Yahoo Tuning Groups Ultimate Backup tuning meantone (please stop now)

Please, can this stop now? This list is potentially a useful resource, and I sometimes send students here when they are interested in tuning--but this is counterproductive and sure to drive people away. "Meantone," like many English words with a long history, has two meanings. One is the restricted one (1/4-comma); the other is the "temperament class", which, outside of the tuning list, does not have its meaning explicitly related to the mapping 4Fifths=Third -- though it amounts to the same thing. Mark Lindley writes this in the New Grove (and it's the consensus definition; it corresponds to how I've seen other contemporary theorists and historians using the terms); see especially the first line of the second paragraph:

MEAN-TONE

A system of temperament or a tuning of the scale, particularly on instruments lacking any capacity for flexibility of intonation during performance, which differs from the equal-tempered system normally used on such instruments today. In its most restricted sense the term refers, like its German equivalent mitteltï¿½nige Temperatur, to a tuning with pure major 3rds (frequency ratio 5:4) divided into two equal whole tones (whereas in Just intonation there are two sizes of whole tone corresponding to the ratios 9:8 and 10:9); to achieve this the tuner must temper the 5ths and 4ths, making the 5ths smaller and the 4ths larger than pure by a quarter of the syntonic comma, hence the label "1/4-comma mean-tone", a more specific name for the same kind of tuning.

A broader and equally legitimate use of the term (dating back to such 18th-century writers as Sauveur and Estï¿½ve) includes any Renaissance or Baroque keyboard tuning in which a major 3rd slightly smaller or, more often, slightly larger than pure is divided into two equal whole tones (see Table 1). [he goes on to describe temperaments of different fractions of a comma]

--Jon Wild

🔗Charles Lucy <lucy@harmonics.com>

Thanks for your comments Jon;

I think you have missed the whole point here of questioning the use
of the term "meantone".

1) So you send students to the tuning; good; the students see
controversy; even better: it shows them that the evolution of tuning
theory and experimentation is live and developing.
2) You are asking for a static (dead - no change) body of work; let's
hope tunings never become that;-)
3) As you illustrate yourself in your quotes below - even using the
secondary meaning of meantone, there is a bias towards tunings which
use integer ratios and hence JI logic.
4) Do we need any further motivation than to resolve these paradoxes?

> [he goes on to describe temperaments of different
> fractions of a comma]

Lighten up Jon, New Grove is not the Koran, or even the Bible.

Change happens and this quest for a better term could actively
involve your students;

(at least those students who can run the gauntlet past the "newbies
know nowt" prunes on the list).

Charles Lucy lucy@lucytune.com

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

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

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

Skype user = lucytune

http://www.myspace.com/lucytuning

On 14 Sep 2007, at 14:58, Jon Wild wrote:

>
> Please, can this stop now? This list is potentially a useful
> resource, and
> I sometimes send students here when they are interested in tuning--but
> this is counterproductive and sure to drive people away.
> "Meantone," like
> many English words with a long history, has two meanings. One is the
> restricted one (1/4-comma); the other is the "temperament class",
> which,
> outside of the tuning list, does not have its meaning explicitly
> related
> to the mapping 4Fifths=Third -- though it amounts to the same
> thing. Mark
> Lindley writes this in the New Grove (and it's the consensus
> definition;
> it corresponds to how I've seen other contemporary theorists and
> historians using the terms); see especially the first line of the
> second
> paragraph:
>
> MEAN-TONE
>
> A system of temperament or a tuning of the scale, particularly on
> instruments lacking any capacity for flexibility of intonation during
> performance, which differs from the equal-tempered system normally
> used on
> such instruments today. In its most restricted sense the term
> refers, like
> its German equivalent mitteltönige Temperatur, to a tuning with
> pure major
> 3rds (frequency ratio 5:4) divided into two equal whole tones
> (whereas in
> Just intonation there are two sizes of whole tone corresponding to the
> ratios 9:8 and 10:9); to achieve this the tuner must temper the
> 5ths and
> 4ths, making the 5ths smaller and the 4ths larger than pure by a
> quarter
> of the syntonic comma, hence the label "1/4-comma mean-tone", a more
> specific name for the same kind of tuning.
>
> A broader and equally legitimate use of the term (dating back to such
> 18th-century writers as Sauveur and Estève) includes any
> Renaissance or
> Baroque keyboard tuning in which a major 3rd slightly smaller or, more
> often, slightly larger than pure is divided into two equal whole tones
> (see Table 1). [he goes on to describe temperaments of different
> fractions of a comma]
>
> --Jon Wild
>
>

🔗Aaron K. Johnson <aaron@akjmusic.com>

🔗Graham Breed <gbreed@gmail.com>

Jon Wild wrote:
> Please, can this stop now? This list is potentially a useful resource, and > I sometimes send students here when they are interested in tuning--but > this is counterproductive and sure to drive people away. "Meantone," like > many English words with a long history, has two meanings. One is the > restricted one (1/4-comma); the other is the "temperament class", which, > outside of the tuning list, does not have its meaning explicitly related > to the mapping 4Fifths=Third -- though it amounts to the same thing. Mark > Lindley writes this in the New Grove (and it's the consensus definition; > it corresponds to how I've seen other contemporary theorists and > historians using the terms); see especially the first line of the second > paragraph:

The discussion will stop when we've finished saying what we have to say. What's counterproductive about discussion on a discussion list?

Ah, but I see you're using it as a device to have the last word.

> A broader and equally legitimate use of the term (dating back to such > 18th-century writers as Sauveur and Estï¿½ve) includes any Renaissance or > Baroque keyboard tuning in which a major 3rd slightly smaller or, more > often, slightly larger than pure is divided into two equal whole tones > (see Table 1). [he goes on to describe temperaments of different > fractions of a comma]

As it stands, that's not equivalent to the meantone temperament class as we understand it. It doesn't specify generation by fifths.

Graham

🔗Carl Lumma <clumma@yahoo.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Jon Wild <wild@music.mcgill.ca>

🔗Graham Breed <gbreed@gmail.com>

Jon Wild wrote:
> Graham wrote:
> > >>The discussion will stop when we've finished saying what we have to say. >>What's counterproductive about discussion on a discussion list?
> > > Nothing wrong with discussion, maybe I was overly crabby--but it just > seems you've got one load of people saying term X means Y, another load of > people saying term X means Z, and many getting fairly nasty at one > another--while offlist, term X is being used by people all the time to > mean both Y *and* Z, with the relevant meaning inferred by context, all > without causing any problems.

I didn't notice people getting nasty. That shows you how differently people interpret the tone of messages. I did see some literature citations (including from you) supporting either viewpoint and as a result my understanding of the debate has altered.

If the term has both meanings offlist that's a good reason to carry on giving it both meanings. At the start of the discussion, at least, that was in question. I'd like to have an overview of the literature that we can use to rebut whoever comes in next to say we're using it wrong.

Daniel W says he brought up the problem several years ago, but most of us have forgotten that and thought there was a consensus. I don't want us to carry on for another 10 years happily using the term and then the debate opens up again. But perhaps the fire had already gone out by the time you posted.

>>Ah, but I see you're using it as a device to have the last word.
> > No, I'm sorry it came across that way. I wrote because I like to read what > people are talking about on the list from time to time, and when it's the > case that anything potentially useful is drowned out by the sheer volume > of angry posts on a topic that's out of anyone's control (i.e., how is a > particular term used), then the utility of the whole list is diminished. > At least for me.

I'm more disappointed that these terminological disputes don't lead anywhere -- that at the end of it we still don't agree on what word to use! This is true for "meantone", "just intonation", "perodicity block", and even it appears "temperament".

Graham

🔗Graham Breed <gbreed@gmail.com>

🔗monz <monz@tonalsoft.com>

🔗Charles Lucy <lucy@harmonics.com>

Your solution only partly solves the problem though Monz;

The "clarified" definitions still contain an integer ratio and comma implication regarding those meantone-type scales, which are not derived from integer ratios;

I am thinking particularly of those meantone-type tunings which are derived from pi, phi and many edo's.

(I am sure that there are other examples, but those are the obvious ones)

Charles Lucy lucy@lucytune.com

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

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

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

Skype user = lucytune

http://www.myspace.com/lucytuning

On 18 Sep 2007, at 06:17, monz wrote:

> Hi Graham,
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> > I'm more disappointed that these terminological disputes
> > don't lead anywhere -- that at the end of it we still don't
> > agree on what word to use! This is true for "meantone",
> > "just intonation", "perodicity block", and even it appears
> > "temperament".
>
> To my way of thinking, the meantone debate did lead somewhere.
> It clarified to me that "meantone" is and should be defined
> both ways, as a single tuning (1/4-comma meantone) and as
> a name for the whole family/class of temperaments which
> temper out the syntonic-comma.
>
> I've already been using it both ways all along in the
> Encyclopedia, but it was good to clarify that the single
> word does indeed carry both definitions. Yes, it's too
> bad that we don't just have two separate words, but that's
> how it is and i can live with it.
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

🔗mikal haley <chipsterthehipster@gmail.com>

🔗Graham Breed <gbreed@gmail.com>

mikal haley wrote:
> GET A PHYSICIST.

There are people with a physics background in the tuning community.

> this is the music of the spheres you are discussing.
> i don't get the integrals, but this is a Goedel Escher Bach
> sort of discussion. i can't even participate, it's out of my personal by -
> ear league
> but you should invite some mathematicians in. it's worth pointing out.

And at least one regular contributor is a professional mathematician. But this is hardly such a difficult problem.

> i would sell plasma for a Lucytuned Guitar.

That's all well and good but they aren't so expensive!

Anyway, to these arguments...

