Yahoo Tuning Groups Ultimate Backup makemicromusic Isomorphic Keyboards

Gentlepersons,

Bill Sethares recommended that I share with you my recent work on
isomorphic keyboards.

There are many known keyboard layouts that have the same fingering in
all 12-ET keys. The Janko keyboard and the Chromatic Button Accordion's
C-System and B-System are well-known.

http://www.thecipher.com/isomorphic_keyboards_cipher.html

Less well-known are the Wicki/Hayden keyboard.

http://www.maccann-duet.com/hayden

.and the keyboard patented by Wesley in 2002.

www.uspto.gov <http://www.uspto.gov/> , patent number
search, # 6,501,011

.and doubtless others of which I am unaware.

On www.thecipher.com <http://www.thecipher.com/> , Roger E. Blumberg
calls these keyboard layouts "isomorphic," from the Greek roots meaning
"same shape," and I've adopted that term. On an isomorphic keyboard,
every occurrence of a given interval has the "same shape" wherever it
occurs (edge conditions aside).

I have attached a PDF file ("Summary of Isomorphic Keyboard Layouts,"
13K) that describes the essential characteristics that can be used to
discriminate among all possible isomorphic keyboards. I have also
attached an image of a three-octave, 19-button-per octave Wicki/Hayden
keyboard (19ButtonName.jpg, 194K).

The Wicki/Hayden layout is a particularly interesting isomorphic layout
because

(a) it exposes the symmetry of the diatonic scale around the second
degree of its Ionian mode (D in C Major)

(b) by sizing, spacing, and shaping the note-controlling buttons
optimally (which is NOT shown in the attached JPG), one can fit a
three-octave range of buttons within the span of a single hand's
fingers, and

(c) it clusters the notes of the diatonic scale into a single
multi-button column, flanked on either side by multi-button columns of
chromatic notes.

By naming one such chromatic column's buttons using flat names, and the
other using sharp names, the isomorphic fingering patterns of scales,
chords, etc. can be consistent with traditional note-naming conventions.

http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf

Bill tells me that microtonalists might be particularly interested in
the observation that if any given isomorphic keyboard (not just the
Wicki/Hayden) uses this system of enharmonic naming (flats on one
"side," sharps on the other) then it will have the same pattern of
note-names in every N-ET tuning if at least N buttons are included per
octave. This is particularly useful for those N that provide a
recognizable diatonic scale. The Wicki/Hayden keyboard displays this
consistency especially clearly, due to its being vertically symmetrical
around D.

More specifically, an electronic instrument that used a
19-button-per-octave Wicki/Hayden keyboard layout (like that shown in
the attached JPG) would present the same pattern of note-names in 12-ET,
17-ET, and 19-ET.

+ In 12-ET, the buttons labeled Cb and E# would be enharmonic with the
diatonic (white) B and F buttons respectively; all of the other black
buttons would be enharmonic with other black buttons (on the other
side).

+ In 17-ET, Cb and E# would still be enharmonic with the diatonic B and
F respectively, but none of the other black buttons would be enharmonic
with any other.

+ In 19-ET, the keyboard would not have any enharmonic buttons; each
button would control a unique pitch.

Because such a keyboard would have the same fingering of diatonic
patterns (the diatonic scale, diatonic chords, etc.) in all such N-ET
tunings, it would be an especially effective tool for introducing
microtonal novices to non-12 ET divisions of the octave. Indeed, if
successful solely on its 12-ET-based merits, such an instrument could be
the Trojan Horse that slips an hidden cargo of microtonality into the
mainstream musical world.

The first question for this group is: is what I've presented in this
email and its attachments already known, or its it novel? I understand
that Erv Wilson has done a lot of work with generalized keyboards, but
what I've read of his work does not seem to parallel mine - unless I'm
missing something, which is more than likely. :-)

Let's take a moment to consider some of the other benefits provided by
an instrument with two keyboards (one for each hand, optionally mirrored
to reflect the mirroring of human hands), each with three-octave,
19-button-per-octave, W/H-optimized button-arrangements.

1) It places three octaves under the span of each hand, so - using both
hands - you can select notes from across a six-octave range
simultaneously. That's about three times the span of two hands over a
piano keyboard.

2) You can press the two adjacent buttons sounding any given P4 or P5
interval (or the three mutually-adjacent buttons sounding any given sus2
or sus4 triad) simultaneously with a single fingertip. Using one hand,
one can play eight or more harmonious notes simultaneously. Look at the
W/H keyboard, and you'll see that this makes single-handed playing of
highly-extended chords possible, without dropping notes.

Because you can play lots of harmonious notes over a wide range on a
Wicki/Hayden layout-based instrument, it is possible to play
(essentially) full orchestra scores on it, whereas such scores have to
be reduced significantly to be played on the piano. This ability has
been demonstrated by performers of W/H-based acoustic concertinas - it's
real, not theoretical.

3) Because the W/H-based keyboards are so small, the entire two-keyboard
(hence six octave) instrument can be remarkably tiny - about the size
and weight of a thick paperback book, partially opened.

The second question for the group is: if you presumed that such a
six-octave, 19-button-per-octave, W/H-layout instrument had all the
usual MIDI keyboard features, was Mac & PC compatible, was compatible
with both hardware and software synths, emitted data via all the usual
physical & wireless interfaces, was highly programmable, had
velocity-sensitive keys and polyphonic aftertouch, supported OSC, and
generally supported every other feature ever seen on any other
MIDI-controller keyboard ever.

+ Would you buy one?

+ What would it worth to you (i.e., what would you be both willing and
capable of paying me for it), given its unique advantages, including its
isomorphic support for microtonality?

+ What among the above described features is of greatest value to you?

+ How many people do you think there are in the world who would buy one
at that price for the same reason(s) you would?

