... wrote:
>
> Anybody know when the identification of Werckmeister III tuning was
first
> identified in history? Barbour used it, but the use of the
copperplate
> monochord to distinguish tunings may be only a modern invention.

Paul: Well, I suppose if you want to call end of the 16th century "modern"
(Zarlino, Salinas, etc.), then yes, it is a modern invention.

Johnny: You misunderstand; I am asking when "Werckmeister III tuning" was
first identified by its order on the copperplate monochord of 1691. It's a
new question.

>
> Otherwise, it can be described as a modified meantone, a rather
meaningless
> identification.

Paul: I don't see how you can call it a modified meantone, other than W.
himself said it was a fast way to convert a 1/4 meantone organ into a
circulating temperament (not to imply that he used the word
"circulating"). But just because the point of departure is meantone,
the basic structure of the temperamet is so utterly different that
calling it a modified meantone really destroys all useful meaning of
the term.

Johnny: This is a little piece in a bigger story. You just gave a reason
from W. himself. Also, you gave us an equation. Does this look right?

modified meantone = point of departure
structure difference

Perhaps the term modified meantone is useful to your harpsichord business,
but it doesn't work for me at all. In the categories I see, WIII is a
modified meantone. How different do you believe it is in terms of structure? You
wouldn't be disingenuous about this, would you?

Paul: Which brings us to the second part of the above sentence. Actually,
the term "modified meantone" is quite useful and has a clear meaning,
provided you don't abuse it by applying it to things like Werckmeister
III. It simply means a temperament in which the basis is regular
meantone, but at some point the logic is abandoned by the introduction
of pure or wide fifths in order to smooth out the wolf fifth and wolf
thirds, like Werckmeister's ...

Johnny: This argument does not hold up. WIII is a natural consequence of
meantone with the precise purpose of escaping wolves, a modified meantone

Surely, after you have your coffee perhaps, no one on this List should feel
censured in questioning the meaning of terms, especially when the term for
WIII tuning simply did not exist before the 20th Century.

Choos,

Johnny

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Dear Paul,

Could have is the operative here. Ibo, as a musicologist, looks for paper
evidence, and you seem to trust his strong assertions. His opinion clearly
twisted Kerala J. Snyder in her 2007 revised biography of Dieterich Buxtehude.

Not incidentally, if you can every compare Armin Schoof playing Buxtehude's
"Te Deum" in WIII on the small Stellwagen organ in St. Jacobi with "Te Deum"
on the CD provided by Snyder with her book the difference is monumental. Ibo
has shamed Kerala into substituting ET for Buxtehude. Awful.

--- In _tuning@yahoogroups.com_
(/tuning/post?postID=n0AMeyQVa8GJK1iucYMNwmvtyRUIRFDwLOHS_UL0E87G7xo1lGzsye79FkpRnZXpcnx
4XOPNyMvCfpxARmTyfA4) , Afmmjr@... wrote:
>

>
> This totally disables the Ortgies premise that there was no
Werckmeister III
> tuning in church organs because there is no evidence in any church
records.
> It didn't have a name.

Paul: I think that is disingenuous to say it "totally disables" Ibo's
assertion that there is no evidence for the application of WIII on
organs. If there is no evidence, there is no evidence. It could have
been referred to in a number of ways, even though it had no specific name.
Ciao, P"

Johnny: No paper evidence for a tuning that was published without a name.
Damn it man, use your imagination for a minute. That's all I am asking.
There are all manner of evidence, no?

Sorge came closest to describing WIII by pointing out there only 4 fifths
quarter of a comma flat, the rest pure. He was the closest, but this is long
after Bach's career was in motion.

choos,

Johnny

BTW, how

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--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
>
> Just as a matter of protocol in reasoning, I have observed it's
> awfully easy to confuse or conflate the credibility of several
> different statements...all of which are attempts to "prove" a negative:
>
> 1. There exists no evidence for X.
>
> 2. I am omniscient and I know of no evidence for X, and therefore
> there isn't any.

[etc]

Me thinks it's more a case of personal ax grinding than any real
difference in logical "protocol", whatever that might mean. To wit:

> Usw.... Make up ten more, all fallacious along similar lines of
> trying to prove a negative about something from another time and >place.

You are trying to score some sort of logic point by stating the
obvious problem of what we call "knowledge", Brad. A negative can
NEVER be "proved" or "known", since the very nature of "proof" is
evidence, and something which does not exist or did not exist by
definition leaves no evidence. Ergo there can be no proof of its
nonexistence. So what else is new? Ho-hum....

But Johnnie's assertion was something altogether different. He posited
that the mere fact that Werckmeister III had no specific name totally
invalids Ibo´s assertion that it was never set on organs (I'm not even
sure he made that particular assertion) because he found no reference
to it in extent organ repair documents. In other words, because a
thing hath not a name, it be impossible to refer to it in ANY way;
therefore the resulting absence of any occurrence of "the name" cannot
be construed as an indication of said thing's nonexistence. This is
simply logical not valid.

As the Bard put it:

A Rose by any other name would smell as sweet.

After all, there is always more than one way to remove the outermost
layer of that small domesticated 4 legged mammal known for its skill
at catching mice, its tendency to sleep in warm spots, and a marked
preference for all manner of dairy products... be it in or out of the bag.

Ciao,

P

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> How nice to hear from you Paul. Thanks to you I have read the
Story of "A"
> by Bruce Haynes. Our mutual friend Leslie Ross leant me her copy.

Do give her my regard! Glad you enjoyed Bruce's book.

Thanks
> also for your response(s), though it should come as no surprise, we
are mostly
> in disagreement.

it apears as though that may be the case. As the I Ching says, No Blame.
>
>
>
> Johnny: You misunderstand; I am asking when "Werckmeister III
tuning" was
> first identified by its order on the copperplate monochord of 1691.
It's a
> new question.

Ok, I get now what you were after.
>
>
> >
> > Otherwise, it can be described as a modified meantone, a rather
> meaningless
> > identification.
>
>
> Johnny: This is a little piece in a bigger story. You just gave a
reason
> from W. himself. Also, you gave us an equation. Does this look right?
>
> modified meantone = point of departure
> structure difference

Very coarsely. Of course, the word "modified" means both difference
and similarity. Which is more significant? I would posit that the
greater the former, the less applicable the word "modified". Rather
like the diference between grand ravalment and petit ravalment. Which
would you call a "modified Ruckers"? Perhaps neither?
>
> Perhaps the term modified meantone is useful to your harpsichord
business,
> but it doesn't work for me at all. In the categories I see, WIII is a
> modified meantone. How different do you believe it is in terms of
structure?

Very much so, to wit:
>
> Johnny: This argument does not hold up. WIII is a natural
consequence of
> meantone with the precise purpose of escaping wolves, a modified
meantone

I disagree. In order to merely "escape wolves", Werckmeister need only
do what he did in his continuo temperament. Actually, he could have
saved a lot more time and money had he simply tweaked the pipes for F,
G, D, A, E, B, F# by the max allowed for by cone tuning, reducing the
tempering of the fifths they produce as much as possible, leaving the
others to be either cut or lengthened to follow a typical scheme of
pure or slightly larger than pure fifths to smooth out the wolves.

Obviously, he was more concerned with rationally eliminating the
Pythagorean comma, which is generally considered to be the essence of
what differentiates circulating or "Well" temperaments from meantones.

Actually, between his continuo temperament and Copperplate III (to use
the modern invention), there is no difference in "escaping wolves", at
least not as long as you are using the modern invention of calling the
fifths the wolves and not the thirds.

;-)

Seriously, though, I consider these two points to be the essence of
ANY meantone, modified or not:

(1) A basis of an unbroken chain of consistently tempered fifths,
located in the natural keys, whose degree of tempering is specified
(either numerically or qualitatively) by the quality of the major
third that four of them produce. It is precisely this unbroken chain
from whence comes the name, for only when there are four fifths of the
same size in a row is the natural and unavoidable result a whole
"tone" which is the geometric "mean" of the major third.

(2) The adherence to a long uninterrupted cycle of such fifths causes
a cumulative over-compensation relative the Pythagorean comma (what
Jorgenson rather amusingly calls "harmonic waste"). In regular
meantones, it is concentrated in 1 wold fifths, 4 wolf major thirds
and 3 wolf minor thirds. In modified meantones, the chain is shorter
and the wolves are diced up more or less so that they seem merely
misbehaved puppies who piss on the carpet and chew the drapes rather
than gnawing off your leg as real wolves do.

Note that none of the copperplate temperaments exhibit either of
these. IV and V do have over-compensation, but it is not produced by
contiguous fifths. Most notably, the tone C-D in Copperplate III is
NOT the geo mean of C-E, and therefore in my book cannot be called any
sort of meantone. Of the three, one could argue that IV is a meantone
derivative, because all he's really done is taken a garden variety 1/6
comma modified meantone and concentrated the total tempering of two
adjacent fifths into every other fifth. Therefore, the tone generally
IS the mean, either through the pattern of t-p-t-p or p-t-p-t.

>
> Surely, after you have your coffee perhaps, no one on this List
should feel
> censured in questioning the meaning of terms,

Well, it's always healthy to question terminology, coffee or no. And
in the absence of some international oversight committee, there may be
some disagreement of terms. Generally, though, there is an agreed-upon
meaning which a large body of those who use the term would recognize
instantly, as in the case with "pure", Brad's aberration not
withstanding. But in any case, one should be able to defend the logic
behind their interpretation. Ball's in your court.

>especially when the term for
> WIII tuning simply did not exist before the 20th Century.

Wrong. One could argue that "III", "Werckmeister's 3rd", or "Erste
richtige Temperature" or some such have all "existed" since 1691.

BTW, its a temperament, not a tuning.

Ciao,

P

Hello Paul,

I will pass on your "hello" to Leslie.

Now that we are getting closer to being on the same page...I must confess; I
have no need for this term, "modified meantone." It wouldn't be the first
time that I did not connect with a particular term. (Pentatonic really
bothers me, for instance.) Ever happen to you...regarding a term?

Your definition for modified meantone was very much appreciated, but seemed
a bit overwrought...a bit of a wrestle. With a different life experience I
see only meantone being modified. But I can't bite because I have no use for
the term. However it is spun, it has never in my entire microtonal life ever
come up. Really. Maybe in the small realm of harpsichord builders and
tuners it is a true buzz term. I just don't feel it.

Paul: I disagree. In order to merely "escape wolves", Werckmeister need only
do what he did in his continuo temperament.

Johnny: Your statement above is not based on Werckmeister's real world of
organ improvisation in Quedlinburg and Halberstadt that required a full circle
of usable keys to do business. It was all about escaping the wolves.

Paul: Obviously, he was more concerned with rationally eliminating the
Pythagorean comma, which is generally considered to be the essence of
what differentiates circulating or "Well" temperaments from meantones.

Johnny: With all due respect, he couldn't care less about the comma.
Werckmeister III is all about escaping wolves. Another small point, what is
"generally considered" has not been very reliable sometimes. As you know, I am
working with some new categories. For example, I want to always distinguish
between irregular tuning that is not a full circle, and irregular tuning that is
in a full circle. To that effect, irregular tuning that is a full circle is
the definition of well temperament. Logically, there is now a complete
difference between irregular tuning and well temperament.

By your definition, I can see why you protest against WIII being considered
a modified meantone. And I thank you for your evaluations. It helps to get
feedback. But the words "modified meantone" as with other List discussions
that argue terms still mean little but a pedigree, often controversial, and
relatively meaningless to the music listener.

I suspect Werckmeister would have been surprised that his natural
consequence of meantone would not be considered a modification. The ball in my court
is a book I am writing, some of it a reevaluation of historic general
consideration.

>especially when the term for
> WIII tuning simply did not exist before the 20th Century.

Paul: Wrong. One could argue that "III", "Werckmeister's 3rd", or "Erste
richtige Temperature" or some such have all "existed" since 1691.

Johnny: You are speaking out of your hat here. Where is it? Who said any
of the descriptions you suggested? No one. Kuhnau is reputed to have said
"Werckmeister's tuning."

Paul: BTW, its a temperament, not a tuning. Ciao, P

Johnny: Yes, this is the ongoing joke. As we all know, these terms have
been interchangeable for a very long time.

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> Sorge came closest to describing WIII by pointing out there only 4
fifths
> quarter of a comma flat, the rest pure. He was the closest, but
this is long
> after Bach's career was in motion.

Not that Sorge's citation of Werckmeister necessarily had anything to
do with Bach, of course! That remains to be shown. Bach's "career
was in motion" by the time Sorge was 4 years old. Bach was 18 years
older than Sorge. Sorge did the writing he did when he was old enough
and competent enough to do so, in his own career and according to his
own interests.

Why should this have any correlation with Bach's, other than the
famous link where Sorge asserted that the (aged) Bach said a regular
1/6 was inadequate for music? Do you have some definite evidence in
which Sorge himself made any connection between Werckmeister's
temperament(s) and Bach's practice(s)?

Brad Lehman

Hi Brad,

Sorge studied with Bach. An old Grove dictionary paints Sorge as a real
sourpuss. But none of this has anything to do with the price of eggs.

Sorge's name came up because he came closest to identifying Werckmeister
with what we now call Werckmeister III tuning, although it could have been
better. It was not prescriptive.

It indicates as well that Werckmeister was not an advocate to equal
temperament at the end. Or not, as it is certainly third hand information long after
Werckmeister had died. It is certainly a curiosity. But the big point for
my posting is that it was near impossible to impossible to put the tuning
down in writing without saying something vague like "Werckmeister's tuning."

best, Johnny

> Sorge came closest to describing WIII by pointing out there only 4
fifths
> quarter of a comma flat, the rest pure. He was the closest, but
this is long
> after Bach's career was in motion.

Not that Sorge's citation of Werckmeister necessarily had anything to
do with Bach, of course! That remains to be shown. Bach's "career
was in motion" by the time Sorge was 4 years old. Bach was 18 years
older than Sorge. Sorge did the writing he did when he was old enough
and competent enough to do so, in his own career and according to his
own interests.

Why should this have any correlation with Bach's, other than the
famous link where Sorge asserted that the (aged) Bach said a regular
1/6 was inadequate for music? Do you have some definite evidence in
which Sorge himself made any connection between Werckmeister's
temperament(s) and Bach's practice(s)?

Brad Lehman

**************Ideas to please picky eaters. Watch video on AOL Living.
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--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
>
> Hello Paul,
>
> I will pass on your "hello" to Leslie.
>
> Now that we are getting closer to being on the same page...I must
confess; I
> have no need for this term, "modified meantone." It wouldn't be
the first
> time that I did not connect with a particular term. (Pentatonic
really
> bothers me, for instance.) Ever happen to you...regarding a term?

All the time. It really drives me around the bend, for instance, when
people use the word "scale" to mean a temperament, a tuning, or a
whole gamut (my preferred term for all the notes taken together), like
19-tET, etc. For me, a scale is only that small selection from the
gamut which is used to make music, like major, minor, dorian (church
modes), enharmonic (Greek modes), or the names of specific maqams, for
example. Whenever somebody says "the Pythagorean scale" I always say,
"Which one?"

>
> Your definition for modified meantone was very much appreciated,
but seemed
> a bit overwrought...a bit of a wrestle. With a different life
experience I
> see only meantone being modified. But I can't bite because I have
no use for
> the term. However it is spun, it has never in my entire microtonal
life ever
> come up. Really. Maybe in the small realm of harpsichord builders
and
> tuners it is a true buzz term. I just don't feel it.

For me, the essence is expressed in Rameau's tuning directions, where
he tells yo to start "the division", which is tuning a row of four
narrow fifths such that yo arrive at a pure third, and you carry on
until "a certain point" where you abandon "the division".
Werckmeister's instruction is essentially a German translation of the
same thing. The point being that instruction to set meantone would
have been exactly the same, except carrying on with "the division".
>
>
> Paul: I disagree. In order to merely "escape wolves", Werckmeister
need only
> do what he did in his continuo temperament.
>
> Johnny: Your statement above is not based on Werckmeister's real
world of
> organ improvisation in Quedlinburg and Halberstadt that required a
full circle
> of usable keys to do business. It was all about escaping the wolves.

Well, temperament is as temperament does, and if yo push
Werckmeister's continuo temperament to the limit of what he says, you
arrive at something that is very close to CopperplateIII. It actually
has less Pythaogrean thirds, of corse at the slight cost to the purity
of the "good"thirds. But everything is plenty usuable, and there is
more variation because you don't have that long chain of pure fifths,
which has always been my complaint about CPIII.
>
> Paul: Obviously, he was more concerned with rationally eliminating the
> Pythagorean comma, which is generally considered to be the essence of
> what differentiates circulating or "Well" temperaments from meantones.
>
> Johnny: With all due respect, he couldn't care less about the comma.

Funny, then, that he went to all that trouble of working out the
string lengths dividing the P comma. Oh well, one of those quirky
things about history, I guess.

Funny also how in his continuo temperament, he specifically says in
this particular instance he doesn't want to talk about this or that
comma, because he wants to keep it simple for the beginning player.
Implying, of course, that in other instances, directed toward a more
sophisticated audience, he DOES deal with this or that particular comma.

> Werckmeister III is all about escaping wolves. Another small
point, what is
> "generally considered" has not been very reliable sometimes.

Well, mixing what is reliable and what is generally undrstood is
mixing apples and oranges. I know that it is totaly unreliable that
Bach wrote the WTC for equal temperament, yet there is STILL a large
number of people who tink it is so, so when speaking to the Great
Unwashed, I know I have to be careful about what is generally understood.

As you know, I am
> working with some new categories. For example, I want to always
distinguish
> between irregular tuning that is not a full circle, and irregular
tuning that is
> in a full circle. To that effect, irregular tuning that is a full
circle is
> the definition of well temperament. Logically, there is now a
complete
> difference between irregular tuning and well temperament.

Well temperament. Another term that drives me around the bend,
especially since I speak German. What a bogus term, invented by a
bunch of dummies who don't know the difference between an adjective
and an adverb.

That much aside, I frankly don't know what the general perception is
about the meaning of well temperament. I always tell my students not
to use it, and everybody else seems foggy on the notion. "You know,
like Werckmeister, or Vallotti/Young, or Kirnberger" is generally the
level of sophistication I encounter.

>
> By your definition, I can see why you protest against WIII being
considered
> a modified meantone. And I thank you for your evaluations. It
helps to get
> feedback. But the words "modified meantone" as with other List
discussions
> that argue terms still mean little but a pedigree, often
controversial, and
> relatively meaningless to the music listener.

I disagree, since many modified meantones SOUND completely meantoney
in the home keys. You only notice it's NOT meantone when the music
wanders into zones normally populated by wolves, or when harmonies
that ought to have pure thirds end up have somewhat wide thirds.
>
> I suspect Werckmeister would have been surprised that his natural
> consequence of meantone would not be considered a modification.

Who knows? I suspect W knew what he was doing, and he knew he was
doing something different. But it is only you and me suspecting.

The ball in my court
> is a book I am writing, some of it a reevaluation of historic general
> consideration.
>
>
> >especially when the term for
> > WIII tuning simply did not exist before the 20th Century.
>
> Paul: Wrong. One could argue that "III", "Werckmeister's 3rd", or
"Erste
> richtige Temperature" or some such have all "existed" since 1691.
>
> Johnny: You are speaking out of your hat here. Where is it? Who
said any
> of the descriptions you suggested? No one.

Umm, Werckmeister himself, right there on the famous Copperplate,
upper right hand corner: "III.IV.V. sint [sic] richtige Temperaturen".

Interesting, that, eh? Who ever takes poor old Mr W seriously with IV
and V? Nobody. Oh well, I guess everybody wants to save a scheckel or
two when it's time to call the organ tuner round to "modifiy" the
meantone, eh?

;-)

Ciao,

P

> Sorge studied with Bach. An old Grove dictionary paints Sorge
> as a real sourpuss. But none of this has anything to do with
> the price of eggs.

"Sorge studied with Bach" exactly when and where, please, and
according to what source? Sorge at age 18, 1721, took a job as court
organist at Lobenstein...and he kept it until his death in 1778. When
did he go and study with Bach?

Yes, both these gentlemen were inducted into Mizler's society within a
month of each other in 1747, and Sorge certainly venerated Bach
(perhaps even before that), and Sorge dedicated some of his own music
to Bach...but that's not the same thing as a direct teacher/pupil
relationship.

Brad Lehman

It would be a mistake to reason that, if something was never talked
about *but did not have a name*, then it is all the more likely to
have actually happened. Perhaps 17th century Germans didn't have a
name for dipping their feet in molasses, painting their eyebrows blue
and dancing the rhumba either, but that doesn't make it more likely
that they did so. One has to have some positive indication.

Regardless of that, I think people could very easily have found a name
for what they were doing if they did set a temperament using
Werckmeister's recipes. We assume that organbuilders and tuners did
sometimes have to talk to other people and didn't dwell in a
perpetually nonverbal world of ratios and monochord lengths.
Perhaps something like 'The organ was tuned not in the old method with
8 pure thirds, but rather according to a new scheme of Hr.
Werckmeister' (etc. etc.).

If indeed these new temperaments did find an increasing range of
application, wouldn't we expect to see something like this somewhere
sometime? [You could call this a Hypothesis...]

Now, if in however many dozens or hundred of historical documents you
never once find anything similar [Test...?] and since we know that
Werckmeister continues in every publication to complain about
organbuilders who fail to pay attention to his temperaments, doesn't
it begin to mean something?

We can never prove that *no-one* in Baroque-era German ever dipped his
feet in molasses, painted his eyebrows blue and started to dance the
rhumba. But we have a pretty good idea as to whether or not this
became a widespread practice. Unless of course it was done by a secret
society to which every town clerk in Thuringia belonged, which would
meet in Halberstadt on the first Friday in April and record its
activities in a small, leather-bound volume that unfortunately was
destroyed in the Second World War.