> On 9/18/07, Charles Lucy <lucy@harmonics.com> wrote:
> >> Your solution only partly solves the problem though Monz;
>>
>>The "clarified" definitions still contain an integer ratio and comma
>>implication regarding those meantone-type scales, which are not derived from
>>integer ratios;
>>
>>I am thinking particularly of those meantone-type tunings which are
>>derived from pi, phi and many edo's.

I see no problem with pi or phi or EDOs that belong to the meantone set. Monz's page does explicitly refer to EDOs (or at least ETs). There would be problems with equal temperaments that don't belong to the meantone set, but otherwise there's be no point in having a definition of "meantone".

>>(I am sure that there are other examples, but those are the obvious ones)

The only real obstacle is the philosophical one that you insist LucyTuning isn't an approximation to integer frequency ratios (despite it being a good one).

Graham

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>(to Charles Lucy)
)
>
> The only real obstacle is the philosophical one that you
> insist LucyTuning isn't an approximation to integer
> frequency ratios (despite it being a good one).

At the risk of stirring up the poo again, I don't think it's
a philosophical issue at all. You must remember that other
people aren't you (hahaha! :-P ): Lucy Tuning doesn't sound or
look like an approximation to integer ratios to Charles Lucy,
nor to myself, therefore it is NOT an approximation to
integer ratios, except to those who choose to view it that way.

A unilateral declaration that 381 cents is an approximation
to 5/4 just won't fly by me, though if it were dictated to be
an approximation of 56/45, then we could start talking about
"philosophical" obstacles.

By the way I suspect that Charles Lucy's interpretation of Harrison's
basic approach, irrespective of the musical quality of Lucy Tuning,
is not what Harrison was actually doing. I do use, every day,
intervals derived in a way I believe serendipitously corresponds
to what Harrison was actually up to, but what tuning theorist would
even care? :-)

take care,

-Cameron Bobro

🔗Graham Breed <gbreed@gmail.com>

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>(to Charles Lucy)
> > )
> >>The only real obstacle is the philosophical one that you >>insist LucyTuning isn't an approximation to integer >>frequency ratios (despite it being a good one).
> > At the risk of stirring up the poo again, I don't think it's
> a philosophical issue at all. You must remember that other
> people aren't you (hahaha! :-P ): Lucy Tuning doesn't sound or
> look like an approximation to integer ratios to Charles Lucy,
> nor to myself, therefore it is NOT an approximation to > integer ratios, except to those who choose to view it that way.

LucyTuned intervals are what they are. How would they sound different if they were or were not approximations to integer ratios? That Lucy *chooses* not to view it as an approximation means that his tuning is not a temperament, and so not a meantone temperament. If he chose to view it a different way the problem of nomenclature would be solved.

> A unilateral declaration that 381 cents is an approximation
> to 5/4 just won't fly by me, though if it were dictated to be
> an approximation of 56/45, then we could start talking about
> "philosophical" obstacles. What difference would it make?

> By the way I suspect that Charles Lucy's interpretation of Harrison's
> basic approach, irrespective of the musical quality of Lucy Tuning, > is not what Harrison was actually doing. I do use, every day, > intervals derived in a way I believe serendipitously corresponds > to what Harrison was actually up to, but what tuning theorist would > even care? :-)

If you have an insight it'd be nice to hear it.

Graham

🔗monz <monz@tonalsoft.com>

Hi Charles,

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Your solution only partly solves the problem though Monz;
>
> The "clarified" definitions still contain an integer
> ratio and comma implication regarding those meantone-type
> scales, which are not derived from integer ratios;
>
> I am thinking particularly of those meantone-type
> tunings which are derived from pi, phi and many edo's.
>
> (I am sure that there are other examples, but those
> are the obvious ones)

In my recent update to my Encyclopedia "meantone" page

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

i did add a section, just under the new Tonescape Lattice
graphics, explaining that some tunings of the meantone
family are not derived from a division of the syntonic-comma.
Thanks to your post, i've just added LucyTuning to list:

>> "Of course, it is not necessary that the amount of
>> tempering be a rational part of the comma -- thus,
>> we have various types of approximations to these
>> theoretical ideals:
>>
>> * EDOs which are close in tuning to fraction-of-a-comma
>> meantones (some theorists prefer to refer to them as
>> ETs for this reason);
>>
>> * TOP meantone, which also tempers the octaves; and
>>
>> * LucyTuning, based on pi, and which is actually not
>> considered by Charles Lucy to represent fraction-of-a-comma
>> meantone."

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

🔗Charles Lucy <lucy@harmonics.com>

Thanks Monz;

Graham is correct about my philosophical objections.
I regret that it was you who had become the victim of my "winding-up" the tuning list; yet the result has been an improvement to your excellent Encyclopedia.

I am pleased to observe that my long-standing claim that integer frequency ratios are more significant in the analysis of beating,
than as a mapping system for "harmonics", has become more widely understood and accepted in recent years.

It's a long haul, yet I am sure that your work is having a significant effect on the progress of microtuning, as it becomes more widely accepted as a viable alternative for future generations.

BTW No-one needs to sell plasma to buy a LucyTuned guitar because:

1) My son claims that he can make his own plasma in our kitchen microwave oven.
2) The guitar specs are free for anyone to use at:

http://www.lucytune.com/guitars_and_frets/frets.html

So LucyTuned guitars are freely available to anyone who wishes to experiment by moving frets.

Best wishes

Charles Lucy lucy@lucytune.com

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

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

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

Skype user = lucytune

http://www.myspace.com/lucytuning

On 18 Sep 2007, at 15:33, monz wrote:

> Hi Charles,
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Your solution only partly solves the problem though Monz;
> >
> > The "clarified" definitions still contain an integer
> > ratio and comma implication regarding those meantone-type
> > scales, which are not derived from integer ratios;
> >
> > I am thinking particularly of those meantone-type
> > tunings which are derived from pi, phi and many edo's.
> >
> > (I am sure that there are other examples, but those
> > are the obvious ones)
>
> In my recent update to my Encyclopedia "meantone" page
>
> http://tonalsoft.com/enc/m/meantone.aspx
>
> i did add a section, just under the new Tonescape Lattice
> graphics, explaining that some tunings of the meantone
> family are not derived from a division of the syntonic-comma.
> Thanks to your post, i've just added LucyTuning to list:
>
> >> "Of course, it is not necessary that the amount of
> >> tempering be a rational part of the comma -- thus,
> >> we have various types of approximations to these
> >> theoretical ideals:
> >>
> >> * EDOs which are close in tuning to fraction-of-a-comma
> >> meantones (some theorists prefer to refer to them as
> >> ETs for this reason);
> >>
> >> * TOP meantone, which also tempers the octaves; and
> >>
> >> * LucyTuning, based on pi, and which is actually not
> >> considered by Charles Lucy to represent fraction-of-a-comma
> >> meantone."
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

🔗Aaron K. Johnson <aaron@akjmusic.com>

🔗Tom Dent <stringph@gmail.com>

I agree with Monz, we can live with both a 'narrow' and a 'broad'
definition, the difference is determined (hopefully) by context.

I even see three possible levels of meaning:

1) 1/4 comma MT as the most commonly described historical meantone
containing the harmonic mean of 9/8 and 10/9.

2) Any regular temperament with fifths narrowed by an amount lying
between 1/3 syntonic comma and (as the extreme case) 1/12 ditonic
comma. The historical range of meantones.

3) Any regular temperament with fifths narrower than 3/2 containing
distinct minor and major thirds produced by three fifths down / four
up resp. This allows such modernities as 2/5-comma or 1/18-comma. One
should put a limit on the flatness, otherwise the thirds - no, the
whole scale - will start to go weird... 7-EDO, anyone?

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
>
> To my way of thinking, the meantone debate did lead somewhere.
> It clarified to me that "meantone" is and should be defined
> both ways, as a single tuning (1/4-comma meantone) and as
> a name for the whole family/class of temperaments which
> temper out the syntonic-comma.
>
> I've already been using it both ways all along in the
> Encyclopedia, but it was good to clarify that the single
> word does indeed carry both definitions. Yes, it's too
> bad that we don't just have two separate words, but that's
> how it is and i can live with it.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Mark Rankin <markrankin95511@yahoo.com>

🔗monz <monz@tonalsoft.com>

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> Octave equivalence has nothing to do with tunings.
> It's related to scales; if they repeat at the octave,
> one may surmise an implicit octave equivalence.

I'm very interested to know more about what you are
referring to here as a difference between tunings
and scales.

The Encyclopedia entries for "tuning", "scale",
and "octave-equivalence" can all be updated with
this.

Your casual manner of referring to this difference
seems to me to indicate that it's a widely-held
perspective. Can you cite references or postings
which show that, if it's true?

Chris and i are really interested in this, because
we have yet to implement a "scale" feature in
Tonescape (which right now deals with tonespaces,
tunings, and musical-pieces), and it's something
we want to add.

> About the only thing I see wrt meantone which
> is relevant to octave equivalence at all is that
> the octave can be taken as one of the generators.

Right ... but while its presence is necessary for
the math calculations, the 2/1 (octave) in meantone
is a generator that doesn't have to appear on the
lattice, precisely *because* it's the identity-interval.

(or equivalence-interval ... while we're on the
subject of Encyclopedia updates: i've always treated
these terms as synonymous, but if folks out there
think they're not, please speak up. I'll create
individual entries for each of them if necessary.)

So how should i change that paragraph in the meantone
page? I'm still confused about your statement that
"Octave equivalence has nothing to do with tunings".
Should i say something like this?:

"Music composed within the meantone paradigm always
implies octave-equivalence, thus the 2/1 ratio
(octave) can be taken as one of the generators."

and be done with it?

