Updated version of Hex available

Hi all - a quick "announcement" that might be of interest (software is
available at www.dynamictonality.com <http://www.dynamictonality.com> )
...

To coincide with the publication of our Computer Music Journal article
about Hex, we have a new version (v1.5)
<http://www.dynamictonality.com/hex.htm> available with some
significant updates.
Hex is a free MIDI sequencer designed to make sequencing music in and
across a large variety of novel tunings as straightforward as it is in
twelve-tone equal temperament. It replaces the piano roll used in
conventional MIDI sequencers with a two-dimensional lattice roll in
order to enable the intuitive visualization and dynamic manipulation of
tuning. It is compatible with the Dynamic Tonality
synths—TransFormSynth, The Viking, and 2032—and, for static
tunings, with any synthesizer that handles channel pitch bend.
The updates include:
- The lattice now shears, rather than rotates, when the tuning is
changed. This looks much neater—particularly for more "extreme"
tunings! - The use of shear means that octaves are always vertically
aligned. It also means that, in addition to vertical distance on the
lattice being proportional to pitch, horizontal distance is proportional
to distance along the cycle of (pseudo-) fifths. - Adjacent Predominant
Seconds (APS) layouts* are now available for any MOS scale** with
nineteen or fewer tones. You choose an MOS scale by selecting its number
of large and small steps in the Setup window, then click on "APS" to
display the appropriate APS note layout for that scale. - Hex now
supports microtonal pitches for standard multitimbral synths. In Setup,
you can select either "DT" (for a Dynamic Tonality synth, like 2032) or
"std" (for a standard multitimbral synth, like the synths built into
Windows and OS X, or SimpleSynth, or Virsyn Tera, etc.). In both cases,
the tones are played at the correct microtonal pitches. When using a
non-DT multitimbral synth, Hex uses pitch bend to get the correct
microtonal pitches. - You can play the hexagons by clicking on them with
a mouse (or finger, if you have a tablet). This is a great way to find
the correct pitch when composing in an unfamiliar scale or tuning. -
Various other small enhancements...
If you want to know more about Hex and its new features, please check
out the CMJ article <http://www.mitpressjournals.org/toc/comj/36/1> or
the free preprint
<http://open.academia.edu/AndrewMilne/Papers/1002899/A_MIDI_sequencer_th\
at_widens_access_to_the_compositional_possibilities_of_novel_tunings> .
* APS layouts are isomorphic generalizations of the Wicki layout, and
are applicable to any MOS scale. In an APS layout, the most common
(predominant) steps (e.g., diatonic wholetones) run along rows, while
the less common steps (e.g., diatonic semitones) are given by a
"carriage return" to the next row above. To learn more about APS
layouts, try the above-mentioned CMJ paper.
** MOS scales (also known as well-formed) have only two steps sizes that
are evenly distributed. Familiar examples are the pentatonic and
diatonic scales—the first has 2 large steps and 3 small, the second
has 5 large steps and 2 small—but there are numerous unfamiliar
possibilities that may hold great musical potential. For a technical
discussion of MOS scales, try our paper Scratching The Scale Labyrinth
<http://www.springerlink.com/content/n257556xw8390457/?CFID=70130633&CFT\
OKEN=29786250> or the free preprint
<http://open.academia.edu/AndrewMilne/Papers/547613/Scratching_the_scale\
_labyrinth> .

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
> Hi all - a quick "announcement" that might be of interest (software is
> available at www.dynamictonality.com <http://www.dynamictonality.com> )
> ...
>
> To coincide with the publication of our Computer Music Journal article
> about Hex, we have a new version (v1.5)
> <http://www.dynamictonality.com/hex.htm> available with some
> significant updates.

Any prospects for running on Linux?

Keenan

There we go, Mike; they are officially "APS layouts". -Carl

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

> * APS layouts are isomorphic generalizations of the Wicki
> layout, and

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> >
> > Hi all - a quick "announcement" that might be of interest (software is
> > available at www.dynamictonality.com <http://www.dynamictonality.com> )
> > ...
> >
> > To coincide with the publication of our Computer Music Journal article
> > about Hex, we have a new version (v1.5)
> > <http://www.dynamictonality.com/hex.htm> available with some
> > significant updates.
>
> Any prospects for running on Linux?
>
> Keenan
>

We are currently working a on a new version built within the QuickTime SDK. In theory, this should be usable on Linux, Android, Windows, and OS X. But no promises - it's still early days...

