Naming intervals - size matters

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_12590.html#33602
>
> >
> > Er _which_ one are you calling the major triad here. For me, the
> only reason 0c:400c:700c is called a major triad in 12-tET is
because
> it's an acceptable approximation _and_ it's the _only_ approximation
> > available.
>
> ****Hi Dave.
>
> Sure, this is logically true. However, in the paragraph above you
> say "the only reason Oc:400c:700c *is* called a major triad..."
>
> That's the crux of it. Whether it makes any sense or not that *is*
> what it's called by almost all practicing musicians today, since
> virtually *all* of them work in 12-tET.

But when they begin to work in Blackjack one should remind them that
although the 12-tET major third is indeed a kind of major third (namely a
wide one) we now have a much better one available, an essentially just one.
You don't seem to have a problem with calling a 4:5 a just major third. One
synonym for "just" is "true". It is the 12-tET one that is the
approximation, not the other way around. I think most musicians are smart
enough to understand this when it's explained to them, even if they are
12-tET trained. At least in this country's universities and conservatoria
they are usually taught briefly about Just scales somewhere in their
training.

> I believe Paul Erlich has
> pointed to studies that show that even *string* players, since the
> advent of many works with strings and piano, particularly, tend to
> play in 12-tET, even though one might think they would play in just
> or Pythagorean.

Is there anyone out there with studies (or even anecdotes) that show that
this can change in a very short time if the string player (or vocalist?) is
asked to play along with other instruments tuned in say Just, meantone or
Pythagorean? It is of course essential that one first retunes the open
strings appropriately.

> > Should we refer to the 1/4 comma meantone major third (4:5) as a
> > twelfth-low major third too?
>
> ****I guess yes, if you were describing in in 72-tET.

72-tET or not is irrelevant. A thought experiment: Assume I have a keyboard
tuned to a 12-note meantone, a little toward 1/3-comma from 1/4-comma, so
that its G:B interval is 383.33 cents (same as the G:Bv interval in
Blackjack). Let's say at first you don't even know how the keyboard is
tuned. I play that interval for you and ask you what kind of third you
think it is. What do you say? Then I lie and say the keyboard is tuned in a
subset of Blackjack. Now what do you call that kind of interval? Then I
tell you I lied and it is actually in a meantone. What do you call it now?
Will you ask, in each case, what notation I am using for the pitches?

The underlying principle of the interval naming scheme I favour did not
originate with me, but apparently with Adriaan Fokker in the 1970s. It is
also the one used in one of our most indispensable tools, Scala.

The priciple is to associate an interval name with a particular interval
width (in cents or ratios), or a small range around that, irrespective of
what scale or tuning the interval is currently a part of. The major third
that is considered not to need a qualifier is the simplest Just one (4:5)
or the best approximation of it in a given tuning (provided it is a good
enough approximation).

So Joseph and Paul, you are apparently the first to object to this
principle in the history of this list. Why only now?

> > You seem to be saying that G-Bv-D is a "correct" major triad, but
> you want to call it a twelfth-low major triad. Seems a
contradiction.
>
> ****Well, Dave, since the "B" is "modified" by a "v" it has to
> be "altered" or "twelfth-low."

Yes the pitch is notated as a twelfth-low B. But that doesn't have to make
the G:Bv interval (essentially a 4:5 in this case) a twelfth-low major
third, when it is in fact a just or true, major third.

In thinking back over other recent posts of yours it becomes apparent to me
that you have a confusion between pitches and intervals. For example you
apparently assumed that because Blackjack has 21 pitches per octave it must
also have 21 kinds of interval per octave, when in fact it has 41. This
seems to be a common confusion, and there is no penalty for such confusion
in 12-tET or indeed any equal temperament. Such confusion is encouraged by
the I II III IV ... system for naming diatonic pitches independent of key.
But if one is to break away from ETs it is a confusion that must be overcome.

> So, yes, I prefer that G-B-D in
> an "unaltered state" be our traditionally wide 12-tET triad.

You said it! I totally agree. G:B:D in 6x12-notated Miracle temperament
represents a "wide" major triad. :-)

> > And so, you want to base your interval nomenclature on those that
> are out of tune? I still don't get it. Why?
>
> ****Why? Because that's what hoards of players in conservatories
and
> music schools have studied and are *used* to. And, I believe that's
> what they are going to study for the conceivable future. I haven't
> heard of any schools, except for isolated cases at the New England
> Conservatory, to offer anything different.
>
> The system that *you* would like where G-B-D *is* 4:5:6 is
> essentially the system advocated by Ben Johnston and we've found
> quite a few inconsistencies trying to reconcile that even to the
> basic Pythagorean-based staff.

