Apocalypse of the two (blackjack) elephants

We have done a marvelous job of agreeing on 72-tET notation in general. (Although I notice Graham has slipped back into using ^ and v, instead of the 72-tET-consistent > and <), as the accidentals for the decimal notation). I think it is time for us to go further and agree on a standard key for Blackjack within the larger 72-tET.

David Clark of MIT has a theory of standards that he calls "The apocalypse of the two elephants". It is illustrated by a graph of activity plotted against time. The curve has two humps (the two elephants).

When a subject is first discovered, there is an explosion of research activity consisting of papers, meetings and discussions. This eventually dies down. Some time later other people (or corporations) become convinced of its value, which leads to an explosion of investment activity.

It is essential that standards be created in the trough between the two "elephants". If they are written too early, before the research is finished, the subject may still be poorly understood, which leads to bad standards [of which, I must now admit, my original D-centered Blackjack proposal, is one].

If they are written too late, so many people may have already made major investments (of time and/or money) in so many different ways of doing the thing, that any standard will simply be ignored, no matter what benefits it might clearly offer.

If the interval between the two elephants is very short (because everyone is in too much of a hurry to get started) the standards will get crushed.

Notational standards are good because they facilitate communication and sharing of new discoveries.

We already have the problem of Joseph unable to make sense of Graham's chords. And we have Alison about to invest in instrument construction using a Blackjack key which is different to Joseph's and Graham's and mine [I know that's partly my fault]. We've got at least four different ways of doing it already.

Four different "languages" requires 6 different translations.

A <-> B
A <-> C
A <-> D
B <-> C
B <-> D
C <-> D

And trying to remember which "language" a particular person uses, is just a headache.

Even if a person chooses to continue using their own key privately (because they can't bear to give up their existing investment) they should at least be willing to use a standard key for communicating with others, assuming they agree that the standard has obvious benefits for newcomers.

Before we start proposing standards we should first discuss how we would know a good standard if we found it. What are the properties that we want of the standard Blackjack key when expressed in (ASCIIfied) Sims notation (I propose we leave decimal notation out of it for now).

The primary concern is that it should minimise the number of accidentals in actual music. But how can we predict what will be needed in actual music? My early D-centered proposal assumed all notes were equally likely and gave minimum accidentals with equal numbers of sharps and flats, in emulation of meantone notation. This was wrong.

Joseph's C-centered proposal seems to assume that the central note of the chain of secors, the one with the small scale steps on both sides of it, is in some sense a "tonic note" for Blackjack. This is wrong. It is certainly a note that is melodically distinguished when the complete Blackjack scale is played, but in actual music, using relatively consonant chords and subset scales capable of forming a melodic gestalt, this note may in fact be the _least_ used! But I agree that our standard Blackjack key _should_ contain a C natural (somewhere) if possible.

If Alison's major requirements are (correct me if I'm wrong) that it have an A natural in it (for tuning reference), and that it contain a major diatonic with no second that is notated with the maximum number of natural notes, then there are several to choose from, one of which should satisfy everyone else too. I suppose also, that Alison wants those instruments built with only subsets of Blackjack to have maximum naturals too. Don't start building those instruments just yet Alison. :-)

So I think we have enough knowledge about the available chords and subset scales now to be able to see how often a given Blackjack key is likely to allow us to use naturals.

The first thing to note is that the naturals must form a single chain of fifths in blackjack. The longest such chain available in blackjack has 4 notes in it. It can occur in 1 of 3 positions. Most relatively consonant chords and most subset scales, will contain fifths. We would prefer to have the _roots_ of chords in particular, being naturals as often as possible. The root will usually be the "lowest" note in any chain of fifths the chord contains.

It also wouldn't hurt if the note most likely to be the root of a consonant chord or the tonic of a subset scale, was a C, or after Partch a G, but this is not essential.