Andy

I think these are generalized Wicki layouts. Note the bit he said
about the "carriage return" and all that. The thing I was talking
about had all seconds adjacent. Like this

http://www.h-pi.com/images/mmBosanquet.gif

Andy, what would you call this sort of layout, but generalized for any
MOS? Something where we lay the whole thing out diagonally.

-Mike

On Fri, Mar 2, 2012 at 1:25 AM, Carl Lumma <carl@...> wrote:
>
> There we go, Mike; they are officially "APS layouts". -Carl
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
> > * APS layouts are isomorphic generalizations of the Wicki
> > layout, and

It might be fun to generalize some of the properties of the Bosanquet layout too.

Andy

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> There we go, Mike; they are officially "APS layouts". -Carl
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > * APS layouts are isomorphic generalizations of the Wicki
> > layout, and
>

On Fri, Mar 2, 2012 at 3:03 AM, andymilneuk <ANDYMILNE@...>
wrote:
>
> It might be fun to generalize some of the properties of the Bosanquet
> layout too.
>
> Andy

Yes! That's what I want. What's this called?

-Mike

Mike - That was good timing! I agree that in the Bosanquet the "carriage return" does not occur - you go up to the next row and continue the left-right trajectory. I'm also not sure if buttons separated by the most numerous steps are adjacent in the same way they are in Wicki - if you use a "proper" hexagonal lattice I think only the vertices are adjacent not the edges. But I may be wrong, I only had a brief look at this some time ago...

Andy

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I think these are generalized Wicki layouts. Note the bit he said
> about the "carriage return" and all that. The thing I was talking
> about had all seconds adjacent. Like this
>
> http://www.h-pi.com/images/mmBosanquet.gif
>
> Andy, what would you call this sort of layout, but generalized for any
> MOS? Something where we lay the whole thing out diagonally.
>
> -Mike
>
>
> On Fri, Mar 2, 2012 at 1:25 AM, Carl Lumma <carl@...> wrote:
> >
> > There we go, Mike; they are officially "APS layouts". -Carl
> >
> > --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> >
> > > * APS layouts are isomorphic generalizations of the Wicki
> > > layout, and
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 3:03 AM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > It might be fun to generalize some of the properties of the Bosanquet
> > layout too.
> >
> > Andy
>
> Yes! That's what I want. What's this called?
>
> -Mike
>

I haven't given it a name. But first, it would need to be properly defined (its salient properties identified), and then checked to see if those properties can be carried across to any arbitrary MOS.

Andy

On Fri, Mar 2, 2012 at 3:09 AM, andymilneuk <ANDYMILNE@...>
wrote:
>
> Mike - That was good timing! I agree that in the Bosanquet the "carriage
> return" does not occur - you go up to the next row and continue the
> left-right trajectory. I'm also not sure if buttons separated by the most
> numerous steps are adjacent in the same way they are in Wicki - if you use a
> "proper" hexagonal lattice I think only the vertices are adjacent not the
> edges. But I may be wrong, I only had a brief look at this some time ago...

What do you mean by this? I'm not sure we're talking about the same thing.

Let's say your three hexagonal unit vectors are called up/down,
up-right/down-left, and up-left/down-right. I'm talking about the
layout where you map one size of second to the "up-right" direction,
and another one to the "down-right" direction. Any affine
transformation of this layout also counts. You can see that the whole
thing will end up tracing out some kind of diagonal line for any MOS.

> I haven't given it a name. But first, it would need to be properly defined
> (its salient properties identified), and then checked to see if those
> properties can be carried across to any arbitrary MOS.

Well, I hope the above definition says it all. I guess the simplest
way to put it is to set the layout up so that two of the three
hexagonal unit vectors correspond to different seconds in the MOS, and
the last one corresponds to the chroma for that MOS (e.g. L-s).

In other words, you want to set it up so that two of your vectors
correspond to the two seconds, and make sure that the way you do it
has it so that the remaining unit vector is not a "third."