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

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Cameron Bobro wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> >>(to Charles Lucy)
> >
> > )
> >
> >>The only real obstacle is the philosophical one that you
> >>insist LucyTuning isn't an approximation to integer
> >>frequency ratios (despite it being a good one).
> >
> > At the risk of stirring up the poo again, I don't think it's
> > a philosophical issue at all. You must remember that other
> > people aren't you (hahaha! :-P ): Lucy Tuning doesn't sound or
> > look like an approximation to integer ratios to Charles Lucy,
> > nor to myself, therefore it is NOT an approximation to
> > integer ratios, except to those who choose to view it that way.
>
> LucyTuned intervals are what they are.

Yes, exactly.

>How would they sound
> different if they were or were not approximations to integer
> ratios?
This is how it seems to me:

When an interval actually is an "approximation" to an integer
ratio directly percievable as such (ie, coincident partials in the
audible range), it's inevitably going to be heard IN TERMS of that
interval (not inevitably "AS" that interval) because it is going
to have substantial characteristics right in the same spot the
pure ratio does. In the case of 5/4, for example, if the
approximation is a hair off of pure, it's going to put a spotlight
on the very fourth and fifth partials that are part of the
5/4 identity. If they slowly "chorus", or do that creamy thing,
you know what I mean, you still have an interval which sounds like
a 5/4 because you have slow and soft movement in the same key
spot where there is near-stillness in a pure 5/4. (Even in a pure
5/4 the is no perfect stillness in this spot unless everything is
perfectly in phase, for example with digital synthesis, and of course
no perfect stillness throughout all partials and all pitch ranges)

But as you move away from the pure interval, you start getting rough
weather in the same spot there once was calm- if calmness is part
of the identity of 5/4, how can you say that an interval that
is not calm is an approximation of 5/4? It's jumping up and down
and waving its arms declaring that it is NOT 5/4. It's a thing
unto itself.

Tempering yet further, it's possible to hit other spots with similar
key characteristics. This is what the Lucy third for example lives,
in my opinion. At 56/45 there's another tiny "soft" region, so it's
5/4-like in that way. But it doesn't have the directness or
vigor or whatever it is of the 5/4, so once again it's not an
approximation, it's a thing unto itself.

I believe, by the way, that all this stuff is why, leaving aside
philosophical and semantic issues, heavy tempering is often
musically superior to mild tempering.

>That Lucy *chooses* not to view it as an
> approximation means that his tuning is not a temperament,
> and so not a meantone temperament. If he chose to view it a
> different way the problem of nomenclature would be solved.

Notation is a different story. In my opinion, if there's a
historical, or simple, or both, way to notate, even if it's
all wrong as far generating principles, it should be used
(I use 34 equal notation with additional + and - signs for
example).
>
> > A unilateral declaration that 381 cents is an approximation
> > to 5/4 just won't fly by me, though if it were dictated to be
> > an approximation of 56/45, then we could start talking about
> > "philosophical" obstacles.
>
> What difference would it make?

Big difference- I wouldn't be able to argue that 381 cents
isn't percieved of as 56/45 (have to check if I can even
differentiate them blind), for I simply don't know and
probably never will whether it is or not, wereas I can and do
argue that it is not an approximation of 5/4 for the
admittedly crude and boneheaded reason that it doesn't sound
like one. Too soft. BTW I'm a fan of 56/45 and the Lucy third.

>
> > By the way I suspect that Charles Lucy's interpretation of
>Harrison's
> > basic approach, irrespective of the musical quality of Lucy
>Tuning,
> > is not what Harrison was actually doing. I do use, every day,
> > intervals derived in a way I believe serendipitously corresponds
> > to what Harrison was actually up to, but what tuning theorist
would
> > even care? :-)
>
> If you have an insight it'd be nice to hear it.

Right off the bat it's obvious that Lucy Tuning isn't what
Harrison was doing. From the wiki:

"He told me he took a thin ruler equal in length to the smallest
string of his base viol. and divided it as a monochord, by taking
the interval of the major IIId, to that of the VIIIth, as the
diameter of a circle, to its circumference. Then by the divisions on
the ruler applied to that string, he adjusted the frets upon the
neck of the viol. and found the harmony of the consonances so
extremely fine that after a very small and gradual lengthening of
the other strings at the nut, by reason of their greater stiffness
he acquiesced in that manner the placing of the frets."

How do get 1200 cents/pi out of that? It's right there in black
and white- divisions of string length, not of cents. Monkey with a
bit, with an actual ruler and monochord (okay I used a measuring
tape and fretless guitar)- this gives you an absolutely gorgeous
third a "fat comma" ("quarter tone") low of 5/4, in keeping with
the original observer's observation. There are a number of
possibilites from there, most sounding very lovely to my ears, don't
know which exact road Harrison took.

None of the possibilities is patentable unless you could find
a very guillible patent office, for they truly are music of the
spheres- whether that's just numerology or something actually
percievable isn't the point. In fact, if the music of spheres is
something natural and percievable it can't be patented any more
than JI could be, or the colors of the rainbow.

I have to score a short film over the next couple of weeks and
I'll try to sneak in some of this pi-bald goofiness, so I'll float
you some tunes and tuning if you'd like.

-Cameron Bobro

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

🔗monz <monz@tonalsoft.com>

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > monz, I believe they already contain Gene's
> > definitions,
>
> The temperament entry has it:
> http://tonalsoft.com/enc/t/temperament.aspx
>
> I'm positive the scale entry used to, but it doesn't
> seem to now:
> http://tonalsoft.com/enc/s/scale.aspx

I don't think it ever did ... i could be wrong,
but i don't think there's another version of this
page. Anyway, the link at the bottom led me to this:

/tuning-math/message/12172

That thread wandered on and on, and my eyes glazed over
before i ever finished reading it. I've added your
short definition to the bottom of my page (along with
the reinsertion of the internal links):

http://tonalsoft.com/enc/s/scale.aspx

Thoughts, criticisms, additions, etc. all welcome.

> There doesn't seem to be an entry for tuning.

Hmm, imagine that! The Encyclopedia which was originally
called "Dictionary of Tuning Terms" ended up never
containing an entry for "tuning" until now! ... oh well:

http://tonalsoft.com/enc/t/tuning.aspx

That's a start ... folks, please help me flesh it out.
And don't forget that the Encyclopedia already has this:

http://tonalsoft.com/enc/t/tuning-map.aspx

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

🔗Aaron K. Johnson <aaron@akjmusic.com>

Carl Lumma wrote:
>> The Encyclopedia entries for "tuning", "scale",
>> and "octave-equivalence" can all be updated with
>> this.
>> >
> monz, I believe they already contain Gene's
> definitions, which I've explained many times on
> this list.
>
> A temperament is a homomorphism -- a mapping from
> a space of generators and periods to JI. There is
> a 1:1 mapping between wedgies and temperaments.
>
> A tuning is a particular tuning of those generators
> and periods -- RMS optimal, TOP, etc.
>
> A scale is a finite number of notes / pitches.
> Usually octave-equivalent, in which case it's a
> finite number of pitch classes.
>
> -Carl
> Do you really think you would be taken seriously opening your mouth in a music classroom and saying 'wedgie'?

These terms have been hijacked, it seems, by tuning-math. I think if you asked "says who", it would be a small core group of tuning-math folks. That's it. Fine to keep using this stuff in tuning-math, but don't expect it to fly untranslated witheveryone else.

A paraphrase of Barbour does the trick for me:

A tuning, as it is understood out in the 'real world' is a rational set of pitches (think the duodene or another such JI set), a temperament is an alteration, or compromise, of one or more JI intervals to create consistent step-sizes. A scale is an ordered pitch set, an abstraction of a set of pitches used for melody/harmony.

I understand the desire to create rigor ala David Hilbert, but to say the word 'homomorphism' when explaining what a temperament is to average musicians, even advanced musicians, let alone the general public, is asking too much, and it is especially asking for extremely poor public relations standards. It would probably elicit only confused, dismissive laughter. Yes, this is unfortunate, especially since the definition is rigorous and accurate. But the laughter is a reality, and if we're smart around here, we ought to consider that. I'll speak for myself---I want to consider that, because I believe that these ideas should and could spread, ridicule-free. Gene, you are great, a math demigod, but c'mon, your page is Greek to anyone without a PhD in higher mathematics. That would mean, oh, only 99.99% of the world.

Also, regarding the place of this list on the larger world stage: a ton of good theory goes on here, a tremendous amount of new thinking has been generated, but to think that what goes on here theory-wise will be disseminated, terminology intact, to the outside world of musicians and the general public is naive at best. It needs translation, for sure.

BTW, Carl, on a technical note: a definition that uses that word being defined in it's body is flawed--see your definition of 'tuning' above.

-A.

🔗Charles Lucy <lucy@harmonics.com>

As far as I know Cameron, I did the arithmetic correctly from what Harrison wrote in the eighteenth century, and have fairly translated his ideas into "modern" terms.

If not please let me know of any errors that you find.

Your quote below "He told me ......." was added to the wiki by an unknown poster (spoiler?).

It is many years since I last looked at Robert Smith's "Harmonics", so I cannot comment on the correctness of the quote, and I am not particularly keen on going back to the

British Library to check on it all again.

To my mind whatever Smith wrote is irrelevant, as there was a disagreement between Smith and Harrison about which of them could claim the "discovery" of this tuning derived from pi.

I did read both books in their entirety about twenty years ago, and came to the conclusion the Smith was relating everything back to integer ratios,

which Harrison regarded as nonsensical. I agree with Harrison.

You can find transcriptions of all of Harrison's writings on music at:

http://www.lucytune.com

When working through the "missing" manuscript about five years ago, I found that Harrison restated his calculations for the tuning derived from pi,

and the results were the same as in his original book on the subject.

The only part of his writings that I have yet to understand are his suggestions on the mathematics of bell-making, which you can find at:

http://www.lucytune.com/academic/manuscript_search.html

So as far as I know I have accurately and honestly represented his concepts.