Oh dear. Now your confusion of intervals and pitches causes you to
misrepresent me. [Thanks Paul for pointing this out while I was away]. I do
_not_ want 4:5:6 (or its nearest approximation in a given tuning) to be
notated G:B:D except in temperaments where the syntonic comma (80:81)
vanishes, i.e. meantones.

I have said before that I do not favour Ben Johnston's notation and
consider that, in any tuning, the 7 nominals FCGDAEB should always be
applied to a chain of approximate 2:3's where these exist. Otherwise
modulation becomes too messy.

> > I'd be saying to the musicians, "No. Not a 12-tET major third, we
> > don't have to put up with that crap any longer. We want a real
> > true just proper pure major third. You know, the kind you can tune by
> > ear. The barbershop harmony kind. _That's_ what we call a major third
> > in _this_ scale."
>
> ***Like I say, that's what Ben Johnston tries to do and he *does*
> get performances. However he mostly *doesn't* get performances.

No that's _not_ what Ben Johnston does. Or at least that's not what Ben
Johston does that's objectionable. Ben Johnston wants to notate the pitches
making up the major third as e.g. G:B. I want them notated as e.g. G:Bv.

> What I'm saying is very obvious and simple: just, for the
notational
> convenience, keep the 12-tET pitches *as is* since they are what
> everybody has practiced and studied, and everything else is
> a "deviation..."

I totally agree (but perhaps for different reaszons). Note that you're
talking here about pitches and scores with notations for pitches, not
intervals or names for intervals.

So I believe the rest of your objections to my _interval_naming_ scheme
were irrelevant since I'm not talking about changing scores, except perhaps
some of the letters above guitar chord diagrams.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com
When remembering the recent horrific acts of violence, let us not forget
that on September 11th there were 35,000 other very innocent victims.
For that is the number of children dying every day from
starvation-related causes. Where is the global outcry, the unprecedented
coalition, the unlimited resources of money, materials, time and will
dedicated to stopping this daily violence? These children are being
killed by commercial and financial terrorism. There can be no other term
for policies which force the poor to sacrifice their children to pay
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to honour its historical and ecological debts to the South.
Jakob von Uexkull

--- In tuning@y..., David C Keenan <d.keenan@u...> wrote:

/tuning/topicId_33799.html#33799

****Hi Dave...

Actually I think part of our disagreement stems from the fact that I
am more concerned with a *notation* than with an "interval naming
system."

I just want a convenient notation that uses 12-tET as a base. I'm
willing to "bastardize" the pure interval nomenclature in order to
make it easier for the players, who are *used* to the "mistuned" 12-
tET intervals as the "normal" ones.

> But when they begin to work in Blackjack one should remind them that
> although the 12-tET major third is indeed a kind of major third
(namely a wide one) we now have a much better one available, an
essentially just one.

****It's only "better" if you except the premise that following the
overtone series is "better." Take Dan Stearns for example: he's
rather "anti overtone" sometimes. For him, Entropy with a big "E"
would be superior to Justice!

> You don't seem to have a problem with calling a 4:5 a just major
third.

****True

One synonym for "just" is "true". It is the 12-tET one that is the
> approximation, not the other way around.

*****If in my *notation* I use 12-tET as a base, I would prefer that
the just third be called:

A-JUST-ED... :)

I think most musicians are smart enough to understand this when it's
explained to them, even if they are 12-tET trained.

****Sure, they're "smart" enough, but they've practiced *ooodles* of
*12-tET* major thirds!

At least in this country's universities and conservatoria
> they are usually taught briefly about Just scales somewhere in their
> training.
>

****Brief is the word for it. I managed to get a so-
called "advanced" education and only encountered *any* of it in *one*
class, taught by John Clough!

>
> > > Should we refer to the 1/4 comma meantone major third (4:5) as
a
> > > twelfth-low major third too?
> >
> > ****I guess yes, if you were describing in in 72-tET.
>
> 72-tET or not is irrelevant.

****Dave, it's *not!* That's the system I'm using for my
*notation.* 72-tET is *never* irrevelant in these cases! :)

A thought experiment: Assume I have a keyboard
> tuned to a 12-note meantone, a little toward 1/3-comma from 1/4-
comma, so that its G:B interval is 383.33 cents (same as the G:Bv
interval in Blackjack). Let's say at first you don't even know how
the keyboard is tuned. I play that interval for you and ask you what
kind of third you think it is. What do you say? Then I lie and say
the keyboard is tuned in a subset of Blackjack. Now what do you call
that kind of interval? Then I tell you I lied and it is actually in a
meantone. What do you call it now? Will you ask, in each case, what
notation I am using for the pitches?