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 3:09 AM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > Mike - That was good timing! I agree that in the Bosanquet the "carriage
> > return" does not occur - you go up to the next row and continue the
> > left-right trajectory. I'm also not sure if buttons separated by the most
> > numerous steps are adjacent in the same way they are in Wicki - if you use a
> > "proper" hexagonal lattice I think only the vertices are adjacent not the
> > edges. But I may be wrong, I only had a brief look at this some time ago...
>
> What do you mean by this? I'm not sure we're talking about the same thing.
>
> Let's say your three hexagonal unit vectors are called up/down,
> up-right/down-left, and up-left/down-right. I'm talking about the
> layout where you map one size of second to the "up-right" direction,
> and another one to the "down-right" direction. Any affine
> transformation of this layout also counts. You can see that the whole
> thing will end up tracing out some kind of diagonal line for any MOS.
>
> > I haven't given it a name. But first, it would need to be properly defined
> > (its salient properties identified), and then checked to see if those
> > properties can be carried across to any arbitrary MOS.
>
> Well, I hope the above definition says it all. I guess the simplest
> way to put it is to set the layout up so that two of the three
> hexagonal unit vectors correspond to different seconds in the MOS, and
> the last one corresponds to the chroma for that MOS (e.g. L-s).
>
> In other words, you want to set it up so that two of your vectors
> correspond to the two seconds, and make sure that the way you do it
> has it so that the remaining unit vector is not a "third."
>
> -Mike
>

OK, that's a nice clear definition. It's not quite what I was thinking (I was thinking of one second being mapped to the up-down vector, the other to the up-left, or something like that!). I can look into implementing generalizations of such layouts in a future version of Hex, time allowing, etc....

On Fri, Mar 2, 2012 at 4:08 AM, andymilneuk <ANDYMILNE@...>
wrote:
>
> OK, that's a nice clear definition. It's not quite what I was thinking (I
> was thinking of one second being mapped to the up-down vector, the other to
> the up-left, or something like that!). I can look into implementing
> generalizations of such layouts in a future version of Hex, time allowing,
> etc....

I think that'd still be the same thing, right? If one vector is up,
and the other is up-left, then you'll end up having all seconds being
unit vectors, and the remaining unit vector will be a chroma (and not
a third). It's equivalent to my up-right/down-right thing up to affine
transformation, which is good enough for me.

Anyway, this is by far my favorite layout for generalized keyboards,
because it makes melodies insanely easy to play. The diatonic-sized
scale is right there in quasi-linear fashion, and then the next MOS up
tends to "cluster" around that MOS (take a look at some examples to
see what I mean). And then, to top it off, chords are still isomorphic
and usually not that bad. Can't go wrong there (except that it's not
very "compact", unfortunately).

-Mike

> We are currently working a on a new version built within the
> QuickTime SDK. In theory, this should be usable on Linux,
> Android, Windows, and OS X. But no promises - it's still
> early days...
>
> Andy

You mean QT (not QuickTime), right? -Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I think these are generalized Wicki layouts. Note the bit he said
> about the "carriage return" and all that. The thing I was talking
> about had all seconds adjacent. Like this
>
> http://www.h-pi.com/images/mmBosanquet.gif

You keep linking to this file even though it's completely
unlabeled! If you're talking about the white notes, they
have a very clear carriage return.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 4:08 AM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > OK, that's a nice clear definition. It's not quite what I was thinking (I
> > was thinking of one second being mapped to the up-down vector, the other to
> > the up-left, or something like that!). I can look into implementing
> > generalizations of such layouts in a future version of Hex, time allowing,
> > etc....
>
> I think that'd still be the same thing, right? If one vector is up,
> and the other is up-left, then you'll end up having all seconds being
> unit vectors, and the remaining unit vector will be a chroma (and not
> a third). It's equivalent to my up-right/down-right thing up to affine
> transformation, which is good enough for me.

I'd be inclined to call them different layouts because, on any given hex lattice, the arrangement of tones of any given MOS would not be the same when moving from one mapping to the other.