If you find any errors, mistakes, or misinterpretations that I have made, please enlighten us.

>
> > > By the way I suspect that Charles Lucy's interpretation of
> >Harrison's
> > > basic approach, irrespective of the musical quality of Lucy
> >Tuning,
> > > is not what Harrison was actually doing. I do use, every day,
> > > intervals derived in a way I believe serendipitously corresponds
> > > to what Harrison was actually up to, but what tuning theorist
> would
> > > even care? :-)
> >
> > If you have an insight it'd be nice to hear it.
>
> Right off the bat it's obvious that Lucy Tuning isn't what
> Harrison was doing. From the wiki:
>
> "He told me he took a thin ruler equal in length to the smallest
> string of his base viol. and divided it as a monochord, by taking
> the interval of the major IIId, to that of the VIIIth, as the
> diameter of a circle, to its circumference. Then by the divisions on
> the ruler applied to that string, he adjusted the frets upon the
> neck of the viol. and found the harmony of the consonances so
> extremely fine that after a very small and gradual lengthening of
> the other strings at the nut, by reason of their greater stiffness
> he acquiesced in that manner the placing of the frets."
>
> How do get 1200 cents/pi out of that? It's right there in black
> and white- divisions of string length, not of cents. Monkey with a
> bit, with an actual ruler and monochord (okay I used a measuring
> tape and fretless guitar)- this gives you an absolutely gorgeous
> third a "fat comma" ("quarter tone") low of 5/4, in keeping with
> the original observer's observation. There are a number of
> possibilites from there, most sounding very lovely to my ears, don't
> know which exact road Harrison took.
>
> None of the possibilities is patentable unless you could find
> a very guillible patent office, for they truly are music of the
> spheres- whether that's just numerology or something actually
> percievable isn't the point. In fact, if the music of spheres is
> something natural and percievable it can't be patented any more
> than JI could be, or the colors of the rainbow.
>
> I have to score a short film over the next couple of weeks and
> I'll try to sneak in some of this pi-bald goofiness, so I'll float
> you some tunes and tuning if you'd like.
>
> -Cameron Bobro
>
>
>

🔗Carl Lumma <carl@lumma.org>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Carl Lumma wrote:
> >> The Encyclopedia entries for "tuning", "scale",
> >> and "octave-equivalence" can all be updated with
> >> this.
> >>
> >
> > monz, I believe they already contain Gene's
> > definitions, which I've explained many times on
> > this list.
> >
> > A temperament is a homomorphism -- a mapping from
> > a space of generators and periods to JI. There is
> > a 1:1 mapping between wedgies and temperaments.
> >
> > A tuning is a particular tuning of those generators
> > and periods -- RMS optimal, TOP, etc.
> >
> > A scale is a finite number of notes / pitches.
> > Usually octave-equivalent, in which case it's a
> > finite number of pitch classes.
> >
> > -Carl
> >
>
> Do you really think you would be taken seriously opening your
> mouth in a music classroom and saying 'wedgie'?

> These terms have been hijacked, it seems, by tuning-math.

I'm not trying to dictate how you use them. However, if you're
interested in regular temperaments, I suggest you learn the
terminology, like any student of any other subject.

> That's it. Fine to keep using this stuff in tuning-math, but don't
> expect it to fly untranslated witheveryone else.

I find it incredible the way the origin of this thread is being
reversed here. It is the folks on your side of the argument who
are trying to dictate terminology!

> A paraphrase of Barbour does the trick for me:
>
> A tuning, as it is understood out in the 'real world' is a
> rational set of pitches

Already completely at odds with anything normal to say around
here, even on this list or MMM. 12-ET isn't a tuning??

> a temperament is
> an alteration, or compromise, of one or more JI intervals
> to create consistent step-sizes.

That's a fine description for common use. No argument from
me (except prehaps that "consistent" is vague).

But if you try to do things like, search the space of
possible 13-limit temperaments rank 2 temperaments, you
will quickly find that you need to reconsider what you
thought a temperament was. Trust me on that.

> A scale is an ordered pitch set, an abstraction
> of a set of pitches used for melody/harmony.

The most important thing about scales, as opposed to tunings
or temperaments, is that they're finite (down to octave
equivalence).

> I understand the desire to create rigor ala David Hilbert,

...Or just to have definitions that work and make sense.

> but to say the word 'homomorphism' when explaining what a
> temperament is to average musicians, even advanced musicians,
> let alone the general public, is asking too much,

There you go again complaining. I'm not saying that the
word homomorphism has to appear in the definition. However,
I do like it because it draws the curious mind in, out of
confusion, to a precise world where things can be manipulated
with ease. At least, that was my experiece so far as I have
taken it.

So the word isn't, and shouldn't be, a hangup. However, the
point is that the tuning-math definitions make a great deal
of *sense*. They correspond -- as much as is possible while
making sense -- to the old meanings of these terms. If you
bothered to learn them well before criticizing, I think you
would agree.

> I'll speak for myself---I want
> to consider that, because I believe that these ideas should
> and could spread, ridicule-free.

This strikes me as a very weak argument. But then again,
if this is what you want, I encourage you to publish your
own definitions and spread them around.

> Gene, you are great, a math demigod, but c'mon,
> your page is Greek to anyone without a PhD in higher
> mathematics. That would mean, oh, only 99.99% of the world.

It's true that communication from tuning-math down to you
pleebs (just kidding!) could be better. However, I wonder
how many have even read and understood The Forms of Tonality,
let alone the Middle Path paper.

> BTW, Carl, on a technical note: a definition that uses that
> word being defined in it's body is flawed--see your definition
> of 'tuning' above.

I knew that when writing it. Like I said, I would have spent
more time if I wasn't doing it between tasks at work.

-Carl

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

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

> I'm very interested to know more about what you are
> referring to here as a difference between tunings
> and scales.

To me, pure octaves and fifths of 5^(1/4), or 696.578 cents, are what
define 1/4-comma meantone. It would still be that if you tuned 19
notes to an octave to twelve steps of 76 cents and seven steps of 41
cents, in a chain of 18 meantone fifths plus one wolf of 661.588
cents. So, the tuning is on a higher level of abstraction than the
scale, which is on a higher level of abstraction that the scale
defined in terms of specific frequencies, which is on a higher level
of abstraction than some application to actual music or a real
instrument. Then, of course, we have levels of abstraction higher
than the tuning, which is what we've been arguing over.
> > About the only thing I see wrt meantone which
> > is relevant to octave equivalence at all is that
> > the octave can be taken as one of the generators.
>
> Right ... but while its presence is necessary for
> the math calculations, the 2/1 (octave) in meantone
> is a generator that doesn't have to appear on the
> lattice, precisely *because* it's the identity-interval.

If what you want is a lattice of pitch classes, yes.

> "Music composed within the meantone paradigm always
> implies octave-equivalence, thus the 2/1 ratio
> (octave) can be taken as one of the generators."
>
> and be done with it?

I've no assurrance music composed within the meantone paradigm always
implies octave equivalence. When I was trying on 3 and 3/2
equivalence for size a few decades back, I was working in 12-et and I
suspect you can find examples of actual music doing that. Actually,
1/4-comma almost asks to be taken as having an equivalence at 5 or
5/2 and a generator of 2; maybe someone should try it.

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Carl Lumma <carl@lumma.org>

🔗djwolf_frankfurt <djwolf@snafu.de>

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

Carl Lumma wrote:

> What the hell is a temperament class??

A set of temperaments with the same mapping from JI.

In The Regular Mapping Paradigm I said "A regular temperament class is a set of regular temperaments that have the same pattern of different sized intervals, but different specific sizes. You can even think of them as being families of equal temperaments..." But that's a stop-gap definition because I hadn't defined "mapping" (or maybe even "JI") at that point. Resolving circular references is left as an exercise for the interested lexicographer.

Note that The Regular Mapping Paradigm is intended to be a sort of regular temperament manifesto, and the fact that the usage of "temperament class" survived unchallenged for this long sets some kind of precedent. Here's the URL:

http://x31eq.com/paradigm.html

I'll now announce that I came to a decision over lunch not to update this page any more. So, for Dave and George, any misrepresentation of the Sagittal notation of blackjack is going to stay that way. You'll have to put a denunciation up somewhere. Any other errors will remain for posterity the same as they would in a printed document. And sorry to Dave for never replying to the message you sent in the summer -- I didn't even get as far as checking what the website currently says.

Graham

🔗Carl Lumma <carl@lumma.org>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> >
> > Scales need not imply octave equivalence.
>
> I agree. And that is what I said.

I also agree, and say so in my Encyclopedia entry.

IMO, the most important things which differentiate
scales from tunings and temperaments is what i put
in the opening statement on that page:

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

Scales are always arranged by pitch, and this is
something which is not necessarily true of either
of the other two entities.

And in fact, that's been pretty much my whole point
from the beginning, in my theoretical writings.
I think it's far easier to understand the harmonic
properties of a tuning or temperament if the pitches
are arranged according to some relevant pitch and/or
interval references (i.e., a tonespace) instead of
pitch-height.

Now, i'm not saying that one representation is superior
over the other; i might as well note that the search
for the "perfect notation" is something which bugs me.
I've always advocated "redundant coding", and strive
to incorporate it into Tonescape. Sound is so much
more abstract than sight, that using multiple different
ways of representing it *simultaneously* is the best
way to visualize what's occuring in a sonic creation.
So, pitch-height, different types of lattices, spreadsheets
of tuning data, and anything else i can think of, all
goes into a Tonescape Musical Piece file.

Anyway, the paradigm of pitch-height order of the notes
is always a property of scales.