+ How price-elastic to you think that demand is? Alternatively put, by
what percentage would I have to lower its price to sell twice as many,
all else being equal?

Hoping that interested readers will respond to the group regarding
novelty (question #1), and to me privately (james@...)
regarding the product/market/pricing issues (question #2), I am

Sincerely Yours,

James

P.S.: I am not able to supply any additional details about the proposed
instrument at this time, but I would welcome your suggestions, sent to
me privately.

P.P.S.: One feature request I know I'll get from this group is to
deliver more than 19 buttons per octave. Sorry, I can't do it. 19 is
the upper bound of what the human hand can span at maximum
button-density - I've checked. In my proposed instrument, if you can't
span it, you can't play it, so there's no point. You're welcome to
build your own isomorphic 22-button-per-octave keyboards, though! :-)

[Non-text portions of this message have been removed]

🔗Kraig Grady <kraiggrady@...>

🔗Rich Holmes <rsholmes@...>

🔗James Plamondon <james@...>

Gentlepersons,

The attachments stripped from my initial email can be found at:

www.jamatronics.com/keyboards.pdf

www.jamatronics.com/19_Button.jpg

I apologize for not realizing that these would be stripped from my
email, and I encourage this group's members to check out the above
documents.

To answer another question: yes, many Wicki/Hayden keyboards exist.

Wicki, being Swiss and having written his patent in German, had his
greatest influence in Germany. It is my understanding (input from a
musical instrument historian would be welcome here) that many German
migrants took their W/H-layout bandoneons to Argentina, where they
became the typical instrument of the tango. Because Wicki did not get
an English patent, and the concertina was already in decline by the time
of his Swiss patent (1896), the Wicki layout was unknown in England
until Hayden discovered it independently 90 years later.

A number of small-scale manufacturers - Stagi, Morse, Dipper, Marcus,
Dickinson, and one other whose name I've misplaced -manufacture
W/H-layout concertinas (invariably described as "Hayden" concertinas,
since the Wicki patent was only "discovered" by Anglophones last year).

There are probably thousands of W/H-layout bandoneons and hundreds of
W/H concertinas in active use. These should not be confused with the
"Anglo"-style concertinas used in Irish folk music! The W/H-layout
concertinas are of the fully-chromatic "duet" type.

The point is NOT that you need to learn about concertinas and bandoneons
- you don't. The point is that these instruments provide an "existence
proof" that the W/H layout can be used for a wide variety of complex and
challenging music.

Thanks! :-)

--- James

-----Original Message-----
From: Kraig Grady [mailto:kraiggrady@...]
Sent: Sunday, 23 January 2005 12:49 AM
To: MakeMicroMusic@yahoogroups.com
Subject: Re: [MMM] Isomorphic Keyboards

The Hayden Keyboard is what Westley came up with later.
except upside down and with buttons ( which is an insignificant
differance) . Erv has the same being the very first keyboard pattern
tuned on it side here. (generator being a fifth)
http://www.anaphoria.com/key.PDF

The Hayden Keyboard appears to be the oldest out of the three compared
to what is in front of me. was any of these ever built

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

_____

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[Non-text portions of this message have been removed]

🔗Rich Holmes <rsholmes@...>

🔗James Plamondon <james@...>

🔗harold_fortuin <harold@...>

James,

Thanks for the details about bandeons, etc. Until George Secor & you
mentioned this, I had no idea that such layouts were already in use
on commonly played instruments.

I'm always pleased to hear about microtonal keyboard projects. I'm
one of the few around to have built one with engineering help: The
Clavette
http://www.geocities.com/harold_fortuin/clavett.htm
(a photo of the keys is posted up here in the Photos folder)

and I also own a Microzone, an 810 key generalized keyboard built
and sold by Starr Labs (developed with input from Erv Wilson)
http://www.starrlabs.com/

You'll note that Starr Labs also has a smaller number-of-keys
keyboard which could also be treated as a generalized keyboard,
which should be much less than the Microzone (which I think today
costs in the upper 4 figures).

As I investigated various tunings, I found I did not want to be
limited to a particular number of notes per octave, although I
haven't yet ventured beyond 31 /octave myself for practical reasons.

I would not want to discourage you from building your own dream
keyboard, but the market of course is so far quite small for these
devices, and of course your keyboard would not be suited to all-
tones-of-the-scale > 19-tone scales, unlike either the Microzone or
Clavette. Also, as a proficient pianist and intermediate-level
generalized keyboard performer, I prefer the Wilsonian horizontal
positioning of the diatonic tones, which of course remains the same
for "fully diatonic" tunings (sorry I don't know the precise term),
those that are 5 * whole step + 2 * half-step. If you'd like to
understand more about the relations of tunings and their layouts on
generalized (or potentially generalized keyboards like yours), you
should speak to Erv Wilson.

At least before venturing into commercial production,
you might be wise to meet with Harvey Starr and Erv Wilson. And in
any case, the anaphoria.com website of Kraig Grady could be a
helpful resource, even if you're determined to keep your keyboard 19-
centric.