****Well, of course, I'm supposed to be *intimidated* by the meantone
example... :) but, frankly, I'm not "buying" it.

The reason is this: I don't believe *meantone* is notated very well,
either!

It brings around an interesting point that we were discussing with Ed
Foote, when he was talking about alternately tuned pianos. And, it
also brings about notation for *early* music.

How is much of this *notated?* It *isn't!* They just *play* the
pianos and harpsichords. Personally, I feel this is a *sloppy*
notation.... It works for past history, but we need more *precision*
if we are to develop accurate and scientific new systems for the
future!

>
> The underlying principle of the interval naming scheme I favour did
not originate with me, but apparently with Adriaan Fokker in the
1970s. It is also the one used in one of our most indispensable
tools, Scala.
>

****Well, now we're getting out the "heavy guns" but, still, my
players will prefer a notation based upon 12-tET. I *guarantee* it!

> The priciple is to associate an interval name with a particular
interval width (in cents or ratios), or a small range around that,
irrespective of what scale or tuning the interval is currently a part
of. The major third that is considered not to need a qualifier is the
simplest Just one (4:5) or the best approximation of it in a given
tuning (provided it is a good enough approximation).

****So? I *still* disagree with that terminology for didactic
purposes when teaching a player! Illogical, yes! Practical? Very!

>
> So Joseph and Paul, you are apparently the first to object to this
> principle in the history of this list. Why only now?
>
> > > You seem to be saying that G-Bv-D is a "correct" major triad,
but you want to call it a twelfth-low major triad. Seems a
> contradiction.
> >
> > ****Well, Dave, since the "B" is "modified" by a "v" it has to
> > be "altered" or "twelfth-low."
>
> Yes the pitch is notated as a twelfth-low B. But that doesn't have
to make the G:Bv interval (essentially a 4:5 in this case) a twelfth-
low major third, when it is in fact a just or true, major third.
>

****Why not, Dave? Then it corresponds with the *notation!* You
see, I feel that is the "root" of the disagreement. We *both* agree
on the *notation* but not on the nomenclature. I want the
nomenclature to mirror the *notation...*

> In thinking back over other recent posts of yours it becomes
apparent to me that you have a confusion between pitches and
intervals. For example you apparently assumed that because Blackjack
has 21 pitches per octave it must also have 21 kinds of interval per
octave, when in fact it has 41.

****Well, Dave, that was only because your chart seemed confusing,
and you have since clarified and elaborated on it, so you must have
thought the same thing! :)

>
> > So, yes, I prefer that G-B-D in
> > an "unaltered state" be our traditionally wide 12-tET triad.
>
> You said it! I totally agree. G:B:D in 6x12-notated Miracle
temperament represents a "wide" major triad. :-)

****So *that's* your *major third,* not your *AD-JUST-ED* major
third! :)

> >
> > The system that *you* would like where G-B-D *is* 4:5:6 is
> > essentially the system advocated by Ben Johnston and we've found
> > quite a few inconsistencies trying to reconcile that even to the
> > basic Pythagorean-based staff.
>
> Oh dear. Now your confusion of intervals and pitches causes you to
> misrepresent me.

****Are you sure that relates, Dave, or are you just "revving up" for
the kill here...? :)

[Thanks Paul for pointing this out while I was away]. I do
> _not_ want 4:5:6 (or its nearest approximation in a given tuning)
to be notated G:B:D except in temperaments where the syntonic comma
(80:81) vanishes, i.e. meantones.
>
> I have said before that I do not favour Ben Johnston's notation and
> consider that, in any tuning, the 7 nominals FCGDAEB should always
be applied to a chain of approximate 2:3's where these exist.
Otherwise modulation becomes too messy.
>
> >
> > ***Like I say, that's what Ben Johnston tries to do and he *does*
> > get performances. However he mostly *doesn't* get performances.
>
> No that's _not_ what Ben Johnston does. Or at least that's not what
Ben Johston does that's objectionable. Ben Johnston wants to notate
the pitches making up the major third as e.g. G:B. I want them
notated as e.g. G:Bv.
>

****So, we *totally* agree. I just want to call G:B a "major third
and you *don't.* And I want to call G:Bv *AD-JUST-ED..* :)

> > What I'm saying is very obvious and simple: just, for the
> notational
> > convenience, keep the 12-tET pitches *as is* since they are what
> > everybody has practiced and studied, and everything else is
> > a "deviation..."
>
> I totally agree (but perhaps for different reaszons). Note that
you're talking here about pitches and scores with notations for
pitches, not intervals or names for intervals.