So, by certain standards of historical reasoning, the Blue-Eyebrow
Molasses Rhumba theory remains intact ... indeed the very lack of
evidence is proof of how obsessively the Terpsichorean Thuringian Town
Clerks protected their dark secrets.
~~~T~~~

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, Afmmjr@ wrote:
> >
> > This totally disables the Ortgies premise that there was no
> Werckmeister III
> > tuning in church organs because there is no evidence in any church
> records.
> > It didn't have a name.
>
> I think that is disingenuous to say it "totally disables" Ibo's
> assertion that there is no evidence for the application of WIII on
> organs. If there is no evidence, there is no evidence. It could have
> been referred to in a number of ways, even though it had no specific
name.
>
> Ciao,
>
> P
>

Hi Brad:

That's what I mean about nothing to do with the price of eggs, etc. Bach
and Sorge were "friends" according to Mark Lindley. The old Grove says: "Sorge
was unfortunately a very conceited man." Brad, if he did study with Bach,
do you think he would admit it, being so conceited and all? Might we say he
studied from J.S. Bach from a distance? : ) J

=========================
Sorge studied with Bach. An old Grove dictionary paints Sorge
> as a real sourpuss. But none of this has anything to do with
> the price of eggs.

"Sorge studied with Bach" exactly when and where, please, and
according to what source? Sorge at age 18, 1721, took a job as court
organist at Lobenstein...and he kept it until his death in 1778. When
did he go and study with Bach?

Yes, both these gentlemen were inducted into Mizler's society within a
month of each other in 1747, and Sorge certainly venerated Bach
(perhaps even before that), and Sorge dedicated some of his own music
to Bach...but that's not the same thing as a direct teacher/pupil
relationship.

Brad Lehman

**************Ideas to please picky eaters. Watch video on AOL Living.
(http://living.aol.com/video/how-to-please-your-picky-eater/rachel-campos-duffy/
2050827?NCID=aolcmp00300000002598)

Hi Tom,

How nice to receive your poetic post. Maybe a few reactions.

Tom: It would be a mistake to reason that, if something was never talked
about *but did not have a name*, then it is all the more likely to
have actually happened. Perhaps 17th century Germans didn't have a
name for dipping their feet in molasses, painting their eyebrows blue
and dancing the rhumba either, but that doesn't make it more likely
that they did so. One has to have some positive indication.

Johnny: By your thinking Andreas Werckmeister didn't exist. There is no
image of him so I have no real evidence that he existed. Jesus, too.

Tom: Regardless of that, I think people could very easily have found a name
for what they were doing if they did set a temperament using
Werckmeister's recipes.

Johnny: Maybe you thought wrong. They did not find a name for what they
were doing. Bach did not have a name for what he was doing. Werckmeister III,
being the first favorite in 1681 was the only thing of its kind....just no
name. The hypothesis makes no sense in light of how the orchestra tuning had
no name either and so went undiscussed.

Tom: Now, if in however many dozens or hundred of historical documents you
never once find anything similar [Test...?] and since we know that
Werckmeister continues in every publication to complain about
organbuilders who fail to pay attention to his temperaments, doesn't
it begin to mean something?

Johnny: It means we don't see things the same way. Werckmeister complained
because the changes were not fast enough. This is a common complaint made
by pioneers, of which Werckmeister is one.

best, johnny

- In _tuning@yahoogroups.com_
(/tuning/post?postID=r7fB5QeJN0XrAa10d_D400fFGCOKUqkpuSF6GMelPenBysHOBNt51PsdW3ttFKYb4qwyx
_HtgY0i5PHGMRW7) , "Paul Poletti" <paul@...> wrote:
>
> --- In _tuning@yahoogroups.com_
(/tuning/post?postID=r7fB5QeJN0XrAa10d_D400fFGCOKUqkpuSF6GMelPenBysHOBNt51PsdW3ttFKYb4
qwyx_HtgY0i5PHGMRW7) , Afmmjr@ wrote:
> >
> > This totally disables the Ortgies premise that there was no
> Werckmeister III
> > tuning in church organs because there is no evidence in any church
> records.
> > It didn't have a name.
>
> I think that is disingenuous to say it "totally disables" Ibo's
> assertion that there is no evidence for the application of WIII on
> organs. If there is no evidence, there is no evidence. It could have
> been referred to in a number of ways, even though it had no specific
name.
>
> Ciao,
>
> P
>

**************Ideas to please picky eaters. Watch video on AOL Living.
(http://living.aol.com/video/how-to-please-your-picky-eater/rachel-campos-duffy/
2050827?NCID=aolcmp00300000002598)

Is not equal temperament "modified Werckmeister"?

Is not meantone "modified just intonation"?

Is not Pythagorean "modified just intonation"?

J

**************Ideas to please picky eaters. Watch video on AOL Living.
(http://living.aol.com/video/how-to-please-your-picky-eater/rachel-campos-duffy/
2050827?NCID=aolcmp00300000002598)

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Is not equal temperament "modified Werckmeister"?
>
> Is not meantone "modified just intonation"?
>
> Is not Pythagorean "modified just intonation"?
>
> J
>
I'd be willing to consider all of the above. however, in the lack of
any supporting argument, these hypothetical postulations remain merely
dust in the wind.

Go for it! Here's your Big Moment, Johnny!

;-)

Ciao,

P

O the witty merry-go-round sarcasm! Will it never end?

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2008 Pazartesi 0:46
Subject: [tuning] Re: Werckmeister III tuning

> --- In tuning@yahoogroups.com, Afmmjr@... wrote:
> >
> > Is not equal temperament "modified Werckmeister"?
> >
> > Is not meantone "modified just intonation"?
> >
> > Is not Pythagorean "modified just intonation"?
> >
> > J
> >
> I'd be willing to consider all of the above. however, in the lack of
> any supporting argument, these hypothetical postulations remain merely
> dust in the wind.
>
> Go for it! Here's your Big Moment, Johnny!
>
> ;-)
>
> Ciao,
>
> P
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> O the witty merry-go-round sarcasm! Will it never end?

It wasn't intended to be sarcastic, Oz, I really wanted Johhny to
explain his thoughts. I mean, I could say something like "Is not
Goerge Bush a modern Mussollini?", and I'm sure lots of people these
days would agree with me instantly. But I haven't really said anything
at all, have I? So what would they be agreeing to?

To argue against Johnny's hypothetical equations, I would say that the
word "modified" in any application has to indicate a basic
characteristic which remains unchanged in some manner AND a variation
in form which does not go so far as to create something completely
different. Thus genetically modified corn can only be called such as
long as it doesn't begin to look like cabbage or taste like strawberries.

A temperament or tuning can be classified in several ways:

(1) the basic acoustical intent, i.e. producing pure thirds, closing
the circle, or as Johnny likes to say, avoiding wolves - or a
combination of more than one intent

(2) a basic structural logic, i.e. distributing the Pythagorean comma,
distributing the Syntonic comma, not dealing with any comma, regular
distribution, irregular distribtuion, etc.

(3) a historical development

(4) whether it is a tuning or a temperament

That's all I can think of at the moment, maybe there are more.

I suppose one could argue the original/modified dichotomy in regards
to any one aspect, but I would posit that the term becomes the more
convincing the more different aspects you can point to.
> > >
> > > Is not equal temperament "modified Werckmeister"?

I don't see how. I assume you mean WIII and not IV or V, but in
regards to them all you could say the point is to make all keys usable
will keeping the natural keys purer than the accidental keys, and the
logic is dividing the Pythagorean comma in a small number of parts
which distributed according to a very irregular scheme, including the
over-distribution which requires the introductin of larger than pure
fifths for correction. ET, on the other hand, intends to make ALL keys
exactly the same, and it does so by distributing the Pythagorean comma
in the most regular method imaginable, and not allowing any
overcompensation t all. Other than the fact that they are both Pyth
comma systems, I don't see any grounds for arguing that the one is a
modified form of the other; for me they are cabbage and strawberries.
> > >
> > > Is not meantone "modified just intonation"?

No. The essence of any form of JI is pure intervals. No prisoners
taken. Those impure intervals which inevitably result are like
collateral casualties, the unfortunate victims of the necessity of
achieving a Higher Case, rigidly following an extremist ideology. It
is a Tuning. Meantone, on the other hand, in any of its various forms,
is a Temperament, and its very essence lies in the idea of compromise.
It's basic approach is the purposeful DEtuning of certain important
consonances in order to arrive at a pure version or near pure (another
compromise) version of other important consonances. JI does not
include an purposeful detuning of anything; some intervals
accidentally end up detuned, but their detuning is an inherent part of
neither the logic nor the methodology.

Actually, I would say that all Tunings are diametrically opposed to
all Temperaments in every possible way.
> > >
> > > Is not Pythagorean "modified just intonation"?
> > >
No. Pythagorean is a subclass of JI. It is 3-limit JI, or to be true
to the original Pythagoreans, it is 4-limit JI in keeping with the
precepts of the Tetrakyts. 5-limit and 7-limit are also a subclasses
of JI. Saying that Pythagorean is modified JI is like saying a cat is
a modified mammal. You're confusing levels in the hierarchical
classification system.

Now, about modified meantones. All meantones use an unbroken chain of
purposely detuned fifths, the size of which is determined by the
desire to arrive at a consistently pure or close to pure major third.
The resulting gap is irrelevant because the resulting bad thirds (the
original wolves) are not intended to be used, except perhaps for
dramatic effect. The temperaments I call modified meantones generally
exhibit a structure which is mostly meantone with a slight variation
in that there is exactly the same long chain intentionally tempered
fifths, the size of which is determined by the desire to arrive at a
consistently pure or close to pure major third, but with the inclusion
of several fifths which do not adhere to this principle, applied to
reduce the harshness of the wolf thirds, making them usable without
the listener cringing, wherein lies the modification both in logic and
intent.

I could also say that in the case of Preatorius, the logic AND intent
are both literally explained as modifications of regular meantone. One
could argue the same for Schlick. Rameau also describes how at a
certain point, one deviates from "the division", i.e. the normal
meantone scheme of dividing the S comma among four consecutive fifths.
So there we've got two and maybe three original sources which say
start with meantone (admittedly without using that modern word) but
modify it at a certain point. Werkmeister says nothing of the sort in
regards to any of the 3 copperplate "richtige temperaturen"; they are
created anew.

On the other hand, his instructions for the continuo temperament can
quite easily be construed to be a deviation from a meantone scheme, in
that the tuner is told to temper ALL of the primary fifths by the same
amount so as to arrive at a certain consistent quality of "good" major
third. This logic is consistently adhered to until the point at which
one modifies it to avoid the appearance of wolves, which is another
thing he literally says in the form of wanting to arrive at
multifunctional thirds produced by the accidentals, which is THE
historical meaning of "avoiding wolves".

That's my take on it. Now I'd be interested in Johhny's.

Go for it, man!

Ciao,

P

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

Thoughts over lunch about "modified" tempering systems...

For me, the final clincher is, can you actually arrive at the new
temperament by practically "modifying" the original temperament? In
other words, suppose someone had already set a beautiful, flawless 1/4
regular meantone on a instrument. Could I go and very quickly, with a
minimum of retuning, say only retouching a few notes, "modify" the
existing temperament so as to arrive at one or another of the
temperaments which I call "modified meantones"? The answer is clearly
yes, as long as it is one of those based on 1/4 comma mean (like
Rameau). The same holds try for Werckmeister's modified meantone (the
1698 continuo temperament) if the instrument has been tuned in any
regular meantone milder than 1/5 comma. In all cases, one only need
tweak a small handful of fifths.

> Is not equal temperament "modified Werckmeister"?

The same cannot be said for "modifying" Werckmeister III, IV, or V so
as to produce Equal, at least not if you are adhering to the
historical practice of keeping C as the unmoving reference (and I have
to say I don't think any other approach has any relevance to the
discussion, as there is no doubt that C was THE starting point for
Werckmeister, as well as many others, including Neidhardt and Sorge,
just to name a few). The fact the tempering is always heavily
concentrated in a small number of fifths on the right half of the
circle mean you are going to have to do a lot of pushing things around
before you can even beginning to reset anything. In fact, not one
single note other than C can be left in its original position. You may
as well chuck the whole thing out and start over again from C. I fail
to see how such a drastic alteration can be viewed as a "modification".
>
> Is not meantone "modified just intonation"?

Exactly the same argument holds here. The only notes which need no
modifying are C and E. ALL of the rest require alterations, and their
JI positions are of no assistance to arriving at their new positions.
In fact, the usual "Just Intonation" of the diatonic scale doesn't
even begin to address the location of the sharps. Once again, except
for the pure third on C-E, you're no worse off if the instrument is
completely out-of-tune when you begin.

Anyway, curious about your logic.

Ciao,

P

newbie question: Are some people here are using the
terms temperament and tuning in a more precise way
than usual? If I Google "temperament definitions", I
get:

quote:

A way of tuning a diatonic scale to produce particular
effects. See the entries for equal and meantone
temperaments and just tuning.
www.hibberts.co.uk/glossary.htm

1. Term denoting a system of tuning in which the
various intervals are tempered or adjusted. The errors
inherent in the chromatic scale of twelve half-steps
are distributed among the intervals in such a way that
each interval has a small error but none sounds
offensive. 2. ...

http://www.google.com/search?hl=en&defl=en&q=define:temperament&sa=X&oi=glossary_definition&ct=title

So, all temperaments are tunings, but not all tunings
are temperaments? (Partch scale is a tuning but not a
temperament)
and if you called Valotti a "tuning" it wouldn't be
*wrong*, merely less precise?

--- Paul Poletti <paul@polettipiano.com> wrote:

> --- In tuning@yahoogroups.com, "Ozan Yarman"
> <ozanyarman@...> wrote:
> >
> > O the witty merry-go-round sarcasm! Will it never
> end?
>
> It wasn't intended to be sarcastic, Oz, I really
> wanted Johhny to
> explain his thoughts. I mean, I could say something
> like "Is not
> Goerge Bush a modern Mussollini?", and I'm sure lots
> of people these
> days would agree with me instantly. But I haven't
> really said anything
> at all, have I? So what would they be agreeing to?
>
> To argue against Johnny's hypothetical equations, I
> would say that the
> word "modified" in any application has to indicate a
> basic
> characteristic which remains unchanged in some
> manner AND a variation
> in form which does not go so far as to create
> something completely
> different. Thus genetically modified corn can only
> be called such as
> long as it doesn't begin to look like cabbage or
> taste like strawberries.
>
> A temperament or tuning can be classified in several
> ways:
>
> (1) the basic acoustical intent, i.e. producing pure
> thirds, closing
> the circle, or as Johnny likes to say, avoiding
> wolves - or a
> combination of more than one intent
>
> (2) a basic structural logic, i.e. distributing the
> Pythagorean comma,
> distributing the Syntonic comma, not dealing with
> any comma, regular
> distribution, irregular distribtuion, etc.
>
> (3) a historical development
>
> (4) whether it is a tuning or a temperament
>
> That's all I can think of at the moment, maybe there
> are more.
>
> I suppose one could argue the original/modified
> dichotomy in regards
> to any one aspect, but I would posit that the term
> becomes the more
> convincing the more different aspects you can point
> to.
> > > >
> > > > Is not equal temperament "modified
> Werckmeister"?
>
> I don't see how. I assume you mean WIII and not IV
> or V, but in
> regards to them all you could say the point is to
> make all keys usable
> will keeping the natural keys purer than the
> accidental keys, and the
> logic is dividing the Pythagorean comma in a small
> number of parts
> which distributed according to a very irregular
> scheme, including the
> over-distribution which requires the introductin of
> larger than pure
> fifths for correction. ET, on the other hand,
> intends to make ALL keys
> exactly the same, and it does so by distributing the
> Pythagorean comma
> in the most regular method imaginable, and not
> allowing any
> overcompensation t all. Other than the fact that
> they are both Pyth
> comma systems, I don't see any grounds for arguing
> that the one is a
> modified form of the other; for me they are cabbage
> and strawberries.
> > > >
> > > > Is not meantone "modified just intonation"?
>
> No. The essence of any form of JI is pure intervals.
> No prisoners
> taken. Those impure intervals which inevitably
> result are like
> collateral casualties, the unfortunate victims of
> the necessity of
> achieving a Higher Case, rigidly following an
> extremist ideology. It
> is a Tuning. Meantone, on the other hand, in any of
> its various forms,
> is a Temperament, and its very essence lies in the
> idea of compromise.
> It's basic approach is the purposeful DEtuning of
> certain important
> consonances in order to arrive at a pure version or
> near pure (another
> compromise) version of other important consonances.
> JI does not
> include an purposeful detuning of anything; some
> intervals
> accidentally end up detuned, but their detuning is
> an inherent part of
> neither the logic nor the methodology.
>
> Actually, I would say that all Tunings are
> diametrically opposed to
> all Temperaments in every possible way.
> > > >
> > > > Is not Pythagorean "modified just intonation"?
> > > >
> No. Pythagorean is a subclass of JI. It is 3-limit
> JI, or to be true
> to the original Pythagoreans, it is 4-limit JI in
> keeping with the
> precepts of the Tetrakyts. 5-limit and 7-limit are
> also a subclasses
> of JI. Saying that Pythagorean is modified JI is
> like saying a cat is
> a modified mammal. You're confusing levels in the
> hierarchical
> classification system.
>
> Now, about modified meantones. All meantones use an
> unbroken chain of
> purposely detuned fifths, the size of which is
> determined by the
> desire to arrive at a consistently pure or close to
> pure major third.
> The resulting gap is irrelevant because the
> resulting bad thirds (the
> original wolves) are not intended to be used, except
> perhaps for
> dramatic effect. The temperaments I call modified
> meantones generally
> exhibit a structure which is mostly meantone with a
> slight variation
> in that there is exactly the same long chain
> intentionally tempered
> fifths, the size of which is determined by the
> desire to arrive at a
> consistently pure or close to pure major third, but
> with the inclusion
> of several fifths which do not adhere to this
> principle, applied to
> reduce the harshness of the wolf thirds, making them
> usable without
> the listener cringing, wherein lies the modification
> both in logic and
> intent.
>
> I could also say that in the case of Preatorius, the
> logic AND intent
> are both literally explained as modifications of
> regular meantone. One
> could argue the same for Schlick. Rameau also
> describes how at a
> certain point, one deviates from "the division",
> i.e. the normal
> meantone scheme of dividing the S comma among four
> consecutive fifths.
> So there we've got two and maybe three original
> sources which say
> start with meantone (admittedly without using that
> modern word) but
> modify it at a certain point. Werkmeister says
> nothing of the sort in
> regards to any of the 3 copperplate "richtige
> temperaturen"; they are
> created anew.
>
> On the other hand, his instructions for the continuo
> temperament can
> quite easily be construed to be a deviation from a
> meantone scheme, in
> that the tuner is told to temper ALL of the primary
> fifths by the same
> amount so as to arrive at a certain consistent
> quality of "good" major
> third. This logic is consistently adhered to until
> the point at which
> one modifies it to avoid the appearance of wolves,
> which is another
> thing he literally says in the form of wanting to
> arrive at
> multifunctional thirds produced by the accidentals,
> which is THE
> historical meaning of "avoiding wolves".
>
> That's my take on it. Now I'd be interested in
> Johhny's.
>
> Go for it, man!
>
>
=== message truncated ===

Caleb,

SNIP

> So, all temperaments are tunings, but not all tunings
> are temperaments? (Partch scale is a tuning but not a
> temperament)
> and if you called Valotti a "tuning" it wouldn't be
> *wrong*, merely less precise?
>

Exactly,
Oz.

--- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>
> newbie question: Are some people here are using the
> terms temperament and tuning in a more precise way
> than usual? If I Google "temperament definitions", I
> get:
>
> quote:
>
> A way of tuning a diatonic scale to produce particular
> effects. See the entries for equal and meantone
> temperaments and just tuning.

Oi! I've seen some bad definitions before, but this one is way up
there! The diatonic scale? Well, THAT certainly makes tings a lot
easier! None of the bluhdy enharmonic accidental stuff to worry about!

Personally, I'm one of those old fuddy duddies who thinks words ought
to have meanings which are not carelessly tossed about, precisely
because it makes communication a lot easier if I say bird and you
don't hear airplane. So for me, "tuning" has two meanings:

(1) The whole series of adjustments one gives all the sound producing
elements of an instrument, as in, "This piano just had a complete tuning."

(2) Specifically with regard to SYSTEMS of fixing the exact pitches of
all the notes, for me a "tuning" is that which is produced by using
pure (i.e."tuned") intervals, such as any stripe of Just Intonation or
Pythagorean. Not all the intervals which result will be pure or "in
tune", mind, it's just that ALL the specific intervals you use to
define ALL of the notes are all pure. The opposite is a temperament,
which is produced by purposely detuning certain intervals, i.e.
"tempering" them. So you can "tune" a harpsichord in any temperament,
or yo can tune it i a tuning. However, I choke on "the Vallotti
tuning", or even worse yet, "the Vallotti scale". Which Vallotti
scale? The minor one? The major one? The whole tone one? Etc etc etc.

Granted, there is no universal agreement on this. I think folks in the
early music biz who know their comma from a whole in the circle more
or less stick to that sort of distinction, but that's only my
experience. Folks in the microtonal movement tend to toss the word
"scale" about rather haphazardly to mean any collection of tones. You
have folks from both environments here, so don't expect there to be
any consistency.

As if it's not confusing enuf already, eh?

Ciao,

P

Hi Paul,

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2008 Pazartesi 10:20
Subject: [tuning] Re: Werckmeister III tuning

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > O the witty merry-go-round sarcasm! Will it never end?
>
> It wasn't intended to be sarcastic, Oz, I really wanted Johhny to
> explain his thoughts. I mean, I could say something like "Is not
> Goerge Bush a modern Mussollini?", and I'm sure lots of people these
> days would agree with me instantly. But I haven't really said anything
> at all, have I? So what would they be agreeing to?
>
> To argue against Johnny's hypothetical equations, I would say that the
> word "modified" in any application has to indicate a basic
> characteristic which remains unchanged in some manner AND a variation
> in form which does not go so far as to create something completely
> different. Thus genetically modified corn can only be called such as
> long as it doesn't begin to look like cabbage or taste like strawberries.
>

Got yer drift. Your analogies are bizzarre and funny though.

> A temperament or tuning can be classified in several ways:
>
> (1) the basic acoustical intent, i.e. producing pure thirds, closing
> the circle, or as Johnny likes to say, avoiding wolves - or a
> combination of more than one intent
>

OK.

> (2) a basic structural logic, i.e. distributing the Pythagorean comma,
> distributing the Syntonic comma, not dealing with any comma, regular
> distribution, irregular distribtuion, etc.
>

Distribtuion, not!

> (3) a historical development
>

How can a tuning or temperament develop (as implying continuity of action)?
Let alone historically? After the theorist designs it, it stays as it is.
The slightest modification thereto automatically qualifies it as another
tuning. Maybe you mean "extension to the tuning" as in going forward by the
generator interval such as is the case with negative meantone temperaments
surpassing 12 regular tones?

> (4) whether it is a tuning or a temperament
>

Good point.

> That's all I can think of at the moment, maybe there are more.
>

Suppose there is, such as the inharmonicity factor, or presence of
relatively strong overtones to achieve beating or the lack thereof.

> I suppose one could argue the original/modified dichotomy in regards
> to any one aspect, but I would posit that the term becomes the more
> convincing the more different aspects you can point to.
> > > >
> > > > Is not equal temperament "modified Werckmeister"?
>
> I don't see how. I assume you mean WIII and not IV or V, but in
> regards to them all you could say the point is to make all keys usable
> will keeping the natural keys purer than the accidental keys, and the
> logic is dividing the Pythagorean comma in a small number of parts
> which distributed according to a very irregular scheme, including the
> over-distribution which requires the introductin of larger than pure
> fifths for correction. ET, on the other hand, intends to make ALL keys
> exactly the same, and it does so by distributing the Pythagorean comma
> in the most regular method imaginable, and not allowing any
> overcompensation t all. Other than the fact that they are both Pyth
> comma systems, I don't see any grounds for arguing that the one is a
> modified form of the other; for me they are cabbage and strawberries.

Surely, a twelve-tone layout can be modified in certain ways to result in
another twelve-tone layout. The process of modification can involve many
steps and pitch manipulations without endangering the concept of
modification.

> > > >
> > > > Is not meantone "modified just intonation"?
>
> No. The essence of any form of JI is pure intervals. No prisoners
> taken. Those impure intervals which inevitably result are like
> collateral casualties, the unfortunate victims of the necessity of
> achieving a Higher Case, rigidly following an extremist ideology. It
> is a Tuning. Meantone, on the other hand, in any of its various forms,
> is a Temperament, and its very essence lies in the idea of compromise.
> It's basic approach is the purposeful DEtuning of certain important
> consonances in order to arrive at a pure version or near pure (another
> compromise) version of other important consonances. JI does not
> include an purposeful detuning of anything; some intervals
> accidentally end up detuned, but their detuning is an inherent part of
> neither the logic nor the methodology.
>

One can surely modify a tuning so that it becomes a temperament. A 12-tone
Pythagorean tuning can be altered in just 2 notes (Eb, Bb) by 2/3 and 1/3
PCs respectively to make it a cyclic temperament. Further modification will
yield other tunings. Thereby, meantone is just as much a modified JI as it
is a modified Pythagorean tuning.

> Actually, I would say that all Tunings are diametrically opposed to
> all Temperaments in every possible way.
> > > >
> > > > Is not Pythagorean "modified just intonation"?
> > > >
> No. Pythagorean is a subclass of JI. It is 3-limit JI, or to be true
> to the original Pythagoreans, it is 4-limit JI in keeping with the
> precepts of the Tetrakyts. 5-limit and 7-limit are also a subclasses
> of JI. Saying that Pythagorean is modified JI is like saying a cat is
> a modified mammal. You're confusing levels in the hierarchical
> classification system.
>

I agree with you here.

> Now, about modified meantones. All meantones use an unbroken chain of
> purposely detuned fifths, the size of which is determined by the
> desire to arrive at a consistently pure or close to pure major third.
> The resulting gap is irrelevant because the resulting bad thirds (the
> original wolves) are not intended to be used, except perhaps for
> dramatic effect. The temperaments I call modified meantones generally
> exhibit a structure which is mostly meantone with a slight variation
> in that there is exactly the same long chain intentionally tempered
> fifths, the size of which is determined by the desire to arrive at a
> consistently pure or close to pure major third, but with the inclusion
> of several fifths which do not adhere to this principle, applied to
> reduce the harshness of the wolf thirds, making them usable without
> the listener cringing, wherein lies the modification both in logic and
> intent.
>

This definition is perfectly suitable for the category of meantone
temperaments that we dub "modified" according to the primary and historical
intent. It does not mean we cannot utilize the concept of modification in
other ways.

> I could also say that in the case of Preatorius, the logic AND intent
> are both literally explained as modifications of regular meantone. One
> could argue the same for Schlick. Rameau also describes how at a
> certain point, one deviates from "the division", i.e. the normal
> meantone scheme of dividing the S comma among four consecutive fifths.
> So there we've got two and maybe three original sources which say
> start with meantone (admittedly without using that modern word) but
> modify it at a certain point. Werkmeister says nothing of the sort in
> regards to any of the 3 copperplate "richtige temperaturen"; they are
> created anew.
>

So, he does not modify a meantone temperament in his original approach to
acquire WIII. That does not mean one cannot arrive at WIII through
modification (no matter how complicated or tedious the procedure may be) of
a meantone temperament.

> On the other hand, his instructions for the continuo temperament can
> quite easily be construed to be a deviation from a meantone scheme, in
> that the tuner is told to temper ALL of the primary fifths by the same
> amount so as to arrive at a certain consistent quality of "good" major
> third. This logic is consistently adhered to until the point at which
> one modifies it to avoid the appearance of wolves, which is another
> thing he literally says in the form of wanting to arrive at
> multifunctional thirds produced by the accidentals, which is THE
> historical meaning of "avoiding wolves".
>
> That's my take on it. Now I'd be interested in Johhny's.
>

See: This definition is perfectly suitable for the category of meantone
temperaments that we dub "modified" according to the primary and historical
intent. It does not mean we cannot utilize the concept of modification in
other ways.

> Go for it, man!
>
> Ciao,
>
> P
>
>

Oz.

Oh my. Why use the word tuning in direct implication of the purity of a JI
interval? A tempered dyad can just as well be in-tune as a pure interval
provided that our satisfaction and criteria are met.

Tuning is not always the elimination of beats. It is rather the set of pure
or tempered pitch adjustments implemented on a musical instrument.

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2008 Pazartesi 21:04
Subject: [tuning] Re: "tuning" vs. "temperament"

> --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
> >
> > newbie question: Are some people here are using the
> > terms temperament and tuning in a more precise way
> > than usual? If I Google "temperament definitions", I
> > get:
> >
> > quote:
> >
> > A way of tuning a diatonic scale to produce particular
> > effects. See the entries for equal and meantone
> > temperaments and just tuning.
>
> Oi! I've seen some bad definitions before, but this one is way up
> there! The diatonic scale? Well, THAT certainly makes tings a lot
> easier! None of the bluhdy enharmonic accidental stuff to worry about!
>
> Personally, I'm one of those old fuddy duddies who thinks words ought
> to have meanings which are not carelessly tossed about, precisely
> because it makes communication a lot easier if I say bird and you
> don't hear airplane. So for me, "tuning" has two meanings:
>
> (1) The whole series of adjustments one gives all the sound producing
> elements of an instrument, as in, "This piano just had a complete tuning."
>
> (2) Specifically with regard to SYSTEMS of fixing the exact pitches of
> all the notes, for me a "tuning" is that which is produced by using
> pure (i.e."tuned") intervals, such as any stripe of Just Intonation or
> Pythagorean. Not all the intervals which result will be pure or "in
> tune", mind, it's just that ALL the specific intervals you use to
> define ALL of the notes are all pure. The opposite is a temperament,
> which is produced by purposely detuning certain intervals, i.e.
> "tempering" them. So you can "tune" a harpsichord in any temperament,
> or yo can tune it i a tuning. However, I choke on "the Vallotti
> tuning", or even worse yet, "the Vallotti scale". Which Vallotti
> scale? The minor one? The major one? The whole tone one? Etc etc etc.
>
> Granted, there is no universal agreement on this. I think folks in the
> early music biz who know their comma from a whole in the circle more
> or less stick to that sort of distinction, but that's only my
> experience. Folks in the microtonal movement tend to toss the word
> "scale" about rather haphazardly to mean any collection of tones. You
> have folks from both environments here, so don't expect there to be
> any consistency.
>
> As if it's not confusing enuf already, eh?
>
> Ciao,
>
> P
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Oh my. Why use the word tuning in direct implication of the purity
of a JI
> interval? A tempered dyad can just as well be in-tune as a pure interval
> provided that our satisfaction and criteria are met.
>
> Tuning is not always the elimination of beats. It is rather the set
of pure
> or tempered pitch adjustments implemented on a musical instrument.

Right. That's more or less my first definition of the word. But I
agree completely with Kirnberger that "the ear cannot know" anything
but a pure interval. We can learn how to produce just about any
interval pretty consistently, and musicians using maqam traditions are
of course far superior to western musicians in this respect. Classical
Indian as well. But the point remain there is nothing there to point
to by which the interval can be objectively perceived; the young
musician must learn it by constant exposure. On the contrary, hearing
a basic pure consonance (up to 7 limit, say) is a simple task once you
copped to the tick of picking out overtones. I've seen students go
from not hearing anything to being able to perfectly tune fifths and
major and minor thirds in less than half an hour.

But as I said, it's a custom fairly common among the Early Music
crowd. You don't have to use it, or even agree with it, but it has a
certain logic.

Ciao,

P

Thank you Oz. I agree.

They seem to have again fallen into the "How close is it to JI?" paradox, as though the only way to "choose" and verify the validity of an interval is by measuring its deviation from "perfect" integer frequency ratio "landmarks".

These "landmarks" do seem to be "sources" of beating, yet for some naive microtonalists, the ratios have become "gospel" exclusive "truths" for interval validation.

These individuals can usually be recognised as those who have yet to be able to visualise tuning/temperaments beyond the integer frequency ratios of JI.

The attitude is conveyed is "If ain't close to a JI; it ain't worth using".

On 3 Mar 2008, at 19:46, Ozan Yarman wrote:

> Oh my. Why use the word tuning in direct implication of the purity > of a JI
> interval? A tempered dyad can just as well be in-tune as a pure > interval
> provided that our satisfaction and criteria are met.
>
> Tuning is not always the elimination of beats. It is rather the set > of pure
> or tempered pitch adjustments implemented on a musical instrument.
>
> Oz.
>
> ----- Original Message -----
> From: "Paul Poletti" <paul@polettipiano.com>
> To: <tuning@yahoogroups.com>
> Sent: 03 Mart 2008 Pazartesi 21:04
> Subject: [tuning] Re: "tuning" vs. "temperament"
>
>
>> --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>>>
>>> newbie question: Are some people here are using the
>>> terms temperament and tuning in a more precise way
>>> than usual? If I Google "temperament definitions", I
>>> get:
>>>
>>> quote:
>>>
>>> A way of tuning a diatonic scale to produce particular
>>> effects. See the entries for equal and meantone
>>> temperaments and just tuning.
>>
>> Oi! I've seen some bad definitions before, but this one is way up
>> there! The diatonic scale? Well, THAT certainly makes tings a lot
>> easier! None of the bluhdy enharmonic accidental stuff to worry >> about!
>>
>> Personally, I'm one of those old fuddy duddies who thinks words ought
>> to have meanings which are not carelessly tossed about, precisely
>> because it makes communication a lot easier if I say bird and you
>> don't hear airplane. So for me, "tuning" has two meanings:
>>
>> (1) The whole series of adjustments one gives all the sound producing
>> elements of an instrument, as in, "This piano just had a complete >> tuning."
>>
>> (2) Specifically with regard to SYSTEMS of fixing the exact pitches >> of
>> all the notes, for me a "tuning" is that which is produced by using
>> pure (i.e."tuned") intervals, such as any stripe of Just Intonation >> or
>> Pythagorean. Not all the intervals which result will be pure or "in
>> tune", mind, it's just that ALL the specific intervals you use to
>> define ALL of the notes are all pure. The opposite is a temperament,
>> which is produced by purposely detuning certain intervals, i.e.
>> "tempering" them. So you can "tune" a harpsichord in any temperament,
>> or yo can tune it i a tuning. However, I choke on "the Vallotti
>> tuning", or even worse yet, "the Vallotti scale". Which Vallotti
>> scale? The minor one? The major one? The whole tone one? Etc etc etc.
>>
>> Granted, there is no universal agreement on this. I think folks in >> the
>> early music biz who know their comma from a whole in the circle more
>> or less stick to that sort of distinction, but that's only my
>> experience. Folks in the microtonal movement tend to toss the word
>> "scale" about rather haphazardly to mean any collection of tones. You
>> have folks from both environments here, so don't expect there to be
>> any consistency.
>>
>> As if it's not confusing enuf already, eh?
>>
>> Ciao,
>>
>> P
>>
>>
>>
>> You can configure your subscription by sending an empty email to one
>> of these addresses (from the address at which you receive the list):
>> tuning-subscribe@yahoogroups.com - join the tuning group.
>> tuning-unsubscribe@yahoogroups.com - leave the group.
>> tuning-nomail@yahoogroups.com - turn off mail from the group.
>> tuning-digest@yahoogroups.com - set group to send daily digests.
>> tuning-normal@yahoogroups.com - set group to send individual emails.
>> tuning-help@yahoogroups.com - receive general help information.
>>
>> Yahoo! Groups Links
>>
>>
>>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Very well put Charles. However, I see fundamental problems in your approach
that states "the further one goes in Lucytuned fifths, the lesser the
consonance". Are there not PI solutions to acquiring the middle seconds of
maqam music other than the cycle of fifths?

Oz.

----- Original Message -----