>
> Anyway, this is by far my favorite layout for generalized keyboards,
> because it makes melodies insanely easy to play. The diatonic-sized
> scale is right there in quasi-linear fashion, and then the next MOS up
> tends to "cluster" around that MOS (take a look at some examples to
> see what I mean). And then, to top it off, chords are still isomorphic
> and usually not that bad. Can't go wrong there (except that it's not
> very "compact", unfortunately).
>
> -Mike
>

We need a 3ft by 1ft tablet :-)

Andy

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
> Mike - That was good timing! I agree that in the Bosanquet the
> "carriage return" does not occur - you go up to the next row
> and continue the left-right trajectory. I'm also not sure if
> buttons separated by the most numerous steps are adjacent in
> the same way they are in Wicki - if you use a "proper" hexagonal
> lattice I think only the vertices are adjacent not the edges.
> But I may be wrong, I only had a brief look at this some
> time ago...
>
> Andy

What angle counts as a carriage return then? -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > We are currently working a on a new version built within the
> > QuickTime SDK. In theory, this should be usable on Linux,
> > Android, Windows, and OS X. But no promises - it's still
> > early days...
> >
> > Andy
>
> You mean QT (not QuickTime), right? -Carl
>

Oh dear, have I committed an Apple faux pas?

> > > We are currently working a on a new version built within the
> > > QuickTime SDK. In theory, this should be usable on Linux,
> > > Android, Windows, and OS X. But no promises - it's still
> > > early days...
> > >
> > > Andy
> >
> > You mean QT (not QuickTime), right? -Carl
>
> Oh dear, have I committed an Apple faux pas?

QT and QuickTime are unrelated. -Carl

On Fri, Mar 2, 2012 at 4:32 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I think these are generalized Wicki layouts. Note the bit he said
> > about the "carriage return" and all that. The thing I was talking
> > about had all seconds adjacent. Like this
> >
> > http://www.h-pi.com/images/mmBosanquet.gif
>
> You keep linking to this file even though it's completely
> unlabeled! If you're talking about the white notes, they
> have a very clear carriage return.

Huh? It's labeled "Bosanquet" on the side of the picture. The carriage
return that Andy's talking about is from the wicki layout, which is
this

http://en.wikipedia.org/wiki/File:Wicki-Hayden_Musical_Note_Layout.png

You can see the actual "carriage return" style break from E to F,
because it doesn't just skip a line, but moves all the way over
horizontally as well.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> >
> > Mike - That was good timing! I agree that in the Bosanquet the
> > "carriage return" does not occur - you go up to the next row
> > and continue the left-right trajectory. I'm also not sure if
> > buttons separated by the most numerous steps are adjacent in
> > the same way they are in Wicki - if you use a "proper" hexagonal
> > lattice I think only the vertices are adjacent not the edges.
> > But I may be wrong, I only had a brief look at this some
> > time ago...
> >
> > Andy
>
> What angle counts as a carriage return then? -Carl
>

The "return" takes you to one of the two buttons that are on the row above and adjacent to the button that starts the run of most numerous steps.

On Fri, Mar 2, 2012 at 4:33 AM, andymilneuk <ANDYMILNE@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I think that'd still be the same thing, right? If one vector is up,
> > and the other is up-left, then you'll end up having all seconds being
> > unit vectors, and the remaining unit vector will be a chroma (and not
> > a third). It's equivalent to my up-right/down-right thing up to affine
> > transformation, which is good enough for me.
>
> I'd be inclined to call them different layouts because, on any given hex
> lattice, the arrangement of tones of any given MOS would not be the same
> when moving from one mapping to the other.

Aren't these two layouts literally just rotated versions of one another?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 4:33 AM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > I think that'd still be the same thing, right? If one vector is up,
> > > and the other is up-left, then you'll end up having all seconds being
> > > unit vectors, and the remaining unit vector will be a chroma (and not
> > > a third). It's equivalent to my up-right/down-right thing up to affine
> > > transformation, which is good enough for me.
> >
> > I'd be inclined to call them different layouts because, on any given hex
> > lattice, the arrangement of tones of any given MOS would not be the same
> > when moving from one mapping to the other.
>
> Aren't these two layouts literally just rotated versions of one another?
>
> -Mike
>

Given a pre-existing physical lattice (that cannot be scaled and sheared, but can be rotated), I don't see how they can be the same. In "my" layout one step size is given by hexagons with adjacent edges, the other step size by hexagons that share only a vertex. In "your" layout, both step sizes are given by hexagons that share edges. Unless, of course, I'm misunderstanding something.