Chain of 21 secors
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
Maximal chains of four fifths
+-----------------+-----------------+-----------------+
+-----------------+-----------------+-----------------+
+-----------------+-----------------+-----------------+
JI Major scales with no second
+-----------------+--+--------------+--T-----------------+
+-----------------+--+--------------+--T-----------------+
JI Minor scales with no fourth
T-----------------+--+--------------+--+-----------------+
T-----------------+--+--------------+--+-----------------+
Maximally consonant chords
5--------------7-----1----otonal-------3-----------------9
5--------------7-----1----otonal-------3-----------------9
1/9---------------1/3------utonal---1/1---1/7------------1/5
1/9---------------1/3------utonal---1/1---1/7------------1/5

I think there's enough information there for anyone to figure out which chain of four fifths should have the naturals, and what those naturals should be. One of us has apparently already figured this out and is already using the resulting key.

By the way Joseph, heres a translation from Graham's to yours. But I think Graham made some typos in some of those chords because the decimal notation doesn't always agree with the Sims notation.

Here they are as chains of secors.

Graham Breed's Blackjack key
Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^
C> D[Eb< Ev F Gb^ G> A[Bb< Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<
Joseph Pehrson's Blackjack key

And now in pitch order.

Graham
Joseph
G A[
G#v A>
Ab^ Bb<
A B[
A> Bv
Bb^ C<
B[ C
Bv C>
C< Db^
C D[
C#v D>
Db^ Eb<
D E[
D> E
Eb^ F<
E[ F
E> F#v
F< Gb^
F] G
F#v G>
G< Ab^

Notice something about Graham's key? Wherever there's a # there's a v next to it and wherever there's a b there's a ^ next to it. So the ^ and v could be omitted if the player was told that # means 5/12 tone sharp and b means 5/12 tone flat. Then we'd never need more than one accidental per note. This isn't the _only_ Blackjack key that has this property. I challenge you to find another.

By the way Alison, here's Graham's key in Hertz.

Name Frequency
(hertz)
----------------
G 195.998
G#v 205.663
Ab^ 209.661
A 220.000
A> 224.277
Bb^ 235.337
B[ 239.912
Bv 244.576
C< 256.636
C 261.626
C#v 274.527
Db^ 279.864
D 293.665
D> 299.374
Eb^ 314.137
E[ 320.244
E> 336.036
F< 342.568
F] 359.461
F#v 366.450
G< 384.520
(G) 391.995

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30143.html#30143

Hello Dave!

A "white elephant" is an American expression, maybe English, of
something out of date. Perhaps you have that expression in Australia
too.

Well, I don't want to be one of those... :)

My point is that I am fully willing to adopt *whatever* convention
the consensus of thinking (hopefully) comes to.

In fact, I would even re-mark *all* the little color stickers on my
full-length synth keyboard... and that's a sacrifice! :)

So I'm all for further developments in this matter and will "convert"
if the standard definitely becomes settled...

>
> It is essential that standards be created in the trough between the
two "elephants". If they are written too early, before the research
is finished, the subject may still be poorly understood, which leads
to bad standards [of which, I must now admit, my original D-centered
Blackjack proposal, is one].
>

It appears you are saying that your original D-centered scale was not
the optimal one. I'm inferring that Graham Breed figured out the
optimal one. Eventually, I'm going to have to get all of this
straight! :)

>
> Notational standards are good because they facilitate communication
and sharing of new discoveries.
>

I'm all for getting this eventually pinned down. However, as you
know, and as Margo Schulter has mentioned on this list, the
gravitational pull of "C" [even moreso, "big daddy" MIDDLE C] has a
profound influence on our Western musical culture.

I particularly like the fact that the "middle C" on my keyboard
matches that of my traditional piano in 12-tET.

However, if "D" would have to be my standard, I guess I could live
with it, but I think the reasons would have to be pretty
significant...

> We already have the problem of Joseph unable to make sense of
Graham's chords. And we have Alison about to invest in instrument
construction using a Blackjack key which is different to Joseph's and
Graham's and mine [I know that's partly my fault]. We've got at least
four different ways of doing it already.
>

It would be difficult for me to argue that this situation is
good... :)

> Before we start proposing standards we should first discuss how we
would know a good standard if we found it.

