Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Re: Symmetrical Keyboard

graham@microtonal.co.uk wrote:

> In-Reply-To: <39A2C59C.AD8670C8@net1plus.com>
> > > It is the exact same keyboard except that I don't rearrange mine for
> > > maximum neatness.
> >
> > Graham mentions the spacing problems he encountered made advantage for
> > navigation.
>
> It makes some difference, but still fits a 12 note pattern.
>

I thought about how the neatness might in fact create more divisions for the mind. Because
what you get are very clear pockets of order. With the messier all rights facing right and all
lefts facing left method, the only order is in the center and that can be easily ignored. It
looks uglier but also it doesn't try to impose any order for the mind. I still can't get my
webpage to work to show the pic I have of the keyboard I thought I discovered and tried to
patent so that I could make billions of money off the sales.

>
>
>
> You do not need web access to participate. You may subscribe through
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--
symmetric keyboard:
http://x31eq.com/instrum.htm

not working website:
http://home.earthlink.net/~troubledoor

🔗Clark <CACCOLA@NET1PLUS.COM>

Hi,

Graham wrote:
> > > It is the exact same keyboard except that I don't rearrange mine for
> > > maximum neatness.
> >
> > Graham mentions the spacing problems he encountered made advantage for
> > navigation.
>
> It makes some difference, but still fits a 12 note pattern.

Except for work like yours, I think it's great that with twelve notes
the standard pattern isn't evenly spaced. I'm very fond of the wide
tails on antique d's.

Troubledoor wrote:
> all rights facing right and all
> lefts facing left method, the only order is in the center and that can be easily ignored

D's are the only non-facing natural keys, typically - g's and c's are
notched more on the right and b's and a's on the left. I don't really
grasp how yours would be, at least in terms of normal touch plates.

> it doesn't try to impose any order for the mind.

The addition of raised keys to the diatonic keyboard permitted a clear,
tactile mapping of its modes; a symmetrical or generalized arrangement
is less imposing, and more mindful in that a knowledge of a scale is
required in order to play it. In its defense, that the Halberstadt form
continues to be retained suggests a certain value in the imposition,
despite the ultimate inconsistencies in transposition.

Clark

🔗Graham Breed <graham@microtonal.co.uk>

On Wed, 23 Aug 2000, Clark wrote:
> Hi,
>
> Graham wrote:
> > > > It is the exact same keyboard except that I don't rearrange mine for
> > > > maximum neatness.
> > >
> > > Graham mentions the spacing problems he encountered made advantage for
> > > navigation.
> >
> > It makes some difference, but still fits a 12 note pattern.
>
> Except for work like yours, I think it's great that with twelve notes
> the standard pattern isn't evenly spaced. I'm very fond of the wide
> tails on antique d's.

Yes, that other message got sent before I was finished with it. When every key
is identical to every other one, it's difficult to orient yourself. The usual
pattern of keys is a big help in this respect, and it's difficult to get by
without it. The slight differences in spacing don't really help much, and are
only really useful for 12 note scales anyway.

I find myself going back to my "normal" keyboard most of the time. There are
plenty of 7- and 5-based scales, octave-based or otherwise, to be getting on
with. A guitar neck isn't nearly as daunting, because everything's relative to
the nut.

>
> Troubledoor wrote:
> > all rights facing right and all
> > lefts facing left method, the only order is in the center and that can be easily ignored
>
> D's are the only non-facing natural keys, typically - g's and c's are
> notched more on the right and b's and a's on the left. I don't really
> grasp how yours would be, at least in terms of normal touch plates.

I'd have to see a photo to know exactly what he's doing. I do have one of
mine, FWIW, still not linked to. Something like

<http://x31eq.com/pics/DX21.jpg>

`> > it doesn't try to impose any order for the mind.
>
> The addition of raised keys to the diatonic keyboard permitted a clear,
> tactile mapping of its modes; a symmetrical or generalized arrangement
> is less imposing, and more mindful in that a knowledge of a scale is
> required in order to play it. In its defense, that the Halberstadt form
> continues to be retained suggests a certain value in the imposition,
> despite the ultimate inconsistencies in transposition.

This is something I've really come to appreciate through having the
alternative. I'm assuming a generalized keyboard would be less of a problem,
provided the keytops are coloured to a useful pattern.