****So that gets back to the *very beginning* of my post. *I'm* more
interested in NOTATION and making the nomenclature consistent with
the notation even if it "corrupts" the idea of the "pure" third as
the "real" one, and *you* don't feel it's necessary to have the
notation and the nomenclature work together.

When a player "ad-JUSTs" he makes a change, he plays the "adjusted"
one G:Bv and the notation *reflects that* just in the addition of
another character!

For me, in this "unreal" "funhouse" world, the corrupt is the true
(Enron?) and G:B *unadorned* is the "real" major third!

Joseph

Dave, all; see reply on metatuning.

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:

/tuning/topicId_33799.html#33818

> Dave, all; see reply on metatuning.
>
> -Carl

***What's the post number, Carl? I'm not seeing it...

JP

>>/tuning/topicId_33799.html#33818
>>
>>Dave, all; see reply on metatuning.
>
>***What's the post number, Carl? I'm not seeing it...

1738 -C.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ****Why not, Dave? Then it corresponds with the *notation!* You
> see, I feel that is the "root" of the disagreement. We *both*
agree
> on the *notation* but not on the nomenclature. I want the
> nomenclature to mirror the *notation...*

i agree with joseph that the interval nomenclature should mirror the
notation -- this is how musicians think, and thinking otherwise would
be kind of like asking a newscaster to learn japanese -- too big an
investment. dave, look at your wilber again. transcend and *include*,
transcend and *include* . . . western musicians have known, for as
long as the terms or their equivalents ('tertia', etc), that four
perfect fifths equals a major third . . . the terms are not ideal for
a system where 80:81 doesn't vanish, but correcting that would
involve, in my opinion, jettisoning the terms 'fifth' and 'third'
altogether . . . so best to leave well enough alone . . .

ideally, the ear training will teach that twelfth-tone alterations
are associated with the consonant ratios of 5, sixth-tone with 7, and
quartertone with 11 . . . the unaltered intervals
represent 'pythagorean', for example the tuning of the open strings
of string instruments . . . this seems clear, logical, consistent,
straighforward, and best of all, it *includes* all the standard
nomenclature and training within it, it doesn't throw any of that
away. this gives our proposal an *immeasurable* practical advantage
over yours.

> From: David C Keenan <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 07, 2002 5:07 PM
> Subject: [tuning] Naming intervals - size matters
>
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > /tuning/topicId_12590.html#33602
> >
> > >
> > > Er _which_ one are you calling the major triad here.
> > > For me, the only reason 0c:400c:700c is called a major
> > > triad in 12-tET is because it's an acceptable approximation
> > > _and_ it's the _only_ approximation available.
> >
> > ****Hi Dave.
> >
> > Sure, this is logically true. However, in the paragraph above you
> > say "the only reason Oc:400c:700c *is* called a major triad..."
> >
> > That's the crux of it. Whether it makes any sense or not that *is*
> > what it's called by almost all practicing musicians today, since
> > virtually *all* of them work in 12-tET.
>
> But when they begin to work in Blackjack one should remind them that
> although the 12-tET major third is indeed a kind of major third (namely a
> wide one) we now have a much better one available, an essentially just
one.
> You don't seem to have a problem with calling a 4:5 a just major third.
One
> synonym for "just" is "true". It is the 12-tET one that is the
> approximation, not the other way around. I think most musicians are smart
> enough to understand this when it's explained to them, even if they are
> 12-tET trained

but these musicians will never have to deal with a 400-cent
interval in blackjack! the only intervals near it that they
will ever get are 350, 383&1/3, and 433&2/3 cents!

> The priciple is to associate an interval name with a particular interval
> width (in cents or ratios), or a small range around that, irrespective of
> what scale or tuning the interval is currently a part of. The major third
> that is considered not to need a qualifier is the simplest Just one (4:5)
> or the best approximation of it in a given tuning (provided it is a good
> enough approximation).

i'm pretty sure i agree with you here, Dave.