Now, that might be good... :)

>
> The primary concern is that it should minimise the number of
accidentals in actual music. But how can we predict what will be
needed in actual music? My early D-centered proposal assumed all
notes were equally likely and gave minimum accidentals with equal
numbers of sharps and flats, in emulation of meantone notation. This
was wrong.
>
> Joseph's C-centered proposal seems to assume that the central note
of the chain of secors, the one with the small scale steps on both
sides of it, is in some sense a "tonic note" for Blackjack. This is
wrong. It is certainly a note that is melodically distinguished when
the complete Blackjack scale is played, but in actual music, using
relatively consonant chords and subset scales capable of forming a
melodic gestalt, this note may in fact be the _least_ used! But I
agree that our standard Blackjack key _should_ contain a C natural
(somewhere) if possible.
>

Well, I can see what you're saying, and C hasn't become "tonicized"
in my Blackjack writing so far, but I think, quite frankly, I am more
concerned about "middle C" being "middle C" on the standard piano
than that the two small scale steps have to surround it... if that's
any help... I understand that Allison wants the standard of "A" for
the same reason...

> >
> The first thing to note is that the naturals must form a single
chain of fifths in blackjack. The longest such chain available in
blackjack has 4 notes in it. It can occur in 1 of 3 positions. Most
relatively consonant chords and most subset scales, will contain
fifths. We would prefer to have the _roots_ of chords in particular,
being naturals as often as possible. The root will usually be
the "lowest" note in any chain of fifths the chord contains.
>
>
> By the way Joseph, heres a translation from Graham's to yours. But
I think Graham made some typos in some of those chords because the
decimal notation doesn't always agree with the Sims notation.

Thanks for this "translation." Graham had some great chords, so this
will be useful...

>
> Here they are as chains of secors.
>
> Graham Breed's Blackjack key
> Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^
> C> D[Eb< Ev F Gb^ G> A[Bb< Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<
> Joseph Pehrson's Blackjack key

Now don't go calling it "my" key until all the results are in! I
just don't know any better! :) As I say, I am more than willing to
change if it's valuable enough to do so. That would be the *key*
(literally!)

>
> And now in pitch order.
>
> Graham
> Joseph
> G A[
> G#v A>
> Ab^ Bb<
> A B[
> A> Bv
> Bb^ C<
> B[ C
> Bv C>
> C< Db^
> C D[
> C#v D>
> Db^ Eb<
> D E[
> D> E
> Eb^ F<
> E[ F
> E> F#v
> F< Gb^
> F] G
> F#v G>
> G< Ab^
>

I believe there is a tiny error here, since I don't have an E. I
believe it should be Ev.

In "my" system, there are three naturals, and in Graham's there
appear to be only FOUR.... so that's only an addition of *one* more
natural. (Better check my math on that, Dave...)

> Notice something about Graham's key? Wherever there's a # there's a
v next to it and wherever there's a b there's a ^ next to it. So the
^ and v could be omitted if the player was told that # means 5/12
tone sharp and b means 5/12 tone flat. Then we'd never need more than
one accidental per note.

Well, quite frankly, I see a tiny problem with this. I think one of
the great "virtues" of Blackjack is that it's a subset of 72-tET, and
one of the great virtues of 72-tET is that it *contains* 12-tET in
all it's glory... So, I would prefer leaving the "original" sharps
and flats of 12 and 72-tET intact and just "add on" from there. In
that sense, I find the "double accidentals" actually *simpler!*

This isn't the _only_ Blackjack key that has this property. I
challenge you to find another.
>

I think I may let Paul do that.... :)

Thanks again, and I assure everybody that *I* will never be the
impediment to progress...

HOWEVER, that being said, and my desire to have consistent "middle
C's" being said I will need:

1) A converted "color sticker" keyboard... I'll do that

2) A converted visual Blackjack lattice of Paul's design, that I use
all the time.

3) The 10 pages or so of Blackjack chords that Paul made all
converted (parallel chords) since I use those all the time, too.

4) The conversion of about 20 to 30 Tuning List posts related to
my "former" key in Blackjack that I frequently use...

Whew!... This had better be worth it, Dave.

So far, Paul Erlich has "weighed in" on the fact that the conversion
isn't really worth the effort, at least that's been my impression.
(I could be mistaken).

So, Paul would have to thrash it out and be convinced first, and then
help me reconstruct all these composing tools.

Then, I guess we would have the "gold standard..." but nobody seems
convinced so far... ?? :)

Thanks!!!