From: "Charles Lucy" <lucy@harmonics.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2008 Pazartesi 22:16
Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI "police"
strike again;-)

> Thank you Oz. I agree.
>
> They seem to have again fallen into the "How close is it to JI?"
> paradox, as though the only way to "choose" and verify the validity of
> an interval is by measuring its deviation from "perfect" integer
> frequency ratio "landmarks".
>
> These "landmarks" do seem to be "sources" of beating, yet for some
> naive microtonalists, the ratios have become "gospel" exclusive
> "truths" for interval validation.
>
> These individuals can usually be recognised as those who have yet to
> be able to visualise tuning/temperaments beyond the integer frequency
> ratios of JI.
>
> The attitude is conveyed is "If ain't close to a JI; it ain't worth
> using".
>
>

Frankly Oz,
I don't know.

What interval are you aiming for? i.e. how many cents?

On 3 Mar 2008, at 20:40, Ozan Yarman wrote:

> Very well put Charles. However, I see fundamental problems in your > approach
> that states "the further one goes in Lucytuned fifths, the lesser the
> consonance". Are there not PI solutions to acquiring the middle > seconds of
> maqam music other than the cycle of fifths?
>
> Oz.
>
> ----- Original Message -----
> From: "Charles Lucy" <lucy@harmonics.com>
> To: <tuning@yahoogroups.com>
> Sent: 03 Mart 2008 Pazartesi 22:16
> Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI "police"
> strike again;-)
>
>
>> Thank you Oz. I agree.
>>
>> They seem to have again fallen into the "How close is it to JI?"
>> paradox, as though the only way to "choose" and verify the validity >> of
>> an interval is by measuring its deviation from "perfect" integer
>> frequency ratio "landmarks".
>>
>> These "landmarks" do seem to be "sources" of beating, yet for some
>> naive microtonalists, the ratios have become "gospel" exclusive
>> "truths" for interval validation.
>>
>> These individuals can usually be recognised as those who have yet to
>> be able to visualise tuning/temperaments beyond the integer frequency
>> ratios of JI.
>>
>> The attitude is conveyed is "If ain't close to a JI; it ain't worth
>> using".
>>
>>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Hi Oz;

Thinking about your "middle seconds", my first thought is to go tothis page, (which lists the most "consonant/concordant/best
concordance" intervals and look at the values at the bottom of the
page.

http://www.lucytune.com/new_to_lt/pitch_02.html

e.g. approx 54¢ bbII; approx approx 123¢ bII; or approx. 68¢ #I?

On 3 Mar 2008, at 21:13, Charles Lucy wrote:

> Frankly Oz,
> I don't know.
>
> What interval are you aiming for? i.e. how many cents?
>
> On 3 Mar 2008, at 20:40, Ozan Yarman wrote:
>
> > Very well put Charles. However, I see fundamental problems in your
> > approach
> > that states "the further one goes in Lucytuned fifths, the lesser
> the
> > consonance". Are there not PI solutions to acquiring the middle
> > seconds of
> > maqam music other than the cycle of fifths?
> >
> > Oz.
> >
> > ----- Original Message -----
> > From: "Charles Lucy" <lucy@harmonics.com>
> > To: <tuning@yahoogroups.com>
> > Sent: 03 Mart 2008 Pazartesi 22:16
> > Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI
> "police"
> > strike again;-)
> >
> >
> >> Thank you Oz. I agree.
> >>
> >> They seem to have again fallen into the "How close is it to JI?"
> >> paradox, as though the only way to "choose" and verify the validity
> >> of
> >> an interval is by measuring its deviation from "perfect" integer
> >> frequency ratio "landmarks".
> >>
> >> These "landmarks" do seem to be "sources" of beating, yet for some
> >> naive microtonalists, the ratios have become "gospel" exclusive
> >> "truths" for interval validation.
> >>
> >> These individuals can usually be recognised as those who have yet
> to
> >> be able to visualise tuning/temperaments beyond the integer
> frequency
> >> ratios of JI.
> >>
> >> The attitude is conveyed is "If ain't close to a JI; it ain't worth
> >> using".
> >>
> >>
> >
> >
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>
> Charles Lucy
> lucy@lucytune.com
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

The intervals are anywhere from roughly 130 to 165 cents. Preferably, we
would want three uniformly seperate pitches in that range which is aptly
called the "mujannab zone".

Oz.

----- Original Message -----
From: "Charles Lucy" <lucy@harmonics.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2008 Pazartesi 23:13
Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI "police"
strike again;-)

> Frankly Oz,
> I don't know.
>
> What interval are you aiming for? i.e. how many cents?
>
> On 3 Mar 2008, at 20:40, Ozan Yarman wrote:
>
> > Very well put Charles. However, I see fundamental problems in your
> > approach
> > that states "the further one goes in Lucytuned fifths, the lesser the
> > consonance". Are there not PI solutions to acquiring the middle
> > seconds of
> > maqam music other than the cycle of fifths?
> >
> > Oz.
> >
> > ----- Original Message -----
> > From: "Charles Lucy" <lucy@harmonics.com>
> > To: <tuning@yahoogroups.com>
> > Sent: 03 Mart 2008 Pazartesi 22:16
> > Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI "police"
> > strike again;-)
> >
> >
> >> Thank you Oz. I agree.
> >>
> >> They seem to have again fallen into the "How close is it to JI?"
> >> paradox, as though the only way to "choose" and verify the validity
> >> of
> >> an interval is by measuring its deviation from "perfect" integer
> >> frequency ratio "landmarks".
> >>
> >> These "landmarks" do seem to be "sources" of beating, yet for some
> >> naive microtonalists, the ratios have become "gospel" exclusive
> >> "truths" for interval validation.
> >>
> >> These individuals can usually be recognised as those who have yet to
> >> be able to visualise tuning/temperaments beyond the integer frequency
> >> ratios of JI.
> >>
> >> The attitude is conveyed is "If ain't close to a JI; it ain't worth
> >> using".
> >>
> >>

Step sizes are not given in cents in the table at the bottom of the page. Is there no other way to acquire Lucy middle seconds than a cycle of Lucytuned fifths?

Oz.

----- Original Message -----
From: Charles Lucy
To: tuning@yahoogroups.com
Sent: 03 Mart 2008 Pazartesi 23:31
Subject: Re: [tuning] Re: "tuning" vs. "temperament" - maqam middle seconds?

Hi Oz;

Thinking about your "middle seconds", my first thought is to go to this page, (which lists the most "consonant/concordant/best concordance" intervals and look at the values at the bottom of the page.

http://www.lucytune.com/new_to_lt/pitch_02.html

e.g. approx 54¢ bbII; approx approx 123¢ bII; or approx. 68¢ #I?

On 3 Mar 2008, at 21:13, Charles Lucy wrote:

Frankly Oz,
I don't know.

What interval are you aiming for? i.e. how many cents?

On 3 Mar 2008, at 20:40, Ozan Yarman wrote:

> Very well put Charles. However, I see fundamental problems in your
> approach
> that states "the further one goes in Lucytuned fifths, the lesser the
> consonance". Are there not PI solutions to acquiring the middle
> seconds of
> maqam music other than the cycle of fifths?
>
> Oz.
>
> ----- Original Message -----
> From: "Charles Lucy" <lucy@harmonics.com>
> To: <tuning@yahoogroups.com>
> Sent: 03 Mart 2008 Pazartesi 22:16
> Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI "police"
> strike again;-)
>
>
>> Thank you Oz. I agree.
>>
>> They seem to have again fallen into the "How close is it to JI?"
>> paradox, as though the only way to "choose" and verify the validity
>> of
>> an interval is by measuring its deviation from "perfect" integer
>> frequency ratio "landmarks".
>>
>> These "landmarks" do seem to be "sources" of beating, yet for some
>> naive microtonalists, the ratios have become "gospel" exclusive
>> "truths" for interval validation.
>>
>> These individuals can usually be recognised as those who have yet to
>> be able to visualise tuning/temperaments beyond the integer frequency
>> ratios of JI.
>>
>> The attitude is conveyed is "If ain't close to a JI; it ain't worth
>> using".
>>
>>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>
> newbie question: Are some people here are using the
> terms temperament and tuning in a more precise way
> than usual?

Yes. I believe Paul posted something about this recently,
but his suggestion was counter to the closest thing we have
to a consensus around here. It was also not very precise.

> So, all temperaments are tunings, but not all tunings
> are temperaments? (Partch scale is a tuning but not a
> temperament) and if you called Valotti a "tuning" it
> wouldn't be *wrong*, merely less precise?

If you want to be precise or you care about aligning with
the literature of the 'regular mapping paradigm' (such as
it is), both Partch's scale and Valotti, by themselves, are
scales -- not tunings and certainly not temperaments.

A temperament is an abstract entity defined by a homomorphism
between its elements and just intonation. For any temperament,
several tunings will support this homomorphism, e.g. 12-ET
and 31-ET both represent tunings of the meantone temperament.

Scales are lists of pitches. If you have something that is
best described with a Scala .scl file, you have a scale.
So 12-ET is a scale that supports the tuning of the meantone
temperament which has 700-cent generators and 1200-cent
periods.

Crystal, I'm sure.

-Carl

Hi Oz;

Yes, I suppose that you could map them using some other pattern (e.g.
steps of thirds), yet the resulting intervals will be the same numberof cents, just expressed in a slightly different order.

That page shows the interval values as cents from A in terms of number
of steps of fourths or fifths.
It shows 21 steps in each direction from A.

Third column from the left for steps of fifths and third column from
the right for steps of fourths in ascending number of steps going down
the page

http://www.lucytune.com/new_to_lt/pitch_02.html

In your range 130 to 165 cents, the only interval that I find is at:

136.903 which is a double sharp (xI) one. (2L-2s) after 14 steps of
fifths.

Since the single sharp i.e. #1 occurs at seven steps (68.45 ¢) it is
doubled to get you into the range that you require.

If it doesn't occur there (to sufficient precision) it will require a
greater number of steps, which requires me to consult one of myFileMaker or other databases to calculate it.

But you're going to get a result with more than 41 steps.

On 3 Mar 2008, at 21:53, Ozan Yarman wrote:

>
> Step sizes are not given in cents in the table at the bottom of the
> page. Is there no other way to acquire Lucy middle seconds than a
> cycle of Lucytuned fifths?
>
> Oz.
>
> ----- Original Message -----
> From: Charles Lucy
> To: tuning@yahoogroups.com
> Sent: 03 Mart 2008 Pazartesi 23:31
> Subject: Re: [tuning] Re: "tuning" vs. "temperament" - maqam middle> seconds?
>
> Hi Oz;
>
> Thinking about your "middle seconds", my first thought is to go to
> this page, (which lists the most "consonant/concordant/best
> concordance" intervals and look at the values at the bottom of the
> page.
>
> http://www.lucytune.com/new_to_lt/pitch_02.html
>
> e.g. approx 54¢ bbII; approx approx 123¢ bII; or approx. 68¢ #I?
>
> On 3 Mar 2008, at 21:13, Charles Lucy wrote:
>
>> Frankly Oz,
>> I don't know.
>>
>> What interval are you aiming for? i.e. how many cents?
>>
>> On 3 Mar 2008, at 20:40, Ozan Yarman wrote:
>>
>> > Very well put Charles. However, I see fundamental problems in your
>> > approach
>> > that states "the further one goes in Lucytuned fifths, the lesser
>> the
>> > consonance". Are there not PI solutions to acquiring the middle
>> > seconds of
>> > maqam music other than the cycle of fifths?
>> >
>> > Oz.
>> >
>> > ----- Original Message -----
>> > From: "Charles Lucy" <lucy@harmonics.com>
>> > To: <tuning@yahoogroups.com>
>> > Sent: 03 Mart 2008 Pazartesi 22:16
>> > Subject: Re: [tuning] Re: "tuning" vs. "temperament" - The JI
>> "police"
>> > strike again;-)
>> >
>> >
>> >> Thank you Oz. I agree.
>> >>
>> >> They seem to have again fallen into the "How close is it to JI?"
>> >> paradox, as though the only way to "choose" and verify the
>> validity
>> >> of
>> >> an interval is by measuring its deviation from "perfect" integer
>> >> frequency ratio "landmarks".
>> >>
>> >> These "landmarks" do seem to be "sources" of beating, yet for some
>> >> naive microtonalists, the ratios have become "gospel" exclusive
>> >> "truths" for interval validation.
>> >>
>> >> These individuals can usually be recognised as those who have
>> yet to
>> >> be able to visualise tuning/temperaments beyond the integer
>> frequency
>> >> ratios of JI.
>> >>
>> >> The attitude is conveyed is "If ain't close to a JI; it ain't
>> worth
>> >> using".
>> >>
>> >>
>> >
>> >
>> >
>> > You can configure your subscription by sending an empty email to
>> one
>> > of these addresses (from the address at which you receive the >> list):
>> > tuning-subscribe@yahoogroups.com - join the tuning group.
>> > tuning-unsubscribe@yahoogroups.com - leave the group.
>> > tuning-nomail@yahoogroups.com - turn off mail from the group.
>> > tuning-digest@yahoogroups.com - set group to send daily digests.
>> > tuning-normal@yahoogroups.com - set group to send individual
>> emails.
>> > tuning-help@yahoogroups.com - receive general help information.
>> >
>> > Yahoo! Groups Links
>> >
>> >
>> >
>> >
>>
>> Charles Lucy
>> lucy@lucytune.com
>>
>> - Promoting global harmony through LucyTuning -
>>
>> for information on LucyTuning go to:
>> http://www.lucytune.com
>>
>> For LucyTuned Lullabies go to:
>> http://www.lullabies.co.uk
>>
>>
>
> Charles Lucy
> lucy@lucytune.com
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
>
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>> So, all temperaments are tunings, but not all tunings
>> are temperaments? (Partch scale is a tuning but not a
>> temperament) and if you called Valotti a "tuning" it
>> wouldn't be *wrong*, merely less precise?
> > If you want to be precise or you care about aligning with
> the literature of the 'regular mapping paradigm' (such as
> it is), both Partch's scale and Valotti, by themselves, are
> scales -- not tunings and certainly not temperaments.

For Partch 43 that's a lax usage of "scale" because it's really a gamut or superscale. At least the way he explained it. But we call it a scale anyway.

Valotti by itself is a tuning of the chromatic scale. As a temperament, it's a tuning of the 12 note well temperament class.

> A temperament is an abstract entity defined by a homomorphism
> between its elements and just intonation. For any temperament,
> several tunings will support this homomorphism, e.g. 12-ET
> and 31-ET both represent tunings of the meantone temperament.

And Valotti shares the same mapping from just intonation as 12-ET.

> Scales are lists of pitches. If you have something that is
> best described with a Scala .scl file, you have a scale.
> So 12-ET is a scale that supports the tuning of the meantone
> temperament which has 700-cent generators and 1200-cent
> periods.
> > Crystal, I'm sure.

Scales are lists of notes. The diatonic or blackjack scales can be tuned many different ways.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
> > --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@> wrote:
> >> So, all temperaments are tunings, but not all tunings
> >> are temperaments? (Partch scale is a tuning but not a
> >> temperament) and if you called Valotti a "tuning" it
> >> wouldn't be *wrong*, merely less precise?
> >
> > If you want to be precise or you care about aligning with
> > the literature of the 'regular mapping paradigm' (such as
> > it is), both Partch's scale and Valotti, by themselves, are
> > scales -- not tunings and certainly not temperaments.
>
> For Partch 43 that's a lax usage of "scale" because it's
> really a gamut or superscale. At least the way he explained
> it. But we call it a scale anyway.

That puts an additional meaning to the term scale that
I didn't know it had. How do you define "gamut"?

> Valotti by itself is a tuning of the chromatic scale.

Generally we don't have tunings of scales, but
rather of maps.

> As a temperament, it's a tuning of the 12 note well
> temperament class.

As a _tuning_ it's a tuning of some unnamed
well temperament (class).

> > A temperament is an abstract entity defined by a homomorphism
> > between its elements and just intonation. For any temperament,
> > several tunings will support this homomorphism, e.g. 12-ET
> > and 31-ET both represent tunings of the meantone temperament.
>
> And Valotti shares the same mapping from just intonation as
> 12-ET.

It has the same mapping, but the scale isn't obtained from
a single tuning of that mapping.

> > Scales are lists of pitches. If you have something that is
> > best described with a Scala .scl file, you have a scale.
> > So 12-ET is a scale that supports the tuning of the meantone
> > temperament which has 700-cent generators and 1200-cent
> > periods.
> >
> > Crystal, I'm sure.
>
> Scales are lists of notes.

What's a "note"? If you mean period-invariant pitch, then
I agree.

-Carl

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

>> For Partch 43 that's a lax usage of "scale" because it's >> really a gamut or superscale. At least the way he explained >> it. But we call it a scale anyway.
> > That puts an additional meaning to the term scale that
> I didn't know it had. How do you define "gamut"?

I thought somebody made the distinction in this thread. A gamut as I take it would be a set of notes you can use to make music -- no special order and no need for them all to be present. Partch talks about this somewhere on one of the Enclosures ... I think he calls it "a source scale".

>> Valotti by itself is a tuning of the chromatic scale.
> > Generally we don't have tunings of scales, but
> rather of maps.

You may, I don't. A tuning is a mapping from notes (or maybe intervals) to pitches. The notes needn't form a scale, and for regular temperaments the tuning is tied to the mapping. But this doesn't work for irregular temperaments and the term would be more useful if it did.

I'd rather say you have a tuning of a temperament class than of a map.

>> As a temperament, it's a tuning of the 12 note well
>> temperament class.
> > As a _tuning_ it's a tuning of some unnamed
> well temperament (class).

It has the same mapping from JI as 12-equal does, so it's a tuning of the natural 12 note well temperament class.

> It has the same mapping, but the scale isn't obtained from
> a single tuning of that mapping.

So it's not a *regular* temperament.

>>> Scales are lists of pitches. If you have something that is
>>> best described with a Scala .scl file, you have a scale.
>>> So 12-ET is a scale that supports the tuning of the meantone
>>> temperament which has 700-cent generators and 1200-cent
>>> periods.
>>>
>>> Crystal, I'm sure.
>> Scales are lists of notes.
> > What's a "note"? If you mean period-invariant pitch, then
> I agree.

A note is something you write down, or something you play. AIUI the term "scale" comes from teaching, not from actual music. If you write down some notes in a given order, and tie the set of notes and order to something musical, then it's a scale. If you tell somebody to practice those notes in the order you gave then it's definitely a scale.

There are Arabic scales that exceed an octave.

Graham

to deepen the ambiguity on all these words we use, i would reserve 'scale' as set of pitches with some sort of melodic (never on the basis of harmonic although this might easily follow) integrity. ex. MOS, Constant structure, diaphonic, tetrachordal etc. perhaps we will always need to define our terms before we discuss them.
but even concrete examples are difficult. in ex. Partch mapped 43 pitches in a way that can be thought of a 41 tone scale with two tones that vary. This is the way it works cause he had to also encompass his harmonic ideas.

Graham Breed wrote:
>
> Carl Lumma wrote:
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > Graham Breed <gbreed@...> wrote:
>
> >> For Partch 43 that's a lax usage of "scale" because it's
> >> really a gamut or superscale. At least the way he explained
> >> it. But we call it a scale anyway.
> >
> > That puts an additional meaning to the term scale that
> > I didn't know it had. How do you define "gamut"?
>
> I thought somebody made the distinction in this thread. A
> gamut as I take it would be a set of notes you can use to
> make music -- no special order and no need for them all to
> be present. Partch talks about this somewhere on one of the
> Enclosures ... I think he calls it "a source scale".
>
> >> Valotti by itself is a tuning of the chromatic scale.
> >
> > Generally we don't have tunings of scales, but
> > rather of maps.
>
> You may, I don't. A tuning is a mapping from notes (or
> maybe intervals) to pitches. The notes needn't form a
> scale, and for regular temperaments the tuning is tied to
> the mapping. But this doesn't work for irregular
> temperaments and the term would be more useful if it did.
>
> I'd rather say you have a tuning of a temperament class than
> of a map.
>
> >> As a temperament, it's a tuning of the 12 note well
> >> temperament class.
> >
> > As a _tuning_ it's a tuning of some unnamed
> > well temperament (class).
>
> It has the same mapping from JI as 12-equal does, so it's a
> tuning of the natural 12 note well temperament class.
>
> > It has the same mapping, but the scale isn't obtained from
> > a single tuning of that mapping.
>
> So it's not a *regular* temperament.
>
> >>> Scales are lists of pitches. If you have something that is
> >>> best described with a Scala .scl file, you have a scale.
> >>> So 12-ET is a scale that supports the tuning of the meantone
> >>> temperament which has 700-cent generators and 1200-cent
> >>> periods.
> >>>
> >>> Crystal, I'm sure.
> >> Scales are lists of notes.
> >
> > What's a "note"? If you mean period-invariant pitch, then
> > I agree.
>
> A note is something you write down, or something you play.
> AIUI the term "scale" comes from teaching, not from actual
> music. If you write down some notes in a given order, and
> tie the set of notes and order to something musical, then
> it's a scale. If you tell somebody to practice those notes
> in the order you gave then it's definitely a scale.
>
> There are Arabic scales that exceed an octave.
>
> Graham
>
> -- 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, Graham Breed <gbreed@...> wrote:
> Carl Lumma wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>
> >> For Partch 43 that's a lax usage of "scale" because it's
> >> really a gamut or superscale. At least the way he explained
> >> it. But we call it a scale anyway.
> >
> > That puts an additional meaning to the term scale that
> > I didn't know it had. How do you define "gamut"?
>
> I thought somebody made the distinction in this thread. A
> gamut as I take it would be a set of notes you can use to
> make music -- no special order and no need for them all to
> be present. Partch talks about this somewhere on one of the
> Enclosures ... I think he calls it "a source scale".

Yes, I believe Paul referred to gamut. But this isn't a
precise definition.

> >> Valotti by itself is a tuning of the chromatic scale.
> >
> > Generally we don't have tunings of scales, but
> > rather of maps.
>
> You may, I don't. A tuning is a mapping from notes (or
> maybe intervals) to pitches.

What's a note?

> I'd rather say you have a tuning of a temperament class than
> of a map.

What's a temperament class? I assume you just mean
temperament (rather than temperament family).

> >> As a temperament, it's a tuning of the 12 note well
> >> temperament class.
> >
> > As a _tuning_ it's a tuning of some unnamed
> > well temperament (class).
>
> It has the same mapping from JI as 12-equal does, so it's a
> tuning of the natural 12 note well temperament class.

What's the "natural well temperament class"? Sounds like
the "31 note regular temperament class"... which is
meaningless.

In the theory of irregular temperaments, there should be
some temperament which Valotti is a tuning of, which is
what I was referring to as "unnamed" above.

> >> Scales are lists of notes.
> >
> > What's a "note"? If you mean period-invariant pitch, then
> > I agree.
>
> A note is something you write down, or something you play.

That sounds equivalent to pitch. So there's redundancy
in your terminology. But the musical meaning of note is
generally a pitch with an octave-invariant name (though
occasionally, I'm sure, you get things like "C4" that are
not octave invariant).

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> to deepen the ambiguity on all these words we use, i would
> reserve 'scale' as set of pitches with some sort of melodic
> (never on the basis of harmonic although this might easily
> follow) integrity. ex. MOS, Constant structure, diaphonic,
> tetrachordal etc.

That's a fine goal, but the definition should be precise.
Do all MOS count? I'm sure I could come up with an MOS that
sounds like heck melodically. Since people are not likely
to agree on what constitutes melodic goodness any time soon,
it should probably be left out of the definition of so
basic a term.

One could perhaps say a scale is a collection of 5-10
10 notes. But then you'd have the musical "set theorists"
complaining that 12-tone rows are melodic entities. And
where would it end?

If you allow it to be up to interpretation, we're
practically back to Gene's definition (any bag of notes).
I'd rather leave value judgments out of it, personally.

-Carl

perhaps we will always need to define our terms before we discuss them.
> but even concrete examples are difficult. in ex. Partch mapped 43
> pitches in a way that can be thought of a 41 tone scale with two tones
> that vary. This is the way it works cause he had to also encompass his
> harmonic ideas.
>
> Graham Breed wrote:
> >
> > Carl Lumma wrote:
> > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
> > Graham Breed <gbreed@> wrote:
> >
> > >> For Partch 43 that's a lax usage of "scale" because it's
> > >> really a gamut or superscale. At least the way he explained
> > >> it. But we call it a scale anyway.
> > >
> > > That puts an additional meaning to the term scale that
> > > I didn't know it had. How do you define "gamut"?
> >
> > I thought somebody made the distinction in this thread. A
> > gamut as I take it would be a set of notes you can use to
> > make music -- no special order and no need for them all to
> > be present. Partch talks about this somewhere on one of the
> > Enclosures ... I think he calls it "a source scale".
> >
> > >> Valotti by itself is a tuning of the chromatic scale.
> > >
> > > Generally we don't have tunings of scales, but
> > > rather of maps.
> >
> > You may, I don't. A tuning is a mapping from notes (or
> > maybe intervals) to pitches. The notes needn't form a
> > scale, and for regular temperaments the tuning is tied to
> > the mapping. But this doesn't work for irregular
> > temperaments and the term would be more useful if it did.
> >
> > I'd rather say you have a tuning of a temperament class than
> > of a map.
> >
> > >> As a temperament, it's a tuning of the 12 note well
> > >> temperament class.
> > >
> > > As a _tuning_ it's a tuning of some unnamed
> > > well temperament (class).
> >
> > It has the same mapping from JI as 12-equal does, so it's a
> > tuning of the natural 12 note well temperament class.
> >
> > > It has the same mapping, but the scale isn't obtained from
> > > a single tuning of that mapping.
> >
> > So it's not a *regular* temperament.
> >
> > >>> Scales are lists of pitches. If you have something that is
> > >>> best described with a Scala .scl file, you have a scale.
> > >>> So 12-ET is a scale that supports the tuning of the meantone
> > >>> temperament which has 700-cent generators and 1200-cent
> > >>> periods.
> > >>>
> > >>> Crystal, I'm sure.
> > >> Scales are lists of notes.
> > >
> > > What's a "note"? If you mean period-invariant pitch, then
> > > I agree.
> >
> > A note is something you write down, or something you play.
> > AIUI the term "scale" comes from teaching, not from actual
> > music. If you write down some notes in a given order, and
> > tie the set of notes and order to something musical, then
> > it's a scale. If you tell somebody to practice those notes
> > in the order you gave then it's definitely a scale.
> >
> > There are Arabic scales that exceed an octave.
> >
> > Graham
> >
> >
>
> --
> 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 wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Carl Lumma wrote:
>>> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
>>>> For Partch 43 that's a lax usage of "scale" because it's >>>> really a gamut or superscale. At least the way he explained >>>> it. But we call it a scale anyway.
>>> That puts an additional meaning to the term scale that
>>> I didn't know it had. How do you define "gamut"?
>> I thought somebody made the distinction in this thread. A >> gamut as I take it would be a set of notes you can use to >> make music -- no special order and no need for them all to >> be present. Partch talks about this somewhere on one of the >> Enclosures ... I think he calls it "a source scale".
> > Yes, I believe Paul referred to gamut. But this isn't a
> precise definition. In that case I'll plead I was only clarifying usage and I don't need a definition for that.

>>>> Valotti by itself is a tuning of the chromatic scale.
>>> Generally we don't have tunings of scales, but
>>> rather of maps.
>> You may, I don't. A tuning is a mapping from notes (or >> maybe intervals) to pitches.
> > What's a note?

Here it's an interval relative to a fixed reference.

>> I'd rather say you have a tuning of a temperament class than >> of a map.
> > What's a temperament class? I assume you just mean
> temperament (rather than temperament family).

Once you have a tuning, then it's a temperament. A temperament class is a set of tunings with the same mapping from just intonation.

>>>> As a temperament, it's a tuning of the 12 note well
>>>> temperament class.
>>> As a _tuning_ it's a tuning of some unnamed
>>> well temperament (class).
>> It has the same mapping from JI as 12-equal does, so it's a >> tuning of the natural 12 note well temperament class.
> > What's the "natural well temperament class"? Sounds like
> the "31 note regular temperament class"... which is
> meaningless.

The natural well temperament class is the one that shares a mapping with the best equal temperament with the same number of notes. It'd be more like the "31 note equal temperament class" which is 31 notes to an octave that needn't be tuned 2:1.

> In the theory of irregular temperaments, there should be
> some temperament which Valotti is a tuning of, which is
> what I was referring to as "unnamed" above.

What temperament is quarter comma meantone a tuning of?

>>>> Scales are lists of notes.
>>> What's a "note"? If you mean period-invariant pitch, then
>>> I agree.
>> A note is something you write down, or something you play.
> > That sounds equivalent to pitch. So there's redundancy
> in your terminology. But the musical meaning of note is
> generally a pitch with an octave-invariant name (though
> occasionally, I'm sure, you get things like "C4" that are
> not octave invariant).

A pitch is tied to a specific frequency, a note needn't be. In everyday music the same notes can be played with different tunings.

Graham

please do come up with an MOS that doesn't sound like a scale. Just because it doesn't sound 'western' does not make it a consistent scale.
you would need to come up with something that sounds like a note is 'left out' or a note should be 'taken out'. I agree that we should take value judgments out of it. there are plenty of even pentatonics i would never use, but they can still have the property of being a scale. too bad we can't have Gene in on this since he is so good at finding the closest ET to just about anything. i would assume we might agree that all ETs are scales.
My problem with the idea of super scales is that what happens if a melody say doesn't use all 7 tones of a diatonic. Does that make it a super scale or gamut, we could add the word array also in the mix.
As far as definite meanings of words the following of Karl Popper might be useful to consider.
http://anaphoria.com/clocksclouds.pdf

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > to deepen the ambiguity on all these words we use, i would
> > reserve 'scale' as set of pitches with some sort of melodic
> > (never on the basis of harmonic although this might easily
> > follow) integrity. ex. MOS, Constant structure, diaphonic,
> > tetrachordal etc.
>
> That's a fine goal, but the definition should be precise.
> Do all MOS count? I'm sure I could come up with an MOS that
> sounds like heck melodically. Since people are not likely
> to agree on what constitutes melodic goodness any time soon,
> it should probably be left out of the definition of so
> basic a term.
>
> One could perhaps say a scale is a collection of 5-10
> 10 notes. But then you'd have the musical "set theorists"
> complaining that 12-tone rows are melodic entities. And
> where would it end?
>
> If you allow it to be up to interpretation, we're
> practically back to Gene's definition (any bag of notes).
> I'd rather leave value judgments out of it, personally.
>
> -Carl
>
> perhaps we will always need to define our terms before we discuss them.
> > but even concrete examples are difficult. in ex. Partch mapped 43
> > pitches in a way that can be thought of a 41 tone scale with two tones
> > that vary. This is the way it works cause he had to also encompass his
> > harmonic ideas.
> >
> > Graham Breed wrote:
> > >
> > > Carl Lumma wrote:
> > > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> > <mailto:tuning%40yahoogroups.com>,
> > > Graham Breed <gbreed@> wrote:
> > >
> > > >> For Partch 43 that's a lax usage of "scale" because it's
> > > >> really a gamut or superscale. At least the way he explained
> > > >> it. But we call it a scale anyway.
> > > >
> > > > That puts an additional meaning to the term scale that
> > > > I didn't know it had. How do you define "gamut"?
> > >
> > > I thought somebody made the distinction in this thread. A
> > > gamut as I take it would be a set of notes you can use to
> > > make music -- no special order and no need for them all to
> > > be present. Partch talks about this somewhere on one of the
> > > Enclosures ... I think he calls it "a source scale".
> > >
> > > >> Valotti by itself is a tuning of the chromatic scale.
> > > >
> > > > Generally we don't have tunings of scales, but
> > > > rather of maps.
> > >
> > > You may, I don't. A tuning is a mapping from notes (or
> > > maybe intervals) to pitches. The notes needn't form a
> > > scale, and for regular temperaments the tuning is tied to
> > > the mapping. But this doesn't work for irregular
> > > temperaments and the term would be more useful if it did.
> > >
> > > I'd rather say you have a tuning of a temperament class than
> > > of a map.
> > >
> > > >> As a temperament, it's a tuning of the 12 note well
> > > >> temperament class.
> > > >
> > > > As a _tuning_ it's a tuning of some unnamed
> > > > well temperament (class).
> > >
> > > It has the same mapping from JI as 12-equal does, so it's a
> > > tuning of the natural 12 note well temperament class.
> > >
> > > > It has the same mapping, but the scale isn't obtained from
> > > > a single tuning of that mapping.
> > >
> > > So it's not a *regular* temperament.
> > >
> > > >>> Scales are lists of pitches. If you have something that is
> > > >>> best described with a Scala .scl file, you have a scale.
> > > >>> So 12-ET is a scale that supports the tuning of the meantone
> > > >>> temperament which has 700-cent generators and 1200-cent
> > > >>> periods.
> > > >>>
> > > >>> Crystal, I'm sure.
> > > >> Scales are lists of notes.
> > > >
> > > > What's a "note"? If you mean period-invariant pitch, then
> > > > I agree.
> > >
> > > A note is something you write down, or something you play.
> > > AIUI the term "scale" comes from teaching, not from actual
> > > music. If you write down some notes in a given order, and
> > > tie the set of notes and order to something musical, then
> > > it's a scale. If you tell somebody to practice those notes
> > > in the order you gave then it's definitely a scale.
> > >
> > > There are Arabic scales that exceed an octave.
> > >
> > > Graham
> > >
> > >
> >
> > --
> > Kraig Grady
> > North American Embassy of Anaphoria Island
> <http://anaphoria.com/index.html <http://anaphoria.com/index.html>>
> > The Wandering Medicine Show
> > KXLU <http://www.kxlu.com/main/index.asp > <http://www.kxlu.com/main/index.asp>> 88.9 FM Wed 8-9 pm Los Angeles
> >
>
> -- 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

> Once you have a tuning, then it's a temperament. A
> temperament class is a set of tunings with the same mapping
> from just intonation.

We say "miracle temperament" and "meantone temperament",
not "miracle temperament class" etc. If just "temperament"
is the tuned thing, then that frees up the term "tuning",
if you have a use for it.

> >>>> As a temperament, it's a tuning of the 12 note well
> >>>> temperament class.
> >>>
> >>> As a _tuning_ it's a tuning of some unnamed
> >>> well temperament (class).
> >>
> >> It has the same mapping from JI as 12-equal does, so it's
> >> a tuning of the natural 12 note well temperament class.
> >
> > What's the "natural well temperament class"? Sounds like
> > the "31 note regular temperament class"... which is
> > meaningless.
>
> The natural well temperament class is the one that shares a
> mapping with the best equal temperament with the same number
> of notes. It'd be more like the "31 note equal temperament
> class" which is 31 notes to an octave that needn't be tuned 2:1.

OK.

> > In the theory of irregular temperaments, there should be
> > some temperament which Valotti is a tuning of, which is
> > what I was referring to as "unnamed" above.
>
> What temperament is quarter comma meantone a tuning of?

meantone

> >>>> Scales are lists of notes.
> >>>
> >>> What's a "note"? If you mean period-invariant pitch,
> >>> then I agree.
> >>
> >> A note is something you write down, or something you play.
> >
> > That sounds equivalent to pitch. So there's redundancy
> > in your terminology. But the musical meaning of note is
> > generally a pitch with an octave-invariant name (though
> > occasionally, I'm sure, you get things like "C4" that are
> > not octave invariant).
>
> A pitch is tied to a specific frequency, a note needn't be.
> In everyday music the same notes can be played with
> different tunings.

I see. So a scale is really an ordering. Well there's
some utility for that. So maybe

Graham's new way Gene's accepted way
----------------------------------------
temperament class temperament
temperament tuning
tuning scale
scale [none -- an ordering]

I still don't think I'm swayed.

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> please do come up with an MOS that doesn't sound like a scale.

Howabout a 2-note MOS?

> My problem with the idea of super scales is that what
> happens if a melody say doesn't use all 7 tones of a diatonic.
> Does that make it a super scale or gamut, we could add the word
> array also in the mix.

Indeed.

-Carl

I am glad to see that the subject of scales has surfaced again.

For those who missed by comments a couple of months ago, here is the link to what I believe will be a very useful system for scalecoding "meantone-type" tunings.

This folder contains databases of 669 unique scales that I have collected.

http://www.lucytune.com/scales/

An explanation of the logic behind the system is here:

http://www.lucytune.com/new_to_lt/pitch_05.html

On 4 Mar 2008, at 07:33, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> >
> > please do come up with an MOS that doesn't sound like a scale.
>
> Howabout a 2-note MOS?
>
> > My problem with the idea of super scales is that what
> > happens if a melody say doesn't use all 7 tones of a diatonic.
> > Does that make it a super scale or gamut, we could add the word
> > array also in the mix.
>
> Indeed.
>
> -Carl
>
>
>
Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Carl Lumma wrote:
>> Once you have a tuning, then it's a temperament. A >> temperament class is a set of tunings with the same mapping >> from just intonation.
> > We say "miracle temperament" and "meantone temperament",
> not "miracle temperament class" etc. If just "temperament"
> is the tuned thing, then that frees up the term "tuning",
> if you have a use for it.

Yes, but I covered this the last time it came up. If "meantone" were the name of a temperament then you should say "the meantone temperament". Leaving out the article is ungrammatical. So plain "meantone temperament" must be short for "the process of tuning by meantone" and that may or may not imply a specific tuning.

Just intonations are tunings but not temperaments.

> I see. So a scale is really an ordering. Well there's
> some utility for that. So maybe

