Yahoo Tuning Groups Ultimate Backup tuning Some thoughts about layouts...

With all this current talk about generalised note layouts, I've posted some pictures taken from the next version of Hex, which can provide a note layout optimised for any MOS scale (with 19 or less tones).

So what do I mean by "layout" and "optimised"?

I'll define a layout to be a specific (spatial) mapping of the period and generator to a basis of an (approximately) hexagonal lattice. For example, in the Wicki layout the period (typically the octave) is mapped to buttons vertically above each other two rows apart, while the generator is mapped to the button diagonally up and right.

Given an appropriate shear, any such layout has some interesting properties:

1. The axis that connects tones octaves apart is a pitch axis - the position of any tone on this axis indicates its pitch.
2. The axis orthogonal to the pitch axis gives the distance in generators (e.g. perfect fifths) between any two tones

But, for any given MOS scale, the actual choice of layout can be "optimised". The Wicki layout is "optimal" for MOS scales where the number of small or large steps is 2 - e.g. the diatonic scale MOS 5L 2S, the pentatonic scale MOS 2L 3S, Mavila scales MOS 2L 5S, etc. It is optimal because the pattern made by the MOS is easy to comprehend, for the following reason (there is another I won't go into, for now):

3. The most common scale steps are traversed by moving stepwise (spatially) across a row, the less common scale steps are traversed by a "carriage return" motion to the next higher row. For example, in Wicki, you start on C go right to D go right to E, do a "carriage return" to the next row above for F, go right to G, go right to A, go right to B, do a carriage return to the next row above for C, and so on.

This third feature can be made available for any given MOS. Here are some links to graphics from the, hopefully, next version of Hex, giving optimised layouts for
MOS 5L 2S http://www.dynamictonality.com/layouts/MOS%205L%202S.jpg
MOS 4L 7S http://www.dynamictonality.com/layouts/MOS%204L%207S.jpg
MOS 3L 7S http://www.dynamictonality.com/layouts/MOS%203L%207S.jpg
MOS 1L 6S http://www.dynamictonality.com/layouts/MOS%201L%206S.jpg
MOS 7L 5S http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg

The mapping of the optimal layout can be quickly determined from the chart that John recently posted - the maximum swathe width (spatial distance between tones an octave apart in units of a the determinant of the lattice's basis) corresponds to the valid tuning range of the MOS scales it is optimal for.

Really I'd love to get this shit onto an iPad to make a multitouch controller...

Andy

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Gene wrote:

> > I'll define a layout to be a specific (spatial) mapping of
> > the period and generator to a basis of an (approximately)
> > hexagonal lattice.
>
> I'm not sure why you bring in periods, generators and a basis,

For 'good' temperaments, these are optimized for conditions
that should also be desirable on keyboards.

It may be a good point of departure for you to review some
of Andy's papers, which are to date the most serious regular
mapping papers we have, and the principle reason any of
this stuff sticks on Wikipedia (thanks Andy!).

This one, perhaps

http://www.thummer.com/ThumTone/Tuning_Invariant_Layouts_Last_Draft.pdf

-Carl

🔗Carl Lumma <carl@...>

Hi Andy!

> With all this current talk about generalised note layouts, I've
> posted some pictures taken from the next version of Hex, which
> can provide a note layout optimised for any MOS scale (with 19
> or less tones).

I was just trying Hex last night. It looks neat, but I had
trouble controlling it (like, entering notes). I also didn't
quite grasp the point. The functional area is still a piano
roll, with the lattice on the left seemingly just a legend
or guide. And since pitch isn't always ascending on the roll,
one has to look back at the guide annoyingly often. Perhaps
I'm being too harsh, and it's possible to learn one's way
around these things. At any rate, it seems to primarily make
sense if one wants to move that slider during performance...
which isn't my cup of tea, so probably I'm not the best
reviewer.

It is, at any rate, extremely encouraging to see software
coming out of the dynamic tonality collaboration!

> But, for any given MOS scale, the actual choice of layout can
> be "optimised". The Wicki layout is "optimal" for MOS scales
> where the number of small or large steps is 2 - e.g. the
> diatonic scale MOS 5L 2S, the pentatonic scale MOS 2L 3S,
> Mavila scales MOS 2L 5S, etc. It is optimal because the
> pattern made by the MOS is easy to comprehend, for the
> following reason (there is another I won't go into, for now):

Can I goad you into going into it? Because the reason you
gave doesn't make much sense to me (2nds and 3rds more common
scale steps than 4ths and 5ths?).

> This third feature can be made available for any given MOS. Here
> are some links to graphics from the, hopefully, next version of
> Hex, giving optimised layouts for

Maybe the hexagons on the left could be labeled with
generator,period coordinates or something?

> The mapping of the optimal layout can be quickly determined
> from the chart that John recently posted - the maximum swathe
> width (spatial distance between tones an octave apart in units
> of a the determinant of the lattice's basis) corresponds to the
> valid tuning range of the MOS scales it is optimal for.

Sorry to hit you with so many critical questions, but I don't
understand why a wider swathe is "optimal".

> Really I'd love to get this shit onto an iPad to make a
> multitouch controller...

I've been playing with a number of 2-D keyboard apps on the
iPad, but the lack of tactile feedback is annoying, as is the
limited overall area (with tactile feedback it'd be easier to
play smaller keys). I thought I had them all, but I just
saw this last night

http://shiverware.com/musix.html

and am about to download it.

-Carl

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Andy!
>
> > With all this current talk about generalised note layouts, I've
> > posted some pictures taken from the next version of Hex, which
> > can provide a note layout optimised for any MOS scale (with 19
> > or less tones).
>
> I was just trying Hex last night. It looks neat, but I had
> trouble controlling it (like, entering notes).

You have to click directly on a lane, but maybe there's a bug - this is still pretty early days for the software...

I also didn't
> quite grasp the point. The functional area is still a piano
> roll, with the lattice on the left seemingly just a legend
> or guide. And since pitch isn't always ascending on the roll,
> one has to look back at the guide annoyingly often.

Height on the lattice should always correspond to pitch height (assuming you're using 2032, which interprets the position of the tuning slider). If it doesn't, you've either discovered a bug, or you're setting things up wrongly?

Perhaps
> I'm being too harsh, and it's possible to learn one's way
> around these things. At any rate, it seems to primarily make
> sense if one wants to move that slider during performance...
> which isn't my cup of tea, so probably I'm not the best
> reviewer.
>
> It is, at any rate, extremely encouraging to see software
> coming out of the dynamic tonality collaboration!
>
> > But, for any given MOS scale, the actual choice of layout can
> > be "optimised". The Wicki layout is "optimal" for MOS scales
> > where the number of small or large steps is 2 - e.g. the
> > diatonic scale MOS 5L 2S, the pentatonic scale MOS 2L 3S,
> > Mavila scales MOS 2L 5S, etc. It is optimal because the
> > pattern made by the MOS is easy to comprehend, for the
> > following reason (there is another I won't go into, for now):
>
> Can I goad you into going into it? Because the reason you
> gave doesn't make much sense to me (2nds and 3rds more common
> scale steps than 4ths and 5ths?).

I'm using "steps" as synonymous with "seconds" - sorry if that wasn't clear. So in the MOS 5L 2S scale (i.e. the familiar diatonic) there are five large steps (major seconds) and two small steps (minor seconds). The large steps are the more common of the two, and in Wicki they are spatially adjacent.

>
> > This third feature can be made available for any given MOS. Here
> > are some links to graphics from the, hopefully, next version of
> > Hex, giving optimised layouts for
>
> Maybe the hexagons on the left could be labeled with
> generator,period coordinates or something?

Sure, I'll add those later and repost...but notes a period apart are on the same vertical line so they are quite easy to spot. In a future version, we'll add some sort of shading to alternate octaves to make this clearer.

>
> > The mapping of the optimal layout can be quickly determined
> > from the chart that John recently posted - the maximum swathe
> > width (spatial distance between tones an octave apart in units
> > of a the determinant of the lattice's basis) corresponds to the
> > valid tuning range of the MOS scales it is optimal for.
>
> Sorry to hit you with so many critical questions, but I don't
> understand why a wider swathe is "optimal".

It's to ensure that the most common seconds of any given MOS are spatially adjacent; when a second is the result of stacking a lot of generators, the swathe width has to be sufficiently wide to make them spatially adjacent. Perhaps if I produce some pictures showing optimal versus non-optimal layouts for a variety of MOS, this will make it clearer.

Andy

>
> > Really I'd love to get this shit onto an iPad to make a
> > multitouch controller...
>
> I've been playing with a number of 2-D keyboard apps on the
> iPad, but the lack of tactile feedback is annoying, as is the
> limited overall area (with tactile feedback it'd be easier to
> play smaller keys). I thought I had them all, but I just
> saw this last night
>
> http://shiverware.com/musix.html
>
> and am about to download it.
>
> -Carl
>

🔗Carl Lumma <carl@...>

Andy wrote:

> You have to click directly on a lane, but maybe there's
> a bug - this is still pretty early days for the software...

I was able to enter them, but not consistently. My 144dpi
monitor and trackpoint maybe weren't helping matters.

> > I also didn't
> > quite grasp the point. The functional area is still a piano
> > roll, with the lattice on the left seemingly just a legend
> > or guide. And since pitch isn't always ascending on the roll,
> > one has to look back at the guide annoyingly often.
>
> Height on the lattice should always correspond to pitch height
> (assuming you're using 2032, which interprets the position of
> the tuning slider). If it doesn't, you've either discovered
> a bug, or you're setting things up wrongly?