Mike wrote:

> > > http://www.h-pi.com/images/mmBosanquet.gif
> >
> > You keep linking to this file even though it's completely
> > unlabeled! If you're talking about the white notes, they
> > have a very clear carriage return.
>
> Huh? It's labeled "Bosanquet" on the side of the picture.

I don't know what that means.

> You can see the actual "carriage return" style break from E to F,
> because it doesn't just skip a line, but moves all the way over
> horizontally as well.

Ok, so for APS the common step has to be one unit on the
keyboard and the rare step has to be one unit *from the
tonic*? The Hex preprint says,

"In any APS layout, the most numerous (i.e., predominant)
scale steps—whether they be large or small—always correspond
to movement along rows, and the least numerous scale steps
always correspond to "carriage returns.""

To me this would include your .gif. It continues

"There is only one such APS layout for each MOS scale,"

Even with the more specific APS definition I suggest above
I don't think this is true.

-Carl

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

>
> Ok, so for APS the common step has to be one unit on the
> keyboard and the rare step has to be one unit *from the
> tonic*? The Hex preprint says,
>
> "In any APS layout, the most numerous (i.e., predominant)
> scale steps—whether they be large or small—always correspond
> to movement along rows, and the least numerous scale steps
> always correspond to "carriage returns.""

The most numerous steps run along rows (each tone is adjacent). At the end of the row, the least numerous step (the "carriage return") leads to a button that is on the row above and adjacent to the first button of the first row.

>
> "There is only one such APS layout for each MOS scale,"
>
> Even with the more specific APS definition I suggest above
> I don't think this is true.

The large and small steps are distributed with maximal evenness in an MOS. This implies that the runs (rows) of most numerous steps have just two different lengths (n and n+1). For example, in the pentatonic scales, there are rows of length 2 and length 3 that alternate; in the diatonic, the rows have lengths 4 and 3 alternating; in the 4L, 3s scale, the rows have length 3 and 2 (there is one row of 3, then 2 rows of 2). These n and n+1 row lengths occur for all MOS scales.

Assuming the rows run from left to right, this means that at the end of a short run (of length n) the carriage return must go to the up-left of that row's start; while at the end of a long run (of length n+1) the carriage return must go to the up-right of that row's start. Hence there is only one mapping, to a given lattice, that will fulfil the definition of APS (ignoring rotations and reflections).

If you have a play around with Hex, this should help to illustrate how this works.

Andy

>
> -Carl
>

On Fri, Mar 2, 2012 at 12:54 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > > > http://www.h-pi.com/images/mmBosanquet.gif
> > >
> > > You keep linking to this file even though it's completely
> > > unlabeled! If you're talking about the white notes, they
> > > have a very clear carriage return.
> >
> > Huh? It's labeled "Bosanquet" on the side of the picture.
>
> I don't know what that means.

What exactly did you want labeled? If it's the note keys that you
wanted labeled, and you can handle Flash, this app lays everything
out: http://monxmood.free.fr/bosanquet/bosanquet.html

I don't know what the actual definition of a "Bosanquet layout" is
anymore after all we discussed, but the one that I see most commonly
used, even if it's a misnomer, corresponds to that. It's built around
meantone[7] and is set up so that one unit vector is a whole step,
another unit vector is a diatonic half step, and the last unit vector
is a chromatic half step, so that the MOS traces out a diagonal line
across the keyboard. The whole thing is typically oriented so that
octaves end up being on a horizontal line that's parallel to the frame
of the keyboard. It's the layout on George Secor's scalatron.

I dont know at this point if that's a "Bosanquet layout," or if it's
just one type of Bosanquet layout, but that's the exact thing I'm
talking about. I want to generalize this by letting the unit vectors
correspond to L, s, and c for some arbitrary MOS.

I don't care which vector corresponds to which, but to make it most
useful, you should try to orient the whole thing so that it roughly
follows the shape of the keyboard, or else you're going to run the
scale right off the end of the layout. On an AXiS this can be hard,
but that's what it is. It still usually gets you about 2 octaves of
most scales for about an octave or two.

For any rotation of the scale you pick, you'll still end up with two
ways to satisfy the above definition which are vertical mirror images
of one another. I've used both in different circumstances, and
consider them both to be the same basic layout. Or in other words, all
affine-transformed versions of this concept are equivalent in my view.