Graham

"I toss therefore I am" -- Sartre

🔗Troubledoor <troubledoor@earthlink.net>

Graham Breed wrote:

> On Wed, 23 Aug 2000, Clark wrote:
> > Hi,
> >
> > Graham wrote:
> > > > > It is the exact same keyboard except that I don't rearrange mine for
> > > > > maximum neatness.
> > > >
> > > > Graham mentions the spacing problems he encountered made advantage for
> > > > navigation.
> > >
> > > It makes some difference, but still fits a 12 note pattern.
> >
> > Except for work like yours, I think it's great that with twelve notes
> > the standard pattern isn't evenly spaced. I'm very fond of the wide
> > tails on antique d's.
>
> Yes, that other message got sent before I was finished with it. When every key
> is identical to every other one, it's difficult to orient yourself. The usual
> pattern of keys is a big help in this respect, and it's difficult to get by
> without it. The slight differences in spacing don't really help much, and are
> only really useful for 12 note scales anyway.
>
> I find myself going back to my "normal" keyboard most of the time. There are
> plenty of 7- and 5-based scales, octave-based or otherwise, to be getting on
> with. A guitar neck isn't nearly as daunting, because everything's relative to
> the nut.
>

My original interest in making the symmetric keyboard was to sound like Alban Berg. Then I
recently discovered that his music is better interpreted not as 12 tones of FREE atonality but
rather as superimpositions of the standard diatonic scales in different keys and modes (much
like jazz improvisation theory). So with this aural perception I too found myself using my
standard C-diatonic keyboard again. Except now I would really like to explore the 72 notes of
the ideal Pythagorean scale (the cycle of 5ths without adjusted temperament produce a scale of
72 notes).

Oooops, I just went to your website and saw your keyboard. You are talking about the symmetric
keyboard still? I'm totally off. I'll keep the above though as my official opinion about Alban
Berg.

My webpage isn't working yet. I'll try to get it working soon. I'll post when it's ready.

>
> >
> > Troubledoor wrote:
> > > all rights facing right and all
> > > lefts facing left method, the only order is in the center and that can be easily ignored
> >
> > D's are the only non-facing natural keys, typically - g's and c's are
> > notched more on the right and b's and a's on the left. I don't really
> > grasp how yours would be, at least in terms of normal touch plates.
>
> I'd have to see a photo to know exactly what he's doing. I do have one of
> mine, FWIW, still not linked to. Something like
>
> <http://x31eq.com/pics/DX21.jpg>
>
> `> > it doesn't try to impose any order for the mind.
> >
> > The addition of raised keys to the diatonic keyboard permitted a clear,
> > tactile mapping of its modes; a symmetrical or generalized arrangement
> > is less imposing, and more mindful in that a knowledge of a scale is
> > required in order to play it. In its defense, that the Halberstadt form
> > continues to be retained suggests a certain value in the imposition,
> > despite the ultimate inconsistencies in transposition.
>
> This is something I've really come to appreciate through having the
> alternative. I'm assuming a generalized keyboard would be less of a problem,
> provided the keytops are coloured to a useful pattern.
>
> Graham
>
> "I toss therefore I am" -- Sartre
>
>
> You do not need web access to participate. You may subscribe through
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symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Troubledoor <troubledoor@earthlink.net>

"Paul H. Erlich" wrote:

> Troubledoor wrote,
>
> (the cycle of 5ths without adjusted temperament produce a scale of
> 72 notes).
>
> You must mean 53. The cycle of fifths doesn't even come close to closing
> after 72 fifths.
>

I know you're going to get your Romulator program out on me but there is a very old tradition
on the number 72 as being the ideal conclusion of the cycle of 4ths or 5ths. Of course, they
didn't have your program and only had abacuses and the like. So I know that they are wrong
compared to your data. But I'm a rationalist of the Platonic/Pythagorean tradition and there
is no way that a percentage program based on a decimal system is going to convince me that the
cycle of 4ths breaks down to 53 notes. The Pythagoreans use an ogdoad or eightfold system
based on a rational octave and produce a more satisfying solution to the puzzle for the
rational MIND. What this does for the ears is another thing. I'm sure your program is probably
more correct. But then again, the goal of the 72 note Pythagorean scale was mastery of the
pitches for MEMORY and as such the ears are not that important once the scales are learned by
memory. It's a mental/memory thing vs. physics/mathematics. I'm more of the psychotic type
who likes abstractions (paranoid schizo) so I'll always say 72. Then I'm going to go out buy
your books and the other authors here and read about the 53 tones. I'm mental. Or more
closely, a rationalist.

>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@egroups.com - join the tuning group.
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> tuning-digest@egroups.com - change your subscription to daily digest mode.
> tuning-normal@egroups.com - change your subscription to individual emails.