Best of luck in your venture,
Harold Fortuin

--- In MakeMicroMusic@yahoogroups.com, "James Plamondon"
<james@p...> wrote:
> Gentlepersons,
>
>
>
> Bill Sethares recommended that I share with you my recent work on
> isomorphic keyboards.
>
>
>
> There are many known keyboard layouts that have the same fingering
in
> all 12-ET keys. The Janko keyboard and the Chromatic Button
Accordion's
> C-System and B-System are well-known.
>
>
http://www.thecipher.com/isomorphic_keyboards_cipher.html
>
>
>
> Less well-known are the Wicki/Hayden keyboard.
>
> http://www.maccann-duet.com/hayden
>
> .and the keyboard patented by Wesley in 2002.
>
> www.uspto.gov <http://www.uspto.gov/> , patent number
> search, # 6,501,011
>
> .and doubtless others of which I am unaware.
>
>
>
> On www.thecipher.com <http://www.thecipher.com/> , Roger E.
Blumberg
> calls these keyboard layouts "isomorphic," from the Greek roots
meaning
> "same shape," and I've adopted that term. On an isomorphic
keyboard,
> every occurrence of a given interval has the "same shape" wherever
it
> occurs (edge conditions aside).
>
>
>
> I have attached a PDF file ("Summary of Isomorphic Keyboard
Layouts,"
> 13K) that describes the essential characteristics that can be used
to
> discriminate among all possible isomorphic keyboards. I have also
> attached an image of a three-octave, 19-button-per octave
Wicki/Hayden
> keyboard (19ButtonName.jpg, 194K).
>
>
>
> The Wicki/Hayden layout is a particularly interesting isomorphic
layout
> because
>
> (a) it exposes the symmetry of the diatonic scale around the second
> degree of its Ionian mode (D in C Major)
>
>
>
> (b) by sizing, spacing, and shaping the note-controlling buttons
> optimally (which is NOT shown in the attached JPG), one can fit a
> three-octave range of buttons within the span of a single hand's
> fingers, and
>
>
>
> (c) it clusters the notes of the diatonic scale into a single
> multi-button column, flanked on either side by multi-button
columns of
> chromatic notes.
>
>
>
> By naming one such chromatic column's buttons using flat names,
and the
> other using sharp names, the isomorphic fingering patterns of
scales,
> chords, etc. can be consistent with traditional note-naming
conventions.
>
>
> http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf
>
>
>
> Bill tells me that microtonalists might be particularly interested
in
> the observation that if any given isomorphic keyboard (not just the
> Wicki/Hayden) uses this system of enharmonic naming (flats on one
> "side," sharps on the other) then it will have the same pattern of
> note-names in every N-ET tuning if at least N buttons are included
per
> octave. This is particularly useful for those N that provide a
> recognizable diatonic scale. The Wicki/Hayden keyboard displays
this
> consistency especially clearly, due to its being vertically
symmetrical
> around D.
>
>
>
> More specifically, an electronic instrument that used a
> 19-button-per-octave Wicki/Hayden keyboard layout (like that shown
in
> the attached JPG) would present the same pattern of note-names in
12-ET,
> 17-ET, and 19-ET.
>
> + In 12-ET, the buttons labeled Cb and E# would be enharmonic with
the
> diatonic (white) B and F buttons respectively; all of the other
black
> buttons would be enharmonic with other black buttons (on the other
> side).
>
> + In 17-ET, Cb and E# would still be enharmonic with the diatonic
B and
> F respectively, but none of the other black buttons would be
enharmonic
> with any other.
>
> + In 19-ET, the keyboard would not have any enharmonic buttons;
each
> button would control a unique pitch.
>
>
>
> Because such a keyboard would have the same fingering of diatonic
> patterns (the diatonic scale, diatonic chords, etc.) in all such N-
ET
> tunings, it would be an especially effective tool for introducing
> microtonal novices to non-12 ET divisions of the octave. Indeed,
if
> successful solely on its 12-ET-based merits, such an instrument
could be
> the Trojan Horse that slips an hidden cargo of microtonality into
the
> mainstream musical world.
>
>
>
> The first question for this group is: is what I've presented in
this
> email and its attachments already known, or its it novel? I
understand
> that Erv Wilson has done a lot of work with generalized keyboards,
but
> what I've read of his work does not seem to parallel mine - unless
I'm
> missing something, which is more than likely. :-)
>
>
>
> Let's take a moment to consider some of the other benefits
provided by
> an instrument with two keyboards (one for each hand, optionally
mirrored
> to reflect the mirroring of human hands), each with three-octave,
> 19-button-per-octave, W/H-optimized button-arrangements.
>
> 1) It places three octaves under the span of each hand, so - using
both
> hands - you can select notes from across a six-octave range
> simultaneously. That's about three times the span of two hands
over a
> piano keyboard.
>
>
>
> 2) You can press the two adjacent buttons sounding any given P4 or
P5
> interval (or the three mutually-adjacent buttons sounding any
given sus2
> or sus4 triad) simultaneously with a single fingertip. Using one
hand,
> one can play eight or more harmonious notes simultaneously. Look
at the
> W/H keyboard, and you'll see that this makes single-handed playing
of
> highly-extended chords possible, without dropping notes.
>
>
>
>
> Because you can play lots of harmonious notes over a wide range on
a
> Wicki/Hayden layout-based instrument, it is possible to play
> (essentially) full orchestra scores on it, whereas such scores
have to
> be reduced significantly to be played on the piano. This ability
has
> been demonstrated by performers of W/H-based acoustic concertinas -
it's
> real, not theoretical.
>
>
>
> 3) Because the W/H-based keyboards are so small, the entire two-
keyboard
> (hence six octave) instrument can be remarkably tiny - about the
size
> and weight of a thick paperback book, partially opened.
>
>
>
> The second question for the group is: if you presumed that such a
> six-octave, 19-button-per-octave, W/H-layout instrument had all the
> usual MIDI keyboard features, was Mac & PC compatible, was
compatible
> with both hardware and software synths, emitted data via all the
usual
> physical & wireless interfaces, was highly programmable, had
> velocity-sensitive keys and polyphonic aftertouch, supported OSC,
and
> generally supported every other feature ever seen on any other
> MIDI-controller keyboard ever.
>
> + Would you buy one?
>
> + What would it worth to you (i.e., what would you be both willing
and
> capable of paying me for it), given its unique advantages,
including its
> isomorphic support for microtonality?
>
> + What among the above described features is of greatest value to
you?
>
> + How many people do you think there are in the world who would
buy one
> at that price for the same reason(s) you would?
>
> + How price-elastic to you think that demand is? Alternatively
put, by
> what percentage would I have to lower its price to sell twice as
many,
> all else being equal?
>
>
>
> Hoping that interested readers will respond to the group regarding
> novelty (question #1), and to me privately (james@p...)
> regarding the product/market/pricing issues (question #2), I am
>
>
>
>
> Sincerely Yours,
>
>
>
>
>
> James
>
>
>
> P.S.: I am not able to supply any additional details about the
proposed
> instrument at this time, but I would welcome your suggestions,
sent to
> me privately.
>
>
>
> P.P.S.: One feature request I know I'll get from this group is to
> deliver more than 19 buttons per octave. Sorry, I can't do it.
19 is
> the upper bound of what the human hand can span at maximum
> button-density - I've checked. In my proposed instrument, if you
can't
> span it, you can't play it, so there's no point. You're welcome to
> build your own isomorphic 22-button-per-octave keyboards,
though! :-)
>
>
>
> [Non-text portions of this message have been removed]