> > You can see the actual "carriage return" style break from E to F,
> > because it doesn't just skip a line, but moves all the way over
> > horizontally as well.
>
> Ok, so for APS the common step has to be one unit on the
> keyboard and the rare step has to be one unit *from the
> tonic*? The Hex preprint says,
>
> "In any APS layout, the most numerous (i.e., predominant)
> scale steps—whether they be large or small—always correspond
> to movement along rows, and the least numerous scale steps
> always correspond to "carriage returns.""
>
> To me this would include your .gif. It continues

I think I see why my picture confused you now. Checkout the Flash app
I linked to above and you'll see why they're not the same.

The thing that Andy's mentioning and the thing that I'm talking about
are totally different. His is supposed to be a generalization of the
Wicki layout, which is really economical and makes it so that you can
go up the long side of the keyboard. If you rotate an AXiS so that the
two arrow buttons are at the bottom, then the Wicki layout for
meantone is played so that major seconds are going to your right, and
the diatonic semitone is two steps to the left and one step up-left.
It's very compact and gives you a ton of range on the keyboard, but at
the cost of being able to easily play chromatic stuff.

The layout I'm talking about, in contrast, sets scales up diagonally,
as in the Flash app I linked you to, so that the whole thing traces
out a rough line and that the next MOS up from it tends to cluster
around it. It's not as good for something like the AXiS (I'm not sure
if it's possible to build an ideal keyboard arrangement around it that
works with a lot of MOS's, actually), but for me, it's the magic
bullet for melody, harmony, and chromaticity all in one. Equating this
with the APS layout basically defeats the purpose of what I was using
it for.

-Mike

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

> The most numerous steps run along rows (each tone is adjacent).
> At the end of the row, the least numerous step (the "carriage
> return") leads to a button that is on the row above and adjacent
> to the first button of the first row.

Got it, thanks.

> > "There is only one such APS layout for each MOS scale,"
> >
> > Even with the more specific APS definition I suggest above
> > I don't think this is true.
>
> The large and small steps are distributed with maximal evenness
> in an MOS. This implies that the runs (rows) of most numerous
> steps have just two different lengths (n and n+1). [snip]
> Assuming the rows run from left to right, this means that at
> the end of a short run (of length n) the carriage return must
> go to the up-left of that row's start; while at the end of a
> long run (of length n+1) the carriage return must go to the
> up-right of that row's start.

Ok, but this "must" is by definition, yes?

-Carl

--- Mike Battaglia <battaglia01@...> wrote:

> What exactly did you want labeled?

In the facebook thread I was looking for note names or some
sort of abstract MOS-step notation like Andy is using. But
it's a side point. The main point is that I think you'll
find melodies even easier to play in an APS layout than a
near-linear one.

> I dont know at this point if that's a "Bosanquet layout,"

I don't think any rigorous definition of the term exists.
More common is what Bosanquet himself called it --
"generalized keyboard" -- but even that is open to some
interpretation.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> but at
> the cost of being able to easily play chromatic stuff.

Yes, that's true. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > The most numerous steps run along rows (each tone is adjacent).
> > At the end of the row, the least numerous step (the "carriage
> > return") leads to a button that is on the row above and adjacent
> > to the first button of the first row.
>
> Got it, thanks.
>
> > > "There is only one such APS layout for each MOS scale,"
> > >
> > > Even with the more specific APS definition I suggest above
> > > I don't think this is true.
> >
> > The large and small steps are distributed with maximal evenness
> > in an MOS. This implies that the runs (rows) of most numerous
> > steps have just two different lengths (n and n+1). [snip]
> > Assuming the rows run from left to right, this means that at
> > the end of a short run (of length n) the carriage return must
> > go to the up-left of that row's start; while at the end of a
> > long run (of length n+1) the carriage return must go to the
> > up-right of that row's start.
>
> Ok, but this "must" is by definition, yes?

The properties of the mapping described in the paragraph starting "The large and small steps ..." are necessary to meet the definition of APS in the paragraph starting "The most numerous steps ...". The purpose of the "The large and small steps ..." paragraph was to demonstrate that, for any given MOS scale and hexagonal lattice, there is only one layout that is APS (ignoring rotation and reflection).

