visual or mathematical

graham@microtonal.co.uk wrote:

> Kraig wrote:
>
> > If you will notice that the notation that Erv Wilson has
> > proposed in Xenharmonikon and
> > elsewhere can have the same bias as Johnson.
>
> Not in "On Linear Notations..." he doesn't. He has the same bias as
> Monzowolfellholtz.

I meant in using a notation of d-a to represent a 40/27. In fact one could have D-A represent any
interval as long as the scale was a constant structure.

>
> > The difference is that Erv
> > notion implies that the
> > scale being used in a Constant Structure. From that point, the notation
> > is based on the melodic
> > consistency (or linear series) of the tuning as opposed to the
> > harmonic, not that this necessarily
> > an opposition.
>
> I don't think they are. What do you intend by drawing the distinction?

The distinction is nothing more than approach to notation. One can base it on harmonic relations
over melodic or visa versa. Both have there advantages. You are correct to imply that the
bosanquet keyboard will steer one toward a good balance between the two.

>
> The Bosanquet layout ensures the two are not in opposition.

>
>
> > The further advantage of his notation is that the logic
> > holds true from tuning to
> > tuning and is consistent with a Bosanquet keyboard.
>
> Of course it's consistent with a Bosanquet keyboard, it's designed for a
> Bosanquet keyboard. It certainly is not consistent from tuning to tuning.
> In positive notation, a 4:5:6 triad is C E- G. In negative notation it's
> C E G. That's an inconsistency and it's a problem.

They also differ in terms of melodic/linear sequence so they should not be called the same thing.
Your point is taken and this shows the advantage of a harmonically based notation, 5/4 will always
be notated the same.

>
> What do you mean the only construction. You said before: "One of the
> things that really got Erv excited about Hanson' s keyboard is that it
> handles 72 where as the Bosanquet does not."

Yes i was not clear here. There is the difference between the keyboard logic design and
physicality of the keyboard. If one has a Bosanquet Keyboard you can put Hansons logic on it

> So Bosanquet can't handle 72. Whereas a keyboard constructed around a
> 10+1 "Miracle" scale could, along with 31 and 41. Why does that not offer
> any promise for moving forward?

where is this keyboard and can't this scale be mapped to one of Hanson's already. Is it not a
generalized?

> If you haven't been following the Miracle discussion, I urge you to look
> back though it. If there's something you don't understand, please ask.

I have no problem following the idea of a 7/72 generator. I have a 72 tone set of tubes tuned to a
Just 72 that contains the Hebdomekontany. With 22 tone you can have an eikosany too. In fact the
22 i have is found within this 72. It has 30 hexanies and 30 tetrads

> > Also a a learning tool it far surpasses in
> > simplicity the use of
> > matrixes to see the unison vectors in any tuning.
>
> I assume that's a swipe at me, as I'm the one who uses matrixes.

not you personally at all. I hadn't followed who used them or didn't. I just find it hard to see
what the scale is without having to map it all out.

> So how
> does this negative notation help me to see the unison vector (4 -1)h?

who uses this notation?. If i look at the keyboard I can see that so many 3/2 will coincide with a
5/4 keyboard rank. Etc. with the other intervals

>
> Look, mathematicians tend to fall into one of two groups. Those who think
> in terms of pictures, and those who think in numbers or symbols. Erv
> looks like he's in the former group, and so are you. I'm in the latter.
> That doesn't stop me drawing diagrams, or Erv using numbers. We can have
> a discussion without either of us having to be wrong.

Perhaps I assume that pictorial is better or more universal. It seems that with a picture it is
easier to decipher. Matrixes require a certain background in math that not all have. I am glad
they work for you . Maybe you look at them and the whole lattice pops out for you. For me and i
imagine others this is not the case and one has to spend quite a time just mapping them out on
paper. If one knows how.

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Kraig Grady wrote:

> > Not in "On Linear Notations..." he doesn't. He has the same bias
as
> > Monzowolfellholtz.
>
> I meant in using a notation of d-a to represent a 40/27. In fact one
could have D-A represent any
> interval as long as the scale was a constant structure.

You could do that. I've suggested doing that as a variation of Erv's
positive notation. But I don't remember Erv ever suggesting it.

> > Of course it's consistent with a Bosanquet keyboard, it's designed
for a
> > Bosanquet keyboard. It certainly is not consistent from tuning to
tuning.
> > In positive notation, a 4:5:6 triad is C E- G. In negative
notation it's
> > C E G. That's an inconsistency and it's a problem.
>
> They also differ in terms of melodic/linear sequence so they should
not be called the same thing.
> Your point is taken and this shows the advantage of a harmonically
based notation, 5/4 will always
> be notated the same.

They differ in linear sequence *on a Bosanquet keyboard*. They don't
in Erlich-Keenan temperament or decimal notation, and so wouldn't on a
keyboard built for it. That's why decimal notation is superior for
11-limit music.

> > What do you mean the only construction. You said before: "One
of the
> > things that really got Erv excited about Hanson' s keyboard is
that it
> > handles 72 where as the Bosanquet does not."
>
> Yes i was not clear here. There is the difference between the
keyboard logic design and
> physicality of the keyboard. If one has a Bosanquet Keyboard you can
put Hansons logic on it

Okay, that's understood.

> > So Bosanquet can't handle 72. Whereas a keyboard constructed
around a
> > 10+1 "Miracle" scale could, along with 31 and 41. Why does that
not offer
> > any promise for moving forward?
>
> where is this keyboard and can't this scale be mapped to one of
Hanson's already. Is it not a
> generalized?