And the fact that scales are generally the entities
comprising the source-set of notes/pitches to be used
in a composition, is also an important consideration.
That's sometimes, but not always, true of tunings,
and temperaments are so abstract that they certainly
would often form a source template for a composition
... i think. I'm willing to open the debate floodgates
on this one.

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

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

Carl Lumma wrote:
> Graham wrote...
> >>If you got it published (as I hope you will) there wouldn't >>be much they could do about it, would there? You'd also set >>a strong precedent for the terms' usage in >>musical-mathematical contexts. Whether they percolate into >>less mathematical contexts is a different matter.
> > What about your own pair of papers? You seem to have
> used the "tuning-math" definitions in them, or am I all wet?

I use definitions as I understood them to be agreed on tuning-math. I use the term "temperament class" and so set a precedent for that. I try not to introduce neologisms were I can help it and I'm careful to distinguish temperaments from temperament classes.

> By the way, publishing means to release to the public, which
> you've done. The way you're using it above is actually a
> bastardization that doesn't date back before 1869.

A paper for Mathematics of Music isn't published until it appears in Mathematics of Music. When it does, it has more weight with mathematicians than a website (let alone a mailing list) because it's more likely to get cited. Anything by Gene in a respected journal is going to become the landmark paper on the mathematical treatment of regular temperaments and an essential citation in the flood of articles we hope will follow it. It'd be much less important for general music theory because you wouldn't expect musicians to understand it and so would be much less likely to refer them to it. It's also going to be less read by the world in general because it's locked away in proprietary journal, which shows you how the spirit of academic publication has changed over the years.

Graham

🔗Graham Breed <gbreed@gmail.com>

Cameron Bobro wrote:

>>How would they sound >>different if they were or were not approximations to integer >>ratios? > > This is how it seems to me:
> > When an interval actually is an "approximation" to an integer
> ratio directly percievable as such (ie, coincident partials in the
> audible range), it's inevitably going to be heard IN TERMS of that > interval (not inevitably "AS" that interval) because it is going
> to have substantial characteristics right in the same spot the
> pure ratio does. In the case of 5/4, for example, if the > approximation is a hair off of pure, it's going to put a spotlight
> on the very fourth and fifth partials that are part of the
> 5/4 identity. If they slowly "chorus", or do that creamy thing,
> you know what I mean, you still have an interval which sounds like
> a 5/4 because you have slow and soft movement in the same key
> spot where there is near-stillness in a pure 5/4. (Even in a pure
> 5/4 the is no perfect stillness in this spot unless everything is > perfectly in phase, for example with digital synthesis, and of course
> no perfect stillness throughout all partials and all pitch ranges)

So they don't sound the same.

> But as you move away from the pure interval, you start getting rough > weather in the same spot there once was calm- if calmness is part
> of the identity of 5/4, how can you say that an interval that
> is not calm is an approximation of 5/4? It's jumping up and down
> and waving its arms declaring that it is NOT 5/4. It's a thing
> unto itself. Yes, that's the sound of "approximation".

> Tempering yet further, it's possible to hit other spots with similar > key characteristics. This is what the Lucy third for example lives,
> in my opinion. At 56/45 there's another tiny "soft" region, so it's
> 5/4-like in that way. But it doesn't have the directness or
> vigor or whatever it is of the 5/4, so once again it's not an > approximation, it's a thing unto itself. You'll have to write a proper introduction of your key characteristics because I don't know what to make of it from these brief mentions. It doesn't relate to anything else I've heard of.

> I believe, by the way, that all this stuff is why, leaving aside > philosophical and semantic issues, heavy tempering is often > musically superior to mild tempering. So you accept the concept of heavy tempering?

>>That Lucy *chooses* not to view it as an >>approximation means that his tuning is not a temperament, >>and so not a meantone temperament. If he chose to view it a >>different way the problem of nomenclature would be solved.
> > Notation is a different story. In my opinion, if there's a > historical, or simple, or both, way to notate, even if it's
> all wrong as far generating principles, it should be used
> (I use 34 equal notation with additional + and - signs for > example).

What does notation have to do with anything?

>>>A unilateral declaration that 381 cents is an approximation
>>>to 5/4 just won't fly by me, though if it were dictated to be
>>>an approximation of 56/45, then we could start talking about
>>>"philosophical" obstacles. >>
>>What difference would it make?
> > Big difference- I wouldn't be able to argue that 381 cents
> isn't percieved of as 56/45 (have to check if I can even > differentiate them blind), for I simply don't know and > probably never will whether it is or not, wereas I can and do
> argue that it is not an approximation of 5/4 for the
> admittedly crude and boneheaded reason that it doesn't sound
> like one. Too soft. BTW I'm a fan of 56/45 and the Lucy third.

Why not? Why can't it be an approximation of 5:4 *and* 56:45? How could it be an approximation if did sound the same? "Approximate" means close but not the same.

Graham

🔗Graham Breed <gbreed@gmail.com>

Aaron K. Johnson wrote:

> Do you really think you would be taken seriously opening your mouth in a > music classroom and saying 'wedgie'?

What does that have to do with anything? This isn't a classroom.

> These terms have been hijacked, it seems, by tuning-math. I think if you > asked "says who", it would be a small core group of tuning-math folks. > That's it. Fine to keep using this stuff in tuning-math, but don't > expect it to fly untranslated witheveryone else.

Discussions are going to leak out of the boxes you try and contain them in.

> A paraphrase of Barbour does the trick for me:
> > A tuning, as it is understood out in the 'real world' is a rational set > of pitches (think the duodene or another such JI set), a temperament is > an alteration, or compromise, of one or more JI intervals to create > consistent step-sizes. A scale is an ordered pitch set, an abstraction > of a set of pitches used for melody/harmony.

But before you said he said the temperament had to be irrational. Now you've dropped that condition. Which definition do you prefer?

In the real world I think you'll find a tuning can be irrational. Otherwise, guitarists would face a logical contradiction every time they tried to tune instruments with conventionally placed frets. Chalk that one up as a peculiarity of Barbour's usage.

> I understand the desire to create rigor ala David Hilbert, but to say > the word 'homomorphism' when explaining what a temperament is to average > musicians, even advanced musicians, let alone the general public, is > asking too much, and it is especially asking for extremely poor public > relations standards. It would probably elicit only confused, dismissive > laughter. Yes, this is unfortunate, especially since the definition is > rigorous and accurate. But the laughter is a reality, and if we're smart > around here, we ought to consider that. I'll speak for myself---I want > to consider that, because I believe that these ideas should and could > spread, ridicule-free. Gene, you are great, a math demigod, but c'mon, > your page is Greek to anyone without a PhD in higher mathematics. That > would mean, oh, only 99.99% of the world.

Right, so don't say it to musicians. When did this list become a branch of somebody's public relations?

Gene's site does a good job of defining things for mathematicians. 0.01% of a global population of 6 billion is, what, 600,000? That's not a bad audience.

> Also, regarding the place of this list on the larger world stage: a ton > of good theory goes on here, a tremendous amount of new thinking has > been generated, but to think that what goes on here theory-wise will be > disseminated, terminology intact, to the outside world of musicians and > the general public is naive at best. It needs translation, for sure.

And the first step is the Tonalsoft Encyclopedia, which is where you came in.

Graham

🔗monz <monz@tonalsoft.com>

Hi Graham and Aaron,

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

> > Also, regarding the place of this list on the
> > larger world stage: a ton of good theory goes
> > on here, a tremendous amount of new thinking has
> > been generated, but to think that what goes on
> > here theory-wise will be disseminated, terminology
> > intact, to the outside world of musicians and
> > the general public is naive at best. It needs
> > translation, for sure.
>
> And the first step is the Tonalsoft Encyclopedia,
> which is where you came in.

And believe me, i strive to translate as much as i
can of what Gene says, into my Encyclopedia. I've
even gone back to school to study math so that i can
get a better understanding of it, but alas, i'm
still a baby at math and much of what he writes is
far beyond what i can grasp.

I'd appreciate it if those Gene and the few of you
out there who do understand his work better would
flag me down with suggested new entries and improvements
to the Encyclopedia. Just put the word "Encyclopedia"
into the subject line and i'll notice it and hopefully
incorporate it.

I've only recently begun doing serious updating to
the Encyclopedia, after a near-hiatus of about two years.
So any help with this would be greatly appreciated.

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

🔗Aaron K. Johnson <aaron@akjmusic.com>

Graham Breed wrote:
> Aaron K. Johnson wrote:
>
> >> Do you really think you would be taken seriously opening your mouth in a >> music classroom and saying 'wedgie'?
>> >
> What does that have to do with anything? This isn't a > classroom.
> Ok, as long as you are comfortable with these terms staying here, and having no effect elsewhere.

>> These terms have been hijacked, it seems, by tuning-math. I think if you >> asked "says who", it would be a small core group of tuning-math folks. >> That's it. Fine to keep using this stuff in tuning-math, but don't >> expect it to fly untranslated witheveryone else.
>> >
> Discussions are going to leak out of the boxes you try and > contain them in.
> Of course, but what I'm objecting to is people saying, committe-style, from tuning-math, 'the term for that is this', inventing neologisms, and then insisting that musicians who have been using say, older 'Barbour-style' terms should be 'upgrading'. Or worse yet, that not using these terms is barbaric. I sense Carl was only half joking when referring to non tuning-mathers
as 'plebs'.
>> A paraphrase of Barbour does the trick for me:
>>
>> A tuning, as it is understood out in the 'real world' is a rational set >> of pitches (think the duodene or another such JI set), a temperament is >> an alteration, or compromise, of one or more JI intervals to create >> consistent step-sizes. A scale is an ordered pitch set, an abstraction >> of a set of pitches used for melody/harmony.
>> >
> But before you said he said the temperament had to be > irrational. Now you've dropped that condition. Which > definition do you prefer?
> Now you're looking for nits. Of course, a temperament is *usually* irrational---this definition is better, in that, one often finds that a rational well-temperament fits nicely (I've designed one myself, which George Secor improved slightly.)