--
Hello,

I have recently discovered a new graphic representation for the
I Ching hexagrams that show that the I Ching was also intended to
be a hologram generator. By hologram, I mean something like the
traditional hieroglyphic style of Chinese writing except that it
has an internal sequence/logic. I accomplished this by representing
the changing lines differently. You can see the new graphic
arrangement at my webpage (it's about 2 paragraphs down):

http://home.earthlink.net/~troubledoor

You can also download the software for free. I use Norton's anti-virus with the
latest software upgrades so the download is virus free.
Please distribute it to your other I Ching friends. Thanks.

symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Troubledoor <troubledoor@earthlink.net>

"Paul H. Erlich" wrote:

> Well, it doesn't take a very complex calculation to show that, since 12
> fifths leave a residue of a Pythagorean comma, 72 fifths will leave a
> residue of 6 Pythagorean commas, or over a semitone!
>

That's the actual usage I've seen in the occult books. Some of them aren't even that occult.
Some are quite exoteric except that its so buried that it will never be found until I blurt it
out but I won't blurt it out here because these are mystical secrets about the the Lambdoma and
that's a religious artifact that should be carefully delivered lest I get shot by a religious
fanatic. The whole subject is so obscured by mysticism that looney zealots are a very real
scare.

Have you actually ever run the circle of fifths around and around until they made an octave?

> However, 72-tET is a wonderful tuning for approximation many non-Pythagorean
> ratios, such as all of Partch's diamond ratios.
>

Do you know anyone who has written on this subject?

Later and thanks.

symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

I wrote,

>> Well, it doesn't take a very complex calculation to show that, since 12
>> fifths leave a residue of a Pythagorean comma, 72 fifths will leave a
>> residue of 6 Pythagorean commas, or over a semitone!

Troubledoor wrote,

>That's the actual usage I've seen in the occult books. Some of them aren't
even that occult.
>Some are quite exoteric except that its so buried that it will never be
found until I blurt it
>out but I won't blurt it out here because these are mystical secrets about
the the Lambdoma and
>that's a religious artifact that should be carefully delivered lest I get
shot by a religious
>fanatic. The whole subject is so obscured by mysticism that looney zealots
are a very real
>scare.

right . . .

>Have you actually ever run the circle of fifths around and around until
they made an octave?

The "circle of fifths" never closes perfectly, but it comes close after 53,
closer after 665, etc . . . see Paul Hahn or Kees van Prooijen's tables.

>> However, 72-tET is a wonderful tuning for approximation many
non-Pythagorean
>> ratios, such as all of Partch's diamond ratios.
>

>Do you know anyone who has written on this subject?

See this 72-tone equal temperament page for a start:
http://sites.netscape.net/ricktagawa/. The Boston microtonal community uses
72-tET.

🔗Clark <CACCOLA@NET1PLUS.COM>

Troubledoor wrote:

> My symmetric keyboard:
> http://home.earthlink.net/~troubledoor

Thanks; it's one thing to invent something, but far better to have it to
use!

Is this the design you submitted? If so, I'm curious why - the neatness
of Halberstadt keyboards springs from efficiency.

John Allen makes a case for less even spacing:
http://www.bikexprt.com/music/refine.htm

> My original interest in making the symmetric keyboard was to sound like Alban Berg. Then I
> recently discovered that his music is better interpreted not as 12 tones of FREE atonality but
> rather as superimpositions of the standard diatonic scales in different keys and modes (much
> like jazz improvisation theory). So with this aural perception I too found myself using my
> standard C-diatonic keyboard again.

I'd think you were better off with the symmetrical in this regard (short
of a Janko); the mental imposition, as it were, is less specific but
there are only two diatonic fingering patterns.

Clark

🔗Clark <CACCOLA@NET1PLUS.COM>

Graham Breed wrote:

> <http://x31eq.com/pics/DX21.jpg>

Great! How do you like it for extended tunings - like how is it to
transpose in 19tET?

> A guitar neck isn't nearly as daunting, because everything's relative to
> the nut.

I think fret spacing plays a role, too. I need to dye the frets on my
viol because with 15+ frets, spacing isn't very apparent.

> When every key
> is identical to every other one, it's difficult to orient yourself. The usual
> pattern of keys is a big help in this respect, and it's difficult to get by
> without it....
> This is something I've really come to appreciate through having the
> alternative. I'm assuming a generalized keyboard would be less of a problem,
> provided the keytops are coloured to a useful pattern.

Isn't yours a generalized keyboard of sorts? GK's are very acceptable,
but not always an optimal choice.

I wonder if the stark contrast in the Halberstadt helped its
entrenchment; I read a quote about a distasteful practice of Americans,
using highly figured ivory and mother of pearl for keytops in the 19th
century.

Regards,

Clark

ps. I wrote:

> I'm very fond of the wide tails on antique d's.

I just noticed my Roland has wide d's!

🔗Clark <CACCOLA@NET1PLUS.COM>

Paul wrote:

> The Boston microtonal community uses
> 72-tET.

My colleague tuned for Sonia Maneri a couple days ago; a former student
of Joe's was visiting, and Gene related an interesting conversation the
three of them held about tunings and keyboards.

His student was somewhat biased toward multiples of 12, but Joe
suggested that his electronic instrument wasn't really useful for
performance and expressed interest in using ones that were - despite
temperament or scale structure!