When this came up before, it was pointed out that scales as usually discussed in music theory do require an ordering -- either ascending or descending. And the two can have different notes. I don't see why the regular mapping paradigm should change that, any more than the idea that a temperament is a specific tuning.

The word "mode" can mean a scale without an ordering, among other things. But if you want to talk about a set of notes you can always say "a set of notes".

> Graham's new way Gene's accepted way
> ----------------------------------------
> temperament class temperament
> temperament tuning
> tuning scale
> scale [none -- an ordering]
> > I still don't think I'm swayed.

The only new thing about my way is "temperament class". Gene's way goes against the standard meanings and isn't at all well accepted.

Graham

Touche!.
I have never been happy with the what i would call the 'formation' period witth MOS. that stage where the interval of equivalence has not been reach at least once. otherwise one could say that the interval of equivalence has not been defined so it might not be a MOS. is it possible past that point? we should throw out also intervals below what we can hear as distinct. which for johnny would have to be less than a cent :) things beyond or below hearing range.

there are two and note melodies but this might be more of a rythmic nature. three more and after that they becme much more prevalent. I am sleepy.........

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > please do come up with an MOS that doesn't sound like a scale.
>
> Howabout a 2-note MOS?
>
> > My problem with the idea of super scales is that what
> > happens if a melody say doesn't use all 7 tones of a diatonic.
> > Does that make it a super scale or gamut, we could add the word
> > array also in the mix.
>
> Indeed.
>
> -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

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
> >> Once you have a tuning, then it's a temperament. A
> >> temperament class is a set of tunings with the same mapping
> >> from just intonation.
> >
> > We say "miracle temperament" and "meantone temperament",
> > not "miracle temperament class" etc. If just "temperament"
> > is the tuned thing, then that frees up the term "tuning",
> > if you have a use for it.
>
> Yes, but I covered this the last time it came up. If
> "meantone" were the name of a temperament then you should
> say "the meantone temperament". Leaving out the article is
> ungrammatical. So plain "meantone temperament" must be
> short for "the process of tuning by meantone"

Nah.

> Just intonations are tunings but not temperaments.

Just intonation isn't precisely defined. Some people
include things like Pythagorean intonation. These admit
regular mapping and could be tunings of a temperament.
Otherwise, they are scales.

> > I see. So a scale is really an ordering. Well there's
> > some utility for that. So maybe
>
> When this came up before, it was pointed out that scales as
> usually discussed in music theory do require an ordering --
> either ascending or descending. And the two can have
> different notes. I don't see why the regular mapping
> paradigm should change that, any more than the idea that a
> temperament is a specific tuning.

Actually I put "none" under Gene's way here, but I think he
used "notation" for this. Gene's site has been down or I'd
double-check it. It was the most controversial of his
definitions but I always thought it was a good one.

> The word "mode" can mean a scale without an ordering, among
> other things. But if you want to talk about a set of notes
> you can always say "a set of notes".
>
> > Graham's new way Gene's accepted way
> > ----------------------------------------
> > temperament class temperament
> > temperament tuning
> > tuning scale
> > scale [none -- an ordering]
> >
> > I still don't think I'm swayed.
>
> The only new thing about my way is "temperament class".
> Gene's way goes against the standard meanings and isn't at
> all well accepted.

Gene's way of temperament has been heavily used for years
on these lists (even before he showed up), including by you.
In fact I've never noticed you to use "temperament class"
in real discourse. Gene's definitions have been passed to
newbies on 3 lists by myself, monz, and others with little
complaint and zero alternatives proposed (until now).

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Touche!.
> I have never been happy with the what i would call the 'formation'
> period witth MOS. that stage where the interval of equivalence
> has not been reach at least once. otherwise one could say that
> the interval of equivalence has not been defined so it might not
> be a MOS. is it possible past that point?

Don't know. With a non-octave period you could probably
get some weird stuff. Or I could make the generator very
close in size to the period, and all the notes would clump up.

> we should throw out
> also intervals below what we can hear as distinct.

Yes. But then you need to define that. It can get a bit
hairy.

Also: how do you handle JI scales? Do you qualify them
with Constant Structures instead of MOS?

-Carl

> Carl Lumma wrote:
> > > please do come up with an MOS that doesn't sound like a scale.
> >
> > Howabout a 2-note MOS?

When it comes to discussing what the terminology should be,
you seem to imply that the discourse on these lists is somehow
insignificant. That isn't what I'd expect from someone who
wrote a paper declaring a new paradigm in music theory. Any
new paradigm has the right and probably the obligation to
practice a precise terminology, using terms either invented
or suitably adapted, and then to extract and publish
definitions from that practice. Gene did the extracting and
monz did the publishing, and there followed 7 years of further
use that seems to be consistent. As Paul points out, in
early some circles a temperament means a 12-tone well temperament.
We can certainly let them.

-Carl

I wrote...
> Graham wrote...
> > The only new thing about my way is "temperament class".
> > Gene's way goes against the standard meanings and isn't at
> > all well accepted.
>
> Gene's way of temperament has been heavily used for years
> on these lists (even before he showed up), including by you.
> In fact I've never noticed you to use "temperament class"
> in real discourse. Gene's definitions have been passed to
> newbies on 3 lists by myself, monz, and others with little
> complaint and zero alternatives proposed (until now).

yes after Wilson

Carl Lumma wrote:
>
>
>
> Also: how do you handle JI scales? Do you qualify them
> with Constant Structures instead of MOS?
>
> -
>
> -- 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

Kraig Grady wrote:
> Touche!.
> I have never been happy with the what i would call the 'formation' > period witth MOS. that stage where the interval of equivalence has not > been reach at least once. otherwise one could say that the interval of > equivalence has not been defined so it might not be a MOS. is it > possible past that point? we should throw out also intervals below what > we can hear as distinct. which for johnny would have to be less than a > cent :) things beyond or below hearing range.

Hmm, I guess something like 3 notes of miracle would make a pretty poor "scale". But then do you need to go all the way to blackjack (21 notes), or is 10 notes good enough? I think there's a point just before the generator becoming the large size step (e.g. 10 notes of miracle, 9 notes of negri, 7 notes of porcupine) where it starts to make sense to treat the MOS as a usable scale.

yes that was attempting to say.
Carl's example of having a very large generator short of the octave might just be considered an inversion of a smaller one or going down instead of up (like the greeks).
BTW way does anyone know if the Persians ever thought downward? i can't remembering hearing so but possible.

Herman Miller wrote:
>
> Kraig Grady wrote:
> > Touche!.
> > I have never been happy with the what i would call the 'formation'
> > period witth MOS. that stage where the interval of equivalence has not
> > been reach at least once. otherwise one could say that the interval of
> > equivalence has not been defined so it might not be a MOS. is it
> > possible past that point? we should throw out also intervals below what
> > we can hear as distinct. which for johnny would have to be less than a
> > cent :) things beyond or below hearing range.
>
> Hmm, I guess something like 3 notes of miracle would make a pretty poor
> "scale". But then do you need to go all the way to blackjack (21 notes),
> or is 10 notes good enough? I think there's a point just before the
> generator becoming the large size step (e.g. 10 notes of miracle, 9
> notes of negri, 7 notes of porcupine) where it starts to make sense to
> treat the MOS as a usable scale.
>
> -- 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" <carl@...> wrote:

>
> That puts an additional meaning to the term scale that
> I didn't know it had. How do you define "gamut"?

Personally, I define gamut in the same way it is used in digital
imaging. Here's the Wikipedia definition:

"In color reproduction, including computer graphics and photography,
the gamut, or color gamut, is a certain complete subset of colors. The
most common usage refers to the subset of colors which can be
accurately represented in a given circumstance, such as within a given
color space or by a certain output device."

In organology, gamut is commonly used to describe the range of pitches
an instrument is capable of producing, say FF-f4 for example (using
the most common organological pitch notation) for a typical Viennese
piano of 1815.

In the field of tuning/temperament, pitch gamut is restricted to an
octave (unless its a system which doesn't repeat at the octave) can be
either virtual or actual. Most western instruments which have fixed or
semi-fixed pitches have a practical gamut which reproduces the
theoretical gamut, but you might just as well have an extended
theoretical system which goes way beyond the standard 12 note gamut,
but the instrument may be capable of producing only a small select
subset of those notes. Your standard kanun is a good example of an
instrument which has a practical gamut which is only a selected subset
from the virtual gamut, a subset which must be chosen before you begin
playing (which of course can be somewhat modified during performance
by the mandals). Another example is an archicembalo, which may
reproduce a limited extension of a much larger theoretical gamut of
extended meantone.

>
> As a _tuning_ it's a tuning of some unnamed
> well temperament (class).

What is a "well" temperament? Is that the tuning of an instrument that
results when you throw it down a well? Or is it the tuning that
results when you can't remember the structure of some system so you
just sort of, you know, well, DO something?

Every time I hear the phrase "well temperament", it reminds me of
those folks who ain't got no proper schoolin', and says things lahk,
"I done tuned up mah geetar, en I dun did it right good!" I dun grewed
up in the central valley a Cal-i-forn-i-ay, so I dun knowed a bunch ah
folk that talked lahk that!

Really, all kidding aside, and apart from the linguistic abomination
of this term, I haven't got the foggiest notion what it is supposed to
mean. Generally, I hear it used by people who have so little real
knowledge of historical temperaments (present company excluded), that
the only thing I can say is that for them it means not meantone, not
Pythagorean, and not Equal. It's just a big bargain basement grab bag
into which they toss anything else, which usually only means WIII,
Kinrberger III, and the ubiquitous two-headed hydra "Vallotti/Young".
If pressed, they will say something like, "It means you can use all
the keys." Some will ad that no fifth can be larger than pure
(harmonically-efficient according to Jorgenson?). Neither definition
provides much light, as there is insufficient information to really
apply the term.

So I'd be curious to know what sort of structure you intended to
describe by your use of the term.

Ciao,

P

The Well-Tempered Clavier

not a cowboy at all

Paul Poletti wrote:
>
>
>
> What is a "well" temperament? Is that the tuning of an instrument that
> results when you throw it down a well? Or is it the tuning that
> results when you can't remember the structure of some system so you
> just sort of, you know, well, DO something?
>
>
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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:
>
>
> The Well-Tempered Clavier
>
>
> not a cowboy at all

Precisely!

In this case, the word "well" is used as an ADVERB - as it properly is.

If you say "a well temperament", you are using it as an adjective.

So if ya gits mah point, pardner, in that case ya wouldn't be talkin'
good, 'cause it wouldn't be no well construction, least not 'ccordin'
to them thar rule thangies they dun tried tah teach me 'bout afore I
dun up 'n' quit school. But shucks, who needs tham thar rule thangies
anyways? Ah kin talk right good enuf without 'em, least ways for
drivin' truck down at Central Feed & Seed. 'N' mah wife, Sarah-Sue,
she kin talk real good, too, 'n' she ain't never had nuthin' more than
8th grade. We gonna teach our kids real good, you just wait 'n' see
whut kinda well English they talk.

Auf Deutsch ist es auch so: das Gut-Temperierte Clavier??

Ciao,

P

Paul Poletti wrote:

> What is a "well" temperament? Is that the tuning of an instrument that
> results when you throw it down a well? Or is it the tuning that
> results when you can't remember the structure of some system so you
> just sort of, you know, well, DO something?

In this case, a rank 1 irregular temperament.

Graham

Paul Poletti wrote:

> In this case, the word "well" is used as an ADVERB - as it properly is.
> > If you say "a well temperament", you are using it as an adjective.

No, you're using a compound noun:

http://www.learnenglish.de/grammar/nouncompound.htm

http://grammar.ccc.commnet.edu/GRAMMAR/compounds.htm

Graham

Herman Miller wrote:

> Hmm, I guess something like 3 notes of miracle would make a pretty poor > "scale". But then do you need to go all the way to blackjack (21 notes), > or is 10 notes good enough? I think there's a point just before the > generator becoming the large size step (e.g. 10 notes of miracle, 9 > notes of negri, 7 notes of porcupine) where it starts to make sense to > treat the MOS as a usable scale.

Magic (major third generator) closes with an augmented triad. 4 notes would certainly be a scale by this definition. And maybe 7 notes is a usable scale although I don't think it's been used in anger yet. But there are other MOSs between there and 19 which I'm not so sure about.

Graham

Carl Lumma wrote:
> When it comes to discussing what the terminology should be,
> you seem to imply that the discourse on these lists is somehow
> insignificant. That isn't what I'd expect from someone who
> wrote a paper declaring a new paradigm in music theory. Any
> new paradigm has the right and probably the obligation to
> practice a precise terminology, using terms either invented
> or suitably adapted, and then to extract and publish
> definitions from that practice. Gene did the extracting and
> monz did the publishing, and there followed 7 years of further
> use that seems to be consistent. As Paul points out, in
> early some circles a temperament means a 12-tone well temperament.
> We can certainly let them.

I wrote a web page explaining the paradigm using terminology that you say is inconsistent with the paradigm. Surely I can speak up about that!

There are cases where terms need to be adapted when they're applied to new things. We do plenty of that (tunings with an infinite number of notes, temperaments with rational intervals, temperaments of inharmonic timbres) but there's no need to make gratuitous changes.

What practice did Gene "extract" definitions from? It looked like he was making up his own definitions.

What did Monz publish? His encyclopedia lists Gene's definition along with three (one of them mine) that say a temperament is a tuning.

What further use? Gene didn't get much beyond the definitions. A Middle Path talks about tunings, but also says they're not essential, suggesting the terminology wasn't fixed then. I've written a web page and a PDF that use "temperament class" and another PDF nearly finished. George Secor talks about the meantone temperament (properly, with the article) as a single tuning. There are also references in the archives that you seem blind to. So every time this issue comes up you argue as if nobody has ever seen the problem before.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
> > In this case, the word "well" is used as an ADVERB - as it
properly is.
> >
> > If you say "a well temperament", you are using it as an adjective.
>
> No, you're using a compound noun:
>
> http://www.learnenglish.de/grammar/nouncompound.htm
>
> http://grammar.ccc.commnet.edu/GRAMMAR/compounds.htm
>
A debatable point. But I notice that NONE of the examples involve the
combination of an adverb and a noun.

But I'm warming to the idea. Let's see, now a job quickly done is a
quickly job. Or work poorly done is poorly work.

Trouble is with English, it is so irregular, and has suffered such
abuse over the centuries. How does one apply a deadly force? Deadlyly?

I give up!

Actually, in certain idomatic constructions, well can be an adjective,
as in "She is not well." Probably just a bastardization of "She is not
feeling well."

Anyway, I still think it's a bit of a botched job, stealing it from a
tittle where it obviously functions adverbilyly.

And what, pray tell, is a class 1 irregular temperament?

Ciao,

P

Paul Poletti wrote:

> Actually, in certain idomatic constructions, well can be an adjective,
> as in "She is not well." Probably just a bastardization of "She is not
> feeling well."

It can also be a noun: "I wish you well!"

> Anyway, I still think it's a bit of a botched job, stealing it from a
> tittle where it obviously functions adverbilyly.

Whether you like it or not it's the term that's in use.

> And what, pray tell, is a class 1 irregular temperament?

I don't know. Is it like a rank 1 irregular temperament?

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
> > Actually, in certain idomatic constructions, well can be an adjective,
> > as in "She is not well." Probably just a bastardization of "She is not
> > feeling well."
>
> It can also be a noun: "I wish you well!"
>
> > Anyway, I still think it's a bit of a botched job, stealing it from a
> > tittle where it obviously functions adverbilyly.
>
> Whether you like it or not it's the term that's in use.
>
Yeah, like military intelligence. Or defense budget.

;-)
>
> I don't know. Is it like a rank 1 irregular temperament?

Obviously a typo on my part. So yeah, tell us what a "rank 1 irregular
temperament" is, please, already. It, on the other hand, does NOT seem
to be a term that's much in use, since as search of the list archives
for "rank 1 irregular" only returns 9 entries, none of which actually
use that particular term.

Ciao,

P

Paul Poletti wrote:

> Obviously a typo on my part. So yeah, tell us what a "rank 1 irregular
> temperament" is, please, already. It, on the other hand, does NOT seem
> to be a term that's much in use, since as search of the list archives
> for "rank 1 irregular" only returns 9 entries, none of which actually
> use that particular term.

Rank 1: just intonation maps to a rank 1 group. So an approximation to any given ratio can be counted as a given number of scale steps, with only one kind of step.

Irregular: the same interval in just intonation can be tuned differently in the temperament. So the steps are tuned differently.

Temperament: an approximation of just intonation.

Usually we call them "well temperaments".

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
>
> Rank 1: just intonation maps to a rank 1 group. So an
> approximation to any given ratio can be counted as a given
> number of scale steps, with only one kind of step.
>
> Irregular: the same interval in just intonation can be tuned
> differently in the temperament. So the steps are tuned
> differently.
>
> Temperament: an approximation of just intonation.

Right. Think I've got it more or less, though rank 1 is still a bit fuzzy.

>
> Usually we call them "well temperaments".

What would you call those temperaments which practicing musicians
refer to as modified meantones?

I assume they are still rank 1, but are they regular or irregular? I
would assume the late, but then why don't you call them "well
temperaments"? Maybe you do.

Ciao,

p

> Every time I hear the phrase "well temperament", it reminds me of
> those folks who ain't got no proper schoolin', and says things lahk,
> "I done tuned up mah geetar, en I dun did it right good!"

I agree the term is not a good one. But it's stuck. Some
people say "circulating temperament", but I don't think that's
much better.

> So I'd be curious to know what sort of structure you intended to
> describe by your use of the term.

We haven't an understanding of them. At least I don't.
Perhaps they can be viewed as irregular tunings of regular
temperaments.

-Carl

I assumed that regular temperaments were those in which every interval in the chain was the same size. Irregular ones where there is variations ( hence makes some distinction between keys). I have only had passing empirical experience with these, but remember i quite like some of Secor's 'equal beating' solutions. Still have one stored away here.

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > Graham Breed <gbreed@...> wrote:
> >
> > Paul Poletti wrote:
> >
> >
> > Rank 1: just intonation maps to a rank 1 group. So an
> > approximation to any given ratio can be counted as a given
> > number of scale steps, with only one kind of step.
> >
> > Irregular: the same interval in just intonation can be tuned
> > differently in the temperament. So the steps are tuned
> > differently.
> >
> > Temperament: an approximation of just intonation.
>
> Right. Think I've got it more or less, though rank 1 is still a bit fuzzy.
>
> >
> > Usually we call them "well temperaments".
>
> What would you call those temperaments which practicing musicians
> refer to as modified meantones?
>
> I assume they are still rank 1, but are they regular or irregular? I
> would assume the late, but then why don't you call them "well
> temperaments"? Maybe you do.
>
> Ciao,
>
> p
>
> -- 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:
> The Well-Tempered Clavier
>
> not a cowboy at all

But here JSB is describing an instrument. "A well-oiled
machine" for example. "Well oilment" is a little funny.

-Carl

> What practice did Gene "extract" definitions from? It
> looked like he was making up his own definitions.

The practice here on these lists, which he observed.

-Carl

Graham wrote...
> There are also references in the archives that you seem blind to.

The usage on the lists is inconsistent, but where it is
consistent it clearly revolves around Gene's definitions.
Things like "meantone temperament" have almost always
referred to an infinite series scales, since the mid 1990s
on this list, and this was extended when we started naming
new temperaments in 2001. "Scale" usually meets Gene's
definition. Scala .scl files are the very embodiment.
"Tuning" is probably the least consistently used of the
three, but "tuning of meantone" can only mean one thing.
"RMS optimum tuning" can only mean one thing. I triple
dog dare you to find more than 5 occurrences of the term
"temperament class" that didn't come from you. And I would
ask you to report the year you first used it. I will eat
a bug if it is < 2006 (but I get to pick which kind).

The terms which are at least debatable are "monz" and "val".
Though if these were coined by Wilson, nobody would be
debating it. So I'm not sure why someone who produced such
a volume of original and groundbreaking literature on the
subject and had the heart to name things after other people
is a target of a militant terminology engineering effort.

-Carl

> I triple
> dog dare you to find more than 5 occurrences of the term
> "temperament class" that didn't come from you.

The most recent such occurrence is from last September, where
George Secor is arguing that "temperament class" should just
be "temperament". And Jon Wild.

In fact I can find exactly two such occurrences where someone
wasn't arguing with you about whether the existing usage
(just temperament) should be replaced by "temperament class".

/tuning/topicId_63252.html#63418
/tuning/topicId_63413.html#63425

As I suspected, I don't see you using it prior to 2006,
except possibly in this one case

/tuning/topicId_8334.html#8425

In the face of much less opposition than this, Gene had
frequently been asked to change his terminology, and he
almost always complied. So... whatd'ya say?

-Carl

"I agree the term is not a good one. But it's stuck. Some
people say "circulating temperament", but I don't think that's
much better."

"Well tempered" is not necessarily a synonymous description for "circulating" and the distinction, however subtle between the two, may well be musically useful.

I think (a) "circulating temperament" describes a very useful property (all of the major/minor scales and tonalities on each tone of the scale or system are usable; caveat: your mileage on "usable" may well vary and "well tempered" presumably adds a positive qualifier, sorting out temperaments with particular properties from among the garden of possible circulating temperaments), and (b) that there is plenty of interesting work to be done in making non-equal circulating temperaments, especially in tuning systems with more than 12 tones.

Daniel Wolf

Carl Lumma wrote:

> The terms which are at least debatable are "monz" and "val".
> Though if these were coined by Wilson, nobody would be
> debating it. So I'm not sure why someone who produced such
> a volume of original and groundbreaking literature on the
> subject and had the heart to name things after other people
> is a target of a militant terminology

Oh, come off it! Who's val? Why do you think I object to the term? Has it ever occurred to you that I want to call it a "gene"?

Graham

Carl Lumma wrote:
> Graham wrote...
>> There are also references in the archives that you seem blind to.
> > The usage on the lists is inconsistent, but where it is
> consistent it clearly revolves around Gene's definitions.
> Things like "meantone temperament" have almost always
> referred to an infinite series scales, since the mid 1990s
> on this list, and this was extended when we started naming
> new temperaments in 2001. "Scale" usually meets Gene's
> definition. Scala .scl files are the very embodiment.
> "Tuning" is probably the least consistently used of the
> three, but "tuning of meantone" can only mean one thing.
> "RMS optimum tuning" can only mean one thing. I triple
> dog dare you to find more than 5 occurrences of the term
> "temperament class" that didn't come from you. And I would
> ask you to report the year you first used it. I will eat
> a bug if it is < 2006 (but I get to pick which kind).

Where are your references then? There's actually an interesting one here:

http://www.robertinventor.com/tuning-math/s___2/msg_1100-1124.html

where I seem to be saying that you *don't* need the tuning to define a temperament, but I haven't found the original. Also I'm quoted as asking whether a temperament is defined as having a tuning, but I can't find the original of that either, or any answers. Mixed in is some stuff about magic temperament and Monz announcing his trip to Europe!

What is your argument for this weird piece of grammar? I speak, and get paid for teaching, the Queen's English. Here's a summary on the use of articles:

http://www.britishcouncil.org/learnenglish-central-grammar-definitions-articles.htm

It says you can leave out the article when you "use uncountable and plural nouns to talk about things generally". Well, a specific temperament isn't "things generally" is it? More like a class of things. Maybe you can pick out the rule you follow from this page:

http://grammar.ccc.commnet.edu/GRAMMAR/determiners/determiners.htm

What is Gene's definition of "scale"? Monzo's looks right:

"A succession of musical pitches arranged in order of pitch-height, generally considered as a source set of pitches for musical composition."

What are Scala files supposed to embody? They're certainly ordered, which was the issue before.

Is there any controversy about "tuning"?

What have "temperament classes" got to do with anything? In fact I was using them before, and you found a reference. So presumably you had a tasty bug ready. Perhaps 2006 was when I was told to stop using "temperament family". I don't remember.

> The terms which are at least debatable are "monz" and "val".
> Though if these were coined by Wilson, nobody would be
> debating it. So I'm not sure why someone who produced such
> a volume of original and groundbreaking literature on the
> subject and had the heart to name things after other people
> is a target of a militant terminology engineering effort.

We're not debating *that* again, are we? And if something nasty's going on you'll have to let me in on the secret.

Now, I had Gene's website open now but I've lost it. The trick is to go to archive.org and search for xenharmony.org and there are several different snapshots.

Graham

Paul Poletti wrote:

> What would you call those temperaments which practicing musicians
> refer to as modified meantones?

I don't know what that means.

> I assume they are still rank 1, but are they regular or irregular? I
> would assume the late, but then why don't you call them "well
> temperaments"? Maybe you do.

If they're modified I take it they aren't regular any more. Meantone is rank 2 even if you take a finite subset within the octave. There's a distinction between perfect fifths and wolves, for example. If you modify them enough for all intervals of a given number of steps to be acceptable, then it'd count as rank 1. I don't have any shares in one definition of "well temperament" but loosely speaking it applies.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
> > What would you call those temperaments which practicing musicians
> > refer to as modified meantones?
>
> I don't know what that means.

Are you just putting me on, or is the void between microtonality and
the field of historical tuning and temperament so vast? I find it hard
to believe that you've never heard of Rameau, or D'Alembert.
Werckmeister's modified meantone I could give you a break on, since
everybody has pretty much ignored it completely until I started
singing its praises some years back, even though it's the first
alternative to ET that was published in the 20th century in any source
dealing with the historical performance of Baroque Music (Arnold, 1931!).

But maybe you're just not interested in historical temperaments, in
which case I could understand. Admittedly, the whole lot of them is
pretty boring and simplistic, compared to more interesting stuff.

>
> > I assume they are still rank 1, but are they regular or irregular? I
> > would assume the late, but then why don't you call them "well
> > temperaments"? Maybe you do.
>
> If they're modified I take it they aren't regular any more.

Now that's a no brainer!

> Meantone is rank 2 even if you take a finite subset within
> the octave. There's a distinction between perfect fifths
> and wolves, for example.

The so-called "wolf" fifth is not a fifth, its either a dimisihed 6th
or an augmented 3rd. Actually, all correct intervals in meantone
(those that can be spelled correctly using the nonenhamronic functions
of the accidentals) are all of the same size, so isn't that rank 1, or
do I misunderstand the ranking of ranks?

Meantone is open-ended, a system which never closes. It just keeps
spiraling. It only "closes" with a "wolf fifth" if you impose the idea
of a 12-tone circular system upon it. The survival of many keyboard
instruments which were tuned in regular meantone and provided with any
number of subsemitones shows that old musicians knew that the 12-tone
version was just a small chunk out of an infinite spiral.

By the way, and I've asked this before, does anybody know by who and
when the word wolf was first applied to the interval Eb-G#. The only
historical use of it I've every read is Preatorius, and he said that
musicians called the augmented second F-G# "the wolf". Not a minor
detail, as resolving the G#/Ab dichotomty pops up again and again in
mod. meantone instructions.

> If you modify them enough for all
> intervals of a given number of steps to be acceptable, then
> it'd count as rank 1.

And how do we define "acceptable"? In other words, playing within the
variations allowed for by Werckmeister's instructions, at what point
do we arrive at a version which makes "all intervals of a given number
of steps acceptable"? The advantage to calling it a modified meantone
is because that name tells you something valid about both its
structure and the practical methodology of actually setting it, yet
doesn't get trapped in any such boggy value judgements.

> I don't have any shares in one
> definition of "well temperament" but loosely speaking it
> applies.

That's my problem. Over and over again I ask people what the hell does
"well" ,mean, and they hem and they haw and they speak loosely in
general terms broadly defined, and finally I just have to reach the
conclusion that it is a totally bogus term, since nobody can clarify
anything.

Thanks for trying, though.

;-)

Ciao,

P

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
> > Graham wrote...
> >> There are also references in the archives that you seem blind to.
> >
> > The usage on the lists is inconsistent, but where it is
> > consistent it clearly revolves around Gene's definitions.
> > Things like "meantone temperament" have almost always
> > referred to an infinite series scales, since the mid 1990s
> > on this list, and this was extended when we started naming
> > new temperaments in 2001. "Scale" usually meets Gene's
> > definition. Scala .scl files are the very embodiment.
> > "Tuning" is probably the least consistently used of the
> > three, but "tuning of meantone" can only mean one thing.
> > "RMS optimum tuning" can only mean one thing. I triple
> > dog dare you to find more than 5 occurrences of the term
> > "temperament class" that didn't come from you. And I would
> > ask you to report the year you first used it. I will eat
> > a bug if it is < 2006 (but I get to pick which kind).
>
> Where are your references then?

I'll get back to you when I've decided which of the 1,000+
potential citations are best fitted to remind you of.

> There's actually an interesting one here:
>
> http://www.robertinventor.com/tuning-math/s___2/msg_1100-1124.html
>
> where I seem to be saying that you *don't* need the tuning
> to define a temperament,

You certainly do. And Dave "totally agrees".

> Also I'm quoted as asking whether a temperament is defined
> as having a tuning, but I can't find the original of that
> either, or any answers.

I don't find such a quote from you on this page.

> What is your argument for this weird piece of grammar?
> I speak, and get paid for teaching, the Queen's English.
> Here's a summary on the use of articles:
> http://www.britishcouncil.org/
> learnenglish-central-grammar-definitions-articles.htm
>
> It says you can leave out the article when you "use
> uncountable and plural nouns to talk about things
> generally". Well, a specific temperament isn't "things
> generally" is it? More like a class of things. Maybe you
> can pick out the rule you follow from this page:
>
> http://grammar.ccc.commnet.edu/GRAMMAR/determiners/determiners.htm

What term are you referring to?

> What is Gene's definition of "scale"?

Scale

A discrete set of real numbers, containing 0, and regarded as
defining tones in a logarithmic measure, such as cents or octaves,
and such that the distance between sucessive elements of the scale
is bounded both below and above by positive real numbers. The least
upper bound of the intervals between successive elements of the
scale is the maximum scale step, and the greatest lower bound is
the minimum scale step. The element of the scale obtained by
counting up n scale steps is the nth degree, by counting down is
the –nth degree; 0 is the 0th degree. The set of positive real
numbers which are the tones so represented is also regarded as the
scale.

> What are Scala files supposed to embody?

They meet Gene's definition, and they're called "scale files".

> They're certainly ordered, which was the issue before.

Yes but you seemed to be talking about just an ordering,
i.e. letter names. So you weren't specifying a tuning.

> Is there any controversy about "tuning"?

Lots of people call things like Valotti and 12-ET "tunings".
Probably the most common term among piano tuners. So you
see, in the world at large terminology is not consistent.
But in each school, it is more consistent. And within a
music theory school heavily dependent on 1. math and 2. e-mail
for communication, ours should be the most consistent.

> What have "temperament classes" got to do with anything?

They're this term you invented and keep using even though
nobody else is.

> In
> fact I was using them before, and you found a reference. So
> presumably you had a tasty bug ready.

It wasn't clear from the context of that message. But if you'll
confirm it, I will eat a bug. However I could probably find on
your website plenty of examples of the Gene's terminology. Oh,
bother...
The only place I find "temperament class" is on your regular
mapping paradigm page. I see plenty of examples of "meantone
temperament" to mean the class, though to be fair you just
about as often use the phrase "meantone temperaments" as well.

Here's a "Catalog of Linear Temperaments"
http://x31eq.com/catalog.htm
not a "catalog of linear temperament classes".

You *do* seem to be using your tuning-invariant definition
of "scale", FWIW.

> Perhaps 2006 was when
> I was told to stop using "temperament family". I don't
> remember.

Yes, because Gene had already published a web page and a
dozen messages to tuning-math using the term for something
else.

-Carl

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
> > What would you call those temperaments which practicing musicians
> > refer to as modified meantones?
>
> I don't know what that means.

They're in the same class as well temperaments, whatever
class that is.

They're not all that interesting theoretically, actually.
I think the term "irregular temperament" should not be
used. They're regular temperaments plus an asymmetrical
tuning.

> > I assume they are still rank 1, but are they regular or
> > irregular? I would assume the late, but then why don't
> > you call them "well temperaments"? Maybe you do.
>
> If they're modified I take it they aren't regular any more.

Modified meantones are well temperaments with mostly
meantone fifths (usually quarter-comma).

> If you modify them enough for all
> intervals of a given number of steps to be acceptable, then
> it'd count as rank 1. I don't have any shares in one
> definition of "well temperament" but loosely speaking it
> applies.

I think a better way is to preserve the mapping (keep them
rank 2) but break a symmetry between the mapping and the
tuning.

-Carl

> > I don't know what that means.
>
> Are you just putting me on, or is the void between microtonality
> and the field of historical tuning and temperament so vast?

So vast.

> I find it heard to believe that you've never heard of Rameau,
> or D'Alembert.

Most of us have heard of Rameau as a composer, and occasionally
as a proponent of 1/3-comma meantone, and occasionally as a
proponent of the virtual pitch theory of dissonance. D'Alembert
I only know of because I'm an early music geek.

-Carl

Carl Lumma schrieb:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Carl Lumma wrote:
>>> Graham wrote...
>>>> There are also references in the archives that you seem blind to.
>>> The usage on the lists is inconsistent, but where it is
>>> consistent it clearly revolves around Gene's definitions.
>>> Things like "meantone temperament" have almost always
>>> referred to an infinite series scales, since the mid 1990s
>>> on this list, and this was extended when we started naming
>>> new temperaments in 2001. "Scale" usually meets Gene's
>>> definition. Scala .scl files are the very embodiment.
>>> "Tuning" is probably the least consistently used of the
>>> three, but "tuning of meantone" can only mean one thing.
>>> "RMS optimum tuning" can only mean one thing. I triple
>>> dog dare you to find more than 5 occurrences of the term
>>> "temperament class" that didn't come from you. And I would
>>> ask you to report the year you first used it. I will eat
>>> a bug if it is < 2006 (but I get to pick which kind).
>> Where are your references then?
> > I'll get back to you when I've decided which of the 1,000+
> potential citations are best fitted to remind you of.
> >> There's actually an interesting one here:
>>
>> http://www.robertinventor.com/tuning-math/s___2/msg_1100-1124.html
>>
>> where I seem to be saying that you *don't* need the tuning >> to define a temperament,