🔗Alexandros Papadopoulos <Alexmoog@...>

🔗harold_fortuin <harold@...>

🔗James Plamondon <james@...>

Harold -

I appreciate your response and feedback. :-)

Actually, the keyboard is resolutely 12-ET-centric for purely commercial
reasons. Its support for 17-ET and 19-ET is an unexpected side-effect of
its geometric consistency (isomorphism) in 12-ET.

Would you say that the geometric conditions necessary for isomorphism (as
described here: www.jamatronics.com/keyboards.pdf) are common knowledge in
the microtonal community?

Thanks! :-)

--- Jim

_____

From: harold_fortuin [mailto:harold@...]
Sent: Wednesday, 26 January 2005 1:42 AM
To: MakeMicroMusic@yahoogroups.com
Subject: [MMM] Re: Isomorphic Keyboards

James,

Thanks for the details about bandeons, etc. Until George Secor & you
mentioned this, I had no idea that such layouts were already in use
on commonly played instruments.

and I also own a Microzone, an 810 key generalized keyboard built
and sold by Starr Labs (developed with input from Erv Wilson)
http://www.starrlabs.com/

As I investigated various tunings, I found I did not want to be
limited to a particular number of notes per octave, although I
haven't yet ventured beyond 31 /octave myself for practical reasons.

Best of luck in your venture,
Harold Fortuin

_____

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* To visit your group on the web, go to:
/makemicromusic/

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[Non-text portions of this message have been removed]

🔗George D. Secor <gdsecor@...>

🔗harold_fortuin <harold@...>

James,

Unfortunately, whenever I attempt to get the keyboards.pdf I get
a "Page not Found" error. Are you sure you didn't post it somewhere
else?

I don't know exactly how widely "the geometric conditions necessary
for isomorphism" are known and understood, but at least many
longtime participants on this list or tuning or similar lists will
have some acquaintance with generalized keyboards, whether or not
they've worked its principles in a formal way.