I was using the built in Windows synth. Does Hex require 2032?

> > > But, for any given MOS scale, the actual choice of layout can
> > > be "optimised". The Wicki layout is "optimal" for MOS scales
> > > where the number of small or large steps is 2 - e.g. the
> > > diatonic scale MOS 5L 2S, the pentatonic scale MOS 2L 3S,
> > > Mavila scales MOS 2L 5S, etc. It is optimal because the
> > > pattern made by the MOS is easy to comprehend, for the
> > > following reason (there is another I won't go into, for now):
> >
> > Can I goad you into going into it? Because the reason you
> > gave doesn't make much sense to me (2nds and 3rds more common
> > scale steps than 4ths and 5ths?).
>
> I'm using "steps" as synonymous with "seconds" - sorry if that
> wasn't clear. So in the MOS 5L 2S scale (i.e. the familiar
> diatonic) there are five large steps (major seconds) and two
> small steps (minor seconds). The large steps are the more
> common of the two, and in Wicki they are spatially adjacent.

Ah, that makes sense. But only from the point of view of
playing scales in order.

> > Maybe the hexagons on the left could be labeled with
> > generator,period coordinates or something?
>
> Sure, I'll add those later and repost...but notes a period
> apart are on the same vertical line so they are quite easy
> to spot. In a future version, we'll add some sort of shading to
> alternate octaves to make this clearer.

Cool.

> > Sorry to hit you with so many critical questions, but I don't
> > understand why a wider swathe is "optimal".
>
> It's to ensure that the most common seconds of any given MOS
> are spatially adjacent; when a second is the result of stacking
> a lot of generators, the swathe width has to be sufficiently
> wide to make them spatially adjacent.

I'm not sure that's such a desirable criterion.

> Perhaps if I produce
> some pictures showing optimal versus non-optimal layouts for
> a variety of MOS, this will make it clearer.

It couldn't hurt!

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
>
> > You have to click directly on a lane, but maybe there's
> > a bug - this is still pretty early days for the software...
>
> I was able to enter them, but not consistently. My 144dpi
> monitor and trackpoint maybe weren't helping matters.

We should probably make the lanes a bit thicker.

>
> > > I also didn't
> > > quite grasp the point. The functional area is still a piano
> > > roll, with the lattice on the left seemingly just a legend
> > > or guide. And since pitch isn't always ascending on the roll,
> > > one has to look back at the guide annoyingly often.
> >
> > Height on the lattice should always correspond to pitch height
> > (assuming you're using 2032, which interprets the position of
> > the tuning slider). If it doesn't, you've either discovered
> > a bug, or you're setting things up wrongly?
>
> I was using the built in Windows synth. Does Hex require 2032?

Absolutely! The Viking will also work as long as you don't go beyond a chain of twelve generators, we will be updating it shortly to make it fully compatible.

>
> > > > But, for any given MOS scale, the actual choice of layout can
> > > > be "optimised". The Wicki layout is "optimal" for MOS scales
> > > > where the number of small or large steps is 2 - e.g. the
> > > > diatonic scale MOS 5L 2S, the pentatonic scale MOS 2L 3S,
> > > > Mavila scales MOS 2L 5S, etc. It is optimal because the
> > > > pattern made by the MOS is easy to comprehend, for the
> > > > following reason (there is another I won't go into, for now):
> > >
> > > Can I goad you into going into it? Because the reason you
> > > gave doesn't make much sense to me (2nds and 3rds more common
> > > scale steps than 4ths and 5ths?).
> >
> > I'm using "steps" as synonymous with "seconds" - sorry if that
> > wasn't clear. So in the MOS 5L 2S scale (i.e. the familiar
> > diatonic) there are five large steps (major seconds) and two
> > small steps (minor seconds). The large steps are the more
> > common of the two, and in Wicki they are spatially adjacent.
>
> Ah, that makes sense. But only from the point of view of
> playing scales in order.

Seconds are very important melodically.

>
> > > Maybe the hexagons on the left could be labeled with
> > > generator,period coordinates or something?
> >
> > Sure, I'll add those later and repost...but notes a period
> > apart are on the same vertical line so they are quite easy
> > to spot. In a future version, we'll add some sort of shading to
> > alternate octaves to make this clearer.
>
> Cool.
>
> > > Sorry to hit you with so many critical questions, but I don't
> > > understand why a wider swathe is "optimal".
> >
> > It's to ensure that the most common seconds of any given MOS
> > are spatially adjacent; when a second is the result of stacking
> > a lot of generators, the swathe width has to be sufficiently
> > wide to make them spatially adjacent.
>
> I'm not sure that's such a desirable criterion.
>
> > Perhaps if I produce
> > some pictures showing optimal versus non-optimal layouts for
> > a variety of MOS, this will make it clearer.
>
> It couldn't hurt!

I'll post some...

Andy

>
> -Carl
>

🔗Carl Lumma <carl@...>

Andy wrote:

> > I was using the built in Windows synth. Does Hex require 2032?
>
> Absolutely! The Viking will also work

Is there a chart somewhere explaining the differences between
the Viking, TFS, and 2032?

> > > > Can I goad you into going into it? Because the reason you
> > > > gave doesn't make much sense to me (2nds and 3rds more common
> > > > scale steps than 4ths and 5ths?).
> > >
> > > I'm using "steps" as synonymous with "seconds" - sorry if that
> > > wasn't clear. So in the MOS 5L 2S scale (i.e. the familiar
> > > diatonic) there are five large steps (major seconds) and two
> > > small steps (minor seconds). The large steps are the more
> > > common of the two, and in Wicki they are spatially adjacent.
> >
> > Ah, that makes sense. But only from the point of view of
> > playing scales in order.
>
> Seconds are very important melodically.

So are 3rds and 4ths...

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

I wrote:

> I've been playing with a number of 2-D keyboard apps on the
> iPad ... I thought I had them all but I just saw this
>
> http://shiverware.com/musix.html

Prior to today, I had

MorphWiz
Harmonizer
Hex OSC Full
iJammer
HexJam HD
RatioKey

This blows them all away.* Chris V. if you're listening,
I strongly recommend this as a companion to your AXiS.

Not only is this a much more polished app, it has the
important option to resize the keys. It can send both
MIDI and OSC (haven't tried either yet) and has important
option of being able to assign any 12-ET interval to each
axis of the keyboard. It has presets for

Gerhard
Park
Wicki
Harmonic table
C-System
B-System
Bayan

I've been playing around with them. C, B, and Bayan are
all rotations or mirrors of one another. Though for some
reason, I seem to prefer C with either hand. That may be
because I've not yet had time to fully explore various
fingering options. And for now all were evaluated in 12-ET
so observations may not hold across tunings (depending too
on how one defines each of these in other tunings).

One way to characterize them is how 'chromatic' they are,
which will be the same as Andy's swathe thickness. I'll
rank them from most to least chromatic:

Gerard
C/B/Bayan
Harmonic
Park
Wicki

In 12-ET, I tend to prefer things toward the top of this
list, because I tend to like to play very chromatic stuff
to escape boredom. However in new systems, I might prefer
a more 'diatonic' option like Wicki, to learn the system
and because there is no longer such a need for novelty
outside the basic scale.

In fact, I will even wonder aloud whether transpositional
invariance is so desirable. It is nice to be able to see
all the major and minor chords of some strange MOS look
the same, as they are in some sense the same from a melodic
or modal point of view. Much like playing the white keys
of the piano makes evident the structure of the
diatonic scale.

-Carl

* MorphWiz and Harmonizer are also pretty polished, and not
quite the same class of instrument.

🔗Carl Lumma <carl@...>

🔗andymilneuk <ANDYMILNE@...>

I've revised the graphics to show the mapping of period and generator (the octave is always vertical), and added the scale degrees of the MOS (the location of scale degree 1 is arbitrary). I've also included two new graphics of MOS 4L 7S and MOS 3L 7S with Wicki layouts for comparison.

MOS 5L 2S http://www.dynamictonality.com/layouts/MOS%205L%202S.jpg
MOS 4L 7S http://www.dynamictonality.com/layouts/MOS%204L%207S.jpg
MOS 3L 7S http://www.dynamictonality.com/layouts/MOS%203L%207S.jpg
MOS 1L 6S http://www.dynamictonality.com/layouts/MOS%201L%206S.jpg
MOS 7L 5S http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg

MOS 4L 7S Wicki http://www.dynamictonality.com/layouts/MOS%204L%207S%20Wicki.jpg
MOS 3L 7S Wicki http://www.dynamictonality.com/layouts/MOS%203L%207S%20Wicki.jpg

I would venture that the scalic structure is much easier to "parse" in the non-Wicki layouts, which have spatially adjacent seconds. Speaking personally, I find it much easier to sequence music in the above non-Wicki layouts. You may disagree...