> > You certainly do. And Dave "totally agrees".
> >> Also I'm quoted as asking whether a temperament is defined >> as having a tuning, but I can't find the original of that >> either, or any answers.
> > I don't find such a quote from you on this page.

May I kindly ask the parties to consider what "to temper" means and what it might be that is tempered?

> >> What is Gene's definition of "scale"?
> > Scale > > A discrete set of real numbers, containing 0, and regarded as
> defining tones in a logarithmic measure, such as cents or octaves,
> and such that the distance between sucessive elements of the scale
> is bounded both below and above by positive real numbers. The least
> upper bound of the intervals between successive elements of the
> scale is the maximum scale step, and the greatest lower bound is
> the minimum scale step. The element of the scale obtained by
> counting up n scale steps is the nth degree, by counting down is
> the �nth degree; 0 is the 0th degree. The set of positive real
> numbers which are the tones so represented is also regarded as the
> scale.
> >> What are Scala files supposed to embody?
> > They meet Gene's definition, and they're called "scale files".

It is not impossible to make a scala file of a gamut, and to order a gamut by pitch. We are all conversing in English here, which is one the few languages distinguished by having terms for both; why not use them both?

For the record, my definition of "gamut" is: All acceptable discrete pitches in a musical culture.

klaus

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > I triple
> > dog dare you to find more than 5 occurrences of the term
> > "temperament class" that didn't come from you.
>
> The most recent such occurrence is from last September, where
> George Secor is arguing that "temperament class" should just
> be "temperament".

Huh? Where? Certainly not here:
/tuning/topicId_72835.html#73129
or here:
/tuning/topicId_72835.html#73314

Sorry, but I've been away for a few days and don't have enough time
to read through the large number of messages in this thread to get
your statement in its full context, so perhaps I've misunderstood
something.

In the above messages I used the term "temperament class", and I'll
continue to do so until such time as some other suitable term
(consisting of a single word other than "temperament" or "family")
can be agreed upon. The bottom line is that "temperament class" has
a clear, unambiguous, meaning (analogous to "pitch class"
and "interval class"), such that it clearly refers to sets of
temperaments defined as having a generator (or generators) and a
period within specified boundaries, whereas "temperament" is a more
general, less rigorous term, such that the mention of "a temperament"
is more likely to be interpreted by a music theorist (outside this
forum) as some particular *tempered tuning* than as some specific set
(or class) of tempered tunings.

To get my thoughts in their full context, you should also review this
message:
/tuning/topicId_72835.html#73069
in which I took issue with using the term "meantone" as a label for a
temperament class (and "meantone temperament" to refer to a
temperament class).

Then (as now) I really didn't have the time or inclination to get
mired down in these particular issues. These were my parting
thoughts from last fall, in which I expressed the hope that the rest
of you might come to terms (pun intended) with common (and widely
accepted) usage that originated outside of this forum:
/tuning/topicId_73148.html#73449

--George

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > I don't know what that means.
> >
> > Are you just putting me on, or is the void between microtonality
> > and the field of historical tuning and temperament so vast?
>
> So vast.

I'm beginnig to get a feel for that vastness.
>
> > I find it heard to believe that you've never heard of Rameau,
> > or D'Alembert.
>
> Most of us have heard of Rameau as a composer, and occasionally
> as a proponent of 1/3-comma meantone,

That's a new one to me. Is there any factual support for this, or is
this just some sort of temperament poodle in the microwave thing?

> D'Alembert
> I only know of because I'm an early music geek.

Right, yeah, I guess other folks would never have hear of him, 'cause
he certainly didn't do anything of any merit in a general sort of
historical sense, ya know, like invent Freedom Fries or baseball
cards. Ah, wait a minute ... wasn't he a contributing editor to The
Rough Guide to Pre-revolutionary France, or somethin' like that? Along
with his girlfriend, Dee de Roo, I think it was...

Happy Trails,

P

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > I triple
> > > dog dare you to find more than 5 occurrences of the term
> > > "temperament class" that didn't come from you.
> >
> > The most recent such occurrence is from last September, where
> > George Secor is arguing that "temperament class" should just
> > be "temperament".
>
> Huh? Where? Certainly not here:
> /tuning/topicId_72835.html#73129
> or here:
> /tuning/topicId_72835.html#73314
>

Very odd... I'm getting a MUCH larger set of results for
"temperament class" than I did the other day. And clearly,
you've been against Gene's definition in these messages.
Moreover, I couldn't find the message (by any author) that
that I'd read the other day and attributed to you.

-Carl

Carl Lumma wrote:

> Very odd... I'm getting a MUCH larger set of results for
> "temperament class" than I did the other day. And clearly,
> you've been against Gene's definition in these messages.
> Moreover, I couldn't find the message (by any author) that
> that I'd read the other day and attributed to you.[George]

It's here:

/tuning/topicId_73148.html#73449

Graham

Klaus Schmirler wrote:

> May I kindly ask the parties to consider what "to temper" means and > what it might be that is tempered?

Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast
Toast toast toast toast

What do you put in a toaster?

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> There's actually an interesting one here:
>>
>> http://www.robertinventor.com/tuning-math/s___2/msg_1100-1124.html
>>
>> where I seem to be saying that you *don't* need the tuning >> to define a temperament,
> > You certainly do. And Dave "totally agrees".

Yes, in 2001. Then, in 2002, we have another discussion where Dave says "So the mapping defines a `temperament class' while specific generators define a `temperament (instance)'. I like that."

http://www.robertinventor.com/tuning-math/s___5/msg_4800-4824.html

>> Also I'm quoted as asking whether a temperament is defined >> as having a tuning, but I can't find the original of that >> either, or any answers.
> > I don't find such a quote from you on this page.

Here, anyway:

http://www.robertinventor.com/tuning-math/s___1/msg__700-_724.html

>> What is your argument for this weird piece of grammar?
>> I speak, and get paid for teaching, the Queen's English.
>> Here's a summary on the use of articles:
>> http://www.britishcouncil.org/
>> learnenglish-central-grammar-definitions-articles.htm
>>
>> It says you can leave out the article when you "use >> uncountable and plural nouns to talk about things >> generally". Well, a specific temperament isn't "things >> generally" is it? More like a class of things. Maybe you >> can pick out the rule you follow from this page:
>>
>> http://grammar.ccc.commnet.edu/GRAMMAR/determiners/determiners.htm
> > What term are you referring to?

"Meantone temperament is a temperament" with respect to "The Article".

>> What is Gene's definition of "scale"?
> > Scale > > A discrete set of real numbers, containing 0, and regarded as
> defining tones in a logarithmic measure, such as cents or octaves,
> and such that the distance between sucessive elements of the scale
> is bounded both below and above by positive real numbers. The least
> upper bound of the intervals between successive elements of the
> scale is the maximum scale step, and the greatest lower bound is
> the minimum scale step. The element of the scale obtained by
> counting up n scale steps is the nth degree, by counting down is
> the �nth degree; 0 is the 0th degree. The set of positive real
> numbers which are the tones so represented is also regarded as the
> scale.

That looks like a special-case definition for a mathematically based theory we haven't seen yet. It talks about real numbers, which suggests a relationship to frequencies, but doesn't define it.

>> What are Scala files supposed to embody?
> > They meet Gene's definition, and they're called "scale files".

They meet pretty much any definition. What else was Manuel supposed to call them back when he started writing Scala?

>> They're certainly ordered, which was the issue before.
> > Yes but you seemed to be talking about just an ordering,
> i.e. letter names. So you weren't specifying a tuning.

No, not just an ordering. I was pointedly not requiring a tuning, which ties in with usages like "the diatonic scale" or "the blackjack scale" but it'd hardly be surprising if other usages conflict with that. I don't know how other people understand it.

>> Is there any controversy about "tuning"?
> > Lots of people call things like Valotti and 12-ET "tunings".
> Probably the most common term among piano tuners. So you
> see, in the world at large terminology is not consistent.
> But in each school, it is more consistent. And within a
> music theory school heavily dependent on 1. math and 2. e-mail
> for communication, ours should be the most consistent.

And they are tunings, aren't they?

>> What have "temperament classes" got to do with anything?
> > They're this term you invented and keep using even though
> nobody else is.

It looks like other people are using it, but if it's under some kind of duress, what of it?

>> In >> fact I was using them before, and you found a reference. So >> presumably you had a tasty bug ready.
> > It wasn't clear from the context of that message. But if you'll
> confirm it, I will eat a bug. However I could probably find on
> your website plenty of examples of the Gene's terminology. Oh,
> bother...
> The only place I find "temperament class" is on your regular
> mapping paradigm page. I see plenty of examples of "meantone
> temperament" to mean the class, though to be fair you just
> about as often use the phrase "meantone temperaments" as well.

I don't remember using the term that early, but the archive clearly shows that I did. The reference I gave above is unambiguous. As is this one from 2001:

http://www.robertinventor.com/tuning-math/s___2/msg_1275-1299.html

But then in 2001 I was also using "temperament" to mean the same thing and "temperament family" for something similar. It's only in 2002 that I can find a reference for "linear temperament family" which is the term I thought I used until it got redefined by the collective. And I was clearly using "temperament class" as well.

I try to be more conservative about the terminology I use on web pages because they're more permanent. Hence the only reference to "temperament class" on an HTML page is on the one I wrote after consciously changing the terminology. But it's also used in regular.zip, primerr.pdf, and complete.pdf so that's hardly the only place on my website. Before the great shift I would have tried to fit what I wanted to say around the word "temperament" with the occasional "family".

> Here's a "Catalog of Linear Temperaments"
> http://x31eq.com/catalog.htm
> not a "catalog of linear temperament classes".

Right, that's a page from 2001, before I had anything else to call them. And it's what I was discussing with Dave when we talked about temperaments being defined by mappings. At that stage the terminology was unclear (consistent with the crisis preceding a paradigm shift).

Also, they should be "rank 2 temperament classes" with the current, strict definition of "linear temperament".

> You *do* seem to be using your tuning-invariant definition
> of "scale", FWIW.

But I may not specify the ordering.

What I think we need is a disambiguation of "pitch". In psychoacoustic terms, it's a subjective quantity associated with a frequency. But isn't it also used in music for things like "C#" or "Gb" where a tuning isn't specified? So the definition of "scale" isn't a problem because a scale's always a list of pitches. The problem is that "pitch" can mean different things.

Unfortunately "pitch class" won't do although I'm sure I heard a definition that was pretty close. I've been using "note" but that's probably not at all accepted. Perhaps it's what you meant by "letter names".

>> Perhaps 2006 was when >> I was told to stop using "temperament family". I don't >> remember.
> > Yes, because Gene had already published a web page and a
> dozen messages to tuning-math using the term for something
> else.

There are still some references to "family" on my website, but I don't think they conflict. It looks like Gene and I were using the term with different meanings in 2004 so the switch to "temperament class" must have been around then. But I had to use a borrowed internet connection late 2004 and early 2005, and then I was in hospital for a month, and had various other disruptions, so it's quite possible I didn't start talking about temperament classes until 2006.

Graham

> > What term are you referring to?
>
> "Meantone temperament is a temperament" with respect to "The
> Article".

If I said that it was strictly a mistake (probably the
result of someone talking to me while I was writing it).

> That looks like a special-case definition for a
> mathematically based theory we haven't seen yet. It talks
> about real numbers, which suggests a relationship to
> frequencies, but doesn't define it.

Some of his proofs may require (or later assume) you've
got reals. Certainly you limit the kinds of caculations
you can do when calculating scales.

He says they're log-pitch. He also goes on in that
message to define things like "periodic scale", "periodic
reduced scale", and "epimorphic scale".

> >> What are Scala files supposed to embody?
> >
> > They meet Gene's definition, and they're called "scale
> > files".
>
> They meet pretty much any definition.

Not at all. You can't put "meantone" in a scale file.

> What else was Manuel
> supposed to call them back when he started writing Scala?

How would the era in which he did it matter? He obviously
felt the abstraction was worth defining a file format around,
and he used the closest existing term for a name, which
turned out to be close enough not to confuse anybody. All
of which mirrors what Gene did.

> >> They're certainly ordered, which was the issue before.
> >
> > Yes but you seemed to be talking about just an ordering,
> > i.e. letter names. So you weren't specifying a tuning.
>
> No, not just an ordering. I was pointedly not requiring a
> tuning, which ties in with usages like "the diatonic scale"
> or "the blackjack scale" but it'd hardly be surprising if
> other usages conflict with that.

So exactly how *do* you define it? I know you've used
xL + ys notation, but that doesn't get you all the way to
"the blackjack scale" (you need to specify L and s and
miracle temperament, or L and s and the distribution of
L & s, or something).

And "the blackjack scale" is something you're apparently
making up. People usually just say "blackjack" (42 vs. 8
matches in my tuning list archives from '03-05).

> I don't know how other
> people understand it.

As Kraig just explained, Wilson starts with Gene's def.
and further requires either MOS or a CS in JI.

> >> Is there any controversy about "tuning"?
> >
> > Lots of people call things like Valotti and 12-ET "tunings".
> > Probably the most common term among piano tuners. So you
> > see, in the world at large terminology is not consistent.
> > But in each school, it is more consistent. And within a
> > music theory school heavily dependent on 1. math and
> > 2. e-mail for communication, ours should be the most
> > consistent.
>
> And they are tunings, aren't they?

You could argue that a restriction to the 12-ET patent val
mapping is taken for granted among piano tuners. In that
case it would be valid usage.

> Before the
> great shift I would have tried to fit what I wanted to say
> around the word "temperament" with the occasional "family".

So you consciously changed it. Did you tell anybody about
your decision at the time?

> Also, they should be "rank 2 temperament classes" with the
> current, strict definition of "linear temperament".

Yes. That's a change I was skeptical of at first, but soon
accepted because it, ahem, made a lot of sense.

> What I think we need is a disambiguation of "pitch". In
> psychoacoustic terms, it's a subjective quantity associated
> with a frequency.

The term could either mean a sound subjectively characterized
by a frequency (and perhaps a confidence interval), or the
class of all sounds someone or some group of people have
or would characterize by a certain frequency (and confidence
interval). The usage isn't consistent.

The terms floating around in this space are "tone", "note",
and "pitch". We could try to standardize them so they make
sense (assign them to 3 concepts that are as different from
one another as possible without breaking a large majority
of prior usage of the term). And then 7 years later somebody
will come along and say we did it all wrong.

> Unfortunately "pitch class" won't do although I'm sure I
> heard a definition that was pretty close.

"Pitch class" is well defined, on the other hand, by
Babbit or whoever. It's the latter meaning of pitch I gave
above plus octave equivalence.

-Carl

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Klaus Schmirler wrote:
>
> > May I kindly ask the parties to consider what "to temper" means and
> > what it might be that is tempered?
>
> Toast toast toast toast
[snip]
>
> What do you put in a toaster?

Bread bread bread bread.

What comes OUT of the toaster after the toasting process is complete?

> Toast toast toast toast

All considering it's a 4 slot toaster, of course.

;-)

Half joking, actually, as I think the analogy is definitely applicable
to the topic of "what is tempering". It's a process of some sort, and
with any process, what goes is not what comes out.

Except in the famous case of bad computer code...

Ciao,

P

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

>
> Most of us have heard of Rameau as a composer, and occasionally
> as a proponent of 1/3-comma meantone,

I've been poking around the internet trying to find some support of
this, since I personally had never heard of it. Haven't found anything
yet. Also thelist archives turn up this statement by you, Carl:

"Also, note that the "1/3-comma meantone" of Rameau (and popular
in Europe during the meantone era) closes very nearly after 19
tones."

from:

/tuning/topicId_49104.html#49217

I am also unaware of any evidence which would indicate that 1/3 comma
meantone EVER was "popular". What's your basis?

Ciao,

P

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Paul Poletti wrote:
>>
>>> What would you call those temperaments which practicing musicians
>>> refer to as modified meantones?
>> I don't know what that means.
> > They're in the same class as well temperaments, whatever
> class that is.
> > They're not all that interesting theoretically, actually.
> I think the term "irregular temperament" should not be
> used. They're regular temperaments plus an asymmetrical
> tuning.

What does the "regular" part mean then?

Graham

Carl Lumma wrote:
>>> What term are you referring to?
>> "Meantone temperament is a temperament" with respect to "The >> Article".
> > If I said that it was strictly a mistake (probably the
> result of someone talking to me while I was writing it).

So what is meantone temperament?

>> That looks like a special-case definition for a >> mathematically based theory we haven't seen yet. It talks >> about real numbers, which suggests a relationship to >> frequencies, but doesn't define it.
> > Some of his proofs may require (or later assume) you've
> got reals. Certainly you limit the kinds of caculations
> you can do when calculating scales.
> > He says they're log-pitch. He also goes on in that
> message to define things like "periodic scale", "periodic
> reduced scale", and "epimorphic scale".

Okay. It's over-precise then.

>>>> What are Scala files supposed to embody?
>>> They meet Gene's definition, and they're called "scale
>>> files".
>> They meet pretty much any definition.
> > Not at all. You can't put "meantone" in a scale file.

There's a difference between scale files containing scales and all scales being compatible with a scale file.

>> What else was Manuel >> supposed to call them back when he started writing Scala?
> > How would the era in which he did it matter? He obviously
> felt the abstraction was worth defining a file format around,
> and he used the closest existing term for a name, which
> turned out to be close enough not to confuse anybody. All
> of which mirrors what Gene did.

We were talking about usage in the context of the regular mapping paradigm. It makes a great deal of difference whether the regular mapping paradigm was in existence. Scala files are an excellent way of recording microtonal scales.

>>>> They're certainly ordered, which was the issue before.
>>> Yes but you seemed to be talking about just an ordering,
>>> i.e. letter names. So you weren't specifying a tuning.
>> No, not just an ordering. I was pointedly not requiring a >> tuning, which ties in with usages like "the diatonic scale" >> or "the blackjack scale" but it'd hardly be surprising if >> other usages conflict with that.
> > So exactly how *do* you define it? I know you've used
> xL + ys notation, but that doesn't get you all the way to
> "the blackjack scale" (you need to specify L and s and
> miracle temperament, or L and s and the distribution of
> L & s, or something).

Why do I need to specify miracle temperament? Why do I need to define anything?

> And "the blackjack scale" is something you're apparently
> making up. People usually just say "blackjack" (42 vs. 8
> matches in my tuning list archives from '03-05).

http://tonalsoft.com/enc/b/blackjack.aspx

http://tonalsoft.com/monzo/blackjack/blackjack.aspx

What is it then?

>> I don't know how other >> people understand it.
> > As Kraig just explained, Wilson starts with Gene's def.
> and further requires either MOS or a CS in JI.

Reference?

>>>> Is there any controversy about "tuning"?
>>> Lots of people call things like Valotti and 12-ET "tunings".
>>> Probably the most common term among piano tuners. So you
>>> see, in the world at large terminology is not consistent.
>>> But in each school, it is more consistent. And within a
>>> music theory school heavily dependent on 1. math and
>>> 2. e-mail for communication, ours should be the most
>>> consistent.
>> And they are tunings, aren't they?
> > You could argue that a restriction to the 12-ET patent val
> mapping is taken for granted among piano tuners. In that
> case it would be valid usage.

When wouldn't it be?

>> Before the >> great shift I would have tried to fit what I wanted to say >> around the word "temperament" with the occasional "family".
> > So you consciously changed it. Did you tell anybody about
> your decision at the time?

I thought I was following the consensus from tuning-math. I don't have the reference. I don't even remember whose suggestion it was.

>> What I think we need is a disambiguation of "pitch". In >> psychoacoustic terms, it's a subjective quantity associated >> with a frequency.
> > The term could either mean a sound subjectively characterized
> by a frequency (and perhaps a confidence interval), or the
> class of all sounds someone or some group of people have
> or would characterize by a certain frequency (and confidence
> interval). The usage isn't consistent.

There you go.

> The terms floating around in this space are "tone", "note",
> and "pitch". We could try to standardize them so they make
> sense (assign them to 3 concepts that are as different from
> one another as possible without breaking a large majority
> of prior usage of the term). And then 7 years later somebody
> will come along and say we did it all wrong.

7 years is pretty good going for tuning terminology. How long before we get a replacement for "unison vector"?

>> Unfortunately "pitch class" won't do although I'm sure I >> heard a definition that was pretty close.
> > "Pitch class" is well defined, on the other hand, by
> Babbit or whoever. It's the latter meaning of pitch I gave
> above plus octave equivalence.

That's what I thought I read, but other people say the only defining feature is octave equivalence.

Graham

Graham Breed schrieb:
> Klaus Schmirler wrote:
> >> May I kindly ask the parties to consider what "to temper" means and >> what it might be that is tempered?
> > Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> Toast toast toast toast
> > What do you put in a toaster?

What do you put in a temperer, if not a tuning? What is it about the thing that comes out which doesn't make it a tuning any more?

klaus

My 2p worth is that there is no such thing as 'tuning' It's a verb
not a noun.

You 'tune' an instrument to a specific intonational scheme of which
some are called 'temperaments'

To temper is to take some just-intonational scheme and deviate from
it in some way, for purposes relating to transposition, or
translating relationships from one part of the intonational scheme
to another.

Equal-temperament as a name isn't really right in that all of the
notes are not tempered by the same amount. what it does do is temper
notes so that all notes are equal in that all the relationships
obtained from one note are identical for all other notes in the
intonational scheme.

Maybe some nomencalture purists will complain. But I have believed
that one 'tunes' an instrument 'to' something...

As for 1/3-comma meantone (and its equal-divisions of the octave
equaivalent 19EDO) It has a had a mixed history, probably based on
the fact that it has unhappy fifths and a poor major third. (And
maybe all that fuss over the sub-hemitonia)

To some it seems a poor choice to increase the number of notes and
end up with what they think is a worse intonational scheme.

Personally, this scale has things to offer, so long as the
composer/performer takes the time to learn its characteristics,
rather than merely write for it using traditional notation and 'hope
for the best'

as I say a lot of this is opinon....

Paul Poletti wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Paul Poletti wrote:
>>
>>> What would you call those temperaments which practicing musicians
>>> refer to as modified meantones?
>> I don't know what that means.
> > Are you just putting me on, or is the void between microtonality and
> the field of historical tuning and temperament so vast? I find it hard
> to believe that you've never heard of Rameau, or D'Alembert.
> Werckmeister's modified meantone I could give you a break on, since
> everybody has pretty much ignored it completely until I started
> singing its praises some years back, even though it's the first
> alternative to ET that was published in the 20th century in any source
> dealing with the historical performance of Baroque Music (Arnold, 1931!).

I know of Rameau, because he's in the basic music histories. I certainly know the name d'Alembert, but I thought he was a mathematician :-O I'll have a look...

Yes, there was certainly a mathematician called d'Alembert. Did he do tuning on the side?

> But maybe you're just not interested in historical temperaments, in
> which case I could understand. Admittedly, the whole lot of them is
> pretty boring and simplistic, compared to more interesting stuff.

There are plenty of things I take an interest in without being an expert.

>>> I assume they are still rank 1, but are they regular or irregular? I
>>> would assume the late, but then why don't you call them "well
>>> temperaments"? Maybe you do.
>> If they're modified I take it they aren't regular any more.
> > Now that's a no brainer!

Unless, of course, the modification's that the fifths are all a different size.

>> Meantone is rank 2 even if you take a finite subset within >> the octave. There's a distinction between perfect fifths >> and wolves, for example.
> > The so-called "wolf" fifth is not a fifth, its either a dimisihed 6th
> or an augmented 3rd. Actually, all correct intervals in meantone
> (those that can be spelled correctly using the nonenhamronic functions
> of the accidentals) are all of the same size, so isn't that rank 1, or
> do I misunderstand the ranking of ranks?

No, that's a sign of rank 2. Not all intervals of the same number of steps are treated the same. If the wolf could be taken as a fifth, it'd be rank 1. And all intervals so described being the same size means it's a regular temperament.

> Meantone is open-ended, a system which never closes. It just keeps
> spiraling. It only "closes" with a "wolf fifth" if you impose the idea
> of a 12-tone circular system upon it. The survival of many keyboard
> instruments which were tuned in regular meantone and provided with any
> number of subsemitones shows that old musicians knew that the 12-tone
> version was just a small chunk out of an infinite spiral.

Right, being "open ended" is another property of the rank being higher than 1. Rank 2 temperaments are a generalization of meantone.

>> If you modify them enough for all
>> intervals of a given number of steps to be acceptable, then >> it'd count as rank 1.
> > And how do we define "acceptable"? In other words, playing within the
> variations allowed for by Werckmeister's instructions, at what point
> do we arrive at a version which makes "all intervals of a given number
> of steps acceptable"? The advantage to calling it a modified meantone
> is because that name tells you something valid about both its
> structure and the practical methodology of actually setting it, yet
> doesn't get trapped in any such boggy value judgements.

It's a subjective judgement, and depends on the person using it. A tuning may or may not be a temperament by similar logic.

Graham

Mark, "tuning" is a verb as well as a noun according to my Microsoft
Bookshelf British Reference Collection. In the context of this thread, it
means both the "act of adjusting tones" and the "sum total of tones thusly
adjusted". Temperament is a type/kind/class of tuning.

Oz.

----- Original Message -----
From: "Mark" <equiton@waitrose.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2008 Cuma 12:31
Subject: [tuning] Re: "tuning" vs. "temperament"

> My 2p worth is that there is no such thing as 'tuning' It's a verb
> not a noun.
>
> You 'tune' an instrument to a specific intonational scheme of which
> some are called 'temperaments'
>
> To temper is to take some just-intonational scheme and deviate from
> it in some way, for purposes relating to transposition, or
> translating relationships from one part of the intonational scheme
> to another.
>
> Equal-temperament as a name isn't really right in that all of the
> notes are not tempered by the same amount. what it does do is temper
> notes so that all notes are equal in that all the relationships
> obtained from one note are identical for all other notes in the
> intonational scheme.
>
> Maybe some nomencalture purists will complain. But I have believed
> that one 'tunes' an instrument 'to' something...
>
> As for 1/3-comma meantone (and its equal-divisions of the octave
> equaivalent 19EDO) It has a had a mixed history, probably based on
> the fact that it has unhappy fifths and a poor major third. (And
> maybe all that fuss over the sub-hemitonia)
>
> To some it seems a poor choice to increase the number of notes and
> end up with what they think is a worse intonational scheme.
>
> Personally, this scale has things to offer, so long as the
> composer/performer takes the time to learn its characteristics,
> rather than merely write for it using traditional notation and 'hope
> for the best'
>
> as I say a lot of this is opinon....
>

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

>
> I know of Rameau, because he's in the basic music histories.

Good! Now if you want to know about his modification of meantone
(which most definitely has nothing whatsoever to do with 1/3 comma),
go check it out:

http://harpsichords.pbwiki.com/Rameau_Ordinaire

> I certainly know the name d'Alembert, but I thought he was
> a mathematician :-O I'll have a look...
>
> Yes, there was certainly a mathematician called d'Alembert.

Mathematician + physicist + philosopher + mechanical theorist +++
co-editor of Encyclopédie, ou dictionnaire raisonné des sciences, des
arts et des métiers, which may just be THE most important publishing
event of the entire 18th century, and certainly one of the most
influential works of all time, being not only a vast collection of
knowledge but also laying out the basic humanitarian principles of the
enlightenment which led to both the American and French revolutions.

> Did he do tuning on the side?

Evidently so. You can read about HIS modification of meantone at:

http://harpsichords.pbwiki.com/dAlembert_Ordinaire

Ciao,

P

Paul Poletti schrieb:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Klaus Schmirler wrote:
>>
>>> May I kindly ask the parties to consider what "to temper" means and >>> what it might be that is tempered?
>> Toast toast toast toast
> [snip]
>> What do you put in a toaster?
> > Bread bread bread bread.
> > What comes OUT of the toaster after the toasting process is complete?
> >> Toast toast toast toast
> > All considering it's a 4 slot toaster, of course.
> > ;-)
> > Half joking, actually, as I think the analogy is definitely applicable
> to the topic of "what is tempering". It's a process of some sort, and
> with any process, what goes is not what comes out.

Ayayay. You understood and yet argue the opposite.

Tempered steel is still steel, but the tensions are gone.

Until someone shows me how to temper an abstract sequence of large and small intervals (restricting "scale" to MOS here) without defining their size first, I say temperament is a process applied to a tuning to make it a slightly different tuning. There's got to be difference between a definition of terms and obfuscation.

Klaus

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Mark, "tuning" is a verb as well as a noun according to my Microsoft
> Bookshelf British Reference Collection.

One need consult a dictionary. It's just a gerund, after all, like a
good tongue lashing, or a good drubbing.

> In the context of this thread, it
> means both the "act of adjusting tones" and the "sum total of tones
thusly
> adjusted". Temperament is a type/kind/class of tuning.

Couldn't agree more.

Ciao,

P

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
>> "Also, note that the "1/3-comma meantone" of Rameau (and popular
>> in Europe during the meantone era) closes very nearly after 19
>> tones."
> I am also unaware of any evidence which would indicate that 1/3 comma
> meantone EVER was "popular". What's your basis?
>
may be, due the
http://en.wikipedia.org/wiki/19_equal_temperament
http://groenewald-berlin.de/text/text_T058.html
http://en.wikipedia.org/wiki/Meantone_temperament
"....Francisco Salinas and Gioseffo Zarlino. Salinas (in De musica
libra septum) describes three different mean tone temperaments: the
1/3 comma system, the 2/7 comma system, and the 1/4 comma system. He
is the likely inventor of the 1/3 system, while he and Zarlino both
wrote on the 2/7 system, apparently independently..."

http://de.wikipedia.org/wiki/Neunzehnstufige_Stimmung
(in german)
Especially attent there the pic. of Zarlino's 19-tone harpsichord:
http://upload.wikimedia.org/wikipedia/commons/3/33/Zarlinocembalo.png

Even today
http://www.denzilwraight.com/
offers again more common classical split keyboard-layout
for having 7 additional accidentials behind the usual dodecatonics:
http://www.denzilwraight.com/roman.htm#cimbalocromatico
http://www.denzilwraight.com/cs19phs3.jpg

To that
http://en.wikipedia.org/wiki/Erv_Wilson
developed an alternative arrangement of the 19 keys for his
"Meantone and other scales assigned to 19-tone clavichord"
http://en.wikipedia.org/wiki/Generalized_keyboard
"Scott Hackelman and Erv Wilson designed a 19-tone generalized
keyboard clavichord with oblong hexagonal keys in 1975, and marketed
it as a kit." as further described in their's original paper:
http://www.anaphoria.com/xen456.PDF

Others realized 19-EDO even on guitars:
http://eceserv0.ece.wisc.edu/~sethares/tet19/guitarchords19.html
http://www.johngzowski.com/19tet%20guitar.html

Sorry, but never the less,
i personally do prefer alike
http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif
the finer graduation of 53 tones per octave
/tuning/topicId_73974.html#73974

Yours Sincerely
A.S.

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > Most of us have heard of Rameau as a composer, and occasionally
> > as a proponent of 1/3-comma meantone,
>
> I've been poking around the internet trying to find some support
> of this, since I personally had never heard of it. Haven't found
> anything yet.

Really? The first Google result for "Rameau 1/3-comma" is

http://www.xs4all.nl/~huygensf/english/temperament.html

where you can download an excerpt of a recent recording of
a stunning Froberger piece in 1/3-comma (I can tell you which
recording if you're interested, since I am the one who told
the author of this page about it).

This mentions Salinas in connection with 1/3-comma meantone,
linking to

http://www.xs4all.nl/~huygensf/english/salinas.html

As does the 2nd Google result

http://wintemper.com/features.htm

Another result is the Wikipedia entry on Zarlino, which
says he described 1/3-comma

http://en.wikipedia.org/wiki/Gioseffo_Zarlino

The entry on meantone confirms Salinas and Zarlino in
connection with 1/3-comma

http://en.wikipedia.org/wiki/Meantone

>Also thelist archives turn up this statement by you, Carl:
>
> "Also, note that the "1/3-comma meantone" of Rameau (and popular
> in Europe during the meantone era) closes very nearly after 19
> tones."
>
> from:
>
> /tuning/topicId_49104.html#49217
>
> I am also unaware of any evidence which would indicate that
> 1/3 comma meantone EVER was "popular". What's your basis?

I was repeating something I read on this list, which may not
be accurate.

-Carl

> > They're not all that interesting theoretically, actually.
> > I think the term "irregular temperament" should not be
> > used. They're regular temperaments plus an asymmetrical
> > tuning.
>
> What does the "regular" part mean then?
>
>
> Graham

The assumption is that any well temperaments will clearly
correspond to exactly one regular temperament. They would
be "well tunings".

-Carl

> >>> What term are you referring to
> >>
> >> "Meantone temperament is a temperament" with respect to "The
> >> Article".
> >
> > If I said that it was strictly a mistake (probably the
> > result of someone talking to me while I was writing it).
>
> So what is meantone temperament?

You lost me.

> >> What else was Manuel
> >> supposed to call them back when he started writing Scala?
> >
> > How would the era in which he did it matter? He obviously
> > felt the abstraction was worth defining a file format around,
> > and he used the closest existing term for a name, which
> > turned out to be close enough not to confuse anybody. All
> > of which mirrors what Gene did.
>
> We were talking about usage in the context of the regular
> mapping paradigm. It makes a great deal of difference
> whether the regular mapping paradigm was in existence.
> Scala files are an excellent way of recording microtonal scales.

Sorry, but I can't make any sense of this comment.

> >>>> They're certainly ordered, which was the issue before.
> >>> Yes but you seemed to be talking about just an ordering,
> >>> i.e. letter names. So you weren't specifying a tuning.
> >> No, not just an ordering. I was pointedly not requiring a
> >> tuning, which ties in with usages like "the diatonic scale"
> >> or "the blackjack scale" but it'd hardly be surprising if
> >> other usages conflict with that.
> >
> > So exactly how *do* you define it? I know you've used
> > xL + ys notation, but that doesn't get you all the way to
> > "the blackjack scale" (you need to specify L and s and
> > miracle temperament, or L and s and the distribution of
> > L & s, or something).
>
> Why do I need to specify miracle temperament? Why do I need
> to define anything?

"blackjack" means 1. twenty-one 2. adjacent 3. miracle
generators with 4. octave equivalence. If you want to call
that a "scale" then your definition of "scale" needs to
demand all four of those elements in one way or another.

If I were using the terms "blackjack" and "scale" together,
I'd say "a blackjack scale" not "the blackjack scale".

> > And "the blackjack scale" is something you're apparently
> > making up. People usually just say "blackjack" (42 vs. 8
> > matches in my tuning list archives from '03-05).
>
> http://tonalsoft.com/enc/b/blackjack.aspx
> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
>
> What is it then?

Perfectly consistent with Gene's definition since here