Andy

On Fri, Mar 2, 2012 at 3:28 PM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > What exactly did you want labeled?
>
> In the facebook thread I was looking for note names or some
> sort of abstract MOS-step notation like Andy is using. But
> it's a side point. The main point is that I think you'll
> find melodies even easier to play in an APS layout than a
> near-linear one.

OK, well did the Flash app clear that up for you? In meantone, one
unit vector is the whole step, another is the diatonic half step, the
other is the chromatic half step. In generalized terms, we say that
one unit vector is L, one is s, and the remaining one is c. So the
shapes C-C#-D-D#-E and C-Db-D-Eb-E are mirror inverses of one another.

I don't see why you say that APS is easier than a near-linear one. In
a near-linear layout, you get not only the chromatic scale, but the
entire enharmonic scale for some albitonic MOS being laid out with
notes at most one key adjacent from the original MOS. For an APS
layout, if I want to play the flight of the bumblebee, my hand is
going to be jumping all over the place. Which might be fine for
something that's repetitious and methodical like the flight of the
bumblebee layout, but will be not fine if I'm soloing and trying to
play highly chromatic bebop lines or something like that.

> > I dont know at this point if that's a "Bosanquet layout,"
>
> I don't think any rigorous definition of the term exists.
> More common is what Bosanquet himself called it --
> "generalized keyboard" -- but even that is open to some
> interpretation.

FWIW, what people have been calling "a Bosanquet layout," in every
instance I've seen the term used before your post on XA, is the thing
I linked to above - specifically for the diatonic scale and in that
layout. If we want to just call that the "diatonic Bosanquet layout,"
or something like that, I'm cool with it, but every time I try to then
talk about a "porcupine Bosanquet layout" or whatever, everyone gets
confused.

What do people think about the term "pseudo-Halberstadt layout" (PHL)
for the general case, where the unit vectors are L, s, and c?

Or, if "Halberstadt" is too loaded as referring only to the chromatic
scale, then the term "pseudo-accretion layout," which has been
advanced as a generalization of Halberstadt. (PAL)

(Of course, to avoid confusion, you could also go with
pseudo-Halberstadt/accretion layout, or PHAL, thus coining a new
generation's worth of dumb inside jokes.)

-Mike

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

> > > The large and small steps are distributed with maximal evenness
> > > in an MOS. This implies that the runs (rows) of most numerous
> > > steps have just two different lengths (n and n+1). [snip]
> > > Assuming the rows run from left to right, this means that at
> > > the end of a short run (of length n) the carriage return must
> > > go to the up-left of that row's start; while at the end of a
> > > long run (of length n+1) the carriage return must go to the
> > > up-right of that row's start.

> The properties of the mapping described in the paragraph starting
> "The large and small steps ..." are necessary to meet the
> definition of APS in the paragraph starting "The most numerous
> steps ...". The purpose of the "The large and small steps ..."
> paragraph was to demonstrate that, for any given MOS scale and
> hexagonal lattice, there is only one layout that is APS (ignoring
> rotation and reflection).
>
> Andy

I'm wondering why the short run must be up and to the left,
rather than up and to the right... -Carl

On Fri, Mar 2, 2012 at 4:35 AM, andymilneuk <ANDYMILNE@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > > We are currently working a on a new version built within the
> > > QuickTime SDK. In theory, this should be usable on Linux,
> > > Android, Windows, and OS X. But no promises - it's still
> > > early days...
> > >
> > > Andy
> >
> > You mean QT (not QuickTime), right? -Carl
> >
>
> Oh dear, have I committed an Apple faux pas?

I think you're talking about this:

http://en.wikipedia.org/wiki/Qt_(framework)

This is pronounced "cute" and is a framework for cross-platform
application development. Quicktime is the other thing that lets you
play movies and such. They're different.