Andy

> > > > Sorry to hit you with so many critical questions, but I don't
> > > > understand why a wider swathe is "optimal".
> > >
> > > It's to ensure that the most common seconds of any given MOS
> > > are spatially adjacent; when a second is the result of stacking
> > > a lot of generators, the swathe width has to be sufficiently
> > > wide to make them spatially adjacent.
> >
> > I'm not sure that's such a desirable criterion.
> >
> > > Perhaps if I produce
> > > some pictures showing optimal versus non-optimal layouts for
> > > a variety of MOS, this will make it clearer.
> >
> > It couldn't hurt!
>
> I'll post some...
>
> Andy
>
>
>
> >
> > -Carl
> >
>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > They are defined by a mapping from a rank two temperament to a
> > standard hexagonal (A2) lattice with distances between the nearest
> > lattice points of one unit. The orientation is normalized so that
> > octaves are precisely along the x-axis. The mapping to the lattice
> > I gave by means of a pair of vals, an "icon" or "mapping to
> > generators" or whatever you want to call it, to two precisely
> > defined lattice basis vectors of length one and 120 degrees apart
> > which I gave explicit formulas for.
>
> Isn't this pair of vals just the period and generator? -Carl
>

No; any pair of vals defining the temperament. Usually you would want smaller steps than period and generator, so you are likely to want to use two equal temperament vals.

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗andymilneuk <ANDYMILNE@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Well, I don't own an iPad but what I bought today, for a bit more money, is
a Digitech Control 8 Midi foot controller.

http://www.digitech.com/classic/Control8.php

this ought to let me control softsynths - for instance get access to
pianoteq's other piano pedals.

My plans are to attempt to used kbm files to remap my AXiS though I'm going
ok in selfless mode in that 90 degree counter-clockwise orientation. I'm
finding though that the velocity sensitivity is... very narrow ranged.

A question I wanted to ask - I had ordered a guitar from Ron Sword in
September - the 20th or before. And I never received it. While NO money has
been exchanged I was told I'd have a guitar by the end of October. I was
never told when or how to send the money. Has anyone else had trouble? He
won't return messages though before I put in the order he was IM'ing me on
facebook all the time. It seems now, via facebook, he is doing stuff in
California.

Chris

On Sat, Nov 20, 2010 at 5:26 PM, Carl Lumma <carl@...> wrote:

>
>
> I wrote:
>
> > I've been playing with a number of 2-D keyboard apps on the
> > iPad ... I thought I had them all but I just saw this
>
> >
> > http://shiverware.com/musix.html
>
> Prior to today, I had
>
> MorphWiz
> Harmonizer
> Hex OSC Full
> iJammer
> HexJam HD
> RatioKey
>
> This blows them all away.* Chris V. if you're listening,
> I strongly recommend this as a companion to your AXiS.
>
>

🔗genewardsmith <genewardsmith@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > Gene wrote:
> >
> > > I don't understand why you want the octave to be vertical.
> > > Wouldn't horizontal make more sense?
> >
> > Why?
>
> A keyboard with pitch increasing to the left is what we are used to, and it seems to me that greater spread horizontally rather than vertically is bound to be easier to finger. Hence a lattice with 2 along the x-axis in positive direction from 1 makes the most sense to me as a lattice intended to correspond to buttons on a keyboard.
>

For the layouts whose images I linked to in my earlier post, you'll see that rotating them 90 deg to make the octave (pitch) axis horizontal would make for very difficult fingering. In practice, I suspect a player would probably rotate the pitch axis slightly off vertical to make the fingering as comfortable as possible for playing both scales and chords.

🔗genewardsmith <genewardsmith@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
>
> > > I was using the built in Windows synth. Does Hex require 2032?
> >
> > Absolutely! The Viking will also work
>
> Is there a chart somewhere explaining the differences between
> the Viking, TFS, and 2032?

For a synth to be fully compatible with Hex, it must respond correctly to the position of Hex's tuning slider, and it must correctly interpret the mapping of period and generator implied by each of Hex's buttons or note lanes. Currently, only 2032 is fully compatible. The Viking and TransForm will be updated shortly to make them so.

In summary, the Dynamic Tonality (DT) synths are:

TransFormSynth is an analysis-resynthesis synth---it analyses an audio sample into its partials and noise components, then retunes those partials according to the settings of its various DT controls, and finally resynthesizes them to make the final sound.

The Viking is an additive-subtractive synth---it emulates a standard subtractive synth (but internally, the waveforms - saw, rect, pwm, triangle, etc are generated additively so their partials can be retuned). It is currently being ported over to Max which will make it compatible with Mac OS X as well as Windows. It currently works with Hex, but only for the central twelve columns of Hex---outside that, the mapping breaks down. This will be fixed in the new version.

2032 is a physical modelling synth (modal synthesis)---it has a bank of tunable resonators, which emulate the modes of a string or column of air, and these are fed through another bank of resonant filters that emulate an instrument body (like a guitar, or cello body). The modes can be excited by models of a hammer/pick, wind, or bow, or by any live audio input (this is actually very cool and worth playing around with---but best to use headphones to avoid feeback!).

Andy

🔗andymilneuk <ANDYMILNE@...>

🔗genewardsmith <genewardsmith@...>

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

> If you get the graphic onto your screen and zoom it so each row is a finger apart, you may then see how easy it is to finger the scales. It's actually very piano like - i.e. left to right as you go up the scale, but with additional "carriage returns" that take you back to the start of the next row above.

This is piano like?

http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg

By the way, in order to make the best sense of your diagram I must subtract 1 from each number; the unison should be a 0 for the math to work out in the easiest way. If you have 1 on the unison and N on an adjacent note, then N is not the generator, N-1 is. You end up with 1, N, 2N-1, 3N-2 on the notes heading off in a given direction, not 0, N, 2N, 3N.

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > If you get the graphic onto your screen and zoom it so each row is a finger apart, you may then see how easy it is to finger the scales. It's actually very piano like - i.e. left to right as you go up the scale, but with additional "carriage returns" that take you back to the start of the next row above.
>
> This is piano like?
>
> http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg

I wrote "It's actually very piano like - i.e. left to right as you go up the scale, but with additional "carriage returns" that take you back to the start of the next row above." In a scale like MOS 7L 5S, there are a lot of carriage returns, in a scale like MOS 3L 7S, MOS 5L 2S, or MOS 1L 6S, there are fewer.

>
> By the way, in order to make the best sense of your diagram I must subtract 1 from each number; the unison should be a 0 for the math to work out in the easiest way. If you have 1 on the unison and N on an adjacent note, then N is not the generator, N-1 is. You end up with 1, N, 2N-1, 3N-2 on the notes heading off in a given direction, not 0, N, 2N, 3N.
>

In conventional music theory, scale degrees often start from 1, and that numbering scheme is probably more familiar to most musicians. But, I agree, from a mathematical perspective starting from 0 is clearer.

🔗Carl Lumma <carl@...>

Gene wrote:

> > > I don't understand why you want the octave to be vertical.
> > > Wouldn't horizontal make more sense?
> >
> > Why?
>
> A keyboard with pitch increasing to the left is what we are
> used to, and it seems to me that greater spread horizontally
> rather than vertically is bound to be easier to finger.

Within the length of a forearm, it's easier to extend the
hands away from the body than strafe them out the sides.
For one thing you don't need wall-eye vision to see both
hands, and for another the wrists stay straight. To keep
the wrists straight when playing a wide compass on the
piano, the shoulders are used, like flapping wings, as you
lean in from the waist. This is much harder than extending
the arms with the elbows. Which is why most keyboard
players don't do it, and often develop wrist problems.

It is also easier to "carriage return" on the Wicki in
the middle of the scale, rather than having to fold a
thumb or finger under the hand as on a piano/Bosanquet.

I'm not saying octaves should be vertical, but it's far
from clear to me they shouldn't.

-Carl

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > I'm not saying octaves should be vertical, but it's far
> > from clear to me they shouldn't.
>
> Is there any reason they shouldn't be either horizontal or vertical?
>

I suspect it is easier for a player to mentally "project" a vertical or horizontal axis onto a button-lattice than it is to mentally project an angled axis. For this reason, it makes sense for an important axis on the button-lattice to be aligned vertically or horizontally.

In the layouts I linked to in earlier posts, the vertical axis is the pitch axis (height on this axis corresponds to pitch); the horizontal axis gives the generator distance. These are both musically important measures. Furthermore, for any MOS scale, the most common seconds are spatially adjacent, which allows for fingering analogous to the Wicki fingering of the diatonic scale (travelling along rows with occasional carriage returns).

🔗Carl Lumma <carl@...>

🔗andymilneuk <ANDYMILNE@...>

🔗Carl Lumma <carl@...>

Hi Andy,

> > Some of the Wicki tunings make it go off at an angle, which
> > seems to me very annoying...
>
> Hi Carl - is this comment directed at me (Hex)?

I was answering Gene's question based on what you say in
your paper ("Northeast"). I wasn't talking about Hex.

> ... In the forthcoming version of Hex (as shown in the
> graphics I posted links to), this no longer occurs because
> we use a shear instead of rotation. This means the pitch
> axis is always vertical, and the generator axis is always
> horizontal (so octaves are always vertically aligned).

Yes, that's good. Hard to do with a physical keyboard,
though a circular tray that turns in the enclosure might
do the job...

-Carl

🔗Carl Lumma <carl@...>

Hi Andy, sorry this got lost in the stack...

> I've revised the graphics to show the mapping of period and
> generator (the octave is always vertical), and added the scale
> degrees of the MOS (the location of scale degree 1 is arbitrary).

Thanks. For studying physical keyboards I think it would
help if you filled out the pane with keys, by adding the
darker-shaded dupes complete with labels. (Understood that
for Hex itself, this is just a distraction.)

> I've also included two new graphics of MOS 4L 7S and MOS 3L 7S
> with Wicki layouts for comparison.

What is the condition telling us whether a given layout
is a Wicki layout?
And what would you call the non-Wicki style of layout here?
It seems they strictly adhere to your idea of making the
rare MOS step vertical and the common MOS step horizontal.
(I thought this was how you were generalizing "Wicki".)