> In the real world I think you'll find a tuning can be > irrational. Otherwise, guitarists would face a logical > contradiction every time they tried to tune instruments with > conventionally placed frets. Chalk that one up as a > peculiarity of Barbour's usage.
> Yes---for clarity---one both 'tunes a piano', and 'sets a temperament', one doesn't 'temper a guitar', etc.

Does this need to be said, or are you picking a fight? ;)

>> I understand the desire to create rigor ala David Hilbert, but to say >> the word 'homomorphism' when explaining what a temperament is to average >> musicians, even advanced musicians, let alone the general public, is >> asking too much, and it is especially asking for extremely poor public >> relations standards. It would probably elicit only confused, dismissive >> laughter. Yes, this is unfortunate, especially since the definition is >> rigorous and accurate. But the laughter is a reality, and if we're smart >> around here, we ought to consider that. I'll speak for myself---I want >> to consider that, because I believe that these ideas should and could >> spread, ridicule-free. Gene, you are great, a math demigod, but c'mon, >> your page is Greek to anyone without a PhD in higher mathematics. That >> would mean, oh, only 99.99% of the world.
>> >
> Right, so don't say it to musicians. When did this list > become a branch of somebody's public relations?
> You're right. But I think it's important to find a consensus among musicians as well, since they are presumably the ones playing the music in the given tuning.
Should that step come into account? There are musicians on this list, not just theorists or mathematicians.

Actually, judging from message volume these days, we are looking at *internal* relations, not public relations.

> Gene's site does a good job of defining things for > mathematicians. 0.01% of a global population of 6 billion > is, what, 600,000? That's not a bad audience.
>
> Like I said, it's all fine and good, but don't expect it to be the colloquial. These tunings have existed as concepts, after all, well before the math was even capable of describing them accurately.

That said, the math is useful---once described, it can be tinkered with in abstract ways---which is where tuning-math comes in. Whethere or not it can be translated back into music on a scale of use anything like what the organic tunings that are 'a priori' in use by musicians remains to be seen.

>> Also, regarding the place of this list on the larger world stage: a ton >> of good theory goes on here, a tremendous amount of new thinking has >> been generated, but to think that what goes on here theory-wise will be >> disseminated, terminology intact, to the outside world of musicians and >> the general public is naive at best. It needs translation, for sure.
>> >
> And the first step is the Tonalsoft Encyclopedia, which is > where you came in.
> I think Monz's work is important, and that's a great resource, but I think it should not be considered the last word on any subject. I'm against committee declarations---let the usage evolve among practitioners, and if it ends up being these neologisms coined in tuning-math out in the world, so be it.

-A.

🔗Carl Lumma <carl@lumma.org>

🔗monz <monz@tonalsoft.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Cameron Bobro wrote:
>
> >>How would they sound
> >>different if they were or were not approximations to integer
> >>ratios?
> >
> > This is how it seems to me:
> >
> > When an interval actually is an "approximation" to an integer
> > ratio directly percievable as such (ie, coincident partials in
the
> > audible range), it's inevitably going to be heard IN TERMS of
that
> > interval (not inevitably "AS" that interval) because it is going
> > to have substantial characteristics right in the same spot the
> > pure ratio does. In the case of 5/4, for example, if the
> > approximation is a hair off of pure, it's going to put a
spotlight
> > on the very fourth and fifth partials that are part of the
> > 5/4 identity. If they slowly "chorus", or do that creamy thing,
> > you know what I mean, you still have an interval which sounds
like
> > a 5/4 because you have slow and soft movement in the same key
> > spot where there is near-stillness in a pure 5/4. (Even in a pure
> > 5/4 the is no perfect stillness in this spot unless everything
is
> > perfectly in phase, for example with digital synthesis, and of
course
> > no perfect stillness throughout all partials and all pitch
ranges)
>
> So they don't sound the same.

No, they sound approximately the same.
>
> > But as you move away from the pure interval, you start getting
rough
> > weather in the same spot there once was calm- if calmness is part
> > of the identity of 5/4, how can you say that an interval that
> > is not calm is an approximation of 5/4? It's jumping up and down
> > and waving its arms declaring that it is NOT 5/4. It's a thing
> > unto itself.
>
> Yes, that's the sound of "approximation".

No, that's the sound of "two different intervals". Is warm
orange approximately cold red? I guess if you're an
interior decorator with a budget drawn from between the
cushions on the sofa, it is. Or maybe working on
data compression algorithms for mobile telephones or
something.

>
> > Tempering yet further, it's possible to hit other spots with
similar
> > key characteristics. This is what the Lucy third for example
lives,
> > in my opinion. At 56/45 there's another tiny "soft" region, so
it's
> > 5/4-like in that way. But it doesn't have the directness or
> > vigor or whatever it is of the 5/4, so once again it's not an
> > approximation, it's a thing unto itself.
>
> You'll have to write a proper introduction of your key
> characteristics because I don't know what to make of it from
> these brief mentions. It doesn't relate to anything else
> I've heard of.
>
> > I believe, by the way, that all this stuff is why, leaving aside
> > philosophical and semantic issues, heavy tempering is often
> > musically superior to mild tempering.
>
> So you accept the concept of heavy tempering?

I accept musical results of heavy tempering, therefore
the act of heavy tempering itself. I don't accept the
idea that a heavily tempered interval "is" the original,
or is an "approximation" of the original. Heavy tempering
succeeds because it fails. This is nothing new or strange
in music or other arts- for example, at this very moment I'm
listening to my 70s discrete-analog "string machine" (a Logan,
for any buffs, and I got it for a 100 Euros, yeah, baby!).
As an approximation to a string section, it's pretty sad, and
that's exactly why it's a cult classic while "realistic"
string samples get continually outdated and updated.
>
> >>That Lucy *chooses* not to view it as an
> >>approximation means that his tuning is not a temperament,
> >>and so not a meantone temperament. If he chose to view it a
> >>different way the problem of nomenclature would be solved.
> >
> > Notation is a different story. In my opinion, if there's a
> > historical, or simple, or both, way to notate, even if it's
> > all wrong as far generating principles, it should be used
> > (I use 34 equal notation with additional + and - signs for
> > example).
>
> What does notation have to do with anything?

Oh, sorry, I read "notation" where Gene had "nomenclature".
Anyway all this about temperaments does have a lot to do
with notation, but whatever.

>
> >>>A unilateral declaration that 381 cents is an approximation
> >>>to 5/4 just won't fly by me, though if it were dictated to be
> >>>an approximation of 56/45, then we could start talking about
> >>>"philosophical" obstacles.
> >>
> >>What difference would it make?
> >
> > Big difference- I wouldn't be able to argue that 381 cents
> > isn't percieved of as 56/45 (have to check if I can even
> > differentiate them blind), for I simply don't know and
> > probably never will whether it is or not, wereas I can and do
> > argue that it is not an approximation of 5/4 for the
> > admittedly crude and boneheaded reason that it doesn't sound
> > like one. Too soft. BTW I'm a fan of 56/45 and the Lucy third.
>
> Why not? Why can't it be an approximation of 5:4 *and*
> 56:45? How could it be an approximation if did sound the
> same? "Approximate" means close but not the same.

Lessee... "approximate":

1. near or approaching a certain state, condition, goal, or
standard.
2. nearly exact; not perfectly accurate or correct: The approximate
time was 10 o'clock.
3. near; close together.
4. very similar; nearly identical.
verb (used with object) 5. to come near to; approach closely to: to
approximate an ideal.
6. to estimate: We approximated the distance at three miles.
7. to simulate; imitate closely: The motions of the stars can be
approximated in a planetarium.
8. to bring near.
verb (used without object) 9. to come near in position, character,
amount, etc

I wasn't able to find "audibly different" in any online dictionary,
and I don't think I'll find it in the hardcover at home, either.

-Cameron Bobro

🔗Carl Lumma <carl@lumma.org>

🔗Aaron K. Johnson <aaron@akjmusic.com>

monz wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> >> <snip> ... but what I'm objecting to is people
>> saying, committe-style, from tuning-math, 'the term
>> for that is this', inventing neologisms, and >> then insisting that musicians who have been
>> using say, older 'Barbour-style' terms should
>> be 'upgrading'. Or worse yet, that not using
>> these terms is barbaric. I sense Carl was only
>> half joking when referring to non tuning-mathers
>> as 'plebs'.
>> >
>
> But if some people decide that "car" is a good name for
> the object that was at first called a "horseless carriage",
> does it really make sense for the folks who are used to
> the older name to object to the new name?
>
> The shorter and more sensible one will ultimately
> replace the older longer one anyway, so why fight it?
> That's a good analogy. But--it takes a critical mass for the shorter and more sensible one to replace the older longer one.

No one has yet made the case that neologisms invented in an internet mailing-list ought to replace terminology that is well understood or short already, and not going to be in the wider vocabulary of musicians and piano tuners everywhere....we must remember that this is simply a Yahoo tuning group, not ANSI or NIST or any such body.

I'll eat my words the day I hear an organ tuner or piano tuner talk about wedgies, and not be referring to painful childhood memories on a school bus. :)

I've yet to see someone explain to me why I shouldn't say '1/6-comma temperament' or '1/6-comma meantone' or even '1/6-comma tuning' and not be understood....who wouldn't assume that an unqualified 'comma' meant 81:80? Isn't it getting a bit pedantic to continue this talk? Everyone here will know what you mean, and anyone who didn't would be ignorant of the subject, or would be just being difficult.

-A

🔗Carl Lumma <carl@lumma.org>

🔗George D. Secor <gdsecor@yahoo.com>

I'm sorry, but I'm going to have to bow out at this point. This
discussion has gone on much longer than I had bargained for, and
there are other things microtonal that I need to get back to.