No, it isn't generalized enough. A simple keyboard for Miracle would
look something like this:

0^
0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ 8^ 9^ 0
0 1 2 3 4 5 6 7 8 9 0v
0v 1v 2v 3v 4v 5v 6v 7v 8v 9v 0w
0w

with the harmonic template

5 7
1 3
9 11

To fit that to a hexagonal keyboard, you need a run of 10 notes all
going in one direction for an octave. With a
U648<http://catalog.com/starrlab/keyboards.html>
, this means you can get about two and a half octaves going diagonally
across the keyboard. So it can be done, but it's a real waste of
resources. I can get the same range with my X5D and a sustain pad.

You can also fit the scale to Modulus 31 or Modulus 41 or Hanson, but
it'll look different each time. So it isn't generalized.

There's a deeper problem with Wilson/Bosanquet in that it's based
around hexagons. When you have neutral thirds or two chains of
generators, a square array becomes more convenient. I've thought
about this before, even mentioned it in a letter to Erv, and
considered it an unfortunate limitation to the Bosanquet concept.
Until the Erlich-Keenan temperament came along, I didn't have a
solution that covered both standard and neutral thirds. I still don't
have it all worked out, that's why I'd prefer you to help us on this
instead of questioning why we're doing it. Of course no physical
keyboard exists specifically for the Erlich-Keenan temperament. Even
the theory didn't exist a fortnight ago.

The best existing keyboard looks like the Z-board
<http://catalog.com/starrlab/keyboards2.html>. They way it's shaped
it'd be better to follow the lattice than the layout I gave above, but
either would work better than on a hexagonal array. In fact, my
preferred "keyboard" now is definitely a Ztar, partly for economic
reasons. I might be able to afford one in the next year or so.

The site's all frames now, and my old MicroZone link's broken <sob>.
So go to <http://catalog.com/starrlab/>. The other links I gave above
do work, but don't give you the navigation.

> > If you haven't been following the Miracle discussion, I urge you
to look
> > back though it. If there's something you don't understand, please
ask.
>
> I have no problem following the idea of a 7/72 generator. I have a
72 tone set of tubes tuned to a
> Just 72 that contains the Hebdomekontany. With 22 tone you can have
an eikosany too. In fact the
> 22 i have is found within this 72. It has 30 hexanies and 30 tetrads

That's not Blackjack, then, but interesting.

> Perhaps I assume that pictorial is better or more universal. It
seems that with a picture it is
> easier to decipher. Matrixes require a certain background in math
that not all have. I am glad
> they work for you . Maybe you look at them and the whole lattice
pops out for you. For me and i
> imagine others this is not the case and one has to spend quite a
time just mapping them out on
> paper. If one knows how.

I think the subject line is wrong. It should be "geometrical or
arithmetical". Geometry *is* mathematics. Erv's ideas seem mostly
aimed at reconciling the arithmetical and geometrical.

Yes, matrixes require a certain background, I find they are useful to
me. I've used Excel's matrix functionality heavily for the Miracle
background and also in looking at some other generators. The
important stuff for the Erlich-Keenan temperament I did on paper
before I got the PC booted, but still using matrixes.

Most of the matrix work does on before the generalized keyboard layout
becomes apparent. So comparing the two isn't really appropriate. By
the time you get a keyboard mapping and template, you dont need the
matrixes.

You can place notes on the lattice from their matrix representation,
but it's still easier to see them on the lattice which is why I use a
lattice. You can also use matrixes to convert between specifications
for a lattice and a generalized keyboard. I find that useful, but
mostly in theory because it isn't something I have to do very often.

Graham

Kraig wrote,

>> It has 30 hexanies and 30 tetrads

Graham wrote,

> That's not Blackjack, then, but interesting.

Kraig (if I may be so bold as to step in and comment) is referring to
the Eikosany with the 30 hexanies and 30 tetrads falling equally into
the 15 categories

1-3-5-7
1-3-5-9
1-3-5-11
1-3-7-9
1-3-7-11
1-3-9-11
1-5-7-9
1-5-7-11
1-5-9-11
1-7-9-11
3-5-7-9
3-5-7-11
3-5-9-11
3-7-9-11
5-7-9-11

For each of the above, the Eikosany has 1 otonal tetrad, 1 utonal
tetrad, and 2 hexanies.

The blackjack scale is very different in that it has far more
hexanies and tetrads in the 1-3-5-7 category. I invite Dave Keenan to
tell us what it has in the other categories.

Paul!
Yes it all depends on what one wants to do. This is where the Art comes in.
One other comment to others (including yourself of course too)
While we can say that there are no bad scales, I do believe that there are inappropriate scales.
Each scale has its plus and minuses and it is up to the artist sensitivity to take them by the
rein. Not picking on anyone in particular, but when i hear a set of pieces running through all the
ET's for instance and they basically sound the same, I feel that something about the scales are
being overlooked. To give credit where credit is due, sometimes what is necessary is to jump in
unprepared and have the courage to misunderstand and reflect on the outcome later. Often in
retrospect enough is done to give one and others an idea just what a scale can do. It all boils
down to what one wants to do and Dave's find offers allot to explore without a doubt. The eikosany
is ideal for exploring a non tonal area with the use of acoustically relevant consonances. Dave
scales will also do this in a more limited way but one will be able to do exact transpositions of
much of the material to other pitch levels. Depending on what one wants to do, each scale is more
appropriate than the other to do its each unique thing.

PERLICH@ACADIAN-ASSET.COM wrote:

> Kraig wrote,
>
> >> It has 30 hexanies and 30 tetrads
>
> Graham wrote,
>
> > That's not Blackjack, then, but interesting.
>
> Kraig (if I may be so bold as to step in and comment) is referring to
> the Eikosany with the 30 hexanies and 30 tetrads falling equally into
> the 15 categories
>
> 1-3-5-7
> 1-3-5-9
> 1-3-5-11
> 1-3-7-9
> 1-3-7-11
> 1-3-9-11
> 1-5-7-9
> 1-5-7-11
> 1-5-9-11
> 1-7-9-11
> 3-5-7-9
> 3-5-7-11
> 3-5-9-11
> 3-7-9-11
> 5-7-9-11
>
> For each of the above, the Eikosany has 1 otonal tetrad, 1 utonal
> tetrad, and 2 hexanies.
>
> The blackjack scale is very different in that it has far more
> hexanies and tetrads in the 1-3-5-7 category. I invite Dave Keenan to
> tell us what it has in the other categories.