> MOS 5L 2S http://www.dynamictonality.com/layouts/MOS%205L%202S.jpg
> MOS 4L 7S http://www.dynamictonality.com/layouts/MOS%204L%207S.jpg
> MOS 3L 7S http://www.dynamictonality.com/layouts/MOS%203L%207S.jpg
> MOS 1L 6S http://www.dynamictonality.com/layouts/MOS%201L%206S.jpg
> MOS 7L 5S http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg

For a physical keyboard, the 7L 5S is getting too tall
I think, and the 1L 6S too wide.

> MOS 4L 7S Wicki http://www.dynamictonality.com/layouts/MOS%204L%207S%20Wicki.jpg
> MOS 3L 7S Wicki http://www.dynamictonality.com/layouts/MOS%203L%207S%20Wicki.jpg

That might be better for a physical keyboard.
More especially in the case of the 7L 5S and 1L 2S.

> I would venture that the scalic structure is much easier to
> "parse" in the non-Wicki layouts, which have spatially adjacent
> seconds. Speaking personally, I find it much easier to sequence
> music in the above non-Wicki layouts. You may disagree...

I agree for the sequencer. Then again I'm not sure any
legend is necessary. The point of scales is that we hear
a 3rd as a 3rd regardless of its size...

-Carl

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Andy, sorry this got lost in the stack...
>
> > I've revised the graphics to show the mapping of period and
> > generator (the octave is always vertical), and added the scale
> > degrees of the MOS (the location of scale degree 1 is arbitrary).
>
> Thanks. For studying physical keyboards I think it would
> help if you filled out the pane with keys, by adding the
> darker-shaded dupes complete with labels. (Understood that
> for Hex itself, this is just a distraction.)
>
> > I've also included two new graphics of MOS 4L 7S and MOS 3L 7S
> > with Wicki layouts for comparison.
>
> What is the condition telling us whether a given layout
> is a Wicki layout?

From my original post in this thread:

> And what would you call the non-Wicki style of layout here?

For the 120 different MOS scales (characterised by their number of large and small steps) with 19 or fewer tones, there are 13 different layouts required to fulfill the adjacent seconds property.

> It seems they strictly adhere to your idea of making the
> rare MOS step vertical and the common MOS step horizontal.
> (I thought this was how you were generalizing "Wicki".)
>
> > MOS 5L 2S http://www.dynamictonality.com/layouts/MOS%205L%202S.jpg
> > MOS 4L 7S http://www.dynamictonality.com/layouts/MOS%204L%207S.jpg
> > MOS 3L 7S http://www.dynamictonality.com/layouts/MOS%203L%207S.jpg
> > MOS 1L 6S http://www.dynamictonality.com/layouts/MOS%201L%206S.jpg
> > MOS 7L 5S http://www.dynamictonality.com/layouts/MOS%207L%205S.jpg
>
> For a physical keyboard, the 7L 5S is getting too tall
> I think, and the 1L 6S too wide.

The lattice can be horizontally or vertically scaled to change the overall profile.

>
> > MOS 4L 7S Wicki http://www.dynamictonality.com/layouts/MOS%204L%207S%20Wicki.jpg
> > MOS 3L 7S Wicki http://www.dynamictonality.com/layouts/MOS%203L%207S%20Wicki.jpg
>
> That might be better for a physical keyboard.
> More especially in the case of the 7L 5S and 1L 2S.
>
> > I would venture that the scalic structure is much easier to
> > "parse" in the non-Wicki layouts, which have spatially adjacent
> > seconds. Speaking personally, I find it much easier to sequence
> > music in the above non-Wicki layouts. You may disagree...
>
> I agree for the sequencer. Then again I'm not sure any
> legend is necessary.

The legend was added to illustrate the pictures, not for Hex.

The point of scales is that we hear
> a 3rd as a 3rd regardless of its size...

Indeed!

Andy

>
> -Carl
>

🔗Carl Lumma <carl@...>

> > What is the condition telling us whether a given layout
> > is a Wicki layout?
>
> From my original post in this thread:
>
> in the Wicki layout the period (typically the octave) is mapped
> to buttons vertically above each other two rows apart, while the
> generator is mapped to the button diagonally up and right.

Thanks. I won't forget this time. :)

> > And what would you call the non-Wicki style of layout here?
>
> For the 120 different MOS scales (characterised by their number
> of large and small steps) with 19 or fewer tones, there are 13
> different layouts required to fulfill the adjacent seconds
> property.

That's good to know. It's not a name however. :)

> > For a physical keyboard, the 7L 5S is getting too tall
> > I think, and the 1L 6S too wide.
>
> The lattice can be horizontally or vertically scaled to
> change the overall profile.

Only by wasting space (assuming a minimum or optimal
key size).

> > > I would venture that the scalic structure is much easier
> > > to "parse" in the non-Wicki layouts, which have spatially
> > > adjacent seconds. Speaking personally, I find it much
> > > easier to sequence music in the above non-Wicki layouts.
> > > You may disagree...
> >
> > I agree for the sequencer. Then again I'm not sure any
> > legend is necessary.
>
> The legend was added to illustrate the pictures, not for Hex.

By legend I meant the entire lattice/keyboard pane (I referred
to it this way in a previous post).

-Carl

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > What is the condition telling us whether a given layout
> > > is a Wicki layout?
> >
> > From my original post in this thread:
> >
> > in the Wicki layout the period (typically the octave) is mapped
> > to buttons vertically above each other two rows apart, while the
> > generator is mapped to the button diagonally up and right.
>
> Thanks. I won't forget this time. :)

>
> > > And what would you call the non-Wicki style of layout here?
> >
> > For the 120 different MOS scales (characterised by their number
> > of large and small steps) with 19 or fewer tones, there are 13
> > different layouts required to fulfill the adjacent seconds
> > property.
>
> That's good to know. It's not a name however. :)

Erm...adjacent seconds layouts?...I'm open to suggestions...

>
> > > For a physical keyboard, the 7L 5S is getting too tall
> > > I think, and the 1L 6S too wide.
> >
> > The lattice can be horizontally or vertically scaled to
> > change the overall profile.
>
> Only by wasting space (assuming a minimum or optimal
> key size).

Not too sure what you mean by wasted space.

>
> > > > I would venture that the scalic structure is much easier
> > > > to "parse" in the non-Wicki layouts, which have spatially
> > > > adjacent seconds. Speaking personally, I find it much
> > > > easier to sequence music in the above non-Wicki layouts.
> > > > You may disagree...
> > >
> > > I agree for the sequencer. Then again I'm not sure any
> > > legend is necessary.
> >
> > The legend was added to illustrate the pictures, not for Hex.
>
> By legend I meant the entire lattice/keyboard pane (I referred
> to it this way in a previous post).

The legend is very helpful when you know the shapes made by important structures (such as major and minor chords) in a given temperament. Or when transferring something you've written on a button-lattice controller to the sequencer - at least that's what I've found. When working in unfamiliar scales and temperaments every possible visual cue helps.

Andy

>
> -Carl
>

🔗Carl Lumma <carl@...>

Andy wrote:

> > > > And what would you call the non-Wicki style of layout here?
[snip]
> Erm...adjacent seconds layouts?...I'm open to suggestions...

Howabout

1. Milne layouts
2. adjacent-2nds layouts
3. MOSopt (MOS-optimal) layouts

> > > > For a physical keyboard, the 7L 5S is getting too tall
> > > > I think, and the 1L 6S too wide.
> > >
> > > The lattice can be horizontally or vertically scaled to
> > > change the overall profile.
> >
> > Only by wasting space (assuming a minimum or optimal
> > key size).
>
> Not too sure what you mean by wasted space.

If we stretch the layout horizontally to make the 7L 5S
unit cell square, the keys regions are wider than optimal.
Or maybe I misunderstood what you meant.

> > By legend I meant the entire lattice/keyboard pane
> > (I referred to it this way in a previous post).
>
> The legend is very helpful when you know the shapes made by
> important structures (such as major and minor chords) in a
> given temperament. Or when transferring something you've
> written on a button-lattice controller to the sequencer - at
> least that's what I've found.

Ok, I'll give it to ya. At least, it's a neat idea.

-Carl

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > I don't understand why you want the octave to be vertical.
> > Wouldn't horizontal make more sense?
>
> Why? I mean, I think we need to define things better...
> Andy and his coauthors have done a good job at improving
> the conversation, but I for one don't have a clear picture
> of how to look at this stuff. Most of the criteria put
> forth by various authors seems rather ad hoc to me.

If the octaves are not horizontal, then the player will, after a short time, experience the discomfort of having the two hands and arms extended at unequal distances most of the time. Furthermore, one arm will often be directly above the other hand, making it necessary for the player to use a less comfortable arm, wrist, and/or hand position to avoid interference with the other hand.

This is no problem if one is designing a layout for a concertina, but I believe that this discussion concerns a single keyboard that will be played by both hands.

--George

🔗Carl Lumma <carl@...>

🔗John Moriarty <JlMoriart@...>

> > Be that as it may, Wicki (e.g. on the Thummer) has roughly
> > vertical octaves too. -Carl
>
> Bosanquet, Janko and Fokker had horizontal octaves, and that is what I had in mind for Bosanquet lattices. Does anyone have any fingering experience to compare here?