> > > You seem to be saying that G-Bv-D is a "correct" major triad,
> > > but you want to call it a twelfth-low major triad. Seems a
> > > contradiction.
> >
> > ****Well, Dave, since the "B" is "modified" by a "v" it has to
> > be "altered" or "twelfth-low."
>
> Yes the pitch is notated as a twelfth-low B. But that doesn't have to make
> the G:Bv interval (essentially a 4:5 in this case) a twelfth-low major
> third, when it is in fact a just or true, major third.
>
> In thinking back over other recent posts of yours it becomes apparent to
me
> that you have a confusion between pitches and intervals. For example you
> apparently assumed that because Blackjack has 21 pitches per octave it
must
> also have 21 kinds of interval per octave, when in fact it has 41. This
> seems to be a common confusion, and there is no penalty for such confusion
> in 12-tET or indeed any equal temperament. Such confusion is encouraged by
> the I II III IV ... system for naming diatonic pitches independent of key.
> But if one is to break away from ETs it is a confusion that must be
overcome.

ah, Dave, i think you've hit on the origin of this kind of confusion.
I II III IV ... is an outgrowth of diatonic thinking, and the
problems with using successive numbers like that to describe
u n e q u a l scale steps is related to staff notation.

humans are often willing to slap a numbering system onto
anything which needs to be described in some kind of order,
without thinking thru all the ramifications of that numbering.

the problem comes in when the numbers are used for analytical
purposes which try to reduce everything to a single unit
basis for measurement. when calculating, we naturally think
of successive numbers as representing a continuous identical
increase.

but this is not the case with diatonic scale numbering!
the I II III IV... ignores the fact that some scale steps
are "whole steps" and some are "half steps", or in our
usual parlance here, some are L and some are s.

i think the quibbling now over what to call different
72edo "major 3rds" has its basis in this.

12edo-based thinking is simply an easy solution to this problem,
because for the diatonic scale it gives you s=1, L=2; in which
case, using Arabic numerals instead of Roman, it's much more
sensible to call the diatonic scale 0 2 4 5 7 9 11. but then,
of course, the diatonic logic is destroyed, because everything
is measured in terms of "half-steps", instead of the diatonic
"scale steps" which can be either "whole" or "half".

would harmonic analysis in blackjack employ Roman numerals
similarly to the way they're used in diatonic music? does the
decatonic blackjack "scale" really function as a scale the
same way the diatonic scale does in diatonic music?

> > So, yes, I prefer that G-B-D in
> > an "unaltered state" be our traditionally wide 12-tET triad.
>
> You said it! I totally agree. G:B:D in 6x12-notated Miracle temperament
> represents a "wide" major triad. :-)
>
> > > And so, you want to base your interval nomenclature on
> > > those that are out of tune? I still don't get it. Why?
> >
> > ****Why? Because that's what hoards of players in conservatories
> > and music schools have studied and are *used* to. And, I believe
> > that's what they are going to study for the conceivable future.
> > I haven't heard of any schools, except for isolated cases at
> > the New England Conservatory, to offer anything different.
> >
> > The system that *you* would like where G-B-D *is* 4:5:6 is
> > essentially the system advocated by Ben Johnston and we've found
> > quite a few inconsistencies trying to reconcile that even to the
> > basic Pythagorean-based staff.
>
> Oh dear. Now your confusion of intervals and pitches causes you to
> misrepresent me. [Thanks Paul for pointing this out while I was away]. I
do
> _not_ want 4:5:6 (or its nearest approximation in a given tuning) to be
> notated G:B:D except in temperaments where the syntonic comma (80:81)
> vanishes, i.e. meantones.
>
> I have said before that I do not favour Ben Johnston's notation and
> consider that, in any tuning, the 7 nominals FCGDAEB should always be
> applied to a chain of approximate 2:3's where these exist. Otherwise
> modulation becomes too messy.

and i certainly agree with that, too.

> > > I'd be saying to the musicians, "No. Not a 12-tET major third, we
> > > don't have to put up with that crap any longer. We want a real
> > > true just proper pure major third. You know, the kind you can tune by
> > > ear. The barbershop harmony kind. _That's_ what we call a major third
> > > in _this_ scale."
> >
> > ***Like I say, that's what Ben Johnston tries to do and he *does*
> > get performances. However he mostly *doesn't* get performances.
>
> No that's _not_ what Ben Johnston does. Or at least that's not what Ben
> Johston does that's objectionable. Ben Johnston wants to notate the
pitches
> making up the major third as e.g. G:B. I want them notated as e.g. G:Bv.
>
> > What I'm saying is very obvious and simple: just, for the
> notational
> > convenience, keep the 12-tET pitches *as is* since they are what
> > everybody has practiced and studied, and everything else is
> > a "deviation..."
>
> I totally agree (but perhaps for different reaszons). Note that you're
> talking here about pitches and scores with notations for pitches, not
> intervals or names for intervals.
>
> So I believe the rest of your objections to my _interval_naming_ scheme
> were irrelevant since I'm not talking about changing scores, except
perhaps
> some of the letters above guitar chord diagrams.