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Graham !
Comments below!

Graham Breed wrote:

> > I meant in using a notation of d-a to represent a 40/27. In fact one
> could have D-A represent any
> > interval as long as the scale was a constant structure.
>
> You could do that. I've suggested doing that as a variation of Erv's
> positive notation. But I don't remember Erv ever suggesting it.

Erv teaches mainly on a a one to one verbal basis, then by letter. If you look at
http://www.anaphoria.com/key.PDF you can see that he shows a basic range of generators going from
phi to equal back to a reciprocal phi.

>
>
>
> 0^
> 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ 8^ 9^ 0
> 0 1 2 3 4 5 6 7 8 9 0v
> 0v 1v 2v 3v 4v 5v 6v 7v 8v 9v 0w
> 0w

I am not sure this lines up. The ascii stuff doesn't work for me as it always gets tweaked

>
>
> with the harmonic template
>
> 5 7
> 1 3
> 9 11
>
> To fit that to a hexagonal keyboard, you need a run of 10 notes all
> going in one direction for an octave. With a
> U648<http://catalog.com/starrlab/keyboards.html>
> , this means you can get about two and a half octaves going diagonally
> across the keyboard. So it can be done, but it's a real waste of
> resources. I can get the same range with my X5D and a sustain pad.

The idea is the one can just tilt this keyboard so that this diagonal would be horizontal.
http://www.anaphoria.com/tres.PDF page 12 is the basic grid to show where the octave would be
depending on the generator. Obviously one can use the keyboard mapping toward the left to map
those "behind" it to the right. One can find samples of this at
http://www.anaphoria.com/key-smpl.PDF . Thus it is possible to map a particular scale in more than
one way. I myself have used three different mappings of 22 at different times. Mapping this scale
out though i get the same keyboard as you (i think) If one didn't care about whether it worked for
31 or 41 other alternatives are possible.

> You can also fit the scale to Modulus 31 or Modulus 41 or Hanson, but
> it'll look different each time. So it isn't generalized.
>
> There's a deeper problem with Wilson/Bosanquet in that it's based
> around hexagons. When you have neutral thirds or two chains of
> generators, a square array becomes more convenient.

I think the ability to slant the whole keyboard is why he picked hexagons so if you have a scale
such as this you just tilt the whole thing.

>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

/tuning/topicId_22183.html#22417

> [Graham Breed]
>
> Some generalised keyboards have been suggested with
> swappable key tops. I don't know if the MicroZone has
> them. It may be a question of economics: better something
> less flexible that exists then a wonderful machine that
> doesn't.
>
> Now we have a mole in the factory, perhaps we could find
> out these tidbits.
>
> I think somebody worked out a design that allowed you to
> change the orientation of the keys as well, but that's
> likely to cost an even larger fortune than the MicroZone
> currently does.

The mole is giving a report here. ;-)

Yes, the MicroZone's key tops can be swapped, so that
black and white (or any other color) keys can be placed
anywhere in the hexagonal honeycomb the user wishes.

Using a variety of colors, I've imagined how to map
Monzo lattices onto the MicroZone keyboard, but haven't
actually tried it yet. My imagination tells me, as Graham
suggests in the post I quote below, that if I tried this
kind of mapping, there would be a lot of empty gaps, thus
wasting much of the resources of the MicroZone.

/tuning/topicId_22430.html#22454

> [Graham Breed]
>
> No, it isn't generalized enough. A simple keyboard for
> Miracle would look something like this:
>
> 0^
> 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ 8^ 9^ 0
> 0 1 2 3 4 5 6 7 8 9 0v
> 0v 1v 2v 3v 4v 5v 6v 7v 8v 9v 0w
> 0w
>
> with the harmonic template
>
> 5 7
> 1 3
> 9 11
>
> ...
>
> There's a deeper problem with Wilson/Bosanquet in that it's
> based around hexagons. When you have neutral thirds or two
> chains of generators, a square array becomes more convenient.
> I've thought about this before, even mentioned it in a
> letter to Erv, and considered it an unfortunate limitation
> to the Bosanquet concept. Until the Erlich-Keenan
> temperament came along, I didn't have a solution that
> covered both standard and neutral thirds. I still don't
> have it all worked out, that's why I'd prefer you to help
> us on this instead of questioning why we're doing it. Of
> course no physical keyboard exists specifically for the
> Erlich-Keenan temperament. Even the theory didn't exist
> a fortnight ago.
>
> The best existing keyboard looks like the Z-board
> <http://catalog.com/starrlab/keyboards2.html>. The way
> it's shaped it'd be better to follow the lattice than
> the layout I gave above, but either would work better
> than on a hexagonal array. In fact, my preferred
> "keyboard" now is definitely a Ztar, partly for economic
> reasons. I might be able to afford one in the next year
> or so.
>
> The site's all frames now, and my old MicroZone link's
> broken <sob>. So go to http://catalog.com/starrlab/>.
> The other links I gave above do work, but don't give you
> the navigation.

(I'm glad Graham posted the link to the Zboard page,
because the Starr Labs site no longer has a link to it.
I'm sure that's just a glitch... I'll mention it
Monday and see if we can put it back in. The Zboard
is definitely still in production.)

> /tuning/topicId_22394.html#22476
>
> [David J. Finnamore]
>
> ... I'm just going to have to rig up a way to play this
> tuning, that's all there is to it.

David, I felt exactly the same way.