monz also demands 5. a specific tuning of the generator.

> >> I don't know how other
> >> people understand it.
> >
> > As Kraig just explained, Wilson starts with Gene's def.
> > and further requires either MOS or a CS in JI.
>
> Reference?

/tuning/topicId_75270.html#75365

and other messages in the thread (and personal communication
with Wilson).

> >>>> Is there any controversy about "tuning"?
> >>> Lots of people call things like Valotti and 12-ET "tunings".
> >>> Probably the most common term among piano tuners. So you
> >>> see, in the world at large terminology is not consistent.
> >>> But in each school, it is more consistent. And within a
> >>> music theory school heavily dependent on 1. math and
> >>> 2. e-mail for communication, ours should be the most
> >>> consistent.
> >>
> >> And they are tunings, aren't they?
> >
> > You could argue that a restriction to the 12-ET patent val
> > mapping is taken for granted among piano tuners. In that
> > case it would be valid usage.
>
> When wouldn't it be?

If you like my suggestion of "well tunings" then perhaps never.

> >> Before the
> >> great shift I would have tried to fit what I wanted to say
> >> around the word "temperament" with the occasional "family".
> >
> > So you consciously changed it. Did you tell anybody about
> > your decision at the time?
>
> I thought I was following the consensus from tuning-math. I
> don't have the reference. I don't even remember whose
> suggestion it was.

I have almost every tuning-math message right here. I'm going
to regex it for "temperament class"... 43 messages found. The
first is from you, on 2002/5/13. In it, you refer to a definition
you apparently wrote in monz's encyclopedia. But it looks like
the encyclopedia entry has changed since then.

http://tonalsoft.com/enc/t/temperament.aspx
(I notice that Joe, you, and John all call a temperament a
kind of tuning, whereas Gene does not. He points out why
it's a bad idea to do so.)

The next hit that wasn't on 2002/5/13 was from Paul E. in
Jan. 2006. Followed by a message from you a few days later,
and its replies. Followed by a message from Gene, where he
says

"An abstract temperament or "temperament class" is..."

Followed by five from you that take us to Sept. 2007, which
I reply to asking, "What's a temperament class?" The next
message that isn't by you or quoting you is from George Secor
in Dec. 2007. There's a quote of that, and then the rest
are from you or quotes of you.

It will be harder to determine which hits for "temperament"
are meaning what you mean by "temperament class", but I'll
bet it dwarfs 43 and the number of authors we see here.

> >> What I think we need is a disambiguation of "pitch". In
> >> psychoacoustic terms, it's a subjective quantity associated
> >> with a frequency.
> >
> > The term could either mean a sound subjectively characterized
> > by a frequency (and perhaps a confidence interval), or the
> > class of all sounds someone or some group of people have
> > or would characterize by a certain frequency (and confidence
> > interval). The usage isn't consistent.
>
> There you go.
>
> > The terms floating around in this space are "tone", "note",
> > and "pitch". We could try to standardize them so they make
> > sense (assign them to 3 concepts that are as different from
> > one another as possible without breaking a large majority
> > of prior usage of the term). And then 7 years later somebody
> > will come along and say we did it all wrong.
>
> 7 years is pretty good going for tuning terminology. How
> long before we get a replacement for "unison vector"?

That one's been around for at least 40 years.

> >> Unfortunately "pitch class" won't do although I'm sure I
> >> heard a definition that was pretty close.
> >
> > "Pitch class" is well defined, on the other hand, by
> > Babbit or whoever. It's the latter meaning of pitch I gave
> > above plus octave equivalence.
>
> That's what I thought I read, but other people say the only
> defining feature is octave equivalence.

Octave equivalence alone doesn't get you anything, so that
doesn't make sense.

-Carl

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Mark, "tuning" is a verb as well as a noun according to my
> Microsoft Bookshelf British Reference Collection.

One of the nice things about English is all verbs are nouns
and vice versa.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > Most of us have heard of Rameau as a composer, and occasionally
> > > as a proponent of 1/3-comma meantone,
> >
> > I've been poking around the internet trying to find some support
> > of this, since I personally had never heard of it. Haven't found
> > anything yet.
>
> Really? The first Google result for "Rameau 1/3-comma" is
>
> http://www.xs4all.nl/~huygensf/english/temperament.html

[etc etc etc]

Right. Of course I'm aware of Salinas, but what I meant was that I
couldn't find any connection between Rameau and 1/3 comma meantone.
> >
> > I am also unaware of any evidence which would indicate that
> > 1/3 comma meantone EVER was "popular". What's your basis?
>
> I was repeating something I read on this list, which may not
> be accurate.

Indeed not. I think the only time it has ever approached "popular" is
among modern players who find it's extreme sound attractive.

Ciao,

P

Paul wrote...

> > Temperament is a type/kind/class of tuning.
>
> Couldn't agree more.

Couldn't disagree more. Tuning is something you do once
you know what you want. Temperament is something that
tells you want you want. You can't tune without a target
to tune to.
Just intonation and temperament are not tunings, they are
mathematical entities that are on equal footing in terms
of 'natural artifacts' we may want to base music on.

-Carl

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> >
> >> "Also, note that the "1/3-comma meantone" of Rameau (and popular
> >> in Europe during the meantone era) closes very nearly after 19
> >> tones."
> > I am also unaware of any evidence which would indicate that 1/3 comma
> > meantone EVER was "popular". What's your basis?

> >
> may be, due the
> http://en.wikipedia.org/wiki/19_equal_temperament
> http://groenewald-berlin.de/text/text_T058.html
> http://en.wikipedia.org/wiki/Meantone_temperament
> "....Francisco Salinas and Gioseffo Zarlino. Salinas (in De musica
> libra septum) describes three different mean tone temperaments: the
> 1/3 comma system, the 2/7 comma system, and the 1/4 comma system. He
> is the likely inventor of the 1/3 system, while he and Zarlino both
> wrote on the 2/7 system, apparently independently..."

None of this, NONE, supports the idea that 1/3 comma meantone was ever
"popular". In fact, you are ignoring that Zarlino himself said that he
found 1/4 more harmonious.

And as to any 19 key harpsichord or organ, that doesn't make it 1/3
comma meantone. It could just as well be 1/4, with all sharps and
flats including E# and Fb.

Am I not making myself clear? I would like to know:

(1) is there is ANY clear irrefutable evidence for 1/3 comma mean even
being used at all, let alone popular?

(2) is there any evidence at all tying Rameau to such an extreme system?

Please don't refer me to another modern bunch of regurgitation or
speculation.

Thanks.

Ciao,

P

One could have a just tuning.
In regard to the subject at large, dictionaries are historical uses of words, they are not set in stone and new words and meanings happen all the time, correct or not. when enough people use them, it gets in. Otherwise they would not need to be updated. Language is quite different than mathematics.

Mark wrote:
>
> My 2p worth is that there is no such thing as 'tuning' It's a verb
> not a noun.
>
> You 'tune' an instrument to a specific intonational scheme of which
> some are called 'temperaments'
>
> To temper is to take some just-intonational scheme and deviate from
> it in some way, for purposes relating to transposition, or
> translating relationships from one part of the intonational scheme
> to another.
>
> Equal-temperament as a name isn't really right in that all of the
> notes are not tempered by the same amount. what it does do is temper
> notes so that all notes are equal in that all the relationships
> obtained from one note are identical for all other notes in the
> intonational scheme.
>
> Maybe some nomencalture purists will complain. But I have believed
> that one 'tunes' an instrument 'to' something...
>
> As for 1/3-comma meantone (and its equal-divisions of the octave
> equaivalent 19EDO) It has a had a mixed history, probably based on
> the fact that it has unhappy fifths and a poor major third. (And
> maybe all that fuss over the sub-hemitonia)
>
> To some it seems a poor choice to increase the number of notes and
> end up with what they think is a worse intonational scheme.
>
> Personally, this scale has things to offer, so long as the
> composer/performer takes the time to learn its characteristics,
> rather than merely write for it using traditional notation and 'hope
> for the best'
>
> as I say a lot of this is opinon....
>
> -- 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

Paul wrote...
> > Really? The first Google result for "Rameau 1/3-comma" is
> >
> > http://www.xs4all.nl/~huygensf/english/temperament.html
>
> [etc etc etc]
>
> Right. Of course I'm aware of Salinas, but what I meant was that I
> couldn't find any connection between Rameau and 1/3 comma meantone.

Oh, sorry.

I'm trying to track down source of the Rameau/France connection
in the archives and on the web. Interestingly, not only is that
Froberger recording French, Parmentier chose 1/3-comma for his
"17th-century French harpsichord" album on Wildboar.

Well, I can't find anything in the archives. I must be
hallucinating again.

-Carl

Carl Lumma schrieb:
> Paul wrote...
> >>> Temperament is a type/kind/class of tuning.
>> Couldn't agree more.
> > Couldn't disagree more. Tuning is something you do once
> you know what you want. Temperament is something that
> tells you want you want. You can't tune without a target
> to tune to.
> Just intonation and temperament are not tunings, they are
> mathematical entities that are on equal footing in terms
> of 'natural artifacts' we may want to base music on.

Horns don't make music? Jaws harps play equations? Isn't the achetypical meantone tuning process to _tune_ fifths and a third, then temper ... what?

klaus

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
>
> > Very odd... I'm getting a MUCH larger set of results for
> > "temperament class" than I did the other day. And clearly,
> > you've been against Gene's definition in these messages.
> > Moreover, I couldn't find the message (by any author) that
> > that I'd read the other day and attributed to you.[George]
>
> It's here:
>
> /tuning/topicId_73148.html#73449
>
> Graham

Yes, I was making a (reluctant) effort to appreciate the merits of
the other side of the debate, specifically that it's possible to use
the terms "temperament", "meantone", and "meantone temperament" to
refer to a set of tempered tunings that are members of the same
temperament (class) in a manner that's both logical and consistent.

I was also "wondering whether the terms 'meantone' and 'meantone
temperament' (without qualifying language) could indeed become
acceptable in a broader sense." In retrospect, I should have used
the word "eventually" instead of "indeed", because I can't agree with
that sort of usage at this point in time. I believe that doing so
would be symptomatic of an evolution in terminology occurring within
only one particular community of individuals who have seemingly
chosen to isolate themselves from (or otherwise disregard the
interests of) the rest of the musical world. As Confucius might say:
It is very difficult to communicate when you and I do not speak the
same language -- but worse yet when we use the same words to mean
different things.

After thinking it over, I'd advise using "meantone-class" rather
than "meantone" as an adjective to describe temperaments such as 19-,
31-, and 12-ET, unless the context makes it absolutely clear that the
latter term is being used to refer to a class of temperaments. Also,
I think that we need to recognize that when one speaks of "a
temperament", it is ordinarily assumed that one is referring to a
single (unspecified) tempered tuning, not a set of tempered tunings
that are members of the same class; if you're thinking of using the
word "temperament" for the latter, then you had better
say "temperament class" to ensure that you won't be misunderstood.

And if you're looking forward to a day when the term "temperament
class" may eventually be shortened to "temperament", then perhaps
using the term "tempered tuning" (when speaking of individual members
of a temperament class) will speed up the process.

--George

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
Hi Paul,
> In fact, you are ignoring that Zarlino himself said that he
> found 1/4 more harmonious.
right,
but in order to find his personal compromise inbetween
the minor-3rd = 6/5 and the major-3rd = 5:4
he developed his own 2/7-SC concept.

>
> And as to any 19 key harpsichord or organ, that doesn't make it 1/3
> comma meantone. It could just as well be 1/4, with all sharps and
> flats including E# and Fb.
That 1/4 subdivsion of the PC approximates the
http://en.wikipedia.org/wiki/31_equal_temperament
instead 19 as in the 1/3 SC case.
Don't confuse that variants.
>
> Am I not making myself clear? I would like to know:
>
> (1) is there is ANY clear irrefutable evidence for 1/3 comma mean even
> being used at all, let alone popular?
So thinks
http://www.christopherstembridge.org/cromatico.htm
in claiming:
" The chromatic harpsichord with 19 keys to the octave was relatively
common in Italy up until the 1640s. "
also
http://ibo.ortgies.googlepages.com/publishedarticles
in
"Pipe Organs with Subsemitones, 1468-1721." and "Historical Organs
with Subsemitones, 1468-1721: Appendix B."
In The Mathematical Theory of Tone Systems, ed. by Ján Haluska. New
York: Marcel Dekker, 2004: 141-146, and 369-374.
/tuning/topicId_20120.html#20120
so far the leading expert in that topic.
>
> Please don't refer me to another modern bunch of regurgitation or
> speculation.
http://www.hetorgel.nl/e2000-06b.htm
"With the rise of circulating temperaments the practice disappeared
soon after 1700."

Even Werckmeister refers to 1/3 SC in his:
http://diapason.xentonic.org/ttl/ttl01.html
on p.37, Chap. XVII
when considering some arithmetical subdivisions of
81:81 for tempering:
"Wenn ein Comma in zwey Theile getheilt wird /
so stehen in kleinesten Zahlen 162. 161. 160.
In drey Theile sind die kleinsten Termini 243. 242. 241. 240.
So es in vier Theile gemachet; stehen die kleinsten Termini 324. 323
322. 322. 320. Die äussersten sind das comma...."
tr:
'If a comma is divided into 2 parts,
then arise in the smallest numbers 162. 161. 160.
In 3 parts the smallest termini become 243. 242. 241 240.
when made into 4 parts, the smallest Termini get 324. 323. 322. 320.
the outer ones represent the comma...'

That refers to the second tuning on p.78
(Die andere N.4)

C~-1/3 G D~-1/3 A E ~-1/3 H F# ~-1/3 C# G# ~+1/3 D# ~+1/3 Bb ~-1/3 F C

A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> >
> Hi Paul,
> > In fact, you are ignoring that Zarlino himself said that he
> > found 1/4 more harmonious.
> right,
> but in order to find his personal compromise inbetween
> the minor-3rd = 6/5 and the major-3rd = 5:4
> he developed his own 2/7-SC concept.

So what? In the Dimostrationii harmoniche of 1571, in which he gives
1/3, 2/7, and 1/4, he says 1/3 is not a sonorous as the other two and
that 1/4 is the easiest to do. The topic is, is there ANY EVIDENCE
THAT 1/3 MEANTONE WAS EVER POPULAR??? Why do I have to keep saying
this over and over again?
>
> >
> > And as to any 19 key harpsichord or organ, that doesn't make it 1/3
> > comma meantone. It could just as well be 1/4, with all sharps and
> > flats including E# and Fb.
> That 1/4 subdivsion of the PC approximates the
> http://en.wikipedia.org/wiki/31_equal_temperament
> instead 19 as in the 1/3 SC case.
> Don't confuse that variants.

I'm not confusing anything. I'm merely saying that a complete set of
subsemitones in 1/4 mean is a perfectly believable way of tuning the
19 tones of an archicembalo. Now, do you have any SPECIFIC EVIDENCE
other than yet another Wikipedia article on yet another EDO system
that 19 keys ALWAYS mean 1/3 comma meantone?

Please, Andreas, DO try to stay on point, man!

> " The chromatic harpsichord with 19 keys to the octave was relatively
> common in Italy up until the 1640s. "

I'm missing the bit about 1/3 coma meantone YET AGAIN!
> >
> > Please don't refer me to another modern bunch of regurgitation or
> > speculation.
> http://www.hetorgel.nl/e2000-06b.htm
> "With the rise of circulating temperaments the practice disappeared
> soon after 1700."

I'm missing the bit about 1/3 coma meantone YET AGAIN!
>
> Even Werckmeister refers to 1/3 SC in his:
> http://diapason.xentonic.org/ttl/ttl01.html
> on p.37, Chap. XVII
> when considering some arithmetical subdivisions of
> 81:81 for tempering:
> "Wenn ein Comma in zwey Theile getheilt wird /
> so stehen in kleinesten Zahlen 162. 161. 160.
> In drey Theile sind die kleinsten Termini 243. 242. 241. 240.
> So es in vier Theile gemachet; stehen die kleinsten Termini 324. 323
> 322. 322. 320. Die äussersten sind das comma...."
> tr:
> 'If a comma is divided into 2 parts,
> then arise in the smallest numbers 162. 161. 160.
> In 3 parts the smallest termini become 243. 242. 241 240.
> when made into 4 parts, the smallest Termini get 324. 323. 322. 320.
> the outer ones represent the comma...'

Yeah, and Neidhardt goes through a whole bunch of useless combinations
of 1/12 PC just to sort of layout all the possibilities. Does this
mean ANYTHING in terms of what was actually done? No.

>
> That refers to the second tuning on p.78
> (Die andere N.4)
>
> C~-1/3 G D~-1/3 A E ~-1/3 H F# ~-1/3 C# G# ~+1/3 D# ~+1/3 Bb ~-1/3 F C
>
Werckmeister's 1/3 PC comma circulating temperament has nothing to do
with regular 1/3 S comma meantone. Why are you even bringing this up?

Please don't give me yet more useless garbage like this! If you
haven't got any real evidence that regular 1/3 comma meantone was ever
popular, which is what I asked for, just be honest and admit it. Or
don't say anything at all.

Jeeeezzzz!!!!

Ciao,

P

Thank you Paul.

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2008 Cuma 18:58
Subject: [tuning] Re: "tuning" vs. "temperament"

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Mark, "tuning" is a verb as well as a noun according to my Microsoft
> > Bookshelf British Reference Collection.
>
> One need consult a dictionary. It's just a gerund, after all, like a
> good tongue lashing, or a good drubbing.
>
> > In the context of this thread, it
> > means both the "act of adjusting tones" and the "sum total of tones
> thusly
> > adjusted". Temperament is a type/kind/class of tuning.
>
> Couldn't agree more.
>
> Ciao,
>
> P
>

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:
>

> Ayayay. You understood and yet argue the opposite.
>
> Tempered steel is still steel, but the tensions are gone.

Not exactly. It's the HARDNESS which is gone. As someone who regularly
does cold forming of metals with a hammer an anvil, I've got a pretty
vast amount of experience with what the word means in regard to metals.
>
> Until someone shows me how to temper an abstract sequence of large and
> small intervals (restricting "scale" to MOS here) without defining
> their size first, I say temperament is a process applied to a tuning
> to make it a slightly different tuning. There's got to be difference
> between a definition of terms and obfuscation.

I think you're almost right. Here's a rather lengthy treatment of the
whole topic I wrote a few days back but never got around to posting:

The other day when I did a session on temperament for general music
students, I told them that there was perhaps no other detail of
musical performance upon which so much ink had been wasted over the
history of western civilization. It's fascinating to see the process
continues with virtual ink.

;-)

But all kidding aside, it's a bit of a waste of time to go through
such contortions and agonizing over such things. As I see it, it's
pretty simple.

Nobody in their right mind can seriously maintain the position that it
is wrong to use the word "tuning" exactly as Oz has stated, i.e. to
mean both the process of adjusting the notes of an instrument and
result of such process. "I just gave the harpsichord in room 305 a
good tuning." "Oh, yeah? How did you tune it?" "I used the quarter
comma meantime temperament." Now, one could just as easily and as far
as I'm concerned CORRECTLY say, "Oh yeah? What tuning did you use?" "I
used the quarter comma meantime temperament." In this context, they
both mean exactly the same thing: what kind of plan or scheme or
template or whatever you want to call it you used to decide exactly
where the notes should be in the process of tuning of the harpsichord.

I personally also maintain that within the specific bounds of talking
about the structural logic of different systems, the word "tuning" can
be used to describe any system by which ALL of the pitches are defined
by intervals which have simple ratios. This of course does not mean
that all of the INTERVALS of the system have simple ratios, nor that
all of these simple generating intervals are taken from the generating
note. Granted, the definition gets fuzzy if we move out into the
further reaches of what many would call extended JI. But almost every
definition or logical system can be pushed to a point where it begins
to break down. So what?

As to what is a temperament and what is being "tempered", I'm plenty
happy with the original meaning as implied (if not precisely stated)
by Werckmeister. Go read either the original German:

http://harpsichords.pbwiki.com/Werckmeister_Anmerckungen_1698

... or my translation:

http://polettipiano.com/Pages/werckengpaul.html

Remember that this is in the context of traditional western white man
harmony of the 17th century, i.e. what folks here would call 5-limit.
So when he says, "it is not possible to have all the consonances pure
if one moves from one chord to another," he simply means you can't
have all our major and minor triads in all keys pure. So what else is
new? So what do we do? We take from the one and give to the other,
i.e. we accept some impurity in some consonances in order to give a
little improvement to the ones that turn out badly distorted.

Now, what precisely is being "tempered", i.e. diluted, softened,
qualified, moderated, etc., all the normal meanings of the word
temper? Is it the hard, rigid stability of the pure intervals, or is
it the harshness of those which come out like hideously deformed
freaks? Hard to know. I would argue that Werckmeister means to
"temper" the rigidity of simple proportions, since at the top of his
tables in the 1681 treatise he says, "hereby the tempering
(temperatur) or hovering (schweben) can be found out in different
ways." And what specific information does said table provide? The
deviation from pure of all of the fifths and major thirds, specified
in fractions of a comma. Seems pretty clear to me. He does not say,
"hereby the improvement of malformed consonances can be found out in
different way," now does he? Ultimately, though, I think it doesn't
really matter as long as we realize we are creating an approximation
of an unreachable ideal, that being the use of pure consonances for
every triad.

I think it is wrong to ask which specific system or which specific
tuning Werckeister had in mind as the starting point to deviate from.
The answer is NO system, just an idealized consistent use of pure
consonances, which is on any instrument which is comprise of discrete
fixed pitch oscillators is unobtainable, unless there are lots and
lots of 'em. That's why I don't agree that a temperament is always an
approximation of some definite tuning. If pressed, I would have to say
that all traditional temperaments are approximations of an
unrestrained flexible 5-limit JI applied independently to each and
every harmony. And yes, that includes sequential harmonies which
contain common notes sustained from one harmony to the other and which
change function as the harmony changes, like a G# becoming an Ab.
These notes would have been altered slightly in pitch at the moment
the harmony changes, precisely as Quantz TELLS us to do. Burney also
sings the praises of an Italian oboist he heard doing precisely that,
remarking at how wonderfully-refined the player's hearing was.

One of my favorite quotes on the topic is that of Roger North (1726):

"If the sounding part [of music] had bin left to the Voice, which
conformes to all truth of accords whereof the ear is judge, there
never had bin any suspicion of such majors, minors, dieses, commas,
and I know not what imaginary devisions of tones, as some clumsye
mechanick devices called Instruments have given occasion to speculate."

In regards to the modern microtonal world, I would use exactly the
same logic, in that any system which has elements defined by intervals
of relatively simply ratios, or a series of relatively simply ratios,
in which case many ratios may well have the appearance of being
complex if we forget how they were arrived at and merely calculate the
ratio to the generating note (a simply Pythagorean tuning of a
diatonic scale being a perfect example).

A temperament is a system which tries to approximate conflicting
issues which are inherent to a tuning system. They can arise from
transposition or simply from internal limitations, like the bad ii
triad in the normal JI tuning of the diatonic scale.

New systems which do not use simple ratios and are created without
reference to anything else need a new word, since they are neither a
tuning (in a structural logic sense of the word) nor a temperament.

Seems simple enuf to me... but then, I'm not used to breathing the
rarefied atmosphere which can only be partaken of from the dizzying
heights of the Ivory Tower of convoluted microtonal structures.

;-)

Me 'umble opinee, but I'm just a grunt down in the trenches with a
tuning hammer in my grubby little hands who likes to read old
treatises on his lunch break

Ciao,

P

>
>
> Klaus
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> recent recording of
> a stunning Froberger piece in 1/3-comma (I can tell you which
> recording if you're interested, since I am the one who told
> the author of this page about it).
>

OK, tell us... I am at least curious.

There is a French harpsichord music recording by Parmentier which is
claimed to be in 1/3-comma, but some people who have listened closely
doubt this.

I have occasionally tuned 2/7 comma, which is fine for full triadic
harmony.

Incidentally the French and Italian words for temperament back in the
Renaissance/Baroque both meant essentially 'dividing up' or 'sharing':
'sistema partecipata' or 'partition'. This relates directly either to
dividing up the comma (mathematically) or sharing out a certain amount
of out-of-tuneness (acoustically).

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > recent recording of
> > a stunning Froberger piece in 1/3-comma (I can tell you which
> > recording if you're interested, since I am the one who told
> > the author of this page about it).
>
> OK, tell us... I am at least curious.

I have this piece on a Christophe Rousset recording on
Harmonia Mundi, but it's at a different pitch. So Manuel
must have sourced this elsewhere. The tuning on my CD
is "French 18th-century", and sounds like either meantone
or modified meantone.

But Manuel did get the "Rossi" fragment (in 1/4-comma) on
that page
http://www.xs4all.nl/~huygensf/english/temperament.html
from me. It's from one of the "Art of Baroque Trumpet"
series on Naxos. M. Rossi... incredible composer.

-Carl

Paul Poletti wrote:

> As to what is a temperament and what is being "tempered", I'm plenty
> happy with the original meaning as implied (if not precisely stated)
> by Werckmeister. Go read either the original German:
> > http://harpsichords.pbwiki.com/Werckmeister_Anmerckungen_1698

Oh, it comes from the German, does it? A word used by Helmholtz, Tanaka and I'm sure others is "Verwechselung" as in "schismatische Verwechselung" and "kleismatische Verwechselung". It takes the place of the English word "temperament" when we call these things "schismatic temperament" or "kleismatic temperament". So what does "Verwechselung" actually mean?

Well, according to a web dictionary:

http://dict.tu-chemnitz.de/dings.cgi?service=deen&query=Verwechselung

it means "mistake" or "confusion". So perhaps we should be talking about "the schismatic mistake" or "the kleismatic confusion"?

Graham

Carl Lumma wrote:

>> So what is meantone temperament?
> > You lost me.

You keep looking for mentions of "meantone temperament" in the archives. What do you expect them to demonstrate?

>>>> What else was Manuel >>>> supposed to call them back when he started writing Scala?
>>> How would the era in which he did it matter? He obviously
>>> felt the abstraction was worth defining a file format around,
>>> and he used the closest existing term for a name, which
>>> turned out to be close enough not to confuse anybody. All
>>> of which mirrors what Gene did.
>> We were talking about usage in the context of the regular >> mapping paradigm. It makes a great deal of difference >> whether the regular mapping paradigm was in existence. >> Scala files are an excellent way of recording microtonal scales.
> > Sorry, but I can't make any sense of this comment.

What are we talking about?

>> Why do I need to specify miracle temperament? Why do I need >> to define anything?
> > "blackjack" means 1. twenty-one 2. adjacent 3. miracle
> generators with 4. octave equivalence. If you want to call
> that a "scale" then your definition of "scale" needs to
> demand all four of those elements in one way or another.

Well that's *one* definition of blackjack. And it'd follow from *one* meaning of scale. Once you have miracle temperament, blackjack's easy to define, anyway. It's 20 generator steps. Why does the definition of scale need to *demand* all four elements? I don't see that at all.

> If I were using the terms "blackjack" and "scale" together,
> I'd say "a blackjack scale" not "the blackjack scale".

There's that at well, but we have a standard blackjack.

>>> And "the blackjack scale" is something you're apparently
>>> making up. People usually just say "blackjack" (42 vs. 8
>>> matches in my tuning list archives from '03-05).
>> http://tonalsoft.com/enc/b/blackjack.aspx
>> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
>>
>> What is it then?
> > Perfectly consistent with Gene's definition since here
> monz also demands 5. a specific tuning of the generator.

And which tuning is that? Some quotes from that single page:

"Blackjack scale: miracle[21], 21-out-of-72-edo"

"The Blackjack generator is also nearly identical to an interval the size of 7 degrees of 72-EDO"

"I will present the Blackjack scale here as 21-out-of-72-EDO. In the 72edo version of blackjack..."

"...those who work in 31edo may easily form blackjack as a subset of that tuning."

"In the 41edo version of blackjack..."

>>>> I don't know how other >>>> people understand it.
>>> As Kraig just explained, Wilson starts with Gene's def.
>>> and further requires either MOS or a CS in JI.
>> Reference?
> > /tuning/topicId_75270.html#75365
> > and other messages in the thread (and personal communication
> with Wilson).

Unfortunately I couldn't reach that page before the weekend, and I still can't reach it this morning. If Erv tells you he used Genes definition, then good for Erv.

I have a message from Kraig to the list saying "Partch mapped 43 pitches in a way that can be thought of [as] a 41 tone scale with two tones that vary". How do varying tones fit Gene's definition?

>>>> Before the >>>> great shift I would have tried to fit what I wanted to say >>>> around the word "temperament" with the occasional "family".
>>> So you consciously changed it. Did you tell anybody about
>>> your decision at the time?
>> I thought I was following the consensus from tuning-math. I >> don't have the reference. I don't even remember whose >> suggestion it was.
> > I have almost every tuning-math message right here. I'm going
> to regex it for "temperament class"... 43 messages found. The
> first is from you, on 2002/5/13. In it, you refer to a definition
> you apparently wrote in monz's encyclopedia. But it looks like
> the encyclopedia entry has changed since then.

Then you missed 20th August 2001.

> http://tonalsoft.com/enc/t/temperament.aspx
> (I notice that Joe, you, and John all call a temperament a
> kind of tuning, whereas Gene does not. He points out why
> it's a bad idea to do so.)

Gene's argument is circular reasoning, for what that's worth.

> The next hit that wasn't on 2002/5/13 was from Paul E. in
> Jan. 2006. Followed by a message from you a few days later,
> and its replies. Followed by a message from Gene, where he
> says
> > "An abstract temperament or "temperament class" is..."

So I picked it up from Paul E then?

> Followed by five from you that take us to Sept. 2007, which
> I reply to asking, "What's a temperament class?" The next
> message that isn't by you or quoting you is from George Secor
> in Dec. 2007. There's a quote of that, and then the rest
> are from you or quotes of you.

The plural of message is "messages".

> It will be harder to determine which hits for "temperament"
> are meaning what you mean by "temperament class", but I'll
> bet it dwarfs 43 and the number of authors we see here.

Sure it's difficult, but you said you could make an argument from usage. And that Gene had already done so, in which case you can refer to his statistics.

Frankly, I'm sure you can find all kinds of things in the archives. When I checked my complete searches paper I found some bad usages of "temperament". I completely avoid the term "equal temperament class" which I'm sure you could argue would be more appropriate in some circumstances. Emails are likely to be checked even less thoroughly. That's why I prefer to use more prominent articles. And even then you have to assume that people might have changed their usage if somebody else had pointed out the error.

But sure, if you have evidence from the archives that people were using the word "temperament" do specify that a mapping doesn't require a tuning, let's see them. One will do for starters.

>>> The terms floating around in this space are "tone", "note",
>>> and "pitch". We could try to standardize them so they make
>>> sense (assign them to 3 concepts that are as different from
>>> one another as possible without breaking a large majority
>>> of prior usage of the term). And then 7 years later somebody
>>> will come along and say we did it all wrong.
>> 7 years is pretty good going for tuning terminology. How >> long before we get a replacement for "unison vector"?
> > That one's been around for at least 40 years.

Yes, but Gene and latterly Aaron H. don't like it.

>>>> Unfortunately "pitch class" won't do although I'm sure I >>>> heard a definition that was pretty close.
>>> "Pitch class" is well defined, on the other hand, by
>>> Babbit or whoever. It's the latter meaning of pitch I gave
>>> above plus octave equivalence.
>> That's what I thought I read, but other people say the only >> defining feature is octave equivalence.
> > Octave equivalence alone doesn't get you anything, so that
> doesn't make sense.

"A pitch class is a pitch under octave equivalence."

Graham

George D. Secor wrote:

> After thinking it over, I'd advise using "meantone-class" rather > than "meantone" as an adjective to describe temperaments such as 19-, > 31-, and 12-ET, unless the context makes it absolutely clear that the > latter term is being used to refer to a class of temperaments. Also, > I think that we need to recognize that when one speaks of "a > temperament", it is ordinarily assumed that one is referring to a > single (unspecified) tempered tuning, not a set of tempered tunings > that are members of the same class; if you're thinking of using the > word "temperament" for the latter, then you had better > say "temperament class" to ensure that you won't be misunderstood.

The tuning doesn't have to be specified then? I'm worried that I've been talking about temperaments in the light of a given error that requires optimization, but not specified that they're optimized. Oh, what a minefield this is!

Furthermore, can you talk about a temperament class having an error? Strictly speaking, error is a property of a temperament. How about badness as a function of the mapping even when there's an implied error?

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >> So what is meantone temperament?
> >
> > You lost me.
>
> You keep looking for mentions of "meantone temperament" in
> the archives. What do you expect them to demonstrate?

Unless (as maybe you were trying to point out) they are
preceded by the article "a", they demonstrate use of the
terminology I'm advocating.

> >>> And "the blackjack scale" is something you're apparently
> >>> making up. People usually just say "blackjack" (42 vs. 8
> >>> matches in my tuning list archives from '03-05).
> >>
> >> http://tonalsoft.com/enc/b/blackjack.aspx
> >> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
> >>
> >> What is it then?
> >
> > Perfectly consistent with Gene's definition since here
> > monz also demands 5. a specific tuning of the generator.
>
> And which tuning is that?

It calls it the "optimal" one. I don't know what it is
but apparently it exists.

> "Blackjack scale: miracle[21], 21-out-of-72-edo"

> "The Blackjack generator is also nearly identical to an
> interval the size of 7 degrees of 72-EDO"

*nearly identical* This explains the double definitions
in the first quote.

> "I will present the Blackjack scale here as
> 21-out-of-72-EDO. In the 72edo version of blackjack..."

*version*

> Unfortunately I couldn't reach that page before the weekend,
> and I still can't reach it this morning. If Erv tells you
> he used Genes definition, then good for Erv.
> I have a message from Kraig to the list saying "Partch
> mapped 43 pitches in a way that can be thought of [as] a 41
> tone scale with two tones that vary". How do varying tones
> fit Gene's definition?

I'm not sure how you got the notion I said Erv was using
Gene's definition. Quite the opposite!

> >> I thought I was following the consensus from tuning-math. I
> >> don't have the reference. I don't even remember whose
> >> suggestion it was.
> >
> > I have almost every tuning-math message right here. I'm going
> > to regex it for "temperament class"... 43 messages found. The
> > first is from you, on 2002/5/13. In it, you refer to a
> > definition you apparently wrote in monz's encyclopedia. But
> > it looks like the encyclopedia entry has changed since then.
>
> Then you missed 20th August 2001.

So I did. I don't see any replies to the relevant aspect
of that message, though.

Out of the 64 results (this time from yahoo), you can't
miss that all but 7 of them date since 2006, and none are
from 2003, 2004, or 2005.

> > http://tonalsoft.com/enc/t/temperament.aspx
> > (I notice that Joe, you, and John all call a temperament a
> > kind of tuning, whereas Gene does not. He points out why
> > it's a bad idea to do so.)
>
> Gene's argument is circular reasoning, for what that's worth.

It'd be worth more if you explained it in some way.

> > Followed by five from you that take us to Sept. 2007, which
> > I reply to asking, "What's a temperament class?" The next
> > message that isn't by you or quoting you is from George Secor
> > in Dec. 2007. There's a quote of that, and then the rest
> > are from you or quotes of you.
>
> The plural of message is "messages".

Huh?

> But sure, if you have evidence from the archives that people
> were using the word "temperament" do specify that a mapping
> doesn't require a tuning, let's see them. One will do for
> starters.

I just showed that they weren't using "temperament class"
for three of the core years. Do you remember any other
terminology that could have been in use during this period?
I don't.

> >>> The terms floating around in this space are "tone", "note",
> >>> and "pitch". We could try to standardize them so they make
> >>> sense (assign them to 3 concepts that are as different from
> >>> one another as possible without breaking a large majority
> >>> of prior usage of the term). And then 7 years later somebody
> >>> will come along and say we did it all wrong.
> >> 7 years is pretty good going for tuning terminology. How
> >> long before we get a replacement for "unison vector"?
> >
> > That one's been around for at least 40 years.
>
> Yes, but Gene and latterly Aaron H. don't like it.

Yeah well, I was never sympathetic to that. Or Gene's
objection to the term "lattice".

> >>>> Unfortunately "pitch class" won't do although I'm sure I
> >>>> heard a definition that was pretty close.
> >>>
> >>> "Pitch class" is well defined, on the other hand, by
> >>> Babbit or whoever. It's the latter meaning of pitch I gave
> >>> above plus octave equivalence.