Clark

Oh, and the schedule for improvised music in Boston, some of it
microtonal, is at http://members.aol.com/Tautology3/BossImpCal.html

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kraig Grady <kraiggrady@anaphoria.com>

Dear Troubledoor;
I assume you are aware of Barbara Hero's wonderful site http://www.lambdoma.com/ also we have
some Lambdoma at http://www.anaphoria.com/lam.html .
Historically it is mostly those of Monotheistic Religions who seem to feel compelled to resort
to weapons as a way of proving there point. Welcome to the Polytheism of the tuning list:)
Secrecy has the advantage of preventing the secularization of sacred "objects", but the
disadvantage of being easily suppressed and/or being destroyed forever . One has to balance the
two cautiously.

Troubledoor wrote:

>
> Some are quite exoteric except that its so buried that it will never be found until I blurt it
> out but I won't blurt it out here because these are mystical secrets about the the Lambdoma and
> that's a religious artifact that should be carefully delivered lest I get shot by a religious
> fanatic.
>
> Have you actually ever run the circle of fifths around and around until they made an octave?
>
> > However, 72-tET is a wonderful tuning for approximation many non-Pythagorean
> > ratios, such as all of Partch's diamond ratios.
> >
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

🔗Clark <CACCOLA@NET1PLUS.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, Troubledoor <troubledoor@e...> wrote:
>
>
It's a mental/memory thing vs. physics/mathematics. I'm
more of the psychotic type who likes abstractions (paranoid schizo)
so I'll always say 72. Then I'm going to go out buy
> your books and the other authors here and read about the 53 tones.
I'm mental. Or more closely, a rationalist.
>
>

Hmmm. I can, unfortunately, kind of understand this... The question
I have here for our Troubadour, or any other mental souls on this
list... is how one actually orients onself to these perfectly
symmetrical keyboards?? As someone who made a living as a
professional pianist for 12 years (yikes!), I would be interested. I
want to play Chopin on it...

_____________ _____ ___ __ _
Joseph Pehrson

🔗Monz <MONZ@JUNO.COM>

Troubledoor recently mentioned an 'ideal 72-tone Pythagorean scale'.
Some of the follow-up:

> [Paul Erlich]
> http://www.egroups.com/message/tuning/11804
>
> I wrote,
>
>>> Well, it doesn't take a very complex calculation to show that,
>>> since 12 fifths leave a residue of a Pythagorean comma, 72
>>> fifths will leave a residue of 6 Pythagorean commas, or over
>>> a semitone!
>
> Troubledoor wrote,
>
>> That's the actual usage I've seen in the occult books. Some of
>> them aren't even that occult. Some are quite exoteric except
>> that its so buried that it will never be found until I blurt it
>> out but I won't blurt it out here because these are mystical
>> secrets about the the Lambdoma and that's a religious artifact
>> that should be carefully delivered lest I get shot by a religious
>> fanatic. The whole subject is so obscured by mysticism that
>> looney zealots are a very real scare.
>
> right . . .
>
>> Have you actually ever run the circle of fifths around and
>> around until they made an octave?
>
> The "circle of fifths" never closes perfectly, but it comes close
> after 53, closer after 665, etc . . . see Paul Hahn or Kees van
> Prooijen's tables.
>

Troubledoor, I questioned you privately a few days ago about
this 'ideal 71-tone Pythagorean scale', asking you why the limit
at 72 tones, and what makes it 'ideal'.

I'm willing to remain open-minded enough to consider some of
the things about which you've posted - indeed, I often skate
dangerously close to mysticism myself in a lot of what I write.

But your answer then sounded like so much occult mumbo-jumbo
that I wanted to wait awhile before responding; I see that
much of the same is being used to answer publicly here.

In addition to the sources cited by Paul, take a look at this:

http://www.egroups.com/files/tuning/monz/Pythagorean-cycle.gif

The number of '5th's in the cycle appears across the bottom as
the x-axis, and the y-axis shows the 'octave'-reduced Semitone
value (Semitones to 2 decimal places show the same thing as
cents, with the 12-tET degree isolated before the decimal point.)

You can see clearly that 12 '5ths' come fairly close to an
'octave' (~23 cents higher, the 'Pythagorean comma'), and that
53 '5ths' come a whole lot closer (only ~4 cents higher), while
72 is, as Paul said, more than a semitone away.

The next closer values, which didn't make it onto my graph, were
306 '5ths' and 359 '5ths', which are ~2 cents lower and higher,
respectively.

While I agree with Paul that 72-tET is a good intonational
resource, the only value I can see in choosing 72 as a limit
in a Pythagorean tuning is that it makes available all the
smaller subsets, like 36, 24, 18, and 12... IMO, this still
doesn't make it all that valuable.

No ancient who bothered to either calculate any of this math
or listen to the result would have had any reason to deliberately
chose a 72-tone *Pythagorean* scale. I suggest you re-evaluate
the ideas you're developing in regard to this 'ideal scale'.