One of those things is that I hope eventually to resume work on my
book. I'll just have to trust this group to arrive at some
consistent definitions that I can accept, whereby I could then take
care to caution the reader to avoid possible pitfalls by explaining
1) how terms have changed in the course of time, and 2) that terms
may still be understood somewhat differently in different venues.

I have a few loose ends to address here.

The term "tuning" has already been used for quite some time to mean
(in my own words) "a set of pitches related by intervals of specific
sizes", so I think it's useless to try to go back to Barbour's
meaning, since 1) we previously had no other word with the present
(more general) meaning, and 2) the term "rational tuning" exactly
meets Barbour's definition.

As Carl pointed out, as language evolves words take on new meanings.
Still, words are often understood to default to their traditional
meanings in the absence of qualifying language. Wherever "comma" is
used in such a way as to indicate a small interval of specific size
(as in "2/7-comma temperament"), it is understood to be 80:81, so
it's not necessary to be more specific than that. Wherever "equal
temperament" is used without specifying either what interval is being
equally divided (or how many parts it's being divided into), it's
universally understood to be one specific tuning, 12-EDO.
Likewise, "meantone temperament" has traditionally understood to mean
1/4-comma temperament, which is basically the hang-up I've been
having with the terms "temperament" and "meantone" being applied to
what Graham calls "temperament class". It would be great
if "temperament" could be extended to refer to classes,
because "tempered tuning" could then be used as a generic term to
refer to a more specific category.

"Tempered tuning" is such a nice foil to the term "rational tuning"
that I'm now wondering whether the terms "meantone" and "meantone
temperament" (without qualifying language) could indeed become
acceptable in a broader sense. We've had something similar happening
with the term "just intonation" (regarding what's considered to be JI
in a practical vs. theoretical sense), such that it's often necessary
to specify "strict JI" to indicate the original (theoretical)
meaning. (On the one hand we have irrational microtemperaments that
sound like JI and on the other hand rational well-temperaments that
don't.) Would "strict meantone" similarly suffice? That's a tough
call. Will everyone outside this group accept that? Probably not,
so we should be prepared to make allowances for that when discussing
these things with others.

Gene, thanks for pointing out that "family" is already taken (I
checked Monz's encyclopedia entry). Likewise, Herman pointed out
that irregular temperaments would still fall into temperament classes
by virtue of sharing the same mapping from JI. I'm wondering whether
there's a single word that would fit the concept of family member,
yet still convey the meaning of class, because I'm still thinking
that extending the term "temperament" to cover temperament class
should be a last resort. Could "family" be replaced with "clan"
and "temperament class" with "family"? Or is it better to
leave "family" as is and find a word that would treat members of the
same temperament class as a "litter" (of temperamental pups). :-)

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> [message #73415]
> ...
> IMO, the most important things which differentiate
> scales from tunings and temperaments is what i put
> in the opening statement on that page:
>
> >> "A succession of musical pitches arranged in order
> >> of pitch-height, generally considered as a source set
> >> of pitches for musical composition."
>
> Scales are always arranged by pitch, and this is
> something which is not necessarily true of either
> of the other two entities.
>
> And in fact, that's been pretty much my whole point
> from the beginning, in my theoretical writings.
> I think it's far easier to understand the harmonic
> properties of a tuning or temperament if the pitches
> are arranged according to some relevant pitch and/or
> interval references (i.e., a tonespace) instead of
> pitch-height.

When defining seemingly simple term such as "scale", it often helps
to identify specific examples of the term and then determine what
these have in common (and from that, also what the term is *not*).
Common examples of scales are major, minor, and chromatic (or if
you're in Java, pelog and slendro). Each of these scales has a
specific number of tones (or tones per period) ordered according to
pitch height, related by specific interval-classes (which help to
distinguish one scale from another), and suitable for composing a
melody. However a scale does not generally require one particular
tuning. Thus a major scale is a major scale regardless of whether
it's played in pythagorean tuning, 12-ET, meantone temperament, 19-
ET, etc., and the definition must take that into account, so as not
to be misleading. Including interval-classes in the definition is
important, because, even though a "pentatonic scale" will allow a
very broad application of the term interval-class, a random selection
of five tones within an octave will probably not

I'll still be reading many of the messages to keep up with what's
happening, but for now I've said my piece.

--George

🔗Graham Breed <gbreed@gmail.com>

Aaron K. Johnson wrote:
> Graham Breed wrote:
> >>Aaron K. Johnson wrote:
>>
>>
>>>Do you really think you would be taken seriously opening your mouth in a >>>music classroom and saying 'wedgie'?
>>
>>What does that have to do with anything? This isn't a >>classroom.
> > Ok, as long as you are comfortable with these terms staying here, and > having no effect elsewhere.

What terms? The only example is "wedgie". I'd be happy if the word "wedgie" were never uttered in a music classroom with the tuning-math meaning because the concept it refers to isn't important to musicians. Maybe Gene disagrees -- we don't think with one mind on tuning-math after all. So what's your argument? I hope you don't want a new word to mean what "wedgie" currently means so that it's more palatable to music students because this is one of the few new terms we actually seem to agree on.

There are places in the world outside mailing lists and music classrooms, you know. Wedgies are more likely to be spoken of in mathematics classrooms, or classrooms teaching hybrid mathematics-of-music courses. "Wedgie" is one of the terms that might not survive the translation into academese because it's obviously light hearted and there are some academics who don't like you to be seen having fun. If it changes, so what?

>>>These terms have been hijacked, it seems, by tuning-math. I think if you >>>asked "says who", it would be a small core group of tuning-math folks. >>>That's it. Fine to keep using this stuff in tuning-math, but don't >>>expect it to fly untranslated witheveryone else.
>>
>>Discussions are going to leak out of the boxes you try and >>contain them in.
> > Of course, but what I'm objecting to is people saying, committe-style, > from tuning-math, 'the term for that is this', inventing neologisms, and > then insisting that musicians who have been using say, older > 'Barbour-style' terms should be 'upgrading'. Or worse yet, that not > using these terms is barbaric. I sense Carl was only half joking when > referring to non tuning-mathers
> as 'plebs'.

Carl uses light-hearted language a lot. As far as I can tell it isn't hiding any malice. You're also stretching it a bit to associate plebeians with barbarians. They were in fact Roman citizens -- among the most civilized people of their time.

Anyway, what terms are you talking about? It's a common convention that if you come up with a new concept you get first dibs on naming it. It happens that some new concepts came about on tuning-math and it would make things simple if you used the tuning-math terms to talk about them.

>>>A paraphrase of Barbour does the trick for me:
>>>
>>>A tuning, as it is understood out in the 'real world' is a rational set >>>of pitches (think the duodene or another such JI set), a temperament is >>>an alteration, or compromise, of one or more JI intervals to create >>>consistent step-sizes. A scale is an ordered pitch set, an abstraction >>>of a set of pitches used for melody/harmony.
>>> >>
>>But before you said he said the temperament had to be >>irrational. Now you've dropped that condition. Which >>definition do you prefer?
>> > > Now you're looking for nits. Of course, a temperament is *usually* > irrational---this definition is better, in that, one often finds that a > rational well-temperament fits nicely (I've designed one myself, which > George Secor improved slightly.)

Indeed you have.

So if you don't follow Barbour's simplistic "rational/irrational" definition where exactly do you disagree with which tuning-math definition? Or is this all hot air?

>>In the real world I think you'll find a tuning can be >>irrational. Otherwise, guitarists would face a logical >>contradiction every time they tried to tune instruments with >>conventionally placed frets. Chalk that one up as a >>peculiarity of Barbour's usage.
> > Yes---for clarity---one both 'tunes a piano', and 'sets a temperament', > one doesn't 'temper a guitar', etc.
> > Does this need to be said, or are you picking a fight? ;)

I'm amazed that anybody would put forward Barbour's definitions as applying in the outside word. I'm sure he was a clever and learned chap but he was a bit idiosyncratic on this point, wasn't he?

I'll echo Carl -- this thread didn't start because a tuning-math member objected to an outside definition. So if Barbour's alternatives are so obviously wrong, what part of what tuning-math definition is who objecting to?

> You're right. But I think it's important to find a consensus among > musicians as well, since they are presumably the ones playing the music > in the given tuning.
> Should that step come into account? There are musicians on this list, > not just theorists or mathematicians.

Why would we care what musicians think about the word "homomorphism"? It's hardly a neologism, anyway.

>>Gene's site does a good job of defining things for >>mathematicians. 0.01% of a global population of 6 billion >>is, what, 600,000? That's not a bad audience.
> > Like I said, it's all fine and good, but don't expect it to be the > colloquial. These tunings have existed as concepts, after all, well > before the math was even capable of describing them accurately.

What tunings? A lot of the temperament classes in Paul's Middle Path paper weren't mentioned anywhere before. Only meantone and 12-equal can have preceded the math to describe them. And that doesn't cover 11-limit temperaments which are even less likely to have been investigated before. I don't think we ever imposed our own name on a temperament class that had an accepted name. Given that, do you think our names won't become the colloquial for those temperament classes?

> That said, the math is useful---once described, it can be tinkered with > in abstract ways---which is where tuning-math comes in. Whethere or not > it can be translated back into music on a scale of use anything like > what the organic tunings that are 'a priori' in use by musicians remains > to be seen.

It isn't that difficult to translate it back. Along the way you lose concepts like wedgies and homomorphisms and a whole lot else. Getting musicians to listen, and help with the translation, is an entirely different question. They'd much rather spend their time objecting to technical terms that inadvertantly rear their heads during the discussion.