--- In MakeMicroMusic@yahoogroups.com, "James Plamondon"
<james@p...> wrote:
> Harold -
>
>
>
> I appreciate your response and feedback. :-)
>
>
>
> Actually, the keyboard is resolutely 12-ET-centric for purely
commercial
> reasons. Its support for 17-ET and 19-ET is an unexpected side-
effect of
> its geometric consistency (isomorphism) in 12-ET.
>
>
>
> Would you say that the geometric conditions necessary for
isomorphism (as
> described here: www.jamatronics.com/keyboards.pdf) are common
knowledge in
> the microtonal community?
>
>
>
> Thanks! :-)
>
>
>
> --- Jim
>
>
>
> _____
>
> From: harold_fortuin [mailto:harold@m...]
> Sent: Wednesday, 26 January 2005 1:42 AM
> To: MakeMicroMusic@yahoogroups.com
> Subject: [MMM] Re: Isomorphic Keyboards
>
>
>
>
> James,
>
> Thanks for the details about bandeons, etc. Until George Secor &
you
> mentioned this, I had no idea that such layouts were already in
use
> on commonly played instruments.
>
> I'm always pleased to hear about microtonal keyboard projects. I'm
> one of the few around to have built one with engineering help: The
> Clavette
> http://www.geocities.com/harold_fortuin/clavett.htm
> (a photo of the keys is posted up here in the Photos folder)
>
> and I also own a Microzone, an 810 key generalized keyboard built
> and sold by Starr Labs (developed with input from Erv Wilson)
> http://www.starrlabs.com/
>
> You'll note that Starr Labs also has a smaller number-of-keys
> keyboard which could also be treated as a generalized keyboard,
> which should be much less than the Microzone (which I think today
> costs in the upper 4 figures).
>
> As I investigated various tunings, I found I did not want to be
> limited to a particular number of notes per octave, although I
> haven't yet ventured beyond 31 /octave myself for practical
reasons.
>
> I would not want to discourage you from building your own dream
> keyboard, but the market of course is so far quite small for these
> devices, and of course your keyboard would not be suited to all-
> tones-of-the-scale > 19-tone scales, unlike either the Microzone
or
> Clavette. Also, as a proficient pianist and intermediate-level
> generalized keyboard performer, I prefer the Wilsonian horizontal
> positioning of the diatonic tones, which of course remains the
same
> for "fully diatonic" tunings (sorry I don't know the precise
term),
> those that are 5 * whole step + 2 * half-step. If you'd like to
> understand more about the relations of tunings and their layouts
on
> generalized (or potentially generalized keyboards like yours), you
> should speak to Erv Wilson.
>
> At least before venturing into commercial production,
> you might be wise to meet with Harvey Starr and Erv Wilson. And in
> any case, the anaphoria.com website of Kraig Grady could be a
> helpful resource, even if you're determined to keep your keyboard
19-
> centric.
>
> Best of luck in your venture,
> Harold Fortuin
>
> --- In MakeMicroMusic@yahoogroups.com, "James Plamondon"
> <james@p...> wrote:
> > Gentlepersons,
> >
> >
> >
> > Bill Sethares recommended that I share with you my recent work on
> > isomorphic keyboards.
> >
> >
> >
> > There are many known keyboard layouts that have the same
fingering
> in
> > all 12-ET keys. The Janko keyboard and the Chromatic Button
> Accordion's
> > C-System and B-System are well-known.
> >
> >
> http://www.thecipher.com/isomorphic_keyboards_cipher.html
> >
> >
> >
> > Less well-known are the Wicki/Hayden keyboard.
> >
> > http://www.maccann-duet.com/hayden
> >
> > .and the keyboard patented by Wesley in 2002.
> >
> > www.uspto.gov <http://www.uspto.gov/> , patent number
> > search, # 6,501,011
> >
> > .and doubtless others of which I am unaware.
> >
> >
> >
> > On www.thecipher.com <http://www.thecipher.com/> , Roger E.
> Blumberg
> > calls these keyboard layouts "isomorphic," from the Greek roots
> meaning
> > "same shape," and I've adopted that term. On an isomorphic
> keyboard,
> > every occurrence of a given interval has the "same shape"
wherever
> it
> > occurs (edge conditions aside).
> >
> >
> >
> > I have attached a PDF file ("Summary of Isomorphic Keyboard
> Layouts,"
> > 13K) that describes the essential characteristics that can be
used
> to
> > discriminate among all possible isomorphic keyboards. I have
also
> > attached an image of a three-octave, 19-button-per octave
> Wicki/Hayden
> > keyboard (19ButtonName.jpg, 194K).
> >
> >
> >
> > The Wicki/Hayden layout is a particularly interesting isomorphic
> layout
> > because
> >
> > (a) it exposes the symmetry of the diatonic scale around the
second
> > degree of its Ionian mode (D in C Major)
> >
> >
> >
> > (b) by sizing, spacing, and shaping the note-controlling buttons
> > optimally (which is NOT shown in the attached JPG), one can fit a
> > three-octave range of buttons within the span of a single hand's
> > fingers, and
> >
> >
> >
> > (c) it clusters the notes of the diatonic scale into a single
> > multi-button column, flanked on either side by multi-button
> columns of
> > chromatic notes.
> >
> >
> >
> > By naming one such chromatic column's buttons using flat names,
> and the
> > other using sharp names, the isomorphic fingering patterns of
> scales,
> > chords, etc. can be consistent with traditional note-naming
> conventions.
> >
> >
> > http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf
> >
> >
> >
> > Bill tells me that microtonalists might be particularly
interested
> in
> > the observation that if any given isomorphic keyboard (not just
the
> > Wicki/Hayden) uses this system of enharmonic naming (flats on one
> > "side," sharps on the other) then it will have the same pattern
of
> > note-names in every N-ET tuning if at least N buttons are
included
> per
> > octave. This is particularly useful for those N that provide a
> > recognizable diatonic scale. The Wicki/Hayden keyboard displays
> this
> > consistency especially clearly, due to its being vertically