but here's the thing i'm totally puzzled about: why such a big
deal over how to label the blackjack interval measured as
3 secors + 1 quomma? it's darn close to the 5:4 ratio, and
the only other intervals which blackjack provides anywhere
near this are:

blackjack interval ~cents

3 secors (a "neutral 3rd") 350
3 secors + 2 quommas 417
{2 secors + 6 quommas 433
{4 secors - 1 quomma 433

i know that Joe Pehrson is concerned about having 12edo-trained
musicians be able to play his blackjack compositions, but the
400-cent "3rd" has nothing to do with blackjack, so why even
invoke it? i personally think that Graham's decimal notation
on a 4-line staff works much better with blackjack; see my example
at <http://www.ixpres.com/interval/monzo/blackjack/blackjack.htm>
and the links to Graham's pages. but i know Joe objects to that
because of the learning curve involved.

Joe, i understand your objections. but you're already using
a *notation* that's based on 12edo (by way of 72edo), so if
you write a piece of music in blackjack and put it in front
of a trained musician, s/he will play Bv a little flatter
than B, and you'll get something close to what you want.
but *since blackjack does not offer a 400-cent interval*,
what's the harm in calling that simply a "major 3rd"?

-monz

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In a message dated 2/8/02 9:59:11 PM Eastern Standard Time, joemonz@yahoo.com
writes:

> but these musicians will never have to deal with a 400-cent
> interval in blackjack! the only intervals near it that they
> will ever get are 350, 383&1/3, and 433&2/3 cents!
>
>
>

Joe, will these musicians ONLY play Blackjack? Would you have musicians
that know only one new tuning? If you want many musicians that can play in
many systems, then you need to keep the 400 cents as an anchor for the mind.
Instead of thinking with a bias either for or against conventional tuning,
try this: music is NEVER exactly played in 12-tET since expressivity is
added which means that notes have direction.

Thinking in 1200 is not thinking in 12. Playing a just third as -14 cents to
a standard will give every bit of 5/4. If individuals insist on changing the
rules for mapping microtonal intervals to the mind there will be more
provincialism if there are performances at all. I have available thousands
of musicians that can understand pitch deviations from a standard. New
notation, as entertaining as Gardner Read's book may be, will not aid in
performances, as easily as it can hinder.

Best, Johnny Reinhard

--- In tuning@y..., David C Keenan <d.keenan@u...> wrote:

/tuning/topicId_33799.html#33799

>
> In thinking back over other recent posts of yours it becomes
apparent to me that you have a confusion between pitches and
intervals. For example you apparently assumed that because Blackjack
has 21 pitches per octave it must also have 21 kinds of interval per
octave, when in fact it has 41. This seems to be a common confusion,
and there is no penalty for such confusion in 12-tET or indeed any
equal temperament. Such confusion is encouraged by the I II III
IV ... system for naming diatonic pitches independent of key. But if
one is to break away from ETs it is a confusion that must be overcome.
>

*****Hello Dave!

I wanted to "revisit" this part of your post again, because it was so
interesting. Actually, it *is* true I am mostly used to ETs (I mean
the "Earthly" kind) and, specially, of course 12-tET.

So your chart which initially showed 41 intervals at first looked
like "StudLoco" to me. However, after Paul Erlich pointed it out, I
quickly saw that the number of *pitches* and number of *intervals*
did not coincide. Your recent "elaboration" with "examples" on this
chart makes the intervallic situation now immediately clear.

Actually, the intervallic multiplicity seems like a real "feature"
not a "bug" of non-equal systems! :) My guess, and you can/should
correct me if I'm wrong, is that the doubling of the interval
possibilities results from the assymetry of the scale caused by the
presence of the *TWO LITTLE* 33-cent intervals right in a row
surrounding B[. That would result in *two different* intervals
associated with any one of the other pitches in the scale, correct?
Hence the "doubling..."

> >
> > The system that *you* would like where G-B-D *is* 4:5:6 is
> > essentially the system advocated by Ben Johnston and we've found
> > quite a few inconsistencies trying to reconcile that even to the
> > basic Pythagorean-based staff.
>
> Oh dear. Now your confusion of intervals and pitches causes you to
> misrepresent me. [Thanks Paul for pointing this out while I was
away]. I do _not_ want 4:5:6 (or its nearest approximation in a given
tuning) to be notated G:B:D except in temperaments where the syntonic
comma (80:81) vanishes, i.e. meantones.
>

***But does it really make sense to notate a 12-tET G:B the *same
way* as a 1/4 comma meantone G:B, for instance?

It would seem the notation would not be so specific in that case, yes?