Graham, I was so excited by this that I printed your
post this morning and took it with me to work. Harvey
Starr and I had a good discussion about making available
a controller that would easily map the blackjack/miracle
scales. Harvey knows a lot about his instruments but not
a lot about tuning, and for me it's vice versa.

After thinking about it all day as I worked on the
MicroZone, and some experimenting with Zboard and Ztar
layouts after work, I decided to settle on mapping the
entire 72-EDO superset to the Ztar keyboard. This
obviates the need to accomodate the odd periodicities of
the 10+1, 21-, 31-, and 41-tone mappings, and in addition
allows full modulation across the entire spectrum of pitches
in this amazing family of tunings.

At first I tried mapping 72-EDO to the Zboard, which
is a matrix of 12 x 23 = 276 keys. Right away the
fact that each column of keys is 12 deep suggested to
me that a 12-EDO whole tone, divided into 12 1/12-tones,
be mapped across the entire column. This resulted in
a 72-EDO adaptation of the van Janko keyboard layout,
with a total range of just under 4 "octaves".

I'll try to get around to making an illustration of
what I did here. Here's a quote describing a regular
Janko keyboard, from
http://afs.wu-wien.ac.at/earlym-l/other.lists/piporg-l/PIPORG-
L.LOG9602E

(use copy and paste to remove the line break)

> Date: Wed, 28 Feb 1996 15:29:17 -0500
> Sender: Pipe Organs and Related Topics
> <PIPORG-L@CNSIBM.ALBANY.EDU>
> From: Paul Opel <POpel@sover.net>
> Subject: Re: Janko keyboards
>
> Paul von Janko', Hungarian pianist and inventor (1856-1919),
> invented the eponymous keyboard layout.
>
> from an Baker's, 5th ed.:
>
>> His keyboard, invented in 1882, is really a new departure
>> in piano-mechanics, though standing in distant relationship
>> the older 'chromatic' keyboard advocated by the society
>> 'Chroma'. It has six rows of keys in steplike succession;
>> the arrangement of the two lowest rows (typical of the
>> other two pairs) is as follows:
>>
>> Second row: c# d# F G A B
>> Lowest row: C D E f# g# a# C
>>
>> the capitals representing white keys, and the small letters
>> black ones.
>>
>> The 3rd and 4th rows, and the 5th and 6th rows, are mere
>> duplications of the 1st and 2nd; and corresponding keys
>> in the 1st, 3rd, and 5th rows, and in the 2nd, 4th, and
>> 6th rows, are on one and the same key-lever, so that
>> any note can be struck in three different places. The
>> fingering of all diatonic scales is alike; chromatic
>> scales are played by striking alternative keys in any
>> two adjoining rows. A full description of the keyboard
>> was published in pamphlet form by its inventor (1886)
>>
>> [then follows a bibliography of articles up to 1905]
>
> As I remember, the keys are the same width as standard
> white keys, making the octave span smaller- so much the
> worse for keyspan chests!
>
>
> I do not find any listing for the 'Chroma' society- but
> I don't have ready access to the New Grove. Anyone have
> anything further?
>
> Paul Opel
>

The major drawback to the Zboard mapping was that it
was quite a stretch of the hand to play some chords
that had notes in both the front and back rows. Also,
the Janko layout is not as familiar, and seemed downright
odd with the microtonal adaptation.

So I decided to try mapping 72-EDO to the Ztar, which
has 6 x 24 = 144 keys. This to me worked much better,
because each column represented a semitone and the
alternation of black and white keys could be made to
more closely resemble the familiar Halberstadt layout.
Here's the beginning of the mapping:

I've made a very realistic JPEG of this mapping
and included it at the end of my Dictionary entry
for 72-EDO:
http://tonalsoft.com/enc/number/72edo.aspx

The total range is 2 audio "octaves".

One of the drawbacks to all these instruments is that
they are expensive. Since I'm not much of a guitarist
and frankly don't need the guitar-like aspects of the
Ztar, I asked Harvey about the possibility of making
an instrument that consisted pretty much of just the
Ztar fingerboard. He said that he gets quite a number
of requests for this, so I'm pretty sure that he's going
to start manufacturing them like that. This should
bring the price down a bit, hopefully around the $1000
range - a great deal more affordable than the $8800
MicroZone.

Go to the Starr Labs site and click on "Custom Designs",
then scroll down to where it says "Y10 Standalone MIDI controller
module shown with a plug-in Ztar fingerboard
attached." The accompanying picture shows a stand-alone
Ztar fingerboard. This is very much along the lines of
what Harvey and I discussed.

I think it would be a great improvement to extend the
Ztar mapping so that more audio "octaves" could be
accomodated. The Zboard would actually work fine in
this regard, as it's columns can simply be divided in
half, with the same patterns of black and white keys
in both halves, and one sounding an "octave" above/below
the other. If Harvey carries out his intention to expand
the Zboard to 12 x 24 = 288 keys, this would give a total
range of 4 "octaves".

Graham's right: between the Ztar and the Zboard, we've
already got a couple of great instruments crying out to
be tuned to these "miracle" scales.

(I've also wondered about mapping 144-EDO to the Ztar,
since the keys are already set up for it.)

Lastly, I tried mapping 72-EDO to the MicroZone, but
alas, it didn't work very well. I've seen commentary
here by Kraig, Paul, and Graham about this, but would
really love to see it explained comprehensively. I could
see in the mapping attempt I made that the problem was
that because of the hexagonal key shape, the same interval
relationships did not hold when traveling from key to
key in a particular direction.

All of the Starr Labs instruments allow comprehensive
MIDI capabilites, including the ability to map any
MIDI note number to any key. All the instruments also
make use of "zones", which can be anywhere from a single
key to the entire keyboard, and can overlap if desired.

With me working together with Harvey on instruments that
serve the needs of the microtonal community, we may end up
with some really useable and affordable instruments. It's
up to us now to make the financial investment so that he
can afford to produce these things.