> symmetrical
> > around D.
> >
> >
> >
> > More specifically, an electronic instrument that used a
> > 19-button-per-octave Wicki/Hayden keyboard layout (like that
shown
> in
> > the attached JPG) would present the same pattern of note-names
in
> 12-ET,
> > 17-ET, and 19-ET.
> >
> > + In 12-ET, the buttons labeled Cb and E# would be enharmonic
with
> the
> > diatonic (white) B and F buttons respectively; all of the other
> black
> > buttons would be enharmonic with other black buttons (on the
other
> > side).
> >
> > + In 17-ET, Cb and E# would still be enharmonic with the
diatonic
> B and
> > F respectively, but none of the other black buttons would be
> enharmonic
> > with any other.
> >
> > + In 19-ET, the keyboard would not have any enharmonic buttons;
> each
> > button would control a unique pitch.
> >
> >
> >
> > Because such a keyboard would have the same fingering of diatonic
> > patterns (the diatonic scale, diatonic chords, etc.) in all such
N-
> ET
> > tunings, it would be an especially effective tool for introducing
> > microtonal novices to non-12 ET divisions of the octave.
Indeed,
> if
> > successful solely on its 12-ET-based merits, such an instrument
> could be
> > the Trojan Horse that slips an hidden cargo of microtonality
into
> the
> > mainstream musical world.
> >
> >
> >
> > The first question for this group is: is what I've presented in
> this
> > email and its attachments already known, or its it novel? I
> understand
> > that Erv Wilson has done a lot of work with generalized
keyboards,
> but
> > what I've read of his work does not seem to parallel mine -
unless
> I'm
> > missing something, which is more than likely. :-)
> >
> >
> >
> > Let's take a moment to consider some of the other benefits
> provided by
> > an instrument with two keyboards (one for each hand, optionally
> mirrored
> > to reflect the mirroring of human hands), each with three-octave,
> > 19-button-per-octave, W/H-optimized button-arrangements.
> >
> > 1) It places three octaves under the span of each hand, so -
using
> both
> > hands - you can select notes from across a six-octave range
> > simultaneously. That's about three times the span of two hands
> over a
> > piano keyboard.
> >
> >
> >
> > 2) You can press the two adjacent buttons sounding any given P4
or
> P5
> > interval (or the three mutually-adjacent buttons sounding any
> given sus2
> > or sus4 triad) simultaneously with a single fingertip. Using
one
> hand,
> > one can play eight or more harmonious notes simultaneously.
Look
> at the
> > W/H keyboard, and you'll see that this makes single-handed
playing
> of
> > highly-extended chords possible, without dropping notes.
> >
> >
> >
> >
> > Because you can play lots of harmonious notes over a wide range
on
> a
> > Wicki/Hayden layout-based instrument, it is possible to play
> > (essentially) full orchestra scores on it, whereas such scores
> have to
> > be reduced significantly to be played on the piano. This
ability
> has
> > been demonstrated by performers of W/H-based acoustic
concertinas -
> it's
> > real, not theoretical.
> >
> >
> >
> > 3) Because the W/H-based keyboards are so small, the entire two-
> keyboard
> > (hence six octave) instrument can be remarkably tiny - about the
> size
> > and weight of a thick paperback book, partially opened.
> >
> >
> >
> > The second question for the group is: if you presumed that such a
> > six-octave, 19-button-per-octave, W/H-layout instrument had all
the
> > usual MIDI keyboard features, was Mac & PC compatible, was
> compatible
> > with both hardware and software synths, emitted data via all the
> usual
> > physical & wireless interfaces, was highly programmable, had
> > velocity-sensitive keys and polyphonic aftertouch, supported
OSC,
> and
> > generally supported every other feature ever seen on any other
> > MIDI-controller keyboard ever.
> >
> > + Would you buy one?
> >
> > + What would it worth to you (i.e., what would you be both
willing
> and
> > capable of paying me for it), given its unique advantages,
> including its
> > isomorphic support for microtonality?
> >
> > + What among the above described features is of greatest value
to
> you?
> >
> > + How many people do you think there are in the world who would
> buy one
> > at that price for the same reason(s) you would?
> >
> > + How price-elastic to you think that demand is? Alternatively
> put, by
> > what percentage would I have to lower its price to sell twice as
> many,
> > all else being equal?
> >
> >
> >
> > Hoping that interested readers will respond to the group
regarding
> > novelty (question #1), and to me privately (james@p...)
> > regarding the product/market/pricing issues (question #2), I am
> >
> >
> >
> >
> > Sincerely Yours,
> >
> >
> >
> >
> >
> > James
> >
> >
> >
> > P.S.: I am not able to supply any additional details about the
> proposed
> > instrument at this time, but I would welcome your suggestions,
> sent to
> > me privately.
> >
> >
> >
> > P.P.S.: One feature request I know I'll get from this group is
to
> > deliver more than 19 buttons per octave. Sorry, I can't do it.
> 19 is
> > the upper bound of what the human hand can span at maximum
> > button-density - I've checked. In my proposed instrument, if
you
> can't
> > span it, you can't play it, so there's no point. You're welcome
to
> > build your own isomorphic 22-button-per-octave keyboards,
> though! :-)
> >
> >
> >
> > [Non-text portions of this message have been removed]
>
>
>
>
>
>
> _____
>
> Yahoo! Groups Links
>
> * To visit your group on the web, go to:
> /makemicromusic/
>
> * To unsubscribe from this group, send an email to:
> MakeMicroMusic-unsubscribe@yahoogroups.com
> <mailto:MakeMicroMusic-unsubscribe@yahoogroups.com?
subject=Unsubscribe>
>
> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service
> <http://docs.yahoo.com/info/terms/> .
>
>
>
> [Non-text portions of this message have been removed]