PS - Where you wrote 'exoteric' you meant 'esoteric'.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Troubledoor <troubledoor@earthlink.net>

Thanks for the links and also thanks to Paul Ehrlich for the links to the 72
tone folks. It is interesting that it is mentioned that Pythagorus learned the
art from Egypt because I was forced to read many Egyptian related books in my
religious practices. Eventually someone will figure out what the Lambdoma is
about but you have to remember that the I Ching is virtually the same method and
it was lost for 3,500 years after the passing of King Wen. He hid it in the I
Ching images but no one found it until I discovered it less than a year ago.
You can go to my webpage below to see the new interpretation of the I Ching that
I am hoping will aid in a holographic/HIEROGLYPHIC microtonal theory based on 16
tones. I'm sure that someone will eventually reconstruct the lost (Chinese
classics or "wing") Book of Music. Just that 3,500 year interims are a long
time to wait.

Kraig Grady wrote:

> Dear Troubledoor;
> I assume you are aware of Barbara Hero's wonderful site
> http://www.lambdoma.com/ also we have some Lambdoma at
> http://www.anaphoria.com/lam.html .
> Historically it is mostly those of Monotheistic Religions who seem to feel
> compelled to resort to weapons as a way of proving there point. Welcome to the
> Polytheism of the tuning list:)
> Secrecy has the advantage of preventing the secularization of sacred
> "objects", but the disadvantage of being easily suppressed and/or being
> destroyed forever . One has to balance the two cautiously.
>
> Troubledoor wrote:
>
>>
>> Some are quite exoteric except that its so buried that it will never be
>> found until I blurt it
>> out but I won't blurt it out here because these are mystical secrets about
>> the the Lambdoma and
>> that's a religious artifact that should be carefully delivered lest I get
>> shot by a religious
>> fanatic.
>>
>> Have you actually ever run the circle of fifths around and around until they
>> made an octave?
>>
>> > However, 72-tET is a wonderful tuning for approximation many
>> non-Pythagorean
>> > ratios, such as all of Partch's diamond ratios.
>> >
>>
>
>
> -- Kraig Grady
> North American Embassy of Anaphoria island
> www.anaphoria.com
> -------------------------------------------------------------------------------
>
> -------------------------------------------------------------------------------
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@egroups.com - join the tuning group.
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> tuning group.
> tuning-digest@egroups.com - change your subscription to daily digest mode.
> tuning-normal@egroups.com - change your subscription to individual emails.
>

--
Hello,

http://home.earthlink.net/~troubledoor

You can also download the software for free. I use Norton's anti-virus with the
latest software upgrades so the download is virus free.
Please distribute it to your other I Ching friends. Thanks.

symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Troubledoor <troubledoor@earthlink.net>

Joseph Pehrson wrote:

> --- In tuning@egroups.com, Troubledoor <troubledoor@e...> wrote:
> >
> >
> It's a mental/memory thing vs. physics/mathematics. I'm
> more of the psychotic type who likes abstractions (paranoid schizo)
> so I'll always say 72. Then I'm going to go out buy
> > your books and the other authors here and read about the 53 tones.
> I'm mental. Or more closely, a rationalist.
> >
> >
>
> Hmmm. I can, unfortunately, kind of understand this... The question
> I have here for our Troubadour, or any other mental souls on this
> list... is how one actually orients onself to these perfectly
> symmetrical keyboards?? As someone who made a living as a
> professional pianist for 12 years (yikes!), I would be interested. I
> want to play Chopin on it...
>

I suck at music. I'm still at the John Coltrane's "Om" phase of my musical development. And I
don't see any harmonious horizons for me any time soon. Really though, the symmetrical
keyboards are best left for 12 tone/atonal improvisations and microtonal music.

>
> _____________ _____ ___ __ _
> Joseph Pehrson
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@egroups.com - join the tuning group.
> tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
> tuning-nomail@egroups.com - put your email message delivery on hold for the tuning group.
> tuning-digest@egroups.com - change your subscription to daily digest mode.
> tuning-normal@egroups.com - change your subscription to individual emails.

--
Hello,

http://home.earthlink.net/~troubledoor

You can also download the software for free. I use Norton's anti-virus with the
latest software upgrades so the download is virus free.
Please distribute it to your other I Ching friends. Thanks.

symmetric keyboard:
http://x31eq.com/instrum.htm

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/11834
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> >
> > In addition to the sources cited by Paul, take a look at this:
> >
> > http://www.egroups.com/files/tuning/monz/Pythagorean-cycle.gif
> >
>
> Hi Monz...
>
> Sorry. I meant to ask... how did you calculate this chart
> graphically?? Distances in centimeters on the page or what??
> How was it done??
>

Wow, it never ceases to amaze me what some of us take for granted.
I was going to send you the file as an attachment, then I realized
... this was so elementary for me that I didn't even save it!