I've had the idea that maybe we could have some sort of
fundraiser to accumulate enough money to get prototypes
up and running. Feedback welcome.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22494

> So I decided to try mapping 72-EDO to the Ztar, which
> has 6 x 24 = 144 keys. This to me worked much better,
> because each column represented a semitone and the
> alternation of black and white keys could be made to
> more closely resemble the familiar Halberstadt layout.
> Here's the beginning of the mapping:
>
> I've made a very realistic JPEG of this mapping
> and included it at the end of my Dictionary entry
> for 72-EDO:
> http://tonalsoft.com/enc/number/72edo.aspx

Oops, my bad. I meant to include some of the mapping in ASCII
here for the benefit of those without web access. Here's the
section from "C" to "G", showing the 72-EDO degree and notation
for each note.

Monzo 72-EDO mapping to Starr Labs Ztar:

2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#> 44 G>
1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+ 43 G+
0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F# 42 G
71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#- 41 G-
70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#< 40 G<
69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ 39 F#^

(Here I consistently use only the "up-arrow" spellings for
the quarter-tones in the bottom row. On the JPG graphic in
the Dictinary entry, both enharmonic spellings are given.)

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22498

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_22430.html#22494
>
> > So I decided to try mapping 72-EDO to the Ztar,
> > ...
> > http://tonalsoft.com/enc/number/72edo.aspx
>
> ...
>
> 2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#> 44 G>
> 1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+ 43 G+
> 0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F# 42 G
> 71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#- 41 G-
> 70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#< 40 G<
> 69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ 39 F#^
>

I was looking at the graphic on the webpage again, and it
suddenly struck me how obvious this makes the "bike gear"
metaphor.

In the same way that 12-EDO can be thought of as a chain of
either "perfect 5ths" or semitones, 72-EDO can be thought of
as 6 such chains, each the same "gear ratio" away from the
next adjacent one (a 1/12-tone, or 16&2/3 cents).

The horizontal rows of keys in this graphic even *look* a
little like bicycle chains to me!

-monz
http://www.monz.org
"All roads lead to n^0"

Monz wrote:

> Using a variety of colors, I've imagined how to map
> Monzo lattices onto the MicroZone keyboard, but haven't
> actually tried it yet. My imagination tells me, as Graham
> suggests in the post I quote below, that if I tried this
> kind of mapping, there would be a lot of empty gaps, thus
> wasting much of the resources of the MicroZone.

[snip]

> Harvey
> Starr and I had a good discussion about making available
> a controller that would easily map the blackjack/miracle
> scales. Harvey knows a lot about his instruments but not
> a lot about tuning, and for me it's vice versa.

Maybe you could collaborate with Harvey and invent the Monzone. :)

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

1st grade, 1901:
See Spot. See Spot run. Run, Spot, run!

1st grade, 2001:
C:\spot
C:\spot\run.exe
RUN spot\run.exe

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22498
>
> Monzo 72-EDO mapping to Starr Labs Ztar:
>
> 2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#> 44 G>
> 1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+ 43 G+
> 0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F# 42 G
> 71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#- 41 G-
> 70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#< 40 G<
> 69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ 39 F#^
>

Well, this is great. Pretty much what Rick Tagawa was doing only
with, obviously, just ONE keyboard!

Could be a new "generalized" keyboard for ALL of us... (??)

________ ________ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_22430.html#22498
> >
> > Monzo 72-EDO mapping to Starr Labs Ztar:
> >
> > 2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#> 44 G>
> > 1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+ 43 G+
> > 0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F# 42 G
> > 71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#- 41 G-
> > 70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#< 40 G<
> > 69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ 39 F#^
> >
>
> Well, this is great. Pretty much what Rick Tagawa was doing only
> with, obviously, just ONE keyboard!
>
> Could be a new "generalized" keyboard for ALL of us... (??)

Weeeell, I'm not sure that a 72-EDO instrument really deserves to be
classified as "MIRACLE". 72 notes per octave is just way too many.
Most folks want more than one and a bit octaves on their instrument
and to fit their fingers between frets.

The point of the MIRACLE generator is that you need less than a third
of that, with double the minimum stepsize, to get a really big chunk
of the 11-limit, and an even bigger chunk of the 9-limit and a bigger
chunk again of the 7-limit. (But you don't get any more 5-limit or
3-limit than the subsets available at the 7-limit).

This increase in numbers of complete consonances with decreasing
odd-limit seems like another miraculous property.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_22430.html#22708

> --- In tuning@y..., jpehrson@r... wrote:
>
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_22430.html#22498
> > >
> > > Monzo 72-EDO mapping to Starr Labs Ztar:
> > >
> > > 2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#>
> > > 1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+
> > > 0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F#
> > > 71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#-
> > > 70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#<
> > > 69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ etc.
> >
> >
> > Well, this is great. Pretty much what Rick Tagawa was doing
> > only with, obviously, just ONE keyboard!
> >
> > Could be a new "generalized" keyboard for ALL of us... (??)
>
> Weeeell, I'm not sure that a 72-EDO instrument really deserves
> to be classified as "MIRACLE". 72 notes per octave is just way
> too many.
>
> Most folks want more than one and a bit octaves on their
> instrument and to fit their fingers between frets.
>
> The point of the MIRACLE generator is that you need less than
> a third of that, with double the minimum stepsize, to get a
> really big chunk of the 11-limit, and an even bigger chunk of
> the 9-limit and a bigger chunk again of the 7-limit. (But you
> don't get any more 5-limit or 3-limit than the subsets available
> at the 7-limit).

Good points, Dave. But keep in mind that the Starr Labs
instruments are only MIDI controllers, with no sound source,
so it's trivial to program the keys to any pitches desired.

The Miracle-31 or Blackjack scales could both be mapped to
the Ztar and have plenty of keys left over for greater range.