I can attest to the ease of vertical octaves and the "steps with carriage returns" scales of the Wicki layout. I've been playing my "jammer" (generic thummer) for a little while now and have found, especially with two keyboards, that playing with vertical ascension in pitch is far more comfortable than playing horizontally on the piano where i have to do much more large muscle movement to go from left to right. It's easier to think about too, IMO. Octaves are up, cardinality extends out to the left and right.

Here are two videos of mine that I think make my point pretty well:

An older video with two keyboards, one per hand:
http://www.youtube.com/watch?v=qyr9Mywnmys

And a more recent one, but before I got both keyboards working at once with my mac:
http://www.youtube.com/watch?v=-sm5dh3fyzQ

John

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
>
> > > > > For a physical keyboard, the 7L 5S is getting too tall
> > > > > I think, and the 1L 6S too wide.
> > > >
> > > > The lattice can be horizontally or vertically scaled to
> > > > change the overall profile.
> > >
> > > Only by wasting space (assuming a minimum or optimal
> > > key size).
> >
> > Not too sure what you mean by wasted space.
>
> If we stretch the layout horizontally to make the 7L 5S
> unit cell square, the keys regions are wider than optimal.
> Or maybe I misunderstood what you meant.

What is a unit cell, and why does it need to be square? I would have thought the only thing that matters is that adjacent buttons in the same row are a "finger" apart. I think the distance betwen rows is less important---a wide range of distances should still allow for an easy carriage return motion. The further the lattice extends vertically the greater the overall pitch range available, so there's no wastage there. Any unused space to the left and right can house a thumb or pinkie controller (for tuning, pitch bend, vibrato, brightness, whatever), so there's no wastage there. But maybe I'm still not getting what you're saying...

(BTW, in case it's not obvious, I'm thinking of these flexible layouts as living in Hex or a multitouch controller, e.g., iPad.)

Andy

🔗Carl Lumma <carl@...>

Andy wrote:
> > If we stretch the layout horizontally to make the 7L 5S
> > unit cell square, the keys regions are wider than optimal.
> > Or maybe I misunderstood what you meant.
>
> What is a unit cell, and why does it need to be square?

It's a connected region of the keyboard containing all the
pitch classes of the scale with as few duplicates as possible
(generally none). Wilson calls it the "modulus".
It doesn't need to be square but if it's very oblong the
fingering will have more or fewer carriage returns than
seems ideal.

> (BTW, in case it's not obvious, I'm thinking of these flexible
> layouts as living in Hex or a multitouch controller, e.g., iPad.)

The convo does seem to drift between the subject of virtual
and physical keyboards. I'm ultimately only interested in
the latter.

-Carl

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
> > > If we stretch the layout horizontally to make the 7L 5S
> > > unit cell square, the keys regions are wider than optimal.
> > > Or maybe I misunderstood what you meant.
> >
> > What is a unit cell, and why does it need to be square?
>
> It's a connected region of the keyboard containing all the
> pitch classes of the scale with as few duplicates as possible
> (generally none).

Wilson calls it the "modulus".
> It doesn't need to be square but if it's very oblong the
> fingering will have more or fewer carriage returns than
> seems ideal.

I think that, given a linear and invertible mapping from 2-D tuning to 2-D button-lattice (such as the ones we've been discussing), any given MOS will have the same number of carriage returns (or advances), whatever the layout. Different layouts affect the extent to which each carriage return (advance) goes away, towards, or beyond, the start of the previous row of seconds.

By making the carriage return an appropriate size, the adjacent seconds layouts seem to minimise the overall "width" (as measured along the rows of seconds) required for any MOS.

(Both these assertions are intuitive, so may be wrong!).

I'm still not sure what you mean by wasted space in the adjacent seconds layouts for the 7L 5S and 1L 6S scales.

>
> > (BTW, in case it's not obvious, I'm thinking of these flexible
> > layouts as living in Hex or a multitouch controller, e.g., iPad.)
>
> The convo does seem to drift between the subject of virtual
> and physical keyboards. I'm ultimately only interested in
> the latter.

Though the design of the latter can be informed by the former.

Andy

>
> -Carl
>

🔗Carl Lumma <carl@...>

Andy wrote:
> > It doesn't need to be square but if it's very oblong the
> > fingering will have more or fewer carriage returns than
> > seems ideal.
>
> I think that, given a linear and invertible mapping from
> 2-D tuning to 2-D button-lattice (such as the ones we've been
> discussing), any given MOS will have the same number of
> carriage returns (or advances), whatever the layout.

Yes of course. It's not actually the carriage returns
that matter. It's fingering chords requiring rotation of
the hand, folding under of a finger, etc. In general it
seems to me the reach of the hand is roughly circular.

> I'm still not sure what you mean by wasted space in the
> adjacent seconds layouts for the 7L 5S and 1L 6S scales.

If you stretch or distort the keys to make the unit cell
square (which is what I thought you were saying) the key
regions just get bigger than what you started with (which is
presumably what you thought was ideal).

> > The convo does seem to drift between the subject of virtual
> > and physical keyboards. I'm ultimately only interested in
> > the latter.
>
> Though the design of the latter can be informed by the former.

Yes!

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

Yep - I'm playing vertical (1/4 turn counter-clockwise) in selfless mode.

Excellent playing by the way!

For some reason though when I mention that... no one hears (ugh) - just like
my question about Sword guitars.

Chris

On Mon, Nov 22, 2010 at 12:58 AM, John Moriarty <JlMoriart@...> wrote:

>
>
> > > Be that as it may, Wicki (e.g. on the Thummer) has roughly
> > > vertical octaves too. -Carl
> >
> > Bosanquet, Janko and Fokker had horizontal octaves, and that is what I
> had in mind for Bosanquet lattices. Does anyone have any fingering
> experience to compare here?
>
> I can attest to the ease of vertical octaves and the "steps with carriage
> returns" scales of the Wicki layout. I've been playing my "jammer" (generic
> thummer) for a little while now and have found, especially with two
> keyboards, that playing with vertical ascension in pitch is far more
> comfortable than playing horizontally on the piano where i have to do much
> more large muscle movement to go from left to right. It's easier to think
> about too, IMO. Octaves are up, cardinality extends out to the left and
> right.
>
> Here are two videos of mine that I think make my point pretty well:
>
> An older video with two keyboards, one per hand:
> http://www.youtube.com/watch?v=qyr9Mywnmys
>
> And a more recent one, but before I got both keyboards working at once with
> my mac:
> http://www.youtube.com/watch?v=-sm5dh3fyzQ
>
> John
>
>
>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
> > > It doesn't need to be square but if it's very oblong the
> > > fingering will have more or fewer carriage returns than
> > > seems ideal.
> >
> > I think that, given a linear and invertible mapping from
> > 2-D tuning to 2-D button-lattice (such as the ones we've been
> > discussing), any given MOS will have the same number of
> > carriage returns (or advances), whatever the layout.
>
> Yes of course. It's not actually the carriage returns
> that matter. It's fingering chords requiring rotation of
> the hand, folding under of a finger, etc. In general it
> seems to me the reach of the hand is roughly circular.

The ease of fingering of chords in a temperament and the ease of fingering its associated MOS scales is something of a lucky dip... I have provided a systematic method to provide layouts that facilitate the playing of different MOS scales - if chords are also easy to finger that's a bonus!

>
> > I'm still not sure what you mean by wasted space in the
> > adjacent seconds layouts for the 7L 5S and 1L 6S scales.
>
> If you stretch or distort the keys to make the unit cell
> square (which is what I thought you were saying) the key
> regions just get bigger than what you started with (which is
> presumably what you thought was ideal).

No, I see no reason to make the unit cell square. The only reasons to use scaling is to make buttons in a row a "finger" apart, and to allow a reasonable pitch range to be easily accessible with minimal hand movement.

Andy

>
> > > The convo does seem to drift between the subject of virtual
> > > and physical keyboards. I'm ultimately only interested in
> > > the latter.
> >
> > Though the design of the latter can be informed by the former.
>
> Yes!
>
> -Carl
>

🔗Carl Lumma <carl@...>

Andy:

> The ease of fingering of chords in a temperament and the
> ease of fingering its associated MOS scales is something
> of a lucky dip...

Not entirely, since presumably one chooses a temperament
low complexity.

> I have provided a systematic method to provide layouts
> that facilitate the playing of different MOS scales - if
> chords are also easy to finger that's a bonus!

I'm afraid I don't think of chords as a bonus.

> The only reasons to use scaling is to make buttons in a row
> a "finger" apart, and to allow a reasonable pitch range to
> be easily accessible with minimal hand movement.

I don't see any reason to rescale either, since it
wastes space. I thought you suggested it.

-Carl

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy:
>
> > The ease of fingering of chords in a temperament and the
> > ease of fingering its associated MOS scales is something
> > of a lucky dip...
>
> Not entirely, since presumably one chooses a temperament
> low complexity.

Just because an MOS scale is easy to finger does not necessarily imply that the chords it embeds are also easy to finger. If the MOS has a spatially compact representation, so will its embedded chords (and the adjacent seconds layouts are spatially compact), and this helps make chords easy to finger. But compactness is just one factor: another important aspect is orientation---the right hand can more easily play shapes that are oriented on a NE line than on a NW line. Sometimes an MOS scale may have an overall NE shape, but its embedded root-position triads a NW shape (e.g., the MOS 3L 7S scale with the Magic temperament). I'm not sure there's any easy way to deal with this melodic-harmonic conflict in a single layout; but when using two controllers, the layouts can be left-right reflected, so in such cases the left hand can easily play chords while the right hand plays melodies.