It was done very simply as a Microsoft Excel spreadsheet chart,
as follows:

- Type a '0' into the top cell of your first column (cell A1).

- Use 'Edit|Fill|Series' to create a column-list of integers
from 0 to wherever you want to stop.

- Use this formula in the second column (cell A2, then copy it):
=mod(log(3^A1)*(12/log(2)),12)

- Format the second column as 'Number' to 2 decimal places,
if you want my Semitone measure; otherwise, leave the decimals.

- Highlight the second column figures and click on the toolbar
button that creates a chart.

- Use 'X-Y Scatter' as the Chart Type.

- Highlight the chart after it's drawn, and use 'File|Save as HTML',
which will create a webpage containing the chart as a graphic.
Then you can just use the graphic by itself.

There ya go, Joe! This is how I've done all the 'Semitone' graphs
on my webpages.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗Joseph Pehrson <pehrson@pubmedia.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

> http://www.egroups.com/files/tuning/monz/Pythagorean-cycle.gif

> Wow, it never ceases to amaze me what some of us take for granted.

Thanks, Monz, for helping me with this. I'm looking forward to being
in such a "state of amazement" myself. Unfortunately, it has not yet
happened...

>
> - Use this formula in the second column (cell A2, then copy it):
> =mod(log(3^A1)*(12/log(2)),12)
>
Ok... so this Excel formula is the crux of it... but I'm still not
getting how it works. Sorry to be so dumb. Maybe a couple of lines
more on this for me??

Oh wait... the log(3^A1) looks suspiciously like the Pythagorean part
and the 12/log(2) is obviously the semitone part (??)

THANKS!!!!

Joe2
________________ ____ __ __ _
Joseph Pehrson

🔗Graham Breed <graham@microtonal.co.uk>

On Fri, 25 Aug 2000, Joseph Pehrson wrote:

> Hmmm. I can, unfortunately, kind of understand this... The question
> I have here for our Troubadour, or any other mental souls on this
> list... is how one actually orients onself to these perfectly
> symmetrical keyboards?? As someone who made a living as a
> professional pianist for 12 years (yikes!), I would be interested. I
> want to play Chopin on it...

With blank video cassettes, you get sheets of stickers with letters on them so
that you can label the tapes. Collect these stickers, and put one behind
each key named by that letter. That helps a bit, but it's a hassle to change
them. Also, they have a habit of falling off. Another thing is to write on the
white keys using a marker pen. I expect enamel paint would do the
same job more permanently.

A thing I do with all keyboards, and it's how I originally learnt to play, is
to write out the scale or chords onto a strip of paper. Then, slide that strip
up and down the keyboard so that you know what to play. The only problem with
this for extended mappings is finding a long enough strip of paper.

This all seems obvious to me, but don't know if other people do it or not.

Graham

"I toss therefore I am" -- Sartre

🔗Graham Breed <graham@microtonal.co.uk>

On Thu, 24 Aug 2000, Clark wrote:
> Graham Breed wrote:
>
> > <http://x31eq.com/pics/DX21.jpg>
>
> Great! How do you like it for extended tunings - like how is it to
> transpose in 19tET?

It works well for equal temperaments with an even number of notes to the
octave. So 14 and 24 work fairly well. But the more notes you have, the
harder it is to remember the structure.

I've got the stickers on for a 19 note scale, but I prefer my guitar for that
kind of thing. I can work out the patterns for particular chords, and so play
them at any position. But playing chord sequences isn't that easy, because
things like "move up a fourth" aren't obvious. Also, playing the same chords
in different inversions isn't obvious, because there's notvisual octave.

> > A guitar neck isn't nearly as daunting, because everything's relative to
> > the nut.
>
> I think fret spacing plays a role, too. I need to dye the frets on my
> viol because with 15+ frets, spacing isn't very apparent.

I've got an unequal fret spacing now, which does help, but I can remember the
days it was in Equal Temperament. But you're suggesting the unequal nature of
a logarithmic scale translated to string lengths helps? You could be right.

> > When every key
> > is identical to every other one, it's difficult to orient yourself. The usual
> > pattern of keys is a big help in this respect, and it's difficult to get by
> > without it....
> > This is something I've really come to appreciate through having the
> > alternative. I'm assuming a generalized keyboard would be less of a problem,
> > provided the keytops are coloured to a useful pattern.
>
> Isn't yours a generalized keyboard of sorts? GK's are very acceptable,
> but not always an optimal choice.

Of sorts, yes, but I was referring to the classical Wilson/Bosanquet layout.
The two-dimensional structure of the keyboard reflects the structure of the
scale, but in a transpositionally-invariant way. I expect keeping the same
size of octave for different numbers of notes would help as well.

> I wonder if the stark contrast in the Halberstadt helped its
> entrenchment; I read a quote about a distasteful practice of Americans,
> using highly figured ivory and mother of pearl for keytops in the 19th
> century.