And on the subject of range, the Ztars that are already in
production have a 6 x 24 layout, so even in 72-EDO they
produce a full 2 "octaves", and the Zboard is 12 x 23, which
will probably become 12 x 24, giving a 4-"octave" range
in 72-EDO. That's not shabby at all, only one "octave" less
than most regular Halberstadt-layout electronic keyboards.
(Does "61-key keyboard" ring a bell to anyone?)

I haven't given it much thought, but a quick first attempt
at mapping Blackjack-21 to the Ztar with no wasted keys
might work like this (giving 72-EDO degrees and notation):

7 C#+ 28 F< 49 G#+ 70 C<
2 C> 23 E- 44 G> 65 B- etc.
0 C 21 Eb^ 42 G 63 Bb^ .
70 C< 16 Eb< 37 F#+ 58 Bb< .
65 B- 14 D> 35 F#- 56 A> .
63 Bb^ 9 C#^ 30 F 51 G#^ 0 C

I could actually see this as being a *very* playable arrangement.
For example, look how comfortably the fingers would lie over
a ~4:5:6:7 tetrad on C:

23 E-
0 C 42 G
58 Bb<

or conversely, a ~1/(4:5:6:7) tetrad with a "root" of C#+
or "guide tone" of B-:

7 C#+
23 E- 65 B-
42 G

The only disadvantage I can see in this mapping is that the
pattern shifts down by 3 keys at the first repetition then
back up to the origin point at the next repetition, so it
gives the appearance of having two chains. But I think one
could easily get used to that, because it's still a quite
regular pattern.

And this mapping gives a range that is only 3 notes shy of
7 "octaves" on the Ztar - quite enough for real musical use,
and just a tiny bit less than the 7&1/3 "octaves" of a full
piano, but in format that is a *LOT* more portable!

Alternatively, since Blackjack can also be viewed as 3
7-tone MOSs, it might be mapped with one "octave" above
and the other below, like this:

7 C#+ 16 Eb< 28 F< 37 F#+ 49 G#+ 58 Bb< 70 C<
2 C> 14 D> 23 E- 35 F#- 44 G> 56 A> 65 B-
0 C 9 C#^ 21 Eb^ 30 F 42 G 51 G#^ 63 Bb^
-------------------------------------------------------------
7 C#+ 16 Eb< 28 F< 37 F#+ 49 G#+ 58 Bb< 70 C<
2 C> 14 D> 23 E- 35 F#- 44 G> 56 A> 65 B-
0 C 9 C#^ 21 Eb^ 30 F 42 G 51 G#^ 63 Bb^ etc.

This gives a strictly regular key pattern, altho at first
glance I don't like it as much as the one above.

Hmmm... I should give some thought to how the Miracle-31
might be mapped onto a Ztar. Now *that* would be a fantastic
instrument. But it's not as straightforward as Blackjack,
since 31 is a prime and therefore won't reconcile with
the Ztar layout easily.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22711

> Hmmm... I should give some thought to how the Miracle-31
> might be mapped onto a Ztar. Now *that* would be a fantastic
> instrument. But it's not as straightforward as Blackjack,
> since 31 is a prime and therefore won't reconcile with
> the Ztar layout easily.

Hmmm... in a sudden flash of insight I realized that there
is an easy and regular way to map Miracle-31 to the Ztar,
but it wastes 5 keys per "octave":

5 10 15 20 25 30 5 10
4 9 14 19 24 29 4 9
3 8 13 18 23 28 3 8
2 7 12 17 22 27 2 7
1 6 11 16 21 26 1 6
0 -- -- -- -- -- 0 -- etc.

(This diagram gives the ordinal 31-tone degree-numbers.
I've been concentrating on Blackjack, and haven't yet worked
out which 72-EDO pitches would be added to make the Miracle-31.)

But even with the wasted keys, the Ztar mapped like this
would give a complete 4 "octave" range. Not bad if you ask me.

I think we have a winner here. Should I have been sending
these posts to the "Practical Microtonality" list instead?

-monz
http://www.monz.org
"All roads lead to n^0"

Joe,

One of the few of the million recent posts I've had time to both read
and reply to!

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> I think we have a winner here. Should I have been sending
> these posts to the "Practical Microtonality" list instead?

How practical is the price range of the instrument? That isn't said
facetiously, I think it is really a significant part of the picture...

Cheers,
Jon

As of Wednesday, Harvey Starr and I entered into a
(so far, still informal) agreement for me to work as a
sales rep for Starr Labs.

In case anyone here is interested in purchasing a Ztar,
Zboard, or MicroZone (OK, so that one's not too likely...)
as a result of the work I've posted here, please be sure
to email me first before contacting Starr Labs, so that
I will be able to receive my proper (and much needed)
commission.

I plan on producing much more in regard to mapping microtonal
scales to Harvey's instruments, both on the Tuning List and
on my webpages, so please keep in mind that I am trying to
earn some money off of this work if it makes people want to
purchase these instruments.

Thanks.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., JSZANTO@A... wrote:

/tuning/topicId_22430.html#22713

> Joe,
>
> One of the few of the million recent posts I've had time to
> both read and reply to!

I know, Jon, sorry... I've been one of the biggest culprits
in the "post overload" this weekend. But I'm inspired!

>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > I think we have a winner here. Should I have been sending
> > these posts to the "Practical Microtonality" list instead?
>
> How practical is the price range of the instrument? That
> isn't said facetiously, I think it is really a significant
> part of the picture...

I agree with you completely, and I know you're not being
the least bit facetious. I've been concentrating my efforts
on the Ztar, precisely because it *is* the most affordable
instrument Harvey makes.