🔗harold_fortuin <harold@...>

Whoops--my mistake. The link works when I don't append a '/' to it,
as I generally do when uploading HTML pages. Interesting comparative
analysis of keyboard layouts.

--- In MakeMicroMusic@yahoogroups.com, "harold_fortuin"
<harold@m...> wrote:
>
> James,
>
> Unfortunately, whenever I attempt to get the keyboards.pdf I get
> a "Page not Found" error. Are you sure you didn't post it
somewhere
> else?
>
> I don't know exactly how widely "the geometric conditions
necessary
> for isomorphism" are known and understood, but at least many
> longtime participants on this list or tuning or similar lists will
> have some acquaintance with generalized keyboards, whether or not
> they've worked its principles in a formal way.
>
>
> --- In MakeMicroMusic@yahoogroups.com, "James Plamondon"
> <james@p...> wrote:
> > Harold -
> >
> >
> >
> > I appreciate your response and feedback. :-)
> >
> >
> >
> > Actually, the keyboard is resolutely 12-ET-centric for purely
> commercial
> > reasons. Its support for 17-ET and 19-ET is an unexpected side-
> effect of
> > its geometric consistency (isomorphism) in 12-ET.
> >
> >
> >
> > Would you say that the geometric conditions necessary for
> isomorphism (as
> > described here: www.jamatronics.com/keyboards.pdf) are common
> knowledge in
> > the microtonal community?
> >
> >
> >
> > Thanks! :-)
> >
> >
> >
> > --- Jim
> >
> >
> >
> > _____
> >
> > From: harold_fortuin [mailto:harold@m...]
> > Sent: Wednesday, 26 January 2005 1:42 AM
> > To: MakeMicroMusic@yahoogroups.com
> > Subject: [MMM] Re: Isomorphic Keyboards
> >
> >
> >
> >
> > James,
> >
> > Thanks for the details about bandeons, etc. Until George Secor &
> you
> > mentioned this, I had no idea that such layouts were already in
> use
> > on commonly played instruments.
> >
> > I'm always pleased to hear about microtonal keyboard projects.
I'm
> > one of the few around to have built one with engineering help:
The
> > Clavette
> > http://www.geocities.com/harold_fortuin/clavett.htm
> > (a photo of the keys is posted up here in the Photos folder)
> >
> > and I also own a Microzone, an 810 key generalized keyboard
built
> > and sold by Starr Labs (developed with input from Erv Wilson)
> > http://www.starrlabs.com/
> >
> > You'll note that Starr Labs also has a smaller number-of-keys
> > keyboard which could also be treated as a generalized keyboard,
> > which should be much less than the Microzone (which I think
today
> > costs in the upper 4 figures).
> >
> > As I investigated various tunings, I found I did not want to be
> > limited to a particular number of notes per octave, although I
> > haven't yet ventured beyond 31 /octave myself for practical
> reasons.
> >
> > I would not want to discourage you from building your own dream
> > keyboard, but the market of course is so far quite small for
these
> > devices, and of course your keyboard would not be suited to all-
> > tones-of-the-scale > 19-tone scales, unlike either the Microzone
> or
> > Clavette. Also, as a proficient pianist and intermediate-level
> > generalized keyboard performer, I prefer the Wilsonian
horizontal
> > positioning of the diatonic tones, which of course remains the
> same
> > for "fully diatonic" tunings (sorry I don't know the precise
> term),
> > those that are 5 * whole step + 2 * half-step. If you'd like to
> > understand more about the relations of tunings and their layouts
> on
> > generalized (or potentially generalized keyboards like yours),
you
> > should speak to Erv Wilson.
> >
> > At least before venturing into commercial production,
> > you might be wise to meet with Harvey Starr and Erv Wilson. And
in
> > any case, the anaphoria.com website of Kraig Grady could be a
> > helpful resource, even if you're determined to keep your
keyboard
> 19-
> > centric.
> >
> > Best of luck in your venture,
> > Harold Fortuin
> >
> > --- In MakeMicroMusic@yahoogroups.com, "James Plamondon"
> > <james@p...> wrote:
> > > Gentlepersons,
> > >
> > >
> > >
> > > Bill Sethares recommended that I share with you my recent work
on
> > > isomorphic keyboards.
> > >
> > >
> > >
> > > There are many known keyboard layouts that have the same
> fingering
> > in
> > > all 12-ET keys. The Janko keyboard and the Chromatic Button
> > Accordion's
> > > C-System and B-System are well-known.
> > >
> > >
> > http://www.thecipher.com/isomorphic_keyboards_cipher.html
> > >
> > >
> > >
> > > Less well-known are the Wicki/Hayden keyboard.
> > >
> > > http://www.maccann-duet.com/hayden
> > >
> > > .and the keyboard patented by Wesley in 2002.
> > >
> > > www.uspto.gov <http://www.uspto.gov/> , patent
number
> > > search, # 6,501,011
> > >
> > > .and doubtless others of which I am unaware.
> > >
> > >
> > >
> > > On www.thecipher.com <http://www.thecipher.com/> , Roger E.
> > Blumberg
> > > calls these keyboard layouts "isomorphic," from the Greek
roots
> > meaning
> > > "same shape," and I've adopted that term. On an isomorphic
> > keyboard,
> > > every occurrence of a given interval has the "same shape"
> wherever
> > it
> > > occurs (edge conditions aside).
> > >
> > >
> > >
> > > I have attached a PDF file ("Summary of Isomorphic Keyboard
> > Layouts,"
> > > 13K) that describes the essential characteristics that can be
> used
> > to
> > > discriminate among all possible isomorphic keyboards. I have
> also
> > > attached an image of a three-octave, 19-button-per octave
> > Wicki/Hayden
> > > keyboard (19ButtonName.jpg, 194K).
> > >
> > >
> > >
> > > The Wicki/Hayden layout is a particularly interesting
isomorphic
> > layout
> > > because
> > >
> > > (a) it exposes the symmetry of the diatonic scale around the
> second
> > > degree of its Ionian mode (D in C Major)
> > >
> > >
> > >
> > > (b) by sizing, spacing, and shaping the note-controlling
buttons
> > > optimally (which is NOT shown in the attached JPG), one can
fit a
> > > three-octave range of buttons within the span of a single
hand's
> > > fingers, and
> > >
> > >
> > >
> > > (c) it clusters the notes of the diatonic scale into a single
> > > multi-button column, flanked on either side by multi-button
> > columns of
> > > chromatic notes.
> > >
> > >
> > >
> > > By naming one such chromatic column's buttons using flat
names,
> > and the
> > > other using sharp names, the isomorphic fingering patterns of
> > scales,
> > > chords, etc. can be consistent with traditional note-naming
> > conventions.
> > >
> > >
> > > http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf
> > >
> > >
> > >
> > > Bill tells me that microtonalists might be particularly
> interested
> > in
> > > the observation that if any given isomorphic keyboard (not
just
> the
> > > Wicki/Hayden) uses this system of enharmonic naming (flats on
one