> >>
> >> That's what I thought I read, but other people say the only
> >> defining feature is octave equivalence.
> >
> > Octave equivalence alone doesn't get you anything, so that
> > doesn't make sense.
>
> "A pitch class is a pitch under octave equivalence."
>
> Graham

Right, you need a pitch and octave equivalence. So you need
a definition of pitch (like the one I gave). Octave equivalence
can't be the "only defining feature".

-Carl

> Furthermore, can you talk about a temperament class having
> an error? Strictly speaking, error is a property of a
> temperament.

Huh? If you stick to the map the number of notes doesn't
matter.

-Carl

Carl Lumma wrote:
>> Furthermore, can you talk about a temperament class having >> an error? Strictly speaking, error is a property of a >> temperament.
> > Huh? If you stick to the map the number of notes doesn't
> matter.

The error measures how close a tuning gets to just intonation. Does it make sense to say that an abstraction that's specifically defined to not have a tuning can still have such an error? Strangely enough, I think it can, or at least I've been using the terms that way.

Graham

Carl Lumma wrote:

>> You keep looking for mentions of "meantone temperament" in >> the archives. What do you expect them to demonstrate?
> > Unless (as maybe you were trying to point out) they are
> preceded by the article "a", they demonstrate use of the
> terminology I'm advocating.

By what grammatical rule?

>>>>> And "the blackjack scale" is something you're apparently
>>>>> making up. People usually just say "blackjack" (42 vs. 8
>>>>> matches in my tuning list archives from '03-05).
>>>> http://tonalsoft.com/enc/b/blackjack.aspx
>>>> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
>>>>
>>>> What is it then?
>>> Perfectly consistent with Gene's definition since here
>>> monz also demands 5. a specific tuning of the generator.
>> And which tuning is that?
> > It calls it the "optimal" one. I don't know what it is
> but apparently it exists.

"There is no single optimum MIRACLE generator..."

>> "I will present the Blackjack scale here as >> 21-out-of-72-EDO. In the 72edo version of blackjack..."
> > *version*

Yes. Are scales not allowed to have different versions now?

>> Unfortunately I couldn't reach that page before the weekend, >> and I still can't reach it this morning. If Erv tells you >> he used Genes definition, then good for Erv.
>> I have a message from Kraig to the list saying "Partch >> mapped 43 pitches in a way that can be thought of [as] a 41 >> tone scale with two tones that vary". How do varying tones >> fit Gene's definition?
> > I'm not sure how you got the notion I said Erv was using
> Gene's definition. Quite the opposite!

Perhaps by the way you said "Wilson starts with Gene's def." but never mind.

>>> http://tonalsoft.com/enc/t/temperament.aspx
>>> (I notice that Joe, you, and John all call a temperament a
>>> kind of tuning, whereas Gene does not. He points out why
>>> it's a bad idea to do so.)
>> Gene's argument is circular reasoning, for what that's worth.
> > It'd be worth more if you explained it in some way.

The argument is "the same people talk of 1/4-comma meantone or 2/7-comma meantone as if they were both meantone". And if they do, that's only true if meantone is a temperament. Which is what Gene's arguing for.

>>> Followed by five from you that take us to Sept. 2007, which
>>> I reply to asking, "What's a temperament class?" The next
>>> message that isn't by you or quoting you is from George Secor
>>> in Dec. 2007. There's a quote of that, and then the rest
>>> are from you or quotes of you.
>> The plural of message is "messages".
> > Huh?

I counted three such messages.

>> But sure, if you have evidence from the archives that people >> were using the word "temperament" do specify that a mapping >> doesn't require a tuning, let's see them. One will do for
>> starters.
> > I just showed that they weren't using "temperament class"
> for three of the core years. Do you remember any other
> terminology that could have been in use during this period?
> I don't.

Yes, "temperament family".

>> "A pitch class is a pitch under octave equivalence."
> > Right, you need a pitch and octave equivalence. So you need
> a definition of pitch (like the one I gave). Octave equivalence
> can't be the "only defining feature".

You need a definition of pitch that specifically allows for different psychoacoustic pitches. And the definition here makes it explicit:

http://solomonsmusic.net/setgloss.htm

Graham

Direct translation is dangerous (especially if you're using an
online dictionary). "Verwechselung" has different implications
than "confusion" or "mistake" do.

"Substitution" or even "exchange", though not
literal translations, would get the point across better in this
case. The native German speakers here, who obviously have an
excellent command of English, can verify that these may not be the
best translations, but they are certainly more accurate in actual
meaning.

The principle problem in translating from German, or understanding
older English for that matter, is that contemporary meanings are
often loaded with value judgements which weren't originally there,
and shouldn't be there now. For example, take "mistake" as a verb.
One meaning can be that one is taking (recognizing) one thing for
another. Is one "making a mistake"? Literally, yes. "One is
mistaking", but there is no value judgement inherent in the
statement. There is nothing "wrong" with mistaking some brushstrokes
of oil and pigment for a beautiful blue sky. With this in mind it is
easy to understand "Verwechselung".

-Cameron Bobro

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Paul Poletti wrote:
>
> > As to what is a temperament and what is being "tempered", I'm
plenty
> > happy with the original meaning as implied (if not precisely
stated)
> > by Werckmeister. Go read either the original German:
> >
> > http://harpsichords.pbwiki.com/Werckmeister_Anmerckungen_1698
>
> Oh, it comes from the German, does it? A word used by
> Helmholtz, Tanaka and I'm sure others is "Verwechselung" as
> in "schismatische Verwechselung" and "kleismatische
> Verwechselung". It takes the place of the English word
> "temperament" when we call these things "schismatic
> temperament" or "kleismatic temperament". So what does
> "Verwechselung" actually mean?
>
> Well, according to a web dictionary:
>
> http://dict.tu-chemnitz.de/
dings.cgi?service=deen&query=Verwechselung
>
> it means "mistake" or "confusion". So perhaps we should be
> talking about "the schismatic mistake" or "the kleismatic
> confusion"?
>
>
> Graham
>

Cameron Bobro wrote:
> Direct translation is dangerous (especially if you're using an
> online dictionary). "Verwechselung" has different implications
> than "confusion" or "mistake" do. > > "Substitution" or even "exchange", though not
> literal translations, would get the point across better in this > case. The native German speakers here, who obviously have an > excellent command of English, can verify that these may not be the > best translations, but they are certainly more accurate in actual > meaning. I assumed it meant something like "substitution" but I don't think I looked it up before.

> The principle problem in translating from German, or understanding > older English for that matter, is that contemporary meanings are > often loaded with value judgements which weren't originally there, > and shouldn't be there now. For example, take "mistake" as a verb. > One meaning can be that one is taking (recognizing) one thing for > another. Is one "making a mistake"? Literally, yes. "One is > mistaking", but there is no value judgement inherent in the > statement. There is nothing "wrong" with mistaking some brushstrokes > of oil and pigment for a beautiful blue sky. With this in mind it is > easy to understand "Verwechselung".

Thanks, that makes sense! But I still think that direct translation is amusing.

Graham

Just looked in Wahrig, and sure enough one of the examples is:
(loosely translated) "they looked so much alike that I thought one
was the other".

In the realm of perception, they're the "same". Mann "verwechselt",
or one tempers, a tuning, and the result is supposed to be, in the
realm of perception, the "same thing". This is why I bitch about
"tempered 5/4"s that don't sound anything like 5/4, hahaha!

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> Direct translation is dangerous (especially if you're using an
> online dictionary). "Verwechselung" has different implications
> than "confusion" or "mistake" do.
>
> "Substitution" or even "exchange", though not
> literal translations, would get the point across better in this
> case. The native German speakers here, who obviously have an
> excellent command of English, can verify that these may not be the
> best translations, but they are certainly more accurate in actual
> meaning.
>
> The principle problem in translating from German, or understanding
> older English for that matter, is that contemporary meanings are
> often loaded with value judgements which weren't originally there,
> and shouldn't be there now. For example, take "mistake" as a verb.
> One meaning can be that one is taking (recognizing) one thing for
> another. Is one "making a mistake"? Literally, yes. "One is
> mistaking", but there is no value judgement inherent in the
> statement. There is nothing "wrong" with mistaking some
brushstrokes
> of oil and pigment for a beautiful blue sky. With this in mind it
is
> easy to understand "Verwechselung".
>
> -Cameron Bobro
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> > Paul Poletti wrote:
> >
> > > As to what is a temperament and what is being "tempered", I'm
> plenty
> > > happy with the original meaning as implied (if not precisely
> stated)
> > > by Werckmeister. Go read either the original German:
> > >
> > > http://harpsichords.pbwiki.com/Werckmeister_Anmerckungen_1698
> >
> > Oh, it comes from the German, does it? A word used by
> > Helmholtz, Tanaka and I'm sure others is "Verwechselung" as
> > in "schismatische Verwechselung" and "kleismatische
> > Verwechselung". It takes the place of the English word
> > "temperament" when we call these things "schismatic
> > temperament" or "kleismatic temperament". So what does
> > "Verwechselung" actually mean?
> >
> > Well, according to a web dictionary:
> >
> > http://dict.tu-chemnitz.de/
> dings.cgi?service=deen&query=Verwechselung
> >
> > it means "mistake" or "confusion". So perhaps we should be
> > talking about "the schismatic mistake" or "the kleismatic
> > confusion"?
> >
> >
> > Graham
> >
>

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

> But I still think that direct
> translation is amusing.

Sometimes I do proofreading and translations from Slovene to English,
and direct translation can have downright embarassing connotations.
I'm sure I've pulled some real boners in Slovene, too. Can't think of
any specific examples at the moment, unfortunately.

Oddly enough, you can do really good and nearly direct translations
using archaic and poetic English (same with German).

Graham Breed schrieb:
> Paul Poletti wrote:
> >> As to what is a temperament and what is being "tempered", I'm plenty
>> happy with the original meaning as implied (if not precisely stated)
>> by Werckmeister. Go read either the original German:
>>
>> http://harpsichords.pbwiki.com/Werckmeister_Anmerckungen_1698
> > Oh, it comes from the German, does it? A word used by > Helmholtz, Tanaka and I'm sure others is "Verwechselung" as > in "schismatische Verwechselung" and "kleismatische > Verwechselung". It takes the place of the English word > "temperament" when we call these things "schismatic > temperament" or "kleismatic temperament". So what does > "Verwechselung" actually mean?
> > Well, according to a web dictionary:
> > http://dict.tu-chemnitz.de/dings.cgi?service=deen&query=Verwechselung
> > it means "mistake" or "confusion". So perhaps we should be > talking about "the schismatic mistake" or "the kleismatic > confusion"?

You forgot to mention that this web dictionary comes from Chemnitz, no doubt the eastern boundary of Johnny's home country of well temperaments.

I can't help but think this post was tongue-in-cheek, but since it created so much response (and since, in hindsight, my involvement here may have to with a t-i-c post that I didn't get) let it be said that Verwechslung most likely (don't know a relevant quote in Helmholtz) means equivalence, as in "enharmonic equivalence". It doesn't mean temperament, but it hints at the interval tempered out.

"Temperament" in German is "Temperatur", but the usual word is "Stimmung" - "tuning". And while the word "Wohltemperatur" almost exists (http://www.googlefight.com/index.php?lang=en_GB&word1=wohltemperatur&word2=wohltemperament), it continues to sound funny and make me think of bath water. Bach wrote the WTC for "wohltemperierte Stimmung" (modern orthography) (and for the grammar debate: that's adverb + past participle used as adjective, noun. But I have always been in awe of English that can make up "well temperament" and get away with it).

klaus

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >> Furthermore, can you talk about a temperament class having
> >> an error? Strictly speaking, error is a property of a
> >> temperament.
> >
> > Huh? If you stick to the map the number of notes doesn't
> > matter.
>
> The error measures how close a tuning gets to just
> intonation. Does it make sense to say that an abstraction
> that's specifically defined to not have a tuning can still
> have such an error? Strangely enough, I think it can, or at
> least I've been using the terms that way.

Error is a property of a map + a tuning. I was thinking your
definition of temperament included a number of notes, but
maybe it doesn't.

-Carl

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> Carl Lumma wrote:
>
> >> You keep looking for mentions of "meantone temperament" in
> >> the archives. What do you expect them to demonstrate?
> >
> > Unless (as maybe you were trying to point out) they are
> > preceded by the article "a", they demonstrate use of the
> > terminology I'm advocating.
>
> By what grammatical rule?

Acceptance of things like, "in meantone temperament, 4 fifths
equal 1 major third" then you're accepting Gene's definition.
For you definition it would have to be "in a meantone
temperament" or "in meantone temperaments". By the way,
I don't put much stock in grammar rules. But if I did, I'd
say you didn't mean "grammatical" there.

> >>>> http://tonalsoft.com/enc/b/blackjack.aspx
> >>>> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
> >>>>
> >>>> What is it then?
> >>>
> >>> Perfectly consistent with Gene's definition since here
> >>> monz also demands 5. a specific tuning of the generator.
> >> And which tuning is that?
> >
> > It calls it the "optimal" one. I don't know what it is
> > but apparently it exists.
>
> "There is no single optimum MIRACLE generator..."

I don't think that's on the same page as the blackjack
definition I'm referring to.

> >> Unfortunately I couldn't reach that page before the weekend,
> >> and I still can't reach it this morning. If Erv tells you
> >> he used Genes definition, then good for Erv.
> >> I have a message from Kraig to the list saying "Partch
> >> mapped 43 pitches in a way that can be thought of [as] a 41
> >> tone scale with two tones that vary". How do varying tones
> >> fit Gene's definition?
> >
> > I'm not sure how you got the notion I said Erv was using
> > Gene's definition. Quite the opposite!
>
> Perhaps by the way you said "Wilson starts with Gene's def."
> but never mind.

It's true.

> >>> http://tonalsoft.com/enc/t/temperament.aspx
> >>> (I notice that Joe, you, and John all call a temperament a
> >>> kind of tuning, whereas Gene does not. He points out why
> >>> it's a bad idea to do so.)
> >> Gene's argument is circular reasoning, for what that's worth.
> >
> > It'd be worth more if you explained it in some way.
>
> The argument is "the same people talk of 1/4-comma meantone
> or 2/7-comma meantone as if they were both meantone". And
> if they do, that's only true if meantone is a temperament.
> Which is what Gene's arguing for.

If you look at the top of this block, you'll see it refers
to Gene's argument for separating tuning and temperament,
not whether temperament should be called "temperament class".

> >>> Followed by five from you that take us to Sept. 2007, which
> >>> I reply to asking, "What's a temperament class?" The next
> >>> message that isn't by you or quoting you is from George Secor
> >>> in Dec. 2007. There's a quote of that, and then the rest
> >>> are from you or quotes of you.
> >>
> >> The plural of message is "messages".
> >
> > Huh?
>
> I counted three such messages.

I don't know what is gained by being cryptic. I say "the
next message" above. Singular.

> >> But sure, if you have evidence from the archives that people
> >> were using the word "temperament" do specify that a mapping
> >> doesn't require a tuning, let's see them. One will do for
> >> starters.
> >
> > I just showed that they weren't using "temperament class"
> > for three of the core years. Do you remember any other
> > terminology that could have been in use during this period?
> > I don't.
>
> Yes, "temperament family".

I recall that never being used during this period, except
to refer to Gene's temperament families.

> >> "A pitch class is a pitch under octave equivalence."
> >
> > Right, you need a pitch and octave equivalence. So you need
> > a definition of pitch (like the one I gave). Octave equivalence
> > can't be the "only defining feature".
>
> You need a definition of pitch that specifically allows for
> different psychoacoustic pitches. And the definition here
> makes it explicit:
>
> http://solomonsmusic.net/setgloss.htm

?? "The predominant frequency in a sound" wouldn't pass
in 'sound perception & hearing 101'. Pitch is a
characteristic frequency in a sound, and it also has units
of confidence. Even better, it would be modeled by n-way
harmonic entropy, where a sound's n partials are the input
and the resulting probabilities under the distribution are
its "pitch".

-Carl

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Carl Lumma wrote:
>>
>>>> You keep looking for mentions of "meantone temperament" in >>>> the archives. What do you expect them to demonstrate?
>>> Unless (as maybe you were trying to point out) they are
>>> preceded by the article "a", they demonstrate use of the
>>> terminology I'm advocating.
>> By what grammatical rule?
> > Acceptance of things like, "in meantone temperament, 4 fifths
> equal 1 major third" then you're accepting Gene's definition.
> For you definition it would have to be "in a meantone
> temperament" or "in meantone temperaments". By the way,
> I don't put much stock in grammar rules. But if I did, I'd
> say you didn't mean "grammatical" there.

No I don't. "Temperament" can be an uncountable noun. For Gene's definition it'd most likely be "in the meantone temperament". But I gave you a link on the correct use of articles and the ball's in your court.

I'd hope if you did put stock in grammatical rules you'd quickly learn the difference between a noun and an adjective.

>>>>>> http://tonalsoft.com/enc/b/blackjack.aspx
>>>>>> http://tonalsoft.com/monzo/blackjack/blackjack.aspx
>>>>>>
>>>>>> What is it then?
>>>>> Perfectly consistent with Gene's definition since here
>>>>> monz also demands 5. a specific tuning of the generator.
>>>> And which tuning is that?
>>> It calls it the "optimal" one. I don't know what it is
>>> but apparently it exists.
>> "There is no single optimum MIRACLE generator..."
> > I don't think that's on the same page as the blackjack
> definition I'm referring to.

I don't know. On what page are you asserting that Monzo demands a specific tuning?

>>>>> http://tonalsoft.com/enc/t/temperament.aspx
>>>>> (I notice that Joe, you, and John all call a temperament a
>>>>> kind of tuning, whereas Gene does not. He points out why
>>>>> it's a bad idea to do so.)
>>>> Gene's argument is circular reasoning, for what that's worth.
>>> It'd be worth more if you explained it in some way.
>> The argument is "the same people talk of 1/4-comma meantone >> or 2/7-comma meantone as if they were both meantone". And >> if they do, that's only true if meantone is a temperament. >> Which is what Gene's arguing for.
> > If you look at the top of this block, you'll see it refers
> to Gene's argument for separating tuning and temperament,
> not whether temperament should be called "temperament class".

It refers to Gene's argument for not calling a temperament a kind of tuning (or not calling a kind of tuning a "temperament").

>>>> But sure, if you have evidence from the archives that people >>>> were using the word "temperament" do specify that a mapping >>>> doesn't require a tuning, let's see them. One will do for
>>>> starters.
>>> I just showed that they weren't using "temperament class"
>>> for three of the core years. Do you remember any other
>>> terminology that could have been in use during this period?
>>> I don't.
>> Yes, "temperament family".
> > I recall that never being used during this period, except
> to refer to Gene's temperament families.

Then your recollection is wrong. Perhaps that's connected with your recollection that a redefinition of "temperament" had become the accepted usage.

>>>> "A pitch class is a pitch under octave equivalence."
>>> Right, you need a pitch and octave equivalence. So you need
>>> a definition of pitch (like the one I gave). Octave equivalence
>>> can't be the "only defining feature".
>> You need a definition of pitch that specifically allows for >> different psychoacoustic pitches. And the definition here >> makes it explicit:
>>
>> http://solomonsmusic.net/setgloss.htm
> > ?? "The predominant frequency in a sound" wouldn't pass
> in 'sound perception & hearing 101'. Pitch is a
> characteristic frequency in a sound, and it also has units
> of confidence. Even better, it would be modeled by n-way
> harmonic entropy, where a sound's n partials are the input
> and the resulting probabilities under the distribution are
> its "pitch".

This isn't Sound Perception & Hearing, it's Set Theory. It doesn't matter how they define "pitch" as a "pitch class" specifically includes "pitches with the same name plus their enharmonic equivalents". I'd like to see Babbitt's original definition because I believe it's similar in this respect. Hence "a scale is a list of pitch classes" would serve us very well and maybe not anger the set theorists too much if we talk about a different (or no) equivalence interval. If not, it's a shame because "pitch class" goes well with "temperament class".

Unfortunately, as most people understand (and some define) "pitch class" they think about twelve scientifically determined pitches within the octave. The wide variety of intonation in practice (which Babbitt may have been thinking of) passes them by. So we can't be sure the term will carry the right connotation.

There's also "abstract pitch" to go with Gene's "abstract temperament" of course ;-)

Graham

Klaus Schmirler wrote:
> Graham Breed schrieb:

>> Oh, it comes from the German, does it? A word used by >> Helmholtz, Tanaka and I'm sure others is "Verwechselung" as >> in "schismatische Verwechselung" and "kleismatische >> Verwechselung". It takes the place of the English word >> "temperament" when we call these things "schismatic >> temperament" or "kleismatic temperament". So what does >> "Verwechselung" actually mean?
>>
>> Well, according to a web dictionary:
>>
>> http://dict.tu-chemnitz.de/dings.cgi?service=deen&query=Verwechselung
>>
>> it means "mistake" or "confusion". So perhaps we should be >> talking about "the schismatic mistake" or "the kleismatic >> confusion"?
> > You forgot to mention that this web dictionary comes from Chemnitz, no > doubt the eastern boundary of Johnny's home country of well temperaments.
>
> I can't help but think this post was tongue-in-cheek, but since it > created so much response (and since, in hindsight, my involvement here > may have to with a t-i-c post that I didn't get) let it be said that > Verwechslung most likely (don't know a relevant quote in Helmholtz) > means equivalence, as in "enharmonic equivalence". It doesn't mean > temperament, but it hints at the interval tempered out.

I'm always happy to use trivial methods to make a serious point. As to the toast post, that was because my first answer to your question was "a temperament" but on consideration I decided you didn't even expect that answer. I was referring to a joke that went round my school, which perhaps the rest of you don't know, where you can trick somebody into saying "toast". If you don't believe it works maybe you could try on your friends.

Anyway, I'd certainly like to know what the original German was intending. You can check Tanaka online:

http://www.anaphoria.com/Shohe.PDF

There's also a rather obscure book by Liberty Manik that discusses the history of the term "schismatische Verwechselung".

From Google Books, it appears Ellis translated "schismatische Verwechse?lung" as "the skhismatic system". There's also a reference to "[a] skhismatic temperament" (but not plain "skhismatic temperament").

Somehow, in these parts at least, it became "schismatic temperament". So the English word "temperament" seems to correspond to three different words in German.

> "Temperament" in German is "Temperatur", but the usual word is > "Stimmung" - "tuning". And while the word "Wohltemperatur" almost > exists > (http://www.googlefight.com/index.php?lang=en_GB&word1=wohltemperatur&word2=wohltemperament), > it continues to sound funny and make me think of bath water. Bach > wrote the WTC for "wohltemperierte Stimmung" (modern orthography) (and > for the grammar debate: that's adverb + past participle used as > adjective, noun. But I have always been in awe of English that can > make up "well temperament" and get away with it).

Then the verbatim translation is "well tempered tuning". Which is grammatically correct with "well" as an adverb modifying "tempered". If you make George's substitution of "temperament" for "tempered tuning" you get "well temperament". Voila! Except "well" now looks like an adjective. Which means the temperament is "in good health; satisfactory state or position, advisable." (The Little Oxford Dictionary)

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> > Acceptance of things like, "in meantone temperament, 4 fifths
> > equal 1 major third" then you're accepting Gene's definition.
> > For you definition it would have to be "in a meantone
> > temperament" or "in meantone temperaments". By the way,
> > I don't put much stock in grammar rules. But if I did, I'd
> > say you didn't mean "grammatical" there.
>
> No I don't. "Temperament" can be an uncountable noun. For
> Gene's definition it'd most likely be "in the meantone
> temperament". But I gave you a link on the correct use of
> articles and the ball's in your court.

I showed that the usage of "temperament class" amounts to
a fart in a windstorm. What more do you want?

> >>>> But sure, if you have evidence from the archives that people
> >>>> were using the word "temperament" do specify that a mapping
> >>>> doesn't require a tuning, let's see them. One will do for
> >>>> starters.
> >>> I just showed that they weren't using "temperament class"
> >>> for three of the core years. Do you remember any other
> >>> terminology that could have been in use during this period?
> >>> I don't.
> >>
> >> Yes, "temperament family".
> >
> > I recall that never being used during this period, except
> > to refer to Gene's temperament families.
>
> Then your recollection is wrong.

Cites?

-Carl

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

> Oh, it comes from the German, does it?
http://de.wikipedia.org/wiki/Enharmonische_Verwechslung
considers in concise original german entry:
"Enharmonische Verwechslung"
aus Wikipedia, der freien Enzyklopädie

Enharmonische Verwechslung nennt man in der Musik die kompositorische
Praxis, Töne als andere Töne, die in gleichstufiger Stimmung gleiche
Höhe, jedoch andere Namen haben, umzudeuten, z. B. Fis als Ges oder
His als C zu betrachten. Dadurch lassen sich der musikalische
Zusammenhang und die Funktion der Töne verändern, z. B. um den Wechsel
in eine andere Tonart (Modulation) herbeizuführen. Der Begriff ist nur
begrenzt gleichzusetzen mit dem Begriff Enharmonik (siehe unten), der
ein weitaus größeres Bedeutungsfeld einnimmt.[1]

Die zwölf Halbtöne der aufsteigenden, chromatisch angereicherten
C-Dur-Tonleiter werden in der zweiten Notenzeile enharmonisch
verwechselt, die übereinander stehenden Töne klingen gleich:

Hier die unterschiedlichen Benennungen für die zwölf Töne der
gleichstufigen Tonleiter; Stammtöne sind hervorgehoben:

His
C
Deses Hisis
Cis
Des Cisis
D
Eses Dis
Es
Feses Disis
E
Fes Eis
F
Geses Eisis
Fis
Ges Fisis
G
Ases
(Asas) Gis
As Gisis
A
Heses
(!) Ais
B
(!)
Ceses Aisis
H
Ces

(Theoretisch lässt sich diese Tabelle nach beiden Seiten erweitern; so
sind z. B. Gis und As gleich klingend mit Fisisis und Heseses.)

Geschichte der Enharmonik und der Enharmonischen Verwechslung:

Enharmonik war in der antiken Musiklehre neben Diatonik und Chromatik
eine Bezeichnung für eine Art der Tonleiterbildung. In der
Musiktheorie der Renaissance wurde der Begriff wieder aufgenommen und
unterschiedlich verwendet. In der Musik des 16. Jahrhunderts finden
wir daher zweierlei Bedeutungen.[1]

* Zum einen waren beispielsweise in der neunzehnstufigen Stimmung
bei Guillaume Costeley mit enharmonischen Tönen Töne unterschiedlicher
Höhe gemeint.
* Zum anderen gab es in den als gleichstufig bezeichneten
Lautenstimmungen derselben Zeit eine Enharmonik mit jeweils denselben
Tonorten.

Gegen Ende des 17. Jahrhundert ermöglichten die Wohltemperierten
Stimmungen sämtliche enharmonischen Verwechslungen auf jeweils
denselben Tonorten. Mit der Möglichkeit, - über die Begrenzungen der
mitteltönigen Stimmungen hinaus - auch Cis und Des, Es und Dis, F und
Eis, Fis und Ges, Gis und As, B und Ais sowie C und His enharmonisch
nicht nur in melodischem, sondern auch in harmonischem Zusammenhang zu
verwenden, standen nun sämtliche Tonarten des Quintenzirkels und deren
Akkorde sogar für ein Musikstück zur Verfügung. Die Rezitative des
Spätbarock sind geradezu geprägt durch ihre intensive Ausnutzung
enharmonischer Fortschreitungen. Als bedeutendes Element der
Modulation mit Hilfe der enharmonischen Verwechslung wurde der
Verminderte Septakkord entdeckt, dessen vier Töne jeweils eine
klingende kleine Terz auseinander stehen und sich vielfältig umdeuten
lassen.

Ob eine Enharmonische Verwechslung durchgeführt werden konnte, hing
also vom verwendeten Stimmungssystem ab. Je näher dieses der
Wohltemperierten Stimmung und schließlich der Gleichstufigen Stimmung
kam, desto zahlreicher und für das Gehör tolerierbarer ließen sich
Enharmonische Verwechslungen verwenden.

In der Musik der Romantik wurde die Tonalität immer mehr erweitert und
begann sich im Laufe des 19. Jahrhunderts bei einigen Komponisten
aufzulösen. Dabei spielte die Enharmonik eine bestimmende Rolle, so z.
B. bei Franz Schubert, Franz Liszt, und Richard Wagner und
weiterführend in das 20. Jahrhundert hinein z. B. bei Gabriel Fauré,
Claude Debussy, Alexander Nikolajewitsch Skrjabin, Max Reger und dem
frühen Arnold Schönberg, denen beispielsweise die enharmonische
Umdeutung alterierter Akkorde fast grenzenlose Modulationen und eine
nicht mehr unbedingt an einen Grundton gebundene Harmonik ermöglichte.[2]

In der weiteren Entwicklung hin zur Atonalität (speziell in der
Dodekaphonie und der ihr folgenden seriellen Kompositionsweise) verlor
die Enharmonik jedoch weitgehend ihre bisherige funktionale Bedeutung.
Bei enharmonischen Verwechslungen ging es oft nur noch um eine
möglichst pragmatische Notation und weniger um eine harmonische
Umdeutungen eines Tones.[3] Folgerichtig wurden neue, zwölfstufige
Notationssysteme erfunden und teilweise in der Praxis verwendet, die
keine enharmonischen Töne mehr enthielten...."

Altavista's
http://de.babelfish.yahoo.com/translate_txt
converts that content almost literally into absolute nonsensial
http://en.wikipedia.org/wiki/Pidgin
in a disharmonic way:

'Enharmoni mistake from Wikipedia, the free encyclopedia changes too:
Navigation, search One calls Enharmoni mistake in the music
kompositorische practice to regard tones as other tones, which have
equivalent height, however different names to reinterpret e.g. Fis
than Ges or His than C in equivalent tendency. Thus the musical
connection and the function of the tones can be changed to cause e.g.
in order the change into another kind of clay/tone (modulation). The
term is only limited to equate with the term Enharmonik (see below),
the one by far greater meaning importance einnimmt.[1 ] The twelve
half-tones of the ascending, chromatically enriched c-Dur-Tonleiter
are confounded in the second note line, the tones standing one above
the other sound enharmonisch directly: align=left Here the different
designations for the twelve tones of the level scale; Naturals are
emphasized: His C Deses Hisis Cis of the Cisis D Eses Dis it Feses
Disis E Fes ice F Geses Eisis Fis Ges Fisis G Ases (Asas) Gis As Gisis
A Heses (!) Ais B (!) Ceses Aisis H Ces (this table can theoretical be
extended after both sides; like that e.g. Gis and As are alike
sounding with Fisisis and Heseses.) History of the Enharmonik and the
Enharmoni mistake [ work on ] Enharmonik was in that antique music
teachings beside Diatonik and Chromatik a name for a kind of the scale
formation. In the music theory of the Renaissance the term was again
taken up and used differently. In the music 16. Century find we
therefore two different Bedeutungen.[1 ] * On the one hand were for
example in the nineteen-level tendency meant with Guillaume Costeley
with enharmonischen tones of tones of different height. * On the other
hand there was a Enharmonik with in each case the same clay/tone
places to than level designated sound tendencies the the same time.
Toward end 17. The tendencies well-being-kept at a moderate
temperature all enharmonischen mistakes on in each case the same
clay/tone places made century possible. With the possibility, - beyond
the delimitations of the mitteltoenigen tendencies - also Cis and, it
and Dis, F and ice, Fis and Ges, Gis and As, B and Ais as well as C
and His enharmonisch not only in melodischem of using but also in
harmonious connection stood now all kinds of clay/tone of the
Quintenzirkels and their chords even for a music piece to the
Verfuegung.[1 ] the Rezitative of the late baroque are almost
coined/shaped by their intensive utilization of enharmonischer
spreads. As important element of the modulation with the help of the
enharmonischen mistake the decreased Septakkord was discovered, whose
four tones in each case a sounding small third can be reinterpreted
apart and variously. Whether a Enharmoni mistake could be
accomplished, depended thus on the used tendency system. The more near
this the tendency well-being-kept at a moderate temperature and
finally the equallevel tendency came, the more numerously and for the
hearing could more tolerable Enharmoni mistakes be used. In the music
of the romance the tonality was extended ever more and began
themselves in the course 19. To dissolve century with some composers.
The Enharmonik played a determining role, so e.g. with Franz Schubert,
Franz Liszt, and Richard wagner and resuming in 20. Century inside
e.g. with Gabriel Fauré, Claude Debussy, Alexander Nikolajewitsch
Skrjabin, max of active and the early Arnold beautiful mountain, those
for example the enharmonische reinterpretation of alterierter chords
nearly boundless modulations and one no longer absolutely to a basic
clay/tone bound Harmonik ermoeglichte.[2 ] _ in the far development to
Atonalitaet (special in the Dodekaphonie and the it following serial
way) lose the Enharmonik however large their past functional meaning.
With enharmonischen mistakes around a if possible pragmatic notation
and around harmonious reinterpretations of a Tones.[3 ] logical were
new, twelve-level notation systems were often only invented less and
in practice partly used, which no more enharmonischen tones contained.
"
...enuf...of that babel-fish -- blah-blah....gibberish...

For an more apt version compare that
to the corresponding reference in the english WIKI entry:
http://en.wikipedia.org/wiki/Enharmonic
or even better to:
http://www.dolmetsch.com/musictheory9.htm
especially there:
"Notes and Keys in Various Languages"
terminology.

'I recommend you to think when at work, not only of the musical but
also of the unmusical public.
You know that for ten true connoisseurs there are a hundred layman
ignoramuses!'
Do not neglect the so-called popular, which tickles long ears.'
so far quoted from:
Leopold Mozart (1719-87) Austrian violinist in Salzburg & Vienna,
advice to his son: Wolfgang Amadeus Mozart (1756-91)

> A word used by
> Helmholtz, Tanaka and I'm sure others is "Verwechselung" as
> in "schismatische Verwechselung" and "kleismatische
> Verwechselung". It takes the place of the English word
> "temperament" when we call these things "schismatic
> temperament" or "kleismatic temperament". So what does
> "Verwechselung" actually mean?
>
> Well, according to a web dictionary:
>
> http://dict.tu-chemnitz.de/dings.cgi?service=deen&query=Verwechselung
>
> it means "mistake" or "confusion". So perhaps we should be
> talking about "the schismatic mistake" or "the kleismatic
> confusion"?
>
That literally "translation" misleads astray
even worser than the above 'babel-fish' attempt.
>
More correct would be in an apt sense:
http://dict.leo.org/ende?lp=ende&p=hPXz..&search=Auswechselung
also spelled as:
http://dict.leo.org/ende?lp=ende&p=hPXz..&search=Auswechslung
http://dict.leo.org/ende?lp=ende&p=hPXz..&search=Tausch
http://dict.leo.org/ende?lp=ende&p=eL4jU.&search=exchange
http://dict.leo.org/ende?lp=ende&p=eL4jU.&search=swap
Denotating an specific kind of
http://dict.leo.org/ende?lp=ende&p=eL4jU.&search=about-face
http://dict.leo.org/ende?lp=ende&p=eL4jU.&search=barter

as for example done by the:
http://en.wikipedia.org/wiki/Tritone_substitution

http://en.wikibooks.org/wiki/Music_Theory/Music_Notation_Systems
"For now, you need only know that a D# and an Eb are enharmonically
equivalent (that is, they have the same pitch, but serve a different
diatonic function) in the oversimplified tuning most commonly used
today." 12-EDO

I hope that contribution helps us to get rid of the
"mistake" or "confusion"
caused by:
http://www.dict.cc/deutsch-englisch/enharmonische+Verwechslung.html

http://www.dolmetsch.com/defse.htm
Enharmonic (noun) enarmono?=a (Spanish), enarmonia (Italian), enharmonie
(French), Enharmonik (German)
(adjective) enharmo?=nico (Spanish), enarmonico (Italian), enharmonique
(French), enharmonisch (German)
(Greek, en, 'in', and harmonia, 'harmony') the capacity for two notes
with different "spellings" and musical functions to be represented by
the same degree of the scale, for example A flat and G sharp, which on
an equal tempered keyboard instrument are played with the same key,
but which on a flexibly tuned instrument, like a violin, can be
perceptibly different where, for example, a note which may be
alternatively expressed as Eb or D#, in the key of B, D# is said to be
'harmonic' to the key of B, while Eb is said to be 'enharmonic' to the
key of B. The distinction is important in how the note would be played
on an unaccompanied non-fixed pitch instrument such as the violin

* Enharmonics
* Enharmonic
(for deeper understanding please follow that links on the original page)

Definitions:
1. Enharmonic change:
the respelling of a note by replacing it with its enharmonic
equivalent, for example, A flat instead of G sharp. This may be
necessary when correctly spelling a chord after a modulation to a new
key the adjustment of the tuning of a note on a stringed or wind
instrument according to whether the note is A flat or G sharp, notes
which in equal temperament would be the same, but which under just
intonation will be different

2. Enharmonic chords:
chords that, in equal temperament, sound the same but differ in the
spelling of their notes....

Conversely in the opposite way around:
http://www-personal.umich.edu/~bpl/temper-examples.html
claims to have solved that problem theoretically by reintroduding
the allegation:
"There is a "wolf" diminished sixth where the circle does not close."
of ~704Cents inbetween A# and F in his own private modern tuning.

Nevertheless: But that's all make belive.

A.S.

Graham Breed schrieb:
> Klaus Schmirler wrote:
>> Graham Breed schrieb:
> >>> Oh, it comes from the German, does it? A word used by >>> Helmholtz, Tanaka and I'm sure others is "Verwechselung" as >>> in "schismatische Verwechselung" and "kleismatische >>> Verwechselung". It takes the place of the English word >>> "temperament" when we call these things "schismatic >>> temperament" or "kleismatic temperament". So what does >>> "Verwechselung" actually mean?
>>>
>>> Well, according to a web dictionary:
>>>
>>> http://dict.tu-chemnitz.de/dings.cgi?service=deen&query=Verwechselung