>
> > I have provided a systematic method to provide layouts
> > that facilitate the playing of different MOS scales - if
> > chords are also easy to finger that's a bonus!
>
> I'm afraid I don't think of chords as a bonus.

Indeed, chords are not a bonus in a musical sense (they are a bonus in terms of the constraints required to get optimal MOS scale fingering)! What I'm saying is that in some temperaments it is straightforward to make the fingering of both their chords and their associated MOS scales easy, in others it is not so straightforward.

>
> > The only reasons to use scaling is to make buttons in a row
> > a "finger" apart, and to allow a reasonable pitch range to
> > be easily accessible with minimal hand movement.
>
> I don't see any reason to rescale either, since it
> wastes space. I thought you suggested it.

I still don't get what you mean by "wastes space". If you can define what you mean I might be able to respond meaningfully to this point.

>
> -Carl
>

🔗Carl Lumma <carl@...>

I wrote:
> I'm afraid I don't think of chords as a bonus.

More to the point, I submit that it's easier to make chords
difficult or impossible to play than scales.

The reach of the fingers (with a static arm) is roughly
circular. If the unit cell is particularly oblong, it means
some intervals will be harder to reach than others. That
may be desired if you want to prioritize some intervals.
But generally I think a roughly square unit cell, with
consonances optimized within it, is a good goal.

Optimizing consonances within the unit cell is not as simple
as making them as short as possible. The "harmonic table"
layout makes 3rds and 5ths one step each. That makes the
major triad harder to play precisely than if they were
farther apart and placed to fall under the natural grasping
motion of the fingers.

The hand is 3-dimensional and so is the ideal keyboard.
However if we ditch the thumbs, a flat keyboard starts to
look better. It is certainly cheaper to make flat keyboards
and transport them. If you're going to go flat I think the
Thummer approach makes a lot of sense -- separate keyboards
for each hand with small keys and a hex layout. Some of the
benefits of this were discussed previously.

But the thumb is a terrible thing to waste, and if a tiered
keyboard like the Daskin ever makes it to market I'll
definitely buy it.

The fingers and the regions of their best (grasping) motion
are rectangular. This is a reason to favor rectangular or
oblong keys -- it lets the hand move while holding a note
(i.e. it makes a given note accessible from more hand
positions). This is also an advantage for rectangular
layouts (90deg), because only on such layouts can a key on
a given row pass *between* keys on adjacent rows. These
considerations are helpful in contrapuntal playing.
I felt their lack on Michael Zarkey's 19-tone harpsichord
and Scott Hackelman's 19-tone clavichord, and it's one
thing I don't like about the otherwise incredible Horvath/
Terpstra design. Rectangular layouts aren't as compact as
hexagonal ones, so that's a disadvantage.

Of course humans are remarkable at doing hard things --
who would have thought modern pianistic fireworks possible
from looking at the halberstadt? It's simply not realistic
to play around with layouts for an hour each and be able to
fairly compare them, especially if they differ in more than
one way (shape of digitals, size of keys, etc etc). You
may be able to compare their initial ease of use, but their
ultimate ease of use is more important.

It took me over a year after quitting cold turkey to reach
my old QWERTY speeds on Dvorak, and I don't think I surpassed
them until the current Apple desktop keyboards came out in
2007 (well, I had them in '07... maybe we didn't ship them
until '08). I hated them at first, but they are objectively
the best keyboards because they require so little force and
so little clearance between keys. So it's hard to evaluate
things. Playing my AXiS today, the desire to ditch it and
sit at the piano instead was overwhelming.

-Carl

🔗Carl Lumma <carl@...>

Hi Andy,

> Just because an MOS scale is easy to finger does not
> necessarily imply that the chords it embeds are also easy to
> finger. If the MOS has a spatially compact representation,
> so will its embedded chords (and the adjacent seconds layouts
> are spatially compact), and this helps make chords easy
> to finger. But compactness is just one factor: another
> important aspect is orientation---the right hand can more
> easily play shapes that are oriented on a NE line than on
> a NW line. Sometimes an MOS scale may have an overall
> NE shape, but its embedded root-position triads a NW shape
> (e.g., the MOS 3L 7S scale with the Magic temperament).
> I'm not sure there's any easy way to deal with this melodic-
> harmonic conflict in a single layout; but when using two
> controllers, the layouts can be left-right reflected, so in
> such cases the left hand can easily play chords while the
> right hand plays melodies.

Good points (I just finished writing some of the same things).

I asked Erv about mirroring layouts in the late '90s, but
he didn't seem to like the idea.

It may be worth saying that a single horizontal keyboard
can be "split" and mirrored too.

> Indeed, chords are not a bonus in a musical sense (they are
> a bonus in terms of the constraints required to get optimal
> MOS scale fingering)! What I'm saying is that in some
> temperaments it is straightforward to make the fingering of
> both their chords and their associated MOS scales easy,
> in others it is not so straightforward.

Agreed, but I would always sacrifice scales, because even
walking a scale with (say) the 1st and ring fingers every
note can be pretty fast, but having to rotate the hand to
reach common chords is an instant prescription for wristola.

> > > The only reasons to use scaling is to make buttons in
> > > a row a "finger" apart, and to allow a reasonable pitch
> > > range to be easily accessible with minimal hand movement.
> >
> > I don't see any reason to rescale either, since it
> > wastes space. I thought you suggested it.
>
> I still don't get what you mean by "wastes space".

As I said, given an optimal key size. Any other key
size wastes space (or doesn't provide enough). QED.

-Carl

🔗andymilneuk <ANDYMILNE@...>

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

> > Indeed, chords are not a bonus in a musical sense (they are
> > a bonus in terms of the constraints required to get optimal
> > MOS scale fingering)! What I'm saying is that in some
> > temperaments it is straightforward to make the fingering of
> > both their chords and their associated MOS scales easy,
> > in others it is not so straightforward.
>
> Agreed, but I would always sacrifice scales, because even
> walking a scale with (say) the 1st and ring fingers every
> note can be pretty fast, but having to rotate the hand to
> reach common chords is an instant prescription for wristola.

I agree. But the adjacent seconds layouts can be oriented to make the generator left or right of the octave to favour chordal over scalic fingering (when they conflict) to avoid the dreaded wristola.

I realise this may all sound very abstract at the moment but, hopefully, I'll soon upload a new version of Hex that should demonstrate these adjacent seconds layouts and how they work.

> > > > The only reasons to use scaling is to make buttons in
> > > > a row a "finger" apart, and to allow a reasonable pitch
> > > > range to be easily accessible with minimal hand movement.
> > >
> > > I don't see any reason to rescale either, since it
> > > wastes space. I thought you suggested it.
> >
> > I still don't get what you mean by "wastes space".
>
> As I said, given an optimal key size. Any other key
> size wastes space (or doesn't provide enough). QED.

I'm not sure there's any such thing as optimal key size. I would rather think in terms of optimal key spacing - i.e., the most common seconds should be a finger width apart, and the less common seconds should be within pinkie-thumb (or pinkie-first finger) distance.

🔗Carl Lumma <carl@...>

> > As I said, given an optimal key size. Any other key
> > size wastes space (or doesn't provide enough). QED.
>
> I'm not sure there's any such thing as optimal key size. I would
> rather think in terms of optimal key spacing

Yes, that's why in 2 previous messages I put the parenthetical
"key regions". "Spacing" is clearer though. I don't know if
you caught the Daskin thread but I think it's desirable to have
a buffer of null space between keys. Actually you can see the
Daskin setup here (plan view):

http://lumma.org/temp/Daskin6.png

with something like 10% vertical and 30% horizontal buffer,
which I reckon is about right for a horizontal keyboard where
horizontal hand placement is less accurate (e.g. playing stride).

-Carl

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> ...
> But the thumb is a terrible thing to waste, ...

One great advantage of the thumb is that it is able to cross under the fingers (and also allows the fingers to cross over it) for the fluent playing of scales. If you don't use the thumb, then your keyboard will have to be constructed in such a way that the fingering patterns for scales and arpeggios do not require any crossing over. This is one great advantage of having the octaves vertically oriented.

However, there are also ways to accomplish this with horizontally oriented octaves. For example, see file AcLh19p3.gif at:
/tuning-math/files/secor/kbds/
This is a variation on the original Bosanquet generalized keyboard, and it's intended as a button system for the left hand of a free-bass accordion. The illustration is for 19 tones/octave (with 3 extra tones at the near & far edges occurring in my multiple-purpose 19+3 temperament).

--George

🔗genewardsmith <genewardsmith@...>

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

> I agree. But the adjacent seconds layouts can be oriented to make the generator left or right of the octave to favour chordal over scalic fingering (when they conflict) to avoid the dreaded wristola.

What's your definition of a "second"? In the myna example I gave, with 10/9 and 8/7 as generators, I presume 10/9 is a second, but what about 8/7? If we used the 36/35-49/49-50/49 (all the same in myna) in place of 8/7, would that be a second?

May I presume "adjacent" means unit vectors 60 degrees apart in the hexagonal lattice setup, and 90 in the square lattice setup? How would you go about choosing adjacent seconds for myna (ie the linear temperament tempering out 126/125 and 1728/1715, with minor thirds as generator?)

🔗John Moriarty <JlMoriart@...>

🔗Graham Breed <gbreed@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > I agree. But the adjacent seconds layouts can be oriented to make the generator left or right of the octave to favour chordal over scalic fingering (when they conflict) to avoid the dreaded wristola.
>
> What's your definition of a "second"? In the myna example I gave, with 10/9 and 8/7 as generators, I presume 10/9 is a second, but what about 8/7? If we used the 36/35-49/49-50/49 (all the same in myna) in place of 8/7, would that be a second?