Aesthetics probably helped, but the main reason for lock-in is the time it
would take to re-learn a different pattern. Not that there's anything wrong
with the Halberstadt for its intended purpose. Nothing that some ergonomic
reshaping couldn't fix, anyway.

> ps. I wrote:
>
> > I'm very fond of the wide tails on antique d's.
>
> I just noticed my Roland has wide d's!

Which end is the tail? My DX21's keys are wider at the back, the significance
of which I only appreciated when I filled the keyboard with them!

Graham

"I toss therefore I am" -- Sartre

🔗Graham Breed <graham@microtonal.co.uk>

On Thu, 24 Aug 2000, Troubledoor wrote:

> > I find myself going back to my "normal" keyboard most of the time. There are
> > plenty of 7- and 5-based scales, octave-based or otherwise, to be getting on
> > with. A guitar neck isn't nearly as daunting, because everything's relative to
> > the nut.
> >
>
> My original interest in making the symmetric keyboard was to sound like Alban Berg. Then I
> recently discovered that his music is better interpreted not as 12 tones of FREE atonality but
> rather as superimpositions of the standard diatonic scales in different keys and modes (much
> like jazz improvisation theory). So with this aural perception I too found myself using my
> standard C-diatonic keyboard again. Except now I would really like to explore the 72 notes of
> the ideal Pythagorean scale (the cycle of 5ths without adjusted temperament produce a scale of
> 72 notes).

I came up with the idea in a free atonal phase as well. Although, by the time
I was able to realize it, I'd learnt to love the broken symmetry of a 7+5
keyboard.

> Oooops, I just went to your website and saw your keyboard. You are talking about the symmetric
> keyboard still? I'm totally off. I'll keep the above though as my official opinion about Alban
> Berg.

The symmetric keyboard isn't the "normal" one.

>
> My webpage isn't working yet. I'll try to get it working soon. I'll post when it's ready.

It's working now, and I think your arrangement makes a lot of sense. It means
each key is in a unique neighbourhood. So, if you want to start a piece on a
particualar note, it's easier to remember that note. If I can remember where I
put the old keys, I might try this out.

Graham

"I toss therefore I am" -- Sartre

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

--- In tuning@egroups.com, Graham Breed <graham@m...> wrote:
>
> A thing I do with all keyboards, and it's how I originally learnt
to play, is
> to write out the scale or chords onto a strip of paper. Then,
slide that strip
> up and down the keyboard so that you know what to play. The only
problem with
> this for extended mappings is finding a long enough strip of paper.
>
> This all seems obvious to me, but don't know if other people do it
or not.
>
> Graham

Graham,

Greetings! I visit you site frequently - thanks!

On the topic of navigation of complex keyboard layouts; the paper
strip concept is something I've used for years to help me to make
music on the "7 white - 5 black". This was interesting to me when I
saw your post - so I thought I'd explain how I use this.

On my midi controller there is about a 2" space above the keys, onto
which I attach (with tape) a long strip of paper that covers the
entire range of the keyboard. On this strip I have drawn a grid that
fits perfectly in reference with the keys below. The first level of
the grid shows the Cents values for the intervals, below this, and in
reference to the cracks between the keys I enter the consecutive
intervals (also in cents). The next level down has the ratios for
each key drawn in. Below this, I have the degree of flattening or
augmentation in cents. An finally at the bottom I have the pitch name
entered.

This allows an immediate visual connection/orientation to what's
going on with any tuning I have mapped to the keyboard - and it helps
me to appreciate in a way that I can see, the subtleties of the Just
Intonation mappings that I use.

The most common kind of tuning that I have used this for (which I'm
sure will sound exceedingly perverse to many) is when I map my 13
Pitch Symmetrical Harmonic Scales to the keys. This particular
approach that I'm speaking of, maps 13 pitches to the octave, where
there are 6 ratios counted up from the 1/1 and 6 counted downward
from the 2/1, in perfect inversional symmetry. A typical scale would
be: 1/1, 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, (10/7, 3/2, 8/5, 5/3, 16/9,
15/8, 2/1). This adds on extra note per octave (2 tritones) - and the
strip really helps to get about on this mapping. But this is only
speaking about just one isolated octave of the total tuning/mapping -
because I will very commonly have a different set of ratios mapped in
every octave going up the keyboard!!! I mention this now, but fear to
be banished to the microtonal wastelands for such dissonant practice
(just joking). It's kind of like a harmonic series sensibility to
mapping the ratios across the keyboard - where the 1/1s and 2/1s act
as a sort of tonal axis. Interestingly too, is that I used to rigidly
adhere to having a 4/3 and 3/2 in each octave (also for tonal
grounding), while all of the other intervals where different in each
successive octave, but of late I'm using many other ratios that fall
within 1/4 tone of 4/3 and 3/2 (to explain the logic of this
construction is beyond what I care to type in this post). Usually
I'll construct about 8 of these scales to cover the midi range. I can
rationalize this practice in no other way than to say that I guess
I'm just a little (over perhaps) enamored with the harmonic series -
and that it can be very interesting and beautiful (to my ears) -
especially in a melodic sense - to hear a number of different timbres
playing at the same time on such a tuning system.