In 72-tET, of course, the example in 1/4 comma meantone would be
close to the "altered" third: G:Bv

Glad we agree, on the overall, that notationed *pitches* aren't
affected by the difference in terminology.

Players think *pitches* not *intervals* when they play, anyway, or at
least they don't think consciously about what they're calling them!

:)

J. Pehrson

> From: <Afmmjr@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, February 09, 2002 7:50 AM
> Subject: Re: [tuning] Naming intervals - size matters
>
>
> In a message dated 2/8/02 9:59:11 PM Eastern Standard Time,
joemonz@yahoo.com
> writes:
>
>
> > but these musicians will never have to deal with a 400-cent
> > interval in blackjack! the only intervals near it that they
> > will ever get are 350, 383&1/3, and 433&2/3 cents!
>
> Joe, will these musicians ONLY play Blackjack? Would you have musicians
> that know only one new tuning? If you want many musicians that can play
in
> many systems, then you need to keep the 400 cents as an anchor for the
mind.
> Instead of thinking with a bias either for or against conventional tuning,
> try this: music is NEVER exactly played in 12-tET since expressivity is
> added which means that notes have direction.

thanks, Johnny ... i know that and agree with you; i was
more or less playing devil's advocate because i noticed that
there is no 400-cent "3rd" in blackjack. personally, for
MIRACLE i prefer canasta anyway, but that doesn't have it
either.

i advocate my own HEWM notation
<http://www.ixpres.com/interval/dict/hewm.htm>
above all others as a sort of "universal standard"
(and p l e a s e mind those quotes!).

but i suppose like many other theorists, i have a
keen interest in designing musical notations simply
for the mental puzzle it presents. i'm having fun.

-monz

_________________________________________________________
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--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_33799.html#33857

>
> would harmonic analysis in blackjack employ Roman numerals
> similarly to the way they're used in diatonic music? does the
> decatonic blackjack "scale" really function as a scale the
> same way the diatonic scale does in diatonic music?
>

****My *intuitive* feeling about this is that it doesn't quite. It
seems, from working with it, that the construction of the
scale "favors" certain harmonic progressions and sounds, and tends to
*push* things more in certain directions than the *global* kind of
transposibility and interconnectivity of 12-tET.

But that is just my impression by *sound* and practice, nothing I've
worked out mathematically. I'll let the cats on the "math list" do
that... :)

I guess that situation would probably pertain to *any* or rather
*many* *unequal* scales.

However, that's just great by me, because the harmonic progressions
are "similar but different" to 12-equal. There are recognizable
patterns that are *very* concordant because they're close to just of
course, but yet the way they work together is totally *ideosyncratic*
to Blackjack itself, so it's really *not* like 12-equal.

That's *great* for me, since I was looking for something "fresh" and
was, finally, quite tired of working in 12-equal. Frankly, I
wouldn't even know what I would want to do in it anymore.

Another great thing about Blackjack is the possibility of *really
strange* xenharmonic effects by the use of the various 33 cent
alterations of the small intervals.

So, while it can be quite concordant and seem to "mimic" 12-equal (of
course 12-equal was trying to "mimic" just ratios) it is still
xenharmonic and has lots of "little interval" effects in it.

What a great scale! I think Kraig Grady is right, though, and a
person should write *many* pieces in a given scale before moving to
something else. I'm still just *starting* to find my way with
Blackjack!

>
> Joe, i understand your objections. but you're already using
> a *notation* that's based on 12edo (by way of 72edo), so if
> you write a piece of music in blackjack and put it in front
> of a trained musician, s/he will play Bv a little flatter
> than B, and you'll get something close to what you want.
> but *since blackjack does not offer a 400-cent interval*,
> what's the harm in calling that simply a "major 3rd"?
>

*****As I said, Joe, in a previous post, it really doesn't make all
tha much difference to me, for the reason that you state above.