The layouts I have been suggesting are defined for MOS scales (not temperaments), in which case the meaning of a second is explicit. In these adjacent seconds layouts, the most common seconds of any MOS are adjacent, the pitch axis is vertical (so equal pitches have the same spatial height), the generator axis is horizontal (so octaves are vertically aligned).

>
> May I presume "adjacent" means unit vectors 60 degrees apart in the hexagonal lattice setup, and 90 in the square lattice setup?

Yes, but I've only considered hexagonal lattices, not square.

> How would you go about choosing adjacent seconds for myna (ie the linear temperament tempering out 126/125 and 1728/1715, with minor thirds as generator?)
>

For any rank-2 temperament, I would find an associated MOS scale, and choose an appropriate adjacent seconds layout.

Andy

🔗Mike Battaglia <battaglia01@...>

Looks like I missed a really interesting discussion.

On Mon, Nov 22, 2010 at 6:41 PM, Carl Lumma <carl@...> wrote:
>
> I wrote:
> > I'm afraid I don't think of chords as a bonus.
>
> More to the point, I submit that it's easier to make chords
> difficult or impossible to play than scales.
>
> The reach of the fingers (with a static arm) is roughly
> circular. If the unit cell is particularly oblong, it means
> some intervals will be harder to reach than others. That
> may be desired if you want to prioritize some intervals.
> But generally I think a roughly square unit cell, with
> consonances optimized within it, is a good goal.
>
> Optimizing consonances within the unit cell is not as simple
> as making them as short as possible. The "harmonic table"
> layout makes 3rds and 5ths one step each. That makes the
> major triad harder to play precisely than if they were
> farther apart and placed to fall under the natural grasping
> motion of the fingers.

I am shamelessly out of the loop here, and I'll have to go through
this massive thread when I have more time, but are you saying that you
generally favor redesigning the keyboard to satisfy various ergonomic
and intuition-pleasing ideals, rather than preserving the "pitch
increases linearly to the right" Halberstadt approach?

The concept of octaves being vertical quite frankly scares the hell
out of me, but maybe I could get used to it.

-Mike

🔗andymilneuk <ANDYMILNE@...>

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

> It may be a good point of departure for you to review some
> of Andy's papers, which are to date the most serious regular
> mapping papers we have, and the principle reason any of
> this stuff sticks on Wikipedia (thanks Andy!).
>
> This one, perhaps
>
> http://www.thummer.com/ThumTone/Tuning_Invariant_Layouts_Last_Draft.pdf
>

Actually I just wanted to point out that the above version (which was our original submission) was superseded by this one

http://homepages.cae.wisc.edu/~sethares/TuningContinua.pdf

which is essentially the same as the version found in the Journal of Math and Music (it contains more sophisticated maths in the first sections and better citations and various other corrections etc).

Andy

🔗Mike Battaglia <battaglia01@...>

On Tue, Nov 23, 2010 at 11:14 AM, andymilneuk <ANDYMILNE@...> wrote:
>
> Actually I just wanted to point out that the above version (which was our original submission) was superseded by this one
>
> http://homepages.cae.wisc.edu/~sethares/TuningContinua.pdf
>
> which is essentially the same as the version found in the Journal of Math and Music (it contains more sophisticated maths in the first sections and better citations and various other corrections etc).

Hi Andy,

Thanks for the cite. I'm trying to wrap my head around the matrices on
page 7. One small erratum I noted, though: The chain of 6 meantone
fourths produces Locrian mode, not Phrygian mode as described. You
have the intervals right (sLLsLLL), but called it Phrygian instead of
Locrian.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗John Moriarty <JlMoriart@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Nov 23, 2010 at 11:14 AM, andymilneuk <ANDYMILNE@...> wrote:
> >
> > Actually I just wanted to point out that the above version (which was our original submission) was superseded by this one
> >
> > http://homepages.cae.wisc.edu/~sethares/TuningContinua.pdf
> >
> > which is essentially the same as the version found in the Journal of Math and Music (it contains more sophisticated maths in the first sections and better citations and various other corrections etc).
>
> Hi Andy,
>
> Thanks for the cite. I'm trying to wrap my head around the matrices on
> page 7. One small erratum I noted, though: The chain of 6 meantone
> fourths produces Locrian mode, not Phrygian mode as described. You
> have the intervals right (sLLsLLL), but called it Phrygian instead of
> Locrian.

Actually I did catch that error just before publication, so it says Locrian in the printed and official (subscription required) web-version. I'm sure there are other errors we didn't catch...I know of at least one!

Andy

>
> -Mike
>

🔗Carl Lumma <carl@...>

🔗chrisvaisvil@...

John,

It looks like in the videos you can exchange the caps on your AXiS. Was it easy to do? Any particular precautions to take?

Thanks

Chris
*

-----Original Message-----
From: "John Moriarty" <JlMoriart@gmail.com>
Sender: tuning@yahoogroups.com
Date: Tue, 23 Nov 2010 19:31:31
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: Some conclusions about layouts...

> But if you have small keys with no space between them, you can easily
> play a chord with one finger.

It seems "One finger harmonies" aren't the thrill we'd thought they'e be, not even on the harmonic table. It's feasible to play them, but too hard to think about, IMO. See in this video:
http://www.youtube.com/watch?v=C9-OSCl7kOc&t=1m0s

Someone asked him why he wasn't using one finger chords in the comments, and he simply answered that he preferred not to. I've found the same thing in using wicki. I could use one finger to play the root-fifth interval, but I don't bother. Easier to think about it with -one finger-per-one note-.

John

🔗Carl Lumma <carl@...>

🔗John Moriarty <JlMoriart@...>

> It looks like in the videos you can exchange the caps on your AXiS. Was it easy to do? Any particular precautions to take?

I have a little bit written up on the process, but no visual documentation (hint hint). Overall, the process is simple and easy. The only downsides are if you manage to lose a piece (which, over hard floors, shouldn't happen) and that it voids your warranty:

____________________________

To physically remap the key-tops of the unit, first the bottom must
removed. This involves the removal of a few screws. Underneath the
bottom you will find the circuit board which must also be removed by
removing some more screws. Semi-attached to the board will be the
buttons that make contact with the board when the key-tops are
depressed. They are all held together in a sort of rubber sheet and
have little stubs that fit into holes in the circuit board to hold
them in place, but they are not physically attached to the board.
(Upon reconstruction of the unit, it is important that they line up
correctly with the board.)

Upon the rubber sheet's removal you are left with the physical keys
and the top half of the unit. The process of remapping the key tops is
dead easy: you just remove a small bottom peg of the key-top that holds it
secure, and the top of the button comes right off the top of the unit.
Do this for every key and place the tops in your new desired pattern.
(If you want to repaint the keys at all, this is the time to do it.)
As you're rearranging the keytops, place the little key bottoms back
on to secure them in place. (This is a point at which you must be
careful. If the little key bottoms are not 100% attached back to the
key-top, that key will stick out a little compared to the rest when
the unit is reassembled and you will have to take the whole thing
apart again and make sure that it is all the way attached. Also, do
this over hard floors so if you drop anything you can find it!)

Finally, once all the key tops and bottoms are all in place, start
reassembling the unit. Make sure that the rubber button contacts are
lined up with the circuit board and reattach them to the unit with
your screws, and then reattach the bottom to the whole unit. Check to
see that all the keys are level, plug it in, and make some music!
________________________________

Let me know if you have any questions.

John

🔗genewardsmith <genewardsmith@...>

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

> > What's your definition of a "second"? In the myna example I gave, with 10/9 and 8/7 as generators, I presume 10/9 is a second, but what about 8/7? If we used the 36/35-49/49-50/49 (all the same in myna) in place of 8/7, would that be a second?
>
> The layouts I have been suggesting are defined for MOS scales (not temperaments), in which case the meaning of a second is explicit.

That strikes me as overly restrictive. The 10/9 and 8/7 system I mention above for myna will not arise from consideration of MOS scales, but it seems to me to be a perfectly reasonable and practical suggestion. But I've no practical experience, so I wonder if you would agree. Perhaps removing the restriction that the scale steps must correspond to the generators would work to get things like 10/9-8/7.

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > > What's your definition of a "second"? In the myna example I gave, with 10/9 and 8/7 as generators, I presume 10/9 is a second, but what about 8/7? If we used the 36/35-49/49-50/49 (all the same in myna) in place of 8/7, would that be a second?
> >
> > The layouts I have been suggesting are defined for MOS scales (not temperaments), in which case the meaning of a second is explicit.
>
> That strikes me as overly restrictive. The 10/9 and 8/7 system I mention above for myna will not arise from consideration of MOS scales, but it seems to me to be a perfectly reasonable and practical suggestion. But I've no practical experience, so I wonder if you would agree. Perhaps removing the restriction that the scale steps must correspond to the generators would work to get things like 10/9-8/7.
>

I need more information about myna to answer this. From previous posts in this thread, I assume myna is a rank-2 temperament which can have a basis of a tempered 2/1 and 6/5, or a basis of a tempered 10/9 and 8/7? If so, what is the advantage of using the second basis?