> > > "side," sharps on the other) then it will have the same
pattern
> of
> > > note-names in every N-ET tuning if at least N buttons are
> included
> > per
> > > octave. This is particularly useful for those N that provide a
> > > recognizable diatonic scale. The Wicki/Hayden keyboard
displays
> > this
> > > consistency especially clearly, due to its being vertically
> > symmetrical
> > > around D.
> > >
> > >
> > >
> > > More specifically, an electronic instrument that used a
> > > 19-button-per-octave Wicki/Hayden keyboard layout (like that
> shown
> > in
> > > the attached JPG) would present the same pattern of note-names
> in
> > 12-ET,
> > > 17-ET, and 19-ET.
> > >
> > > + In 12-ET, the buttons labeled Cb and E# would be enharmonic
> with
> > the
> > > diatonic (white) B and F buttons respectively; all of the
other
> > black
> > > buttons would be enharmonic with other black buttons (on the
> other
> > > side).
> > >
> > > + In 17-ET, Cb and E# would still be enharmonic with the
> diatonic
> > B and
> > > F respectively, but none of the other black buttons would be
> > enharmonic
> > > with any other.
> > >
> > > + In 19-ET, the keyboard would not have any enharmonic
buttons;
> > each
> > > button would control a unique pitch.
> > >
> > >
> > >
> > > Because such a keyboard would have the same fingering of
diatonic
> > > patterns (the diatonic scale, diatonic chords, etc.) in all
such
> N-
> > ET
> > > tunings, it would be an especially effective tool for
introducing
> > > microtonal novices to non-12 ET divisions of the octave.
> Indeed,
> > if
> > > successful solely on its 12-ET-based merits, such an
instrument
> > could be
> > > the Trojan Horse that slips an hidden cargo of microtonality
> into
> > the
> > > mainstream musical world.
> > >
> > >
> > >
> > > The first question for this group is: is what I've presented
in
> > this
> > > email and its attachments already known, or its it novel? I
> > understand
> > > that Erv Wilson has done a lot of work with generalized
> keyboards,
> > but
> > > what I've read of his work does not seem to parallel mine -
> unless
> > I'm
> > > missing something, which is more than likely. :-)
> > >
> > >
> > >
> > > Let's take a moment to consider some of the other benefits
> > provided by
> > > an instrument with two keyboards (one for each hand,
optionally
> > mirrored
> > > to reflect the mirroring of human hands), each with three-
octave,
> > > 19-button-per-octave, W/H-optimized button-arrangements.
> > >
> > > 1) It places three octaves under the span of each hand, so -
> using
> > both
> > > hands - you can select notes from across a six-octave range
> > > simultaneously. That's about three times the span of two
hands
> > over a
> > > piano keyboard.
> > >
> > >
> > >
> > > 2) You can press the two adjacent buttons sounding any given
P4
> or
> > P5
> > > interval (or the three mutually-adjacent buttons sounding any
> > given sus2
> > > or sus4 triad) simultaneously with a single fingertip. Using
> one
> > hand,
> > > one can play eight or more harmonious notes simultaneously.
> Look
> > at the
> > > W/H keyboard, and you'll see that this makes single-handed
> playing
> > of
> > > highly-extended chords possible, without dropping notes.
> > >
> > >
> > >
> > >
> > > Because you can play lots of harmonious notes over a wide
range
> on
> > a
> > > Wicki/Hayden layout-based instrument, it is possible to play
> > > (essentially) full orchestra scores on it, whereas such scores
> > have to
> > > be reduced significantly to be played on the piano. This
> ability
> > has
> > > been demonstrated by performers of W/H-based acoustic
> concertinas -
> > it's
> > > real, not theoretical.
> > >
> > >
> > >
> > > 3) Because the W/H-based keyboards are so small, the entire
two-
> > keyboard
> > > (hence six octave) instrument can be remarkably tiny - about
the
> > size
> > > and weight of a thick paperback book, partially opened.
> > >
> > >
> > >
> > > The second question for the group is: if you presumed that
such a
> > > six-octave, 19-button-per-octave, W/H-layout instrument had
all
> the
> > > usual MIDI keyboard features, was Mac & PC compatible, was
> > compatible
> > > with both hardware and software synths, emitted data via all
the
> > usual
> > > physical & wireless interfaces, was highly programmable, had
> > > velocity-sensitive keys and polyphonic aftertouch, supported
> OSC,
> > and
> > > generally supported every other feature ever seen on any other
> > > MIDI-controller keyboard ever.
> > >
> > > + Would you buy one?
> > >
> > > + What would it worth to you (i.e., what would you be both
> willing
> > and
> > > capable of paying me for it), given its unique advantages,
> > including its
> > > isomorphic support for microtonality?
> > >
> > > + What among the above described features is of greatest value
> to
> > you?
> > >
> > > + How many people do you think there are in the world who
would
> > buy one
> > > at that price for the same reason(s) you would?
> > >
> > > + How price-elastic to you think that demand is?
Alternatively
> > put, by
> > > what percentage would I have to lower its price to sell twice
as
> > many,
> > > all else being equal?
> > >
> > >
> > >
> > > Hoping that interested readers will respond to the group
> regarding
> > > novelty (question #1), and to me privately (james@p...)
> > > regarding the product/market/pricing issues (question #2), I am
> > >
> > >
> > >
> > >
> > > Sincerely Yours,
> > >
> > >
> > >
> > >
> > >
> > > James
> > >
> > >
> > >
> > > P.S.: I am not able to supply any additional details about
the
> > proposed
> > > instrument at this time, but I would welcome your suggestions,
> > sent to
> > > me privately.
> > >
> > >
> > >
> > > P.P.S.: One feature request I know I'll get from this group
is
> to
> > > deliver more than 19 buttons per octave. Sorry, I can't do
it.
> > 19 is
> > > the upper bound of what the human hand can span at maximum
> > > button-density - I've checked. In my proposed instrument, if
> you
> > can't
> > > span it, you can't play it, so there's no point. You're
welcome
> to
> > > build your own isomorphic 22-button-per-octave keyboards,
> > though! :-)
> > >
> > >
> > >
> > > [Non-text portions of this message have been removed]
> >
> >
> >
> >
> >
> >
> > _____
> >
> > Yahoo! Groups Links
> >
> > * To visit your group on the web, go to:
> > /makemicromusic/
> >
> > * To unsubscribe from this group, send an email to:
> > MakeMicroMusic-unsubscribe@yahoogroups.com
> > <mailto:MakeMicroMusic-unsubscribe@yahoogroups.com?
> subject=Unsubscribe>
> >
> > * Your use of Yahoo! Groups is subject to the Yahoo! Terms of
> Service
> > <http://docs.yahoo.com/info/terms/> .
> >
> >
> >
> > [Non-text portions of this message have been removed]