The smallest and most low-end version of the Ztar, the Mini-Z
(<http://www.starrlabs.com/miniz.html>, bigger picture at
<http://www.starrlabs.com/5.html>), is currently listed at
$1595. This is a huge leap downward from the $8800 MicroZone,
within the reach of a lot of musicians and comparable to
many other "regular" instruments on the market. And the
price would certainly drop lower if sales continued to increase.

Harvey and I have also discussed the very likely possibility
of creating a new instrument consisting of just the Ztar
fingerboard, which might retail for just over $1000.
I'd buy one of those in a second.

-monz
http://www.monz.org
"All roads lead to n^0"

Joe,

Just checking to make sure I didn't tweak you, and I see I didn't,
which is good!

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> I agree with you completely, and I know you're not being
> the least bit facetious. I've been concentrating my efforts
> on the Ztar, precisely because it *is* the most affordable
> instrument Harvey makes.

And to wrap up, I completely understand that the amount of money
needed to ramp up a 'new' venture that is aimed at what could be
ultra-conservatively termed a "niche market" is nothing to smirk at.
I only hope, for those of you that want one, that either enough get
sold to bring these soundless contollers into the realm of
affordability, or Starr finds a sugar-daddy investor to grease the
skids.

I felt the same way about the Buchla 'mallet instrument'-style
contoller, the name of which I forget. Beautiful instrument,
incredible specs in terms of programability, obviously brilliantly
engineered considering the source. Just too damn expensive to
justify...

Rats!

Cheers,
Jon

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22712

> Hmmm... in a sudden flash of insight I realized that there
> is an easy and regular way to map Miracle-31 to the Ztar,
> but it wastes 5 keys per "octave":
>
> 5 10 15 20 25 30 5 10
> 4 9 14 19 24 29 4 9
> 3 8 13 18 23 28 3 8
> 2 7 12 17 22 27 2 7
> 1 6 11 16 21 26 1 6
> 0 -- -- -- -- -- 0 -- etc.
>
>
> (This diagram gives the ordinal 31-tone degree-numbers.
> I've been concentrating on Blackjack, and haven't yet worked
> out which 72-EDO pitches would be added to make the Miracle-31.)

I've decided that the mini-Z version of the Starr Labs Ztar
is going to be the microtonal keyboard for me.
(and Graham Breed has, too)

While the Blackjack scale is a good one, and I've already
devoted quite a bit of work to presenting some features of
it, *and* it maps well to the Ztar layout, mapping the
Blackjack to an instrument with this many keys is somewhat
pointless, because the Ztar can easily accomodate the full
31-tone Miracle scale, as shown above. The Blackjack is
good for other instruments with a more limited keyboard.

So now my question is: what extra 5 notes would be the
best ones to add to the Miracle scale to fill in the blank
spots on my Ztar layout?

(Sure wish I had spent my time making webpages and mp3's
of Miracle tuning rather than Blackjack...)

-monz
http://www.monz.org
"All roads lead to n^0"

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22752

>
> While the Blackjack scale is a good one, and I've already
> devoted quite a bit of work to presenting some features of
> it, *and* it maps well to the Ztar layout, mapping the
> Blackjack to an instrument with this many keys is somewhat
> pointless, because the Ztar can easily accomodate the full
> 31-tone Miracle scale, as shown above. The Blackjack is
> good for other instruments with a more limited keyboard.
>
> So now my question is: what extra 5 notes would be the
> best ones to add to the Miracle scale to fill in the blank
> spots on my Ztar layout?
>
>
> (Sure wish I had spent my time making webpages and mp3's
> of Miracle tuning rather than Blackjack...)
>

I still believe, Monz, that of the various "miracles," "blackjack"
with only 21 notes, is the most practical, particularly since most of
us don't have these "accelerated" keyboards yet.

Maybe someday we all will, and will practice them diligently in the
conservatories... but, until then, most of us are still stuck with
the Halberstadt!

For that reason, I am DELIGHTED that you have devoted that much web
space to "blackjack..."

I just hope that someday you have some kind of complete INDEX right
on your home page... since you have SO MANY interesting pages that
get lost out in cyberspace someplace!...

best,

Joe

_________ _______ ______ ____
Joseph Pehrson

monz wrote:

> I've decided that the mini-Z version of the Starr Labs Ztar
> is going to be the microtonal keyboard for me.
> (and Graham Breed has, too)

I didn't say a mini-Z. If you sit them in front of me, I might go for one
of the big boys.

> While the Blackjack scale is a good one, and I've already
> devoted quite a bit of work to presenting some features of
> it, *and* it maps well to the Ztar layout, mapping the
> Blackjack to an instrument with this many keys is somewhat
> pointless, because the Ztar can easily accomodate the full
> 31-tone Miracle scale, as shown above. The Blackjack is
> good for other instruments with a more limited keyboard.

Hmm. Well, I've found a way of tuning the strings on my meantone guitar
to suit Miracle temperament. Like this:

Decimal note Meantone/31 cents from 12-equal (for 31-equal)

6 E E-3
3 C^ C+48
8 Gb F#+29
5 D# D#-19
0 A A+0
6 E E-3

The decimal column is transposed to be all nominals, although usually 0
corresponds to C.

The idea is that the open strings form a tight structure on the lattice,
and connected only by 11-limit intervals.

The first impression was that I'd made the guitar horribly out of tune.
Also, the B string gets very tight and I wondered if it would snap. After
playing it melodically for a while, I quite like it. I've even found some
good chords, although not with all strings. One thing you have to watch
out for is that G-B becomes a tritone, so melodic steps between them
become expanded.

I also find that playing the open strings through some warm distortion
sounds quite good. Hey, and letting the vibrato arm come up when you do
so is wonderful!

It's intended for a Blackjack fretting, of which I only have the top half.
If you have a 31-fretted guitar you can try it out. For the Ztar, try
emulating a Blackjack fretting with the "wolf" placed to give both a minor
third and perfect fourth, as I showed before.