Players rarely think about the terminology of an interval when they
play...

best,

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., David C Keenan <d.keenan@u...> wrote:
> *****Hello Dave!
>
> I wanted to "revisit" this part of your post again, because it was
so
> interesting. Actually, it *is* true I am mostly used to ETs (I mean
> the "Earthly" kind) and, specially, of course 12-tET.
>
> So your chart which initially showed 41 intervals at first looked
> like "StudLoco" to me. However, after Paul Erlich pointed it out, I
> quickly saw that the number of *pitches* and number of *intervals*
> did not coincide. Your recent "elaboration" with "examples" on this
> chart makes the intervallic situation now immediately clear.
>
> Actually, the intervallic multiplicity seems like a real "feature"
> not a "bug" of non-equal systems! :) My guess, and you can/should
> correct me if I'm wrong, is that the doubling of the interval
> possibilities results from the assymetry of the scale caused by the
> presence of the *TWO LITTLE* 33-cent intervals right in a row
> surrounding B[. That would result in *two different* intervals
> associated with any one of the other pitches in the scale, correct?
> Hence the "doubling..."

Yes. That's certainly one way of looking at it.

> > >
> > > The system that *you* would like where G-B-D *is* 4:5:6 is
> > > essentially the system advocated by Ben Johnston and we've found
> > > quite a few inconsistencies trying to reconcile that even to the
> > > basic Pythagorean-based staff.
> >
> > Oh dear. Now your confusion of intervals and pitches causes you to
> > misrepresent me. [Thanks Paul for pointing this out while I was
> away]. I do _not_ want 4:5:6 (or its nearest approximation in a
given
> tuning) to be notated G:B:D except in temperaments where the
syntonic
> comma (80:81) vanishes, i.e. meantones.
> >
>
> ***But does it really make sense to notate a 12-tET G:B the *same
> way* as a 1/4 comma meantone G:B, for instance?

It does to me, and a helluva lot of other people.

> It would seem the notation would not be so specific in that case,
yes?
>
> In 72-tET, of course, the example in 1/4 comma meantone would be
> close to the "altered" third: G:Bv

Yes. But what is notated as B depends only on the chain of approximate
fifths, not whether it is near 4:5 or 400 cents or whatever.

> Glad we agree, on the overall, that notationed *pitches* aren't
> affected by the difference in terminology.
>
> Players think *pitches* not *intervals* when they play, anyway, or
at
> least they don't think consciously about what they're calling them!

I was aware of that, so wondered why the 12-tET-based interval naming
was so important to you.

Of course many guitar players think chords, not pitches.

> In a message dated 2/8/02 9:59:11 PM Eastern Standard Time,
joemonz@y...
> writes:
>
>
> > but these musicians will never have to deal with a 400-cent
> > interval in blackjack! the only intervals near it that they
> > will ever get are 350, 383&1/3, and 433&2/3 cents!

also 416 & 2/3 cents . . .

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 12:57 PM
> Subject: [tuning] Re: Naming intervals - size matters
>
>
> > In a message dated 2/8/02 9:59:11 PM EST, joemonz@y... writes:
> >
> >
> > > but these musicians will never have to deal with a 400-cent
> > > interval in blackjack! the only intervals near it that they
> > > will ever get are 350, 383&1/3, and 433&2/3 cents!
>
> also 416 & 2/3 cents . . .

hmm . . . i had noticed -- i thought it was before i sent it --
that i had left that one out. thought i'd added it in,
guess i didn't. thanks.

-monz

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Hi Margo,

You (and possibly Paul and Joseph) seem to have made a case for
calling anything from about 380 cents to about 440 cents an
(unqualified) major third merely because it is generated by a chain of
four approximate 2:3s in the particular tuning under consideration.

Whereas I would prefer to qualify those more than about 8 cents wider
than 4:5 with terms like equal, Pythagorean and septimal (as Scala
does), or in another system: wide, narrow-super, super. I'm happy to
drop the "wide"s and "narrow"s if a tuning only has one kind, but not
the "super"s.

So, Margo, Paul, Joseph or anyone,
How about neutral thirds? How do you define them? Does their size
depend on what scale they are in (e.g. how many whatevers generate
them) or how it is notated?

I'd say a good definition would be 351 +-8 cents.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_33799.html#33953

> > >
> >
> > ***But does it really make sense to notate a 12-tET G:B the *same
> > way* as a 1/4 comma meantone G:B, for instance?
>
> It does to me, and a helluva lot of other people.
>
> > It would seem the notation would not be so specific in that case,
> yes?
> >
> > In 72-tET, of course, the example in 1/4 comma meantone would be
> > close to the "altered" third: G:Bv
>
> Yes. But what is notated as B depends only on the chain of
approximate fifths, not whether it is near 4:5 or 400 cents or
whatever.
>

****Sure, that makes sense... but it might be nice if somebody were
to let us know the size of the fifth before we sit down at the
instrument... :)

JP