Anyway, I think the paper strip method of keyboard navigation can be
a great tool for making music with microtunings. Sometimes I wonder
if my musical guests think I have some kind of "big note" scheme on
my keyboard, because I don't know the notes. An amusing thought.

I wish everyone well today. I'm off to see a performance of
international artists in Carrboro, NC this evening. I'll let you know
what I saw and heard.

Good Day!!!

Jacky

🔗kdoyle9162@aol.com

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, Graham Breed <graham@m...> wrote:
> On Fri, 25 Aug 2000, Joseph Pehrson wrote:

> A thing I do with all keyboards, and it's how I originally learnt
to play, is to write out the scale or chords onto a strip of paper.
Then, slide that strip up and down the keyboard so that you know what
to play. The only problem with this for extended mappings is finding
a long enough strip of paper.
>
> This all seems obvious to me, but don't know if other people do it
or not.
>

Thank you, Graham, for your commentary. Admittedly, our standard 2+3
keyboard is quite biased just by looking at it... suitable, of
course,
for the "altered Pythagorean," but definitely not other systems...

Hmmm. Maybe at some point manufacturers would also include some kind
of "alterable" windows with pitch names or other nomenclature right
above the keys, changable by moving wheels or whatever... I guess it
might be desirable.

Thanks for the response!

_________ _____ ___ __ __
Joseph Pehrson

🔗Graham Breed <graham@microtonal.co.uk>

On Sat, 26 Aug 2000, Joseph Pehrson wrote:

> Thank you, Graham, for your commentary. Admittedly, our standard 2+3
> keyboard is quite biased just by looking at it... suitable, of
> course,
> for the "altered Pythagorean," but definitely not other systems...

Pshah! That's defeatist talk! The keyboard is suited for a number of other
systems as well.

The most obvious are the doubly-negative temperaments. In these, the fifth is
tempered flat of 12-equal, like a meantone, but also divided into two equal
parts. On the keyboard, the white keys play the normal diatonic, and each
black key equally splits the interval between the neighbouring white keys.
Tune to 14-equal, and this gives you 7-equal on the white keys: an entirely
logical tuning. To 38- or 50-equal, the white keys are excellent meantone
diatonic scales, and the black keys give you 7-limit alternatives.

And wasn't it you, Joseph, who was "surprised [by] the satisfactory
results for 26, 27and 29"? Well, get this: 26 is another doubly-negative
temperament. See how well those "satisfactory" intervals fit this
mapping!

As for 29, well, you don't know the half of it. As a perfect fourth is 12
steps from 29, this fits a 7+5 keyboard very well indeed, as covered in
<http://x31eq.com/schv12.htm>.

A lot of the other scales on my website have 7 notes, and so are still
eminently playable on a regular keyboard. So much so, that my problem is not
finding scales to play, but finding the time to explore them all.

> Hmmm. Maybe at some point manufacturers would also include some kind
> of "alterable" windows with pitch names or other nomenclature right
> above the keys, changable by moving wheels or whatever... I guess it
> might be desirable.

LCDs would be very useful, but I doubt the demand's there. And controllable
via MIDI or somesuch. A simple system might even be useful to those learning
traditional scales, as the display could adjust to the key signature. With a
generalized keyboard, making each key an LCD sounds like an excellent idea.

David J. Finnamore wrote:

>Hi, Graham and Joseph! Two words: masking tape.

Such an obvious idea, but I never thought of it. Thanks, David!

Graham

"I toss therefore I am" -- Sartre

🔗Jacky Ligon <jacky_ekstasis@yahoo.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, Graham Breed <graham@m...> wrote:
> On Sat, 26 Aug 2000, Joseph Pehrson wrote:
>
> As for 29, well, you don't know the half of it. As a perfect
fourth is 12 steps from 29, this fits a 7+5 keyboard very well
indeed,
as covered in
> <http://x31eq.com/schv12.htm>.
>
> A lot of the other scales on my website have 7 notes, and so are
still eminently playable on a regular keyboard. So much so, that my
problem is notfinding scales to play, but finding the time to explore
them all.
>
Thanks, Grahm, for your experienced comments concerning alternate
(and unalternate!)keyboards. I feel much better about my "7+5"
already. I was going to spend a sleepless night about it like
Monzo...
but I'm feel much more relaxed already....
>
> "I toss therefore I am" -- Sartre

____________ ____ __ __ _
Joseph Pehrson