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
> >
> > > > What's your definition of a "second"? In the myna example I gave, with 10/9 and 8/7 as generators, I presume 10/9 is a second, but what about 8/7? If we used the 36/35-49/49-50/49 (all the same in myna) in place of 8/7, would that be a second?
> > >
> > > The layouts I have been suggesting are defined for MOS scales (not temperaments), in which case the meaning of a second is explicit.
> >
> > That strikes me as overly restrictive. The 10/9 and 8/7 system I mention above for myna will not arise from consideration of MOS scales, but it seems to me to be a perfectly reasonable and practical suggestion. But I've no practical experience, so I wonder if you would agree. Perhaps removing the restriction that the scale steps must correspond to the generators would work to get things like 10/9-8/7.
> >
>
> I need more information about myna to answer this. From previous posts in this thread, I assume myna is a rank-2 temperament which can have a basis of a tempered 2/1 and 6/5, or a basis of a tempered 10/9 and 8/7? If so, what is the advantage of using the second basis?

The advantage is that 8/7-10/9 can be used as a pair of adjacent seconds on a button lattice. Some other good possibilities would be 7/6-8/7, 7/6-36/35, 8/7-36/35 and 10/9-36/35.

Myna tempers out 126/125 and 1728/1715. (6/5)^10 equates to 6, (6/5)^9 to 5, and (6/5)^7 to 7/2, which requires the 6/5 generator to be flat. The minimax generator, which gives JI octaves and fifths, has it at 6^(1/10), or 310.1955 cents. The pure octaves TE tuning has it at 310.1459 cents.

🔗Carl Lumma <carl@...>

Thanks John. If I ever settle on a layout I'll rearrange
to it. -Carl

> To physically remap the key-tops of the unit, first the bottom must
> removed. This involves the removal of a few screws. Underneath the
> bottom you will find the circuit board which must also be removed by
> removing some more screws. Semi-attached to the board will be the
> buttons that make contact with the board when the key-tops are
> depressed. They are all held together in a sort of rubber sheet and
> have little stubs that fit into holes in the circuit board to hold
> them in place, but they are not physically attached to the board.
> (Upon reconstruction of the unit, it is important that they line up
> correctly with the board.)
>
> Upon the rubber sheet's removal you are left with the physical keys
> and the top half of the unit. The process of remapping the key tops
> is dead easy: you just remove a small bottom peg of the key-top
> that holds it secure, and the top of the button comes right off the
> top of the unit. Do this for every key and place the tops in your
> new desired pattern.
> (If you want to repaint the keys at all, this is the time to do it.)
> As you're rearranging the keytops, place the little key bottoms back
> on to secure them in place. (This is a point at which you must be
> careful. If the little key bottoms are not 100% attached back to the
> key-top, that key will stick out a little compared to the rest when
> the unit is reassembled and you will have to take the whole thing
> apart again and make sure that it is all the way attached. Also, do
> this over hard floors so if you drop anything you can find it!)
>
> Finally, once all the key tops and bottoms are all in place, start
> reassembling the unit. Make sure that the rubber button contacts are
> lined up with the circuit board and reattach them to the unit with
> your screws, and then reattach the bottom to the whole unit. Check
> to see that all the keys are level, plug it in, and make some music!
> ________________________________
>
> Let me know if you have any questions.
>
> John
>

🔗andymilneuk <ANDYMILNE@...>

🔗genewardsmith <genewardsmith@...>

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andy wrote:
>
> > I need more information about myna to answer this. From previous
> > posts in this thread, I assume myna is a rank-2 temperament which
> > can have a basis of a tempered 2/1 and 6/5, or a basis of a
> > tempered 10/9 and 8/7? If so, what is the advantage of using the
> > second basis?
>
> I'm not sure I understand Gene's question. Your Wicki layouts
> would work with either basis. Your adjacent-2nds layouts would
> require a MOS. Myna has a 7-tone MOS LsLsLsL, L = approx 7/6
> and s = approx 36/35. I presume you'd use that. Maybe Gene
> just means there are other possible mappings that might be good.

http://www.dynamictonality.com/layouts/MOS%204L%203S%20(myna).jpg

...this is what an adjacent seconds layout for MOS 4L 3S looks like (with a generator of 310 cents).

Andy

🔗andymilneuk <ANDYMILNE@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "andymilneuk" <ANDYMILNE@> wrote:
>
> > > The advantage is that 8/7-10/9 can be used as a pair of adjacent seconds on a button lattice.
> >
> > So, to be sure I understand, are you suggesting the tempered 8/7 could be mapped one adjacent button (e.g., North East), and the tempered 10/9 to another (e.g., East)?
> >
>
> Precisely.
>

The graphic I linked to in my previous post (adjacent seconds layout for MOS 4L 3S generator 310 cents) would, at first sight, seem to have both the tempered 8/7 and the tempered 10/9 as spatially adjacent buttons - which is what you've suggested. (But I don't know what the mappings of myna are, so I don't know if that is actually the case.)

Here's the link again...

http://www.dynamictonality.com/layouts/MOS%204L%203S%20(myna).jpg

🔗genewardsmith <genewardsmith@...>

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

> The graphic I linked to in my previous post (adjacent seconds layout for MOS 4L 3S generator 310 cents) would, at first sight, seem to have both the tempered 8/7 and the tempered 10/9 as spatially adjacent buttons - which is what you've suggested. (But I don't know what the mappings of myna are, so I don't know if that is actually the case.)

It seems it makes the most sense to look at the whole hexagon, and not just an adjacent pair. Following that logic, counterclockwise around from 10/9 we would get 10/9, 8/7, 36/35, 9/10, 7/8, 35/36. So we have both 10/9-8/7 and 8/7-36/35 as adjacent pairs; the first corresponding to an 18-note non-MOS and the second to an 11-note MOS. Pairs like 36/35-9/10 correspond to non-adjacent (120 degree) pairs such as 10/9-36/35. So you could indeed get the 10/9-8/7 pair at second hand, so to speak, from the 4L7s MOS. The 4L3s MOS corresponds to 7/6-36/35, which gives a hexagon 7/6, 36/35, 7/8, 6/7, 35/36, 8/7, which also has adjacent 8/7-7/6, with a 10-note non-MOS scale, or modulus, or whatever you wish to call it.

🔗Chris Vaisvil <chrisvaisvil@...>

Thanks John!!

Wow - this is pretty involved!

On Tue, Nov 23, 2010 at 3:44 PM, John Moriarty <JlMoriart@...> wrote:

>
>
> > It looks like in the videos you can exchange the caps on your AXiS. Was
> it easy to do? Any particular precautions to take?
>
> I have a little bit written up on the process, but no visual documentation
> (hint hint). Overall, the process is simple and easy. The only downsides are
> if you manage to lose a piece (which, over hard floors, shouldn't happen)
> and that it voids your warranty:
>
> ____________________________
>
> To physically remap the key-tops of the unit, first the bottom must
> removed. This involves the removal of a few screws. Underneath the
> bottom you will find the circuit board which must also be removed by
> removing some more screws. Semi-attached to the board will be the
> buttons that make contact with the board when the key-tops are
> depressed. They are all held together in a sort of rubber sheet and
> have little stubs that fit into holes in the circuit board to hold
> them in place, but they are not physically attached to the board.
> (Upon reconstruction of the unit, it is important that they line up
> correctly with the board.)
>
> Upon the rubber sheet's removal you are left with the physical keys
> and the top half of the unit. The process of remapping the key tops is
> dead easy: you just remove a small bottom peg of the key-top that holds it
> secure, and the top of the button comes right off the top of the unit.
> Do this for every key and place the tops in your new desired pattern.
> (If you want to repaint the keys at all, this is the time to do it.)
> As you're rearranging the keytops, place the little key bottoms back
> on to secure them in place. (This is a point at which you must be
> careful. If the little key bottoms are not 100% attached back to the
> key-top, that key will stick out a little compared to the rest when
> the unit is reassembled and you will have to take the whole thing
> apart again and make sure that it is all the way attached. Also, do
> this over hard floors so if you drop anything you can find it!)
>
> Finally, once all the key tops and bottoms are all in place, start
> reassembling the unit. Make sure that the rubber button contacts are
> lined up with the circuit board and reattach them to the unit with
> your screws, and then reattach the bottom to the whole unit. Check to
> see that all the keys are level, plug it in, and make some music!
> ________________________________
>
> Let me know if you have any questions.
>
> John
>
>
>

🔗genewardsmith <genewardsmith@...>

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

> It seems it makes the most sense to look at the whole hexagon, and not just an adjacent pair. Following that logic, counterclockwise around from 10/9 we would get 10/9, 8/7, 36/35, 9/10, 7/8, 35/36. So we have both 10/9-8/7 and 8/7-36/35 as adjacent pairs; the first corresponding to an 18-note non-MOS and the second to an 11-note MOS. Pairs like 36/35-9/10 correspond to non-adjacent (120 degree) pairs such as 10/9-36/35. So you could indeed get the 10/9-8/7 pair at second hand, so to speak, from the 4L7s MOS. The 4L3s MOS corresponds to 7/6-36/35, which gives a hexagon 7/6, 36/35, 7/8, 6/7, 35/36, 8/7, which also has adjacent 8/7-7/6, with a 10-note non-MOS scale, or modulus, or whatever you wish to call it.
>

Most often 2 will be inside one of the 1/6 pie pie-slices for a generator pair, which is presumably the canonical pair for that particular hexagon. That would mean 8/7-36/35 with the 4L7s MOS for the first of these hexagons, and 7/6-36/35 with the 4L3s MOS for the second. It would be nice to have either a proof the canonical pair is always a MOS, or an example of where it isn't. I have an idea of how you might prove it, but this is getting off-topic for the tuning list.