BTW, if you're going to mess with Qt4, I highly, highly, highly
recommend you consider looking at JUCE, which is like Qt but comes
with so many additional audio and networking and "everything" features
that it's almost unreal. You can make write-once, run anywhere
VST/AU/RTAS plugins as well. You should check it out, it's at
http://www.rawmaterialsoftware.com.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > > > The large and small steps are distributed with maximal evenness
> > > > in an MOS. This implies that the runs (rows) of most numerous
> > > > steps have just two different lengths (n and n+1). [snip]
> > > > Assuming the rows run from left to right, this means that at
> > > > the end of a short run (of length n) the carriage return must
> > > > go to the up-left of that row's start; while at the end of a
> > > > long run (of length n+1) the carriage return must go to the
> > > > up-right of that row's start.
>
> > The properties of the mapping described in the paragraph starting
> > "The large and small steps ..." are necessary to meet the
> > definition of APS in the paragraph starting "The most numerous
> > steps ...". The purpose of the "The large and small steps ..."
> > paragraph was to demonstrate that, for any given MOS scale and
> > hexagonal lattice, there is only one layout that is APS (ignoring
> > rotation and reflection).
> >
> > Andy
>
> I'm wondering why the short run must be up and to the left,
> rather than up and to the right... -Carl
>

Imagine we've got to the end of a short run and then we do a carriage return to the hexagon that is above-right of the start of the run. Now imagine we've got to the end of a long run (which is one note longer) and apply the same carriage return move - the resulting hexagon will be not be adjacent to the start of the previous row - it will be one hexagon too far to the right. Andy

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 4:35 AM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > > We are currently working a on a new version built within the
> > > > QuickTime SDK. In theory, this should be usable on Linux,
> > > > Android, Windows, and OS X. But no promises - it's still
> > > > early days...
> > > >
> > > > Andy
> > >
> > > You mean QT (not QuickTime), right? -Carl
> > >
> >
> > Oh dear, have I committed an Apple faux pas?
>
> I think you're talking about this:
>
> http://en.wikipedia.org/wiki/Qt_(framework)
>
> This is pronounced "cute" and is a framework for cross-platform
> application development. Quicktime is the other thing that lets you
> play movies and such. They're different.
>
> BTW, if you're going to mess with Qt4, I highly, highly, highly
> recommend you consider looking at JUCE, which is like Qt but comes
> with so many additional audio and networking and "everything" features
> that it's almost unreal. You can make write-once, run anywhere
> VST/AU/RTAS plugins as well. You should check it out, it's at
> http://www.rawmaterialsoftware.com.
>
> -Mike
>

Thanks - I'll pass it on... (I'm not doing the programming, which may be rather obvious!)

On Fri, Mar 2, 2012 at 4:26 PM, andymilneuk <ANDYMILNE@...>
wrote:
>
> Imagine we've got to the end of a short run and then we do a carriage
> return to the hexagon that is above-right of the start of the run. Now
> imagine we've got to the end of a long run (which is one note longer) and
> apply the same carriage return move - the resulting hexagon will be not be
> adjacent to the start of the previous row - it will be one hexagon too far
> to the right. Andy

What about for scales in which the "rare second" isn't an even number? Say 5L3s.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Mar 2, 2012 at 4:26 PM, andymilneuk <ANDYMILNE@...>
> wrote:
> >
> > Imagine we've got to the end of a short run and then we do a carriage
> > return to the hexagon that is above-right of the start of the run. Now
> > imagine we've got to the end of a long run (which is one note longer) and
> > apply the same carriage return move - the resulting hexagon will be not be
> > adjacent to the start of the previous row - it will be one hexagon too far
> > to the right. Andy
>
> What about for scales in which the "rare second" isn't an even number? Say 5L3s.
>
> -Mike

No difference.

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
> Imagine we've got to the end of a short run and then we do a
> carriage return to the hexagon that is above-right of the start
> of the run. Now imagine we've got to the end of a long run (which
> is one note longer) and apply the same carriage return move - the
> resulting hexagon will be not be adjacent to the start of the
> previous row - it will be one hexagon too far to the right. Andy

Thank you! -Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I don't see why you say that APS is easier than a near-linear one. In
> a near-linear layout, you get not only the chromatic scale, but the
> entire enharmonic scale for some albitonic MOS being laid out with
> notes at most one key adjacent from the original MOS. For an APS
> layout, if I want to play the flight of the bumblebee, my hand is
> going to be jumping all over the place. Which might be fine for
> something that's repetitious and methodical like the flight of the
> bumblebee layout, but will be not fine if I'm soloing and trying to
> play highly chromatic bebop lines or something like that.
>

Something worth pointing out is that the APS layout for the 7L,5s or 5L,7s (i.e., chromatic) scale is identical to the Bosanquet layout (i.e., all seconds of the diatonic 5L,2s are adjacent).

Andy