>>>
>>> it means "mistake" or "confusion". So perhaps we should be >>> talking about "the schismatic mistake" or "the kleismatic >>> confusion"?
>> You forgot to mention that this web dictionary comes from Chemnitz, no >> doubt the eastern boundary of Johnny's home country of well temperaments.
> >
>> I can't help but think this post was tongue-in-cheek, but since it >> created so much response (and since, in hindsight, my involvement here >> may have to with a t-i-c post that I didn't get) let it be said that >> Verwechslung most likely (don't know a relevant quote in Helmholtz) >> means equivalence, as in "enharmonic equivalence". It doesn't mean >> temperament, but it hints at the interval tempered out.
> > I'm always happy to use trivial methods to make a serious > point. As to the toast post, that was because my first > answer to your question was "a temperament" but on > consideration I decided you didn't even expect that answer. > I was referring to a joke that went round my school, which > perhaps the rest of you don't know, where you can trick > somebody into saying "toast". If you don't believe it works > maybe you could try on your friends.

Yes, I got that later. We do it with colors, but the matter is more complicated because at least in my idiolect, "Brot" is more likely to be a sour dough loaf, whereas the fluffy, pre-cut stuff that is meant to be toasted is already toast when still in its plastic bag. You can have your toast untoasted here.

> > Anyway, I'd certainly like to know what the original German > was intending. You can check Tanaka online:
> > http://www.anaphoria.com/Shohe.PDF

It is as I thought. "Schismatic" and "kleismic" "Verwechslung" means that tones differing by 32805/32768 and 15625/1552 are to be regarded as the same tone. He lists their equivalent names, but there is no mention of a temperament. In "System der 53 reinen Intervalle" he introduces the "Focker block" you see in figure III, where tones at the ends of a row differ by a schisma, and tones at the ends of a column differ by a kleisma. Only then does he propose a 53 tone temperament. He admits it is best realized by simply dividing the octave, but he meant to show that the 53 comma tuning is not just a place where the circle of fifths approximates closure, but that its necessity arises from "harmony".

> > There's also a rather obscure book by Liberty Manik that > discusses the history of the term "schismatische Verwechselung".
> > From Google Books, it appears Ellis translated > "schismatische Verwechse?lung" as "the skhismatic system". > There's also a reference to "[a] skhismatic temperament" > (but not plain "skhismatic temperament").

Since it means systematically taking one note for the other, why not?

I never looked into Google books, but I will have to. Apparently, no library in Germany has the Ellis translation, only the original Helmholtz.

To your all's well-being, and good night,

klaus

> > Somehow, in these parts at least, it became "schismatic > temperament". So the English word "temperament" seems to > correspond to three different words in German.
> >> "Temperament" in German is "Temperatur", but the usual word is >> "Stimmung" - "tuning". And while the word "Wohltemperatur" almost >> exists >> (http://www.googlefight.com/index.php?lang=en_GB&word1=wohltemperatur&word2=wohltemperament), >> it continues to sound funny and make me think of bath water. Bach >> wrote the WTC for "wohltemperierte Stimmung" (modern orthography) (and >> for the grammar debate: that's adverb + past participle used as >> adjective, noun. But I have always been in awe of English that can >> make up "well temperament" and get away with it).
> > Then the verbatim translation is "well tempered tuning". > Which is grammatically correct with "well" as an adverb > modifying "tempered". If you make George's substitution of > "temperament" for "tempered tuning" you get "well > temperament". Voila! Except "well" now looks like an > adjective. Which means the temperament is "in good health; > satisfactory state or position, advisable." (The Little > Oxford Dictionary)
> > > Graham

> No I don't. "Temperament" can be an uncountable noun. For
> Gene's definition it'd most likely be "in the meantone
> temperament". But I gave you a link on the correct use of
> articles and the ball's in your court.

Here's a quick survey (of complete matches, including spaces
on either end of the target) of my Tuning, Tuning-math, and
Tuning-math2 mailboxes. Not conclusive by any means, but
suggestive:

"meantone temperament" = 122 matches
"meantone temperaments" = 17 matches

"miracle temperament" = 23 matches
"miracle temperaments" = 1 match

"magic temperament" = 6 matches
"magic temperaments" = 1 match

"schismatic temperament" = 6 matches
"schismatic temperaments" = 0 matches

"pajara temperament" = 10 matches
"pajara temperaments" = 2 matches

-Carl

Klaus Schmirler wrote:

>> http://www.anaphoria.com/Shohe.PDF
> > It is as I thought. "Schismatic" and "kleismic" "Verwechslung" means > that tones differing by 32805/32768 and 15625/1552 are to be regarded > as the same tone. He lists their equivalent names, but there is no > mention of a temperament. In "System der 53 reinen Intervalle" he > introduces the "Focker block" you see in figure III, where tones at > the ends of a row differ by a schisma, and tones at the ends of a > column differ by a kleisma. Only then does he propose a 53 tone > temperament. He admits it is best realized by simply dividing the > octave, but he meant to show that the 53 comma tuning is not just a > place where the circle of fifths approximates closure, but that its > necessity arises from "harmony".

He shows a chain of minor thirds, so he has the basic property of kleismatic temperament. Maybe he didn't think of tempering it but the unison vector (presumably what the Verwechselung indicates) is in enough to define a temperament class.

>> There's also a rather obscure book by Liberty Manik that >> discusses the history of the term "schismatische Verwechselung".
>>
>> From Google Books, it appears Ellis translated >> "schismatische Verwechse?lung" as "the skhismatic system". >> There's also a reference to "[a] skhismatic temperament" >> (but not plain "skhismatic temperament").
> > Since it means systematically taking one note for the other, why not?

It loses the meaning of equivalence, though. Hence "schismatic temperament" became the term in English instead of "schismatic equivalence". What would it be in German?

Graham

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >> Oh, it comes from the German, does it? > http://de.wikipedia.org/wiki/Enharmonische_Verwechslung
> considers in concise original german entry:
> "Enharmonische Verwechslung"
> aus Wikipedia, der freien Enzyklop�die
<snip>

Okay, "Enharmonische Verwechslung" is the term for enharmonic equivalence, then. But you rarely hear "schismatic equivalence" in English. (Google says that Monzo used it twice, compared to about a thousand hits for "schismatic temperament". And only one has it happens for "schismatische Verwechse?lung", which is to this thread.)

Graham

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

> Okay, "Enharmonische Verwechslung" is the term for
> enharmonic equivalence, then. But you rarely hear
> "schismatic equivalence" in English.

Naturally, because one rarely discusses the schisma, while enharmonic
equivalence plays a role in familiar repertoire as well as theory.

(Google says that
> Monzo used it twice, compared to about a thousand hits for
> "schismatic temperament". And only one has it happens for
> "schismatische Verwechse?lung", which is to this thread.)
>

When Erv and Larry asked me for a rough translation of parts of the
Tanaka (which was published in Xenharmonikon without my permission;
I'd have preferred to finish and polish the thing), too many years
ago, I was sorely tempted to translate Verwechselung as "pun", in
order to capture both the sense of substitution and of confusion, but
gave in to music-theoretic convention and chose "equivalence".

Now, I recognize that equivalence has one real advantage, and that is
it makes the idea more approachable by those who already have a
theory background, and encourages them to become both a bit more
accurate in their terminology and more flexible in their ideas. In
fact, building on the idea, X-equivalence is a very useful way of
getting tonal theorists to appreciate the utility of recognizing
tempered-out intervals in tonal progressions, and ultimately,
becoming more familiar with the entire landscape or scenario (or
whatever you're calling it) of such equivalences.

Dnaiel Wolf

--- In tuning@yahoogroups.com, "djwolf_frankfurt" <djwolf@...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
>
> > Okay, "Enharmonische Verwechslung" is the term for
> > enharmonic equivalence, then. But you rarely hear
> > "schismatic equivalence" in English.
>
> Naturally, because one rarely discusses the schisma, while
enharmonic
> equivalence plays a role in familiar repertoire as well as theory.
>
>
> (Google says that
> > Monzo used it twice, compared to about a thousand hits for
> > "schismatic temperament". And only one has it happens for
> > "schismatische Verwechse?lung", which is to this thread.)
> >
>
> When Erv and Larry asked me for a rough translation of parts of the
> Tanaka (which was published in Xenharmonikon without my permission;
> I'd have preferred to finish and polish the thing), too many years
> ago, I was sorely tempted to translate Verwechselung as "pun", in
> order to capture both the sense of substitution and of confusion,
but
> gave in to music-theoretic convention and chose "equivalence".
>
> Now, I recognize that equivalence has one real advantage, and that
is
> it makes the idea more approachable by those who already have a
> theory background, and encourages them to become both a bit more
> accurate in their terminology and more flexible in their ideas. In
> fact, building on the idea, X-equivalence is a very useful way of
> getting tonal theorists to appreciate the utility of recognizing
> tempered-out intervals in tonal progressions, and ultimately,
> becoming more familiar with the entire landscape or scenario (or
> whatever you're calling it) of such equivalences.
>
> Dnaiel Wolf
>

Good post. "Equivalence" is good, check out the etymology.

BTW "unison vector" is a waste of time, "enharmonic vector" is
truer and clearer.

-Cameron Bobro

Here's one example of a use of "temperament family", which I
happened to run into today when looking up diaschismic
temperament...

http://www.robertinventor.com/tuning-math/s___7/msg_6700-6724.html#6718

Searching for the term, I see Herman, Gene, Monz, and Paul E.
using Gene's definition. I only see Graham and George Secor
using the other definition, and the total number of uses is
much smaller (very much smaller if we discount messages where
Graham and George are only arguing for their definition).
Graham does appear to be using it first (in 2002), but it
still confuses Paul E. in in 2006, and the next day Graham
offers to change over to "temperament class".

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > No I don't. "Temperament" can be an uncountable noun. For
> > Gene's definition it'd most likely be "in the meantone
> > temperament". But I gave you a link on the correct use of
> > articles and the ball's in your court.
>
> Here's a quick survey (of complete matches, including spaces
> on either end of the target) of my Tuning, Tuning-math, and
> Tuning-math2 mailboxes. Not conclusive by any means, but
> suggestive:
>
> "meantone temperament" = 122 matches
> "meantone temperaments" = 17 matches
>
> "miracle temperament" = 23 matches
> "miracle temperaments" = 1 match
>
> "magic temperament" = 6 matches
> "magic temperaments" = 1 match
>
> "schismatic temperament" = 6 matches
> "schismatic temperaments" = 0 matches
>
> "pajara temperament" = 10 matches
> "pajara temperaments" = 2 matches
>
> -Carl
>

Hi Cameron,

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

> BTW "unison vector" is a waste of time,
> "enharmonic vector" is truer and clearer.

I totally disagree with that.

"Unison vector" is a term that was coined by Fokker (AFAIK),
and expresses perfectly the concept he was writing about:
the closure of the theoretically infinite JI lattice
by equating notes outside the periodicity-block with
those inside it.

"Enharmonic" has only come to mean "the same" in the
context of 12-edo as a member of the augmented family
(or class, if "family" has been deprecated).

The term "enharmonic" of course originated with the
ancient Greek theorists, who used it to characterize
a class of genera, which featured what we today would
call quarter-tones.

It so happens that in 5-limit JI, the "enharmonic diesis"
of ratio 128:125 is ~41 cents, roughly the right size
to fit into the Greek enharmonic genus. This was
recognized in the 1500s by such theorists as Vicentino,
who were exploring 5-limit JI and its associated meantone
temperaments, and using those tunings to relate to and
explain the ancient Greek theories.

It's only because 12-edo tempers out the enharmonic diesis
that "enharmonic" came to refer to a type of pitch
equivalence.

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

Carl Lumma wrote:
> Here's one example of a use of "temperament family", which I
> happened to run into today when looking up diaschismic
> temperament...
> > http://www.robertinventor.com/tuning-math/s___7/msg_6700-6724.html#6718
> > Searching for the term, I see Herman, Gene, Monz, and Paul E.
> using Gene's definition. I only see Graham and George Secor
> using the other definition, and the total number of uses is
> much smaller (very much smaller if we discount messages where
> Graham and George are only arguing for their definition).
> Graham does appear to be using it first (in 2002), but it
> still confuses Paul E. in in 2006, and the next day Graham
> offers to change over to "temperament class".

There you go, 2006. There is one case where I was evil enough to trick Gene into using my meaning of "family", although maybe not about temperaments:

http://www.robertinventor.com/tuning-math/s__11/msg_10600-10624.html

Graham

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Hi Cameron,
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
>
> > BTW "unison vector" is a waste of time,
> > "enharmonic vector" is truer and clearer.
>
>
> I totally disagree with that.
>
> "Unison vector" is a term that was coined by Fokker (AFAIK),
> and expresses perfectly the concept he was writing about:
> the closure of the theoretically infinite JI lattice
> by equating notes outside the periodicity-block with
> those inside it.
>
> "Enharmonic" has only come to mean "the same" in the
> context of 12-edo as a member of the augmented family
> (or class, if "family" has been deprecated).
>
> The term "enharmonic" of course originated with the
> ancient Greek theorists, who used it to characterize
> a class of genera, which featured what we today would
> call quarter-tones.
>
> It so happens that in 5-limit JI, the "enharmonic diesis"
> of ratio 128:125 is ~41 cents, roughly the right size
> to fit into the Greek enharmonic genus. This was
> recognized in the 1500s by such theorists as Vicentino,
> who were exploring 5-limit JI and its associated meantone
> temperaments, and using those tunings to relate to and
> explain the ancient Greek theories.
>
> It's only because 12-edo tempers out the enharmonic diesis
> that "enharmonic" came to refer to a type of pitch
> equivalence.

Unfortunately, "enharmonic" HAS come to refer to pitch
equivalences, whereas "unison" refers to both actual
unison (and octave "equivalences", in practice).

Better than either in this case would be something along the
lines of "mergence". "Unison" simply does not "express
perfectly" the "closings" in an infinite JI lattice.

-Cameron Bobro

Carl Lumma wrote:
> Here's one example of a use of "temperament family", which I
> happened to run into today when looking up diaschismic
> temperament...
> > http://www.robertinventor.com/tuning-math/s___7/msg_6700-6724.html#6718
> > Searching for the term, I see Herman, Gene, Monz, and Paul E.
> using Gene's definition. I only see Graham and George Secor
> using the other definition, and the total number of uses is
> much smaller (very much smaller if we discount messages where
> Graham and George are only arguing for their definition).
> Graham does appear to be using it first (in 2002), but it
> still confuses Paul E. in in 2006, and the next day Graham
> offers to change over to "temperament class".

Monzo was the first to use it in tuning-math and Paul E. wasn't confused:

http://www.robertinventor.com/tuning-math/s___1/msg____0-__24.html#16

So when you say "still" you mean "now".

Graham

> http://www.robertinventor.com/tuning-math/s___1/msg____0-__24.html#16

"Temperament family" doesn't occur on this page, nor anything like
it in Monz's message.

> So when you say "still" you mean "now".

Where do you get these from?

-Carl

Hi Cameron,

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

> Unfortunately, "enharmonic" HAS come to refer to pitch
> equivalences, whereas "unison" refers to both actual
> unison (and octave "equivalences", in practice).
>
> Better than either in this case would be something along the
> lines of "mergence". "Unison" simply does not "express
> perfectly" the "closings" in an infinite JI lattice.

Your points are noted, but i still disagree.

Fokker's concept is that the reference periodicity-block
*is* the *finite* JI lattice, and that all similar blocks
lying outside the reference block (in the theoretically
infinite lattice) are considered to be *the same*.
In other words, they don't even exist, and therefore,
they are all unisons with the notes inside the reference
periodicity-block.

Of course, in real JI, they are theoretically equivalent,
but are not real unisons. However, in a temperament,
when a unison-vector (which many folks around here like
to call a "comma") vanishes, they *are* real unisons.
This was all part of Fokker's plan, because he was
showing 31-tone periodicity-blocks in 7-limit JI as
a preliminary to developing 31-edo as 31-et of 7-limit JI.

The only reason "enharmonic" has taken on the meaning
of "equivalence" is because 12-edo arose in its first
prominent usage as a member of the meantone family, and
musicians insisted on spelling the enharmonically-equivalent
pairs of notes with their meantone spellings. But in
12-edo, these pairs of notes really are unisons (if that
word is taken in its literal meaning of "one sound").

It would have been better to adopt a base-12 system
of notation for 12-edo, which in fact finally did happen
in the mid-1900s (using the integers 0 to 11), but that
usage is pretty narrowly confined to academia. I've
been exploring it more recently, as on this page:

http://tonalsoft.com/enc/p/pc-set.aspx

This concept appeals to me because of its extendability
to other EDOs, and that's what i've been working on lately.

Anyway, i suppose it's necessary to acknowledge that
"enharmonic" has evolved to mean "equivalent" -- and
indeed, i did that years ago by putting pages about it
into my Encyclopedia -- but i still argue that "unison-vector"
is a perfectly logical and reasonable term.

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

Hi Carl (and Graham),

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > http://www.robertinventor.com/tuning-math/s___1/msg____0-__24.html#16
>
> "Temperament family" doesn't occur on this page, nor anything like
> it in Monz's message.
>
> > So when you say "still" you mean "now".
>
> Where do you get these from?

I think Graham is referring to this question i asked:

"Did we ever take a serious look at 11-odd-limit
approximations in the MIRACLE family?"

True, i didn't write exactly the phrase "temperament family",
but by the definition of "miracle", that's clearly what i was
referring to.

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

Graham Breed schrieb:
> Klaus Schmirler wrote:
> >>> http://www.anaphoria.com/Shohe.PDF
>> It is as I thought. "Schismatic" and "kleismic" "Verwechslung" means >> that tones differing by 32805/32768 and 15625/1552 are to be regarded >> as the same tone. He lists their equivalent names, but there is no >> mention of a temperament. In "System der 53 reinen Intervalle" he >> introduces the "Focker block" you see in figure III, where tones at >> the ends of a row differ by a schisma, and tones at the ends of a >> column differ by a kleisma. Only then does he propose a 53 tone >> temperament. He admits it is best realized by simply dividing the >> octave, but he meant to show that the 53 comma tuning is not just a >> place where the circle of fifths approximates closure, but that its >> necessity arises from "harmony".
> > He shows a chain of minor thirds, so he has the basic > property of kleismatic temperament. Maybe he didn't think > of tempering it but the unison vector (presumably what the > Verwechselung indicates) is in enough to define a > temperament class.
> >>> There's also a rather obscure book by Liberty Manik that >>> discusses the history of the term "schismatische Verwechselung".
>>>
>>> From Google Books, it appears Ellis translated >>> "schismatische Verwechse?lung" as "the skhismatic system". >>> There's also a reference to "[a] skhismatic temperament" >>> (but not plain "skhismatic temperament").
>> Since it means systematically taking one note for the other, why not?
> > It loses the meaning of equivalence, though. Why? "Verwechslung" basically means "mistaken identity" The mistaking can be a matter of course (if the identity is indeed given in a temperament), or it can be between different, but negligibly different, entities. Ellis looks at the whole picture, where all the skhismata have a definite distance in the interval grid, already having in mind it will be bridged, Tanaka just lists where skhismata occur.

I have the feeling that enharmonic equivalence is used less in English than in German. This may be because I learned to read music in German. But if it's true, it could motivate a translator to look for another word that also conveys the idea. "System" can be a general stand-in for so much ...

Hence
> "schismatic temperament" became the term in English instead > of "schismatic equivalence". What would it be in German?

I could be ... or ... But I'm not telling because I don't know former usages of either term.

klaus

> > "Temperament family" doesn't occur on this page, nor anything like
> > it in Monz's message.
> >
> > > So when you say "still" you mean "now".
> >
> > Where do you get these from?
>
> I think Graham is referring to this question i asked:
>
> "Did we ever take a serious look at 11-odd-limit
> approximations in the MIRACLE family?"
>
> True, i didn't write exactly the phrase "temperament family",
> but by the definition of "miracle", that's clearly what i was
> referring to.

You're right, sorry I missed that.

Do you recall if you meant family as in...

1. 31/41/72 notes of the same generator, or

2. 31/41/72 ETs, or

3. ways of extending the 7-limit miracle map to the 11-limit

or some combination thereof?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Here's one example of a use of "temperament family", which I
> happened to run into today when looking up diaschismic
> temperament...
>
> http://www.robertinventor.com/tuning-math/s___7/msg_6700-
6724.html#6718
>
> Searching for the term, I see Herman, Gene, Monz, and Paul E.
> using Gene's definition. I only see Graham and George Secor
> using the other definition, and the total number of uses is
> much smaller (very much smaller if we discount messages where
> Graham and George are only arguing for their definition).
> Graham does appear to be using it first (in 2002), but it
> still confuses Paul E. in in 2006, and the next day Graham
> offers to change over to "temperament class".
>
> -Carl

In this message:
/tuning/topicId_73148.html#73449
I wrote, "Gene, thanks for pointing out that 'family' is already
taken."

By making that statement, my intention was to indicate that I had
abandoned the idea of using the term "temperament family" for what
Graham calls a temperament class, since that would conflict with
Gene's definition.

--George

> In this message:
> /tuning/topicId_73148.html#73449
> I wrote, "Gene, thanks for pointing out that 'family' is already
> taken."
>
> By making that statement, my intention was to indicate that I had
> abandoned the idea of using the term "temperament family" for what
> Graham calls a temperament class, since that would conflict with
> Gene's definition.

Yes, saw that. The particular nitpicking craziness Graham and
I have been reduced to discussing in this case, is how widely
used any term other than just "temperament" (class or family)
was used.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > "Temperament family" doesn't occur on this page, nor anything like
> > > it in Monz's message.
> > >
Hi Carl,

> > [monz, me, wrote:]
> >
> > I think Graham is referring to this question i asked:
> >
> > "Did we ever take a serious look at 11-odd-limit
> > approximations in the MIRACLE family?"
> >
> > True, i didn't write exactly the phrase "temperament family",
> > but by the definition of "miracle", that's clearly what i was
> > referring to.
>
> You're right, sorry I missed that.
>
> Do you recall if you meant family as in...
>
> 1. 31/41/72 notes of the same generator, or
>
> 2. 31/41/72 ETs, or
>
> 3. ways of extending the 7-limit miracle map to the 11-limit
>
> or some combination thereof?

I'm pretty sure that i meant a combination of all three.
At the time i wrote that, i was focusing mainly on
31/41/72 ETs, because i was just beginning to understand
the whole concept of tunings related by being different
MOS of the same generator. But the whole group of us who
were discussing miracle (me, you, Paul E., Graham, Gene,
and Dave Keenan ... hopefully i'm not leaving anyone out)
were talking about it as a "family" of tunings.

Honestly, at this point i'm totally confused about any
difference (if there is one) between a temperament "class"
and a temperament "family". I wrote a page about "family"
in my Encyclopedia early on, in hopes that it would help
to standardize the terminology. But when Graham introduced
"class" i think i was mostly on hiatus from these lists
(which has happened several times in the last 3 years as
i've had to work on my website and on Tonescape) and i
missed it.

Any help in clarifying would be appreciated -- specifically,
with a view towards my putting a "class" page into the
Encyclopedia with a good explanation of the differences
between "class" and "family" ... or an explanation of
why both terms are used if they do mean the same thing.

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

> I'm pretty sure that i meant a combination of all three.
> At the time i wrote that, i was focusing mainly on
> 31/41/72 ETs, because i was just beginning to understand
> the whole concept of tunings related by being different
> MOS of the same generator. But the whole group of us who
> were discussing miracle (me, you, Paul E., Graham, Gene,
> and Dave Keenan ... hopefully i'm not leaving anyone out)
> were talking about it as a "family" of tunings.
>
> Honestly, at this point i'm totally confused about any
> difference (if there is one) between a temperament "class"
> and a temperament "family".

"Temperament class" is a term promoted by Graham and
George Secor, which means "temperament".

"Temperament family" is a term coined by Gene, about
which you can see his web pages (use archive.org for now)
or search the archives. It's about how to extend
temperaments into higher limits.

> Any help in clarifying would be appreciated -- specifically,
> with a view towards my putting a "class" page into the
> Encyclopedia with a good explanation of the differences
> between "class"

Your current definition of "temperament" needs work.
"Temperament class" could goes as an a.k.a. there, if you
were feeling generous.

> and "family" ...

The family concept isn't complete, but Gene's page is
an excellent definition of that. I'm in the process of
mirroring Gene's site. When it's up, you can link to it.
You can link to the archive.org backup for now.

-Carl

monz wrote:

> I'm pretty sure that i meant a combination of all three.
> At the time i wrote that, i was focusing mainly on
> 31/41/72 ETs, because i was just beginning to understand
> the whole concept of tunings related by being different
> MOS of the same generator. But the whole group of us who
> were discussing miracle (me, you, Paul E., Graham, Gene,
> and Dave Keenan ... hopefully i'm not leaving anyone out)
> were talking about it as a "family" of tunings.

The top of your "family" definition seems to be about classes. But as it could also apply to equal temperament families it isn't definitively wrong. Depending on what a "family" of equal temperaments actually is. See below.

> Honestly, at this point i'm totally confused about any
> difference (if there is one) between a temperament "class"
> and a temperament "family". I wrote a page about "family"
> in my Encyclopedia early on, in hopes that it would help
> to standardize the terminology. But when Graham introduced
> "class" i think i was mostly on hiatus from these lists
> (which has happened several times in the last 3 years as
> i've had to work on my website and on Tonescape) and i
> missed it.

Unfortunately I'm now getting confused as well. I thought "equal temperament family" and "rank 2 temperament class" were roughly synonymous, but now I'm not so sure.

> Any help in clarifying would be appreciated -- specifically,
> with a view towards my putting a "class" page into the
> Encyclopedia with a good explanation of the differences
> between "class" and "family" ... or an explanation of
> why both terms are used if they do mean the same thing.

You can add "temperament class" and I think "a set of tempered tunings with the same mapping from just intonation" is good enough as a definition. At least, its meaning isn't in question.

The new meaning of "family" is Gene's, and so you'll have to defer to his definition. But it's the next level of abstraction beyond "class". Temperament classes of the same family will have the same mapping for most, but not all, primes. For example, in http://x31eq.com/diaschis.htm I talk about different 7-limit mappings. So you could describe them as different temperament classes of the diaschismic family.

Now, there's *another* meaning of "equal temperament family" as I alluded to above. Here, it consists of different equal temperaments that belong to the same higher rank class. Hence 12, 19, 31, e.t.c. belong to the meantone family. This is a term I still use on my website. I don't intend to make revisionist changes so they'll have to count as obsolete usages if this is deemed to be obsolete.

I assumed that Gene's idea of temperament families was a natural extension of equal temperament families to a higher rank. Maybe it is if you think about unison vectors (or whatever we're supposed to call them this week). Equal temperaments belonging to the same rank 2 class will share unison vectors, as will different rank 2 temperament classes belonging to the same family.

The older meaning of "linear temperament family" isn't something you need to document because it was never widely used and is no longer accepted. There are probably all kinds of uses of the word "family" for different things in the archives. Another is a family of MOS scales (or equivalent terms) which means they share the same pattern of large and small intervals but different tunings.

Graham

P.S. I've got three articles on my website with glossaries:

http://x31eq.com/paradigm.html#gloss
http://x31eq.com/primerr.pdf
http://x31eq.com/complete.pdf

Although they aren't intended to be strict definitions you can certainly use them in the encyclopedia.

Carl Lumma wrote:

>> Any help in clarifying would be appreciated -- specifically,
>> with a view towards my putting a "class" page into the
>> Encyclopedia with a good explanation of the differences
>> between "class"
> > Your current definition of "temperament" needs work.
> "Temperament class" could goes as an a.k.a. there, if you
> were feeling generous.

Here Carl's trying to drag you (the Monz) into a terminology dispute. He thinks "temperament" shouldn't (nay, already doesn't) imply "tuning" and I oppose such a barbarity (even though my usage was lax in the past).

Note that Gene also proposed "abstract temperament" for "temperament without a tuning". That's similar to "temperament class" but not the same because Gene didn't like to think about an infinite set of tunings, rather a concept with tuning abstracted out.

Graham

Hi Carl,

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

> > [monz (me) wrote:]
> >
> > Honestly, at this point i'm totally confused about any
> > difference (if there is one) between a temperament "class"
> > and a temperament "family".
>
> "Temperament class" is a term promoted by Graham and
> George Secor, which means "temperament".
>
> "Temperament family" is a term coined by Gene, about
> which you can see his web pages (use archive.org for now)
> or search the archives. It's about how to extend
> temperaments into higher limits.

Ok, thanks. I never understood "family" to be specifically
about extending into higher limits. I always thought it
just was a way to group together temperaments in which
the same unison-vector (comma) vanishes.

> > Any help in clarifying would be appreciated -- specifically,
> > with a view towards my putting a "class" page into the
> > Encyclopedia with a good explanation of the differences
> > between "class"
>
> Your current definition of "temperament" needs work.
> "Temperament class" could goes as an a.k.a. there, if you
> were feeling generous.

I'd be happy to accept any contributions from folks here
that would improve it.

> > and "family" ...
>
> The family concept isn't complete, but Gene's page is
> an excellent definition of that. I'm in the process of
> mirroring Gene's site. When it's up, you can link to it.
> You can link to the archive.org backup for now.

Thanks so much for mirroring Gene's site! I was very
disappointed to find that it no longer exists. And
i'm also wondering what happened to Gene. He seems to
still be around, posting on sci-fi lists, but he sure
did vanish from the tuning community very suddenly
and very completely, which seems awfully weird to me.

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

Hi Graham,

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

> You can add "temperament class" and I think "a set of
> tempered tunings with the same mapping from just intonation"
> is good enough as a definition. At least, its meaning isn't
> in question.
>
> <snip>
>
> P.S. I've got three articles on my website with glossaries:
>
> http://x31eq.com/paradigm.html#gloss
> http://x31eq.com/primerr.pdf
> http://x31eq.com/complete.pdf
>
> Although they aren't intended to be strict definitions you
> can certainly use them in the encyclopedia.

Thanks very much for all of that!
... including what i snipped.

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

Graham wrote...

> The top of your "family" definition seems to be about
> classes. But as it could also apply to equal temperament
> families it isn't definitively wrong.
//
> Unfortunately I'm now getting confused as well. I thought
> "equal temperament family" and "rank 2 temperament class"
> were roughly synonymous, but now I'm not so sure.
//
> I assumed that Gene's idea of temperament families was a
> natural extension of equal temperament families to a higher
> rank.

WTF is an "equal temperament family", and do you really think
anyone but you has used it in a precise manner?

> You can add "temperament class" and I think "a set of
> tempered tunings with the same mapping from just intonation"
> is good enough as a definition. At least, its meaning isn't
> in question.

That's not going to work, since I can 'refactor' all the
mappings and presumably still have things you'd say are in
the same temperament class. You need wedgies.

-Carl

> >> Any help in clarifying would be appreciated -- specifically,
> >> with a view towards my putting a "class" page into the
> >> Encyclopedia with a good explanation of the differences
> >> between "class"
> >
> > Your current definition of "temperament" needs work.
> > "Temperament class" could goes as an a.k.a. there, if you
> > were feeling generous.
>
> Here Carl's trying to drag you (the Monz) into a terminology
> dispute.

Any more than you (by giving him wording for his encyclopedia
in a previous message) are?

> He thinks "temperament" shouldn't (nay, already
> doesn't) imply "tuning" and I oppose such a barbarity (even
> though my usage was lax in the past).

Before we can have this kind of argument, we need to decide
what should be the basis of a definition. Is it descriptive
of past use? Or should it prescribe the most logical use?
I submit that Gene's definition wins on both these counts,
but it clearly wins (as we've seen with all these statistics
recently) on the former. The only question is what percent
of prior use do you need to get added as an alternate
definition.

-Carl

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Hi Carl,
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > > [monz (me) wrote:]
> > >
> > > Honestly, at this point i'm totally confused about any
> > > difference (if there is one) between a temperament "class"
> > > and a temperament "family".
> >
> > "Temperament class" is a term promoted by Graham and
> > George Secor, which means "temperament".
> >
> > "Temperament family" is a term coined by Gene, about
> > which you can see his web pages (use archive.org for now)
> > or search the archives. It's about how to extend
> > temperaments into higher limits.
>
> Ok, thanks. I never understood "family" to be specifically
> about extending into higher limits. I always thought it
> just was a way to group together temperaments in which
> the same unison-vector (comma) vanishes.

There's presumably a core comma or commas that remain
in the kernel as you extend the family. For example, if
septimal meantone has commas 81/80 & 126/125, then
huygens is 81/80, 126/125 & 99/98.

> > > and "family" ...
> >
> > The family concept isn't complete, but Gene's page is
> > an excellent definition of that. I'm in the process of
> > mirroring Gene's site. When it's up, you can link to it.
> > You can link to the archive.org backup for now.
>
> Thanks so much for mirroring Gene's site!

Well, it isn't mirrored yet, so thank me when it's done!

-Carl

Carl Lumma wrote:

>> Here Carl's trying to drag you (the Monz) into a terminology >> dispute.
> > Any more than you (by giving him wording for his encyclopedia
> in a previous message) are?

Where did this come from? The wording I chose was "tempered tunings" which specifically avoids this issue.

>> He thinks "temperament" shouldn't (nay, already >> doesn't) imply "tuning" and I oppose such a barbarity (even >> though my usage was lax in the past).
> > Before we can have this kind of argument, we need to decide
> what should be the basis of a definition. Is it descriptive
> of past use? Or should it prescribe the most logical use?
> I submit that Gene's definition wins on both these counts,
> but it clearly wins (as we've seen with all these statistics
> recently) on the former. The only question is what percent
> of prior use do you need to get added as an alternate
> definition.

I'll point out now that Carl's statistics are bogus and he's ignored my argument about the grammar.

Graham

Carl Lumma wrote:
> Graham wrote...

>> I assumed that Gene's idea of temperament families was a >> natural extension of equal temperament families to a higher >> rank.
> > WTF is an "equal temperament family", and do you really think
> anyone but you has used it in a precise manner?

Why does it matter?

>> You can add "temperament class" and I think "a set of >> tempered tunings with the same mapping from just intonation" >> is good enough as a definition. At least, its meaning isn't >> in question.
> > That's not going to work, since I can 'refactor' all the
> mappings and presumably still have things you'd say are in
> the same temperament class. You need wedgies.

If it's a different mapping I'd take it to be a different temperament class, or maybe not a temperament class. What does "refactor" mean? I really don't think I need wedgies.

Graham

Carl Lumma wrote:

> That's not going to work, since I can 'refactor' all the
> mappings and presumably still have things you'd say are in
> the same temperament class. You need wedgies.

Oh, I get it. Gene's supplied a wacky definition of "prime mapping" as well, so different representations are different mappings. Well, fine, but I didn't say "prime mapping".

"Mapping" means what it's always meant. From dictionary.com:

"""
4. Mathematics.
...
b. Also called multiple-value function. a relation between two sets in which two or more elements of the second set are assigned to each element of the first set, as y2 = x2, which assigns to every x the two values y = +x and y = −x.
...
"""