Graham

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Graham Breed <gbreed@gmail.com>

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

<snip>
>>>pure ratio does. In the case of 5/4, for example, if the >>>approximation is a hair off of pure, it's going to put a > spotlight
>>>on the very fourth and fifth partials that are part of the
>>>5/4 identity. If they slowly "chorus", or do that creamy thing,
>>>you know what I mean, you still have an interval which sounds > like
>>>a 5/4 because you have slow and soft movement in the same key
>>>spot where there is near-stillness in a pure 5/4. (Even in a pure
>>>5/4 the is no perfect stillness in this spot unless everything > is >>>perfectly in phase, for example with digital synthesis, and of > course
>>>no perfect stillness throughout all partials and all pitch > ranges)
> >>So they don't sound the same.
> > No, they sound approximately the same.

Right, that establishes what they mean by "approximate". Maybe it's testable.

>>>But as you move away from the pure interval, you start getting > rough >>>weather in the same spot there once was calm- if calmness is part
>>>of the identity of 5/4, how can you say that an interval that
>>>is not calm is an approximation of 5/4? It's jumping up and down
>>>and waving its arms declaring that it is NOT 5/4. It's a thing
>>>unto itself. >>
>>Yes, that's the sound of "approximation".
> > No, that's the sound of "two different intervals". Is warm
> orange approximately cold red? I guess if you're an
> interior decorator with a budget drawn from between the > cushions on the sofa, it is. Or maybe working on
> data compression algorithms for mobile telephones or
> something. Who are you to tell me what I mean by a word?

> I accept musical results of heavy tempering, therefore
> the act of heavy tempering itself. I don't accept the > idea that a heavily tempered interval "is" the original,
> or is an "approximation" of the original. Heavy tempering
> succeeds because it fails. This is nothing new or strange
> in music or other arts- for example, at this very moment I'm > listening to my 70s discrete-analog "string machine" (a Logan,
> for any buffs, and I got it for a 100 Euros, yeah, baby!).
> As an approximation to a string section, it's pretty sad, and
> that's exactly why it's a cult classic while "realistic"
> string samples get continually outdated and updated. What do you think heavy tempering fails at? What motives are you divining?

>>>>>A unilateral declaration that 381 cents is an approximation
>>>>>to 5/4 just won't fly by me, though if it were dictated to be
>>>>>an approximation of 56/45, then we could start talking about
>>>>>"philosophical" obstacles. >>>>
>>>>What difference would it make?
>>>
>>>Big difference- I wouldn't be able to argue that 381 cents
>>>isn't percieved of as 56/45 (have to check if I can even >>>differentiate them blind), for I simply don't know and >>>probably never will whether it is or not, wereas I can and do
>>>argue that it is not an approximation of 5/4 for the
>>>admittedly crude and boneheaded reason that it doesn't sound
>>>like one. Too soft. BTW I'm a fan of 56/45 and the Lucy third.
>>
>>Why not? Why can't it be an approximation of 5:4 *and* >>56:45? How could it be an approximation if did sound the >>same? "Approximate" means close but not the same.
> > Lessee... "approximate":
> > 1. near or approaching a certain state, condition, goal, or > standard. > 2. nearly exact; not perfectly accurate or correct: The approximate > time was 10 o'clock. > 3. near; close together. > 4. very similar; nearly identical. > ï¿½verb (used with object) 5. to come near to; approach closely to: to > approximate an ideal. > 6. to estimate: We approximated the distance at three miles. > 7. to simulate; imitate closely: The motions of the stars can be > approximated in a planetarium. > 8. to bring near. > ï¿½verb (used without object) 9. to come near in position, character, > amount, etc That's admirably detailed. I'll take 1(b), "approaching a .. goal". I can also take 1(a), "near a certain ... goal" provided you don't argue that 4 cents isn't "near".

The Oxford thing that came with my computer has an admirably succinct definition for the verb: "come close or be similar to something in quality, nature, or quantity". So you're talking abut quality and we're talking about quantity -- or maybe a different quality. (Note that we usually say "approximate" as a verb, but you've cleverly slided in a definition of the adjective, which has some definitions more to your liking.)

> I wasn't able to find "audibly different" in any online dictionary,
> and I don't think I'll find it in the hardcover at home, either.

So which orifice did you pull "audibly different" out of?

Graham

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Cameron Bobro wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> >>Cameron Bobro wrote:
>
> <snip>
> >>>pure ratio does. In the case of 5/4, for example, if the
> >>>approximation is a hair off of pure, it's going to put a
> > spotlight
> >>>on the very fourth and fifth partials that are part of the
> >>>5/4 identity. If they slowly "chorus", or do that creamy thing,
> >>>you know what I mean, you still have an interval which sounds
> > like
> >>>a 5/4 because you have slow and soft movement in the same key
> >>>spot where there is near-stillness in a pure 5/4. (Even in a
pure
> >>>5/4 the is no perfect stillness in this spot unless everything
> > is
> >>>perfectly in phase, for example with digital synthesis, and of
> > course
> >>>no perfect stillness throughout all partials and all pitch
> > ranges)
> >
> >>So they don't sound the same.
> >
> > No, they sound approximately the same.
>
> Right, that establishes what they mean by "approximate".
> Maybe it's testable.

Who's "they"? Sure it's testable, but it must be subjective.

>
> >>>But as you move away from the pure interval, you start getting
> > rough
> >>>weather in the same spot there once was calm- if calmness is
part
> >>>of the identity of 5/4, how can you say that an interval that
> >>>is not calm is an approximation of 5/4? It's jumping up and down
> >>>and waving its arms declaring that it is NOT 5/4. It's a thing
> >>>unto itself.
> >>
> >>Yes, that's the sound of "approximation".
> >
> > No, that's the sound of "two different intervals". Is warm
> > orange approximately cold red? I guess if you're an
> > interior decorator with a budget drawn from between the
> > cushions on the sofa, it is. Or maybe working on
> > data compression algorithms for mobile telephones or
> > something.
>
> Who are you to tell me what I mean by a word?

Nice little straw man there- I wasn't telling you what
you mean by the word, but what the word means. Sorry I
won't buy your misunderstanding or misuse but help
yourself to it. :-)
>
> > I accept musical results of heavy tempering, therefore
> > the act of heavy tempering itself. I don't accept the
> > idea that a heavily tempered interval "is" the original,
> > or is an "approximation" of the original. Heavy tempering
> > succeeds because it fails. This is nothing new or strange
> > in music or other arts- for example, at this very moment I'm
> > listening to my 70s discrete-analog "string machine" (a Logan,
> > for any buffs, and I got it for a 100 Euros, yeah, baby!).
> > As an approximation to a string section, it's pretty sad, and
> > that's exactly why it's a cult classic while "realistic"
> > string samples get continually outdated and updated.
>
> What do you think heavy tempering fails at? What motives
> are you divining?

It fails at "approximating", obviously. Which is just fine.
I don't know what you mean by "motives" here, but the historical
motives of tempering you know very well.
>
> >>>>>A unilateral declaration that 381 cents is an approximation
> >>>>>to 5/4 just won't fly by me, though if it were dictated to be
> >>>>>an approximation of 56/45, then we could start talking about
> >>>>>"philosophical" obstacles.
> >>>>
> >>>>What difference would it make?
> >>>
> >>>Big difference- I wouldn't be able to argue that 381 cents
> >>>isn't percieved of as 56/45 (have to check if I can even
> >>>differentiate them blind), for I simply don't know and
> >>>probably never will whether it is or not, wereas I can and do
> >>>argue that it is not an approximation of 5/4 for the
> >>>admittedly crude and boneheaded reason that it doesn't sound
> >>>like one. Too soft. BTW I'm a fan of 56/45 and the Lucy third.
> >>
> >>Why not? Why can't it be an approximation of 5:4 *and*
> >>56:45? How could it be an approximation if did sound the
> >>same? "Approximate" means close but not the same.
> >
> > Lessee... "approximate":
> >
> > 1. near or approaching a certain state, condition, goal, or
> > standard.
> > 2. nearly exact; not perfectly accurate or correct: The
approximate
> > time was 10 o'clock.
> > 3. near; close together.
> > 4. very similar; nearly identical.
> > verb (used with object) 5. to come near to; approach closely
to: to
> > approximate an ideal.
> > 6. to estimate: We approximated the distance at three miles.
> > 7. to simulate; imitate closely: The motions of the stars can be
> > approximated in a planetarium.
> > 8. to bring near.
> > verb (used without object) 9. to come near in position,
character,
> > amount, etc
>
> That's admirably detailed. I'll take 1(b), "approaching a
> .. goal". I can also take 1(a), "near a certain ... goal"
> provided you don't argue that 4 cents isn't "near".

Four cents high or four cents low, in light of which particular
musical characteristics you're after? Anyway, shall we take
a look at the "middle path" papers and see if the
purported approximations are all within 4 cents of their
stated goals?

>
> The Oxford thing that came with my computer has an admirably
> succinct definition for the verb: "come close or be similar
> to something in quality, nature, or quantity". So you're
> talking abut quality and we're talking about quantity -- or
> maybe a different quality. (Note that we usually say
> "approximate" as a verb, but you've cleverly slided in a
> definition of the adjective, which has some definitions more
> to your liking.)

Man, a definition of the verb is right there in front of you,
of course I was careful to include it as well. Nor are the
definitions of the adjective and verb contradictory in any way,
in fact one can be gleaned immediately from the other. There are
intelligent and educated people reading this list and
surely there going to wonder why you insist on cladding
yourself in motley.

Yes of course I'm talking about quality and not quantity, that's
the whole point.

>
> > I wasn't able to find "audibly different" in any online
dictionary,
> > and I don't think I'll find it in the hardcover at home, either.
>
> So which orifice did you pull "audibly different" out of?

The horse's mouth, obviously.

-Cameron Bobro