Joseph

David C Keenan wrote:

> It is essential that standards be created in the trough between the two "elephants". If they are written too early, before the research is finished, the subject may still be poorly understood, which leads to bad standards [of which, I must now admit, my original D-centered Blackjack proposal, is one].
>
> If they are written too late, so many people may have already made major investments (of time and/or money) in so many different ways of doing the thing, that any standard will simply be ignored, no matter what benefits it might clearly offer.

That's nearly me but I'd be willing to call it R&D time.

>
> Even if a person chooses to continue using their own key privately (because they can't bear to give up their existing investment) they should at least be willing to use a standard key for communicating with others, assuming they agree that the standard has obvious benefits for newcomers.

I agree entirely with the principle of a standard. It might encourage the exchange of scores in the future.

> Before we start proposing standards we should first discuss how we would know a good standard if we found it. What are the properties that we want of the standard Blackjack key when expressed in (ASCIIfied) Sims notation (I propose we leave decimal notation out of it for now).

1. Ease of use for the composer - that means for those of us like Joseph who exploits his familiarity with a standard keyboard and likes his middle C and those of us like myself who want an A natural at A440 in order to have a clear point of connection at afuture date with 'conventional' string, wind and brass players. I would tend to agree with Joseph that from the working composer's point of view it does matter that we have a 'tonic' with the small step on either side. He's chosen C. I chose A, then changed to F] .

Having said that, I'm not too clear in my own mind as to the relevance of 'key' and 'tonic' in most of my own music. I don't follow common practice tonal musical structures and therefore fast and elaborate modulations are not part of my language. There might be composers out there who like to know what 'key' they are in and they might have different notational needs from me.

2. Ease of use by the player. I know that I'm going to have to do a lot of persuasive dancing around with performers. A clear, logical and consistent notation will help to bridge the 'fear of the new' gap that we all have to cross in new music ventures. An orchestral percussionist faced with 36 steel tubes tuned to a subset of 72et should have as many familiar points of reference as possible.

> The primary concern is that it should minimise the number of accidentals in actual music. But how can we predict what will be needed in actual music? My early D-centered proposal assumed all notes were equally likely and gave minimum accidentals with equal numbers of sharps and flats, in emulation of meantone notation. This was wrong.
>
> Joseph's C-centered proposal seems to assume that the central note of the chain of secors, the one with the small scale steps on both sides of it, is in some sense a "tonic note" for Blackjack. This is wrong. It is certainly a note that is melodically distinguished when the complete Blackjack scale is played, but in actual music, using relatively consonant chords and subset scales capable of forming a melodic gestalt, this note may in fact be the _least_ used! But I agree that our standard Blackjack key _should_ contain a C natural (somewhere) if possible.
>
> If Alison's major requirements are (correct me if I'm wrong) that it have an A natural in it (for tuning reference), and that it contain a major diatonic with no second that is notated with the maximum number of natural notes, then there are several to choose from, one of which should satisfy everyone else too. I suppose also, that Alison wants those instruments built with only subsets of Blackjack to have maximum naturals too. Don't start building those instruments just yet Alison. :-)

I don't need the major diatonic with no second. That was a misunderstanding. I do want the A natural though. The strings are strung and tuned to their various subsets. They can be retuned because a shift to a new standard shouldn't involve any drastic changes. As for the fixed pitch department I've cut and tuned a few tubes but I've enough steel for a full set so I can hold on for some discussion on a new standard.

>
> By the way Alison, here's Graham's key in Hertz.
>
> Name Frequency
> (hertz)
> ----------------
> G 195.998
> G#v 205.663
> Ab^ 209.661
> A 220.000
> A> 224.277
> Bb^ 235.337
> B[ 239.912
> Bv 244.576
> C< 256.636
> C 261.626
> C#v 274.527
> Db^ 279.864
> D 293.665
> D> 299.374
> Eb^ 314.137
> E[ 320.244
> E> 336.036
> F< 342.568
> F] 359.461
> F#v 366.450
> G< 384.520
> (G) 391.995
>
> Regards,
> -- Dave Keenan
> Brisbane, Australia
> http://dkeenan.com

Thanks Dave for starting this one off. I look forward to the ongoing discussion.

Kind Regards