> So now my question is: what extra 5 notes would be the
> best ones to add to the Miracle scale to fill in the blank
> spots on my Ztar layout?

It partly depends on what 31 note scale you're working with. As I have
it, there are gaps between notes 10 and 11 and 20 and 21 that can be
filled. But otherwise, it'd have to be single steps of 72.

This mapping doesn't "work" for me at all.

For the Ztar, I thought about using one of the mappings with a big drift,
and allowing it to wrap around. It might take a bit of getting used to,
but all the notes would be there.

Any chance of a cylindrical neck?

Graham

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_22430.html#22763

> monz wrote:
>
> > I've decided that the mini-Z version of the Starr Labs Ztar
> > is going to be the microtonal keyboard for me.
> > (and Graham Breed has, too)
>
> I didn't say a mini-Z. If you sit them in front of me,
> I might go for one of the big boys.

Oops... my bad again. Sorry. I added that parenthetical
comment as an afterthought, but it was obviously more "after"
and less "thought". :)

Gotta go... will respond to the rest of this later.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., graham@m... wrote:
> Hmm. Well, I've found a way of tuning the strings on my meantone
guitar
> to suit Miracle temperament. Like this:
>
> Decimal note Meantone/31 cents from 12-equal (for
31-equal)
>
> 6 E E-3
> 3 C^ C+48
> 8 Gb F#+29
> 5 D# D#-19
> 0 A A+0
> 6 E E-3
>
> The decimal column is transposed to be all nominals, although
usually 0
> corresponds to C.
>
> The idea is that the open strings form a tight structure on the
lattice,
> and connected only by 11-limit intervals.

Could you draw the lattice segment? Or show it on the chain of 7/72
oct?

> The first impression was that I'd made the guitar horribly out of
tune.

Well 31-EDO _is_ horribly out of tune at the 11-limit. 3 times the max
error of Canasta (= MIRACLE-31). What if you tune the open strings to
the appropriate 72-EDO degrees?

> Also, the B string gets very tight and I wondered if it would snap.
After
> playing it melodically for a while, I quite like it.

Yes it should at least give _some_ feel for Blackjack melodies.

> I also find that playing the open strings through some warm
distortion
> sounds quite good. Hey, and letting the vibrato arm come up when
you do
> so is wonderful!

But doesn't that work to hide _most_ tuning deficiencies. :-)

Monz wrote:

> > So now my question is: what extra 5 notes would be the
> > best ones to add to the Miracle scale to fill in the blank
> > spots on my Ztar layout?

Just continue the chain of 7/72 oct generators for another 5 notes,
say 3 up and 2 down. For scales of 29 notes or more, a continuous
chain will always give best results. The real limit (to keep the above
statement true) is probably lower than 29 notes too.

-- Dave Keenan

Dave!
I remember the 11/9 being quite good with the 9 and 11 off in the same direction. For some
reason it never caused me as much problem as the 9

Dave Keenan wrote:

>
>
> Well 31-EDO _is_ horribly out of tune at the 11-limit. 3 times the max
> error of Canasta (= MIRACLE-31). -- Dave Keenan

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

BTW, for those confused by the terminology --

Partch used the term 11-limit to mean the set of all:

Ratios of 1 (1:1)
Ratios of 3 (3:1)
Ratios of 5 (5:1, 5:3),
Ratios of 7 (7:1, 7:3, 7:5),
Ratios of 9 (9:1, 9:5, 9:7),
Ratios of 11 (11:1, 11:3, 11:5, 11:7, 11:9),

(including, in each case, all the octave-eqivalents obtained by
multiplying or dividing any of these ratios by any power of two.

That's why it's called a "limit" -- it means all odd numbers up to 11
may be used in both the numerator, and the denominator, of the ratios.

People sometimes say "11-limit" when they mean "Ratios of 11". I've
been guilty of that myself. I think this stuff is confusing enough
without ambiguous terminology.
Let's stick to 11-limit in Partch's sense -- 9:8 is included.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Dave!
> I remember the 11/9 being quite good with the 9 and 11 off in
the same direction. For some
> reason it never caused me as much problem as the 9

Kraig!

Sure. I was referring to the maximum error over all 11-limit ratios.
Yes the 31-EDO 9:11 is essentially just. The 6:11 is not too bad
either and the 7-limit ratios are OK. But ratios of 9 and the other
ratios of 11 are way worse than they are in MIRACLE temperament.

Dave Keenan wrote:

> Could you draw the lattice segment? Or show it on the chain of 7/72
> oct?

Lattice segment is

0 3 6

5 8

I think these are the 72 degrees:

A C+3 E

D#-1 F#+2

> > The first impression was that I'd made the guitar horribly out of
> tune.
>
> Well 31-EDO _is_ horribly out of tune at the 11-limit. 3 times the max
> error of Canasta (= MIRACLE-31). What if you tune the open strings to
> the appropriate 72-EDO degrees?

I think this is an 11-limit sound rather than a temperament sound. The
fretting's roughly in 31-equal, so the strings go with that. You could
try 72-equal, but it's difficult to get that level of accuracy on a
guitar. Especially when it's in a new tuning.

It's really a way of getting 11-limit intervals from a meantone fretting.

> > I also find that playing the open strings through some warm
> distortion
> > sounds quite good. Hey, and letting the vibrato arm come up when
> you do
> > so is wonderful!
>
> But doesn't that work to hide _most_ tuning deficiencies. :-)

You can tell the difference between good and bad chords, so something must
be right.

Graham

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_22430.html#22708

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_22430.html#22498
> > >
> > > Monzo 72-EDO mapping to Starr Labs Ztar:
> > >
> > > 2 C> 8 C#> 14 D> 20 Eb> 26 E> 32 F> 38 F#> 44 G>
> > > 1 C+ 7 C#+ 13 D+ 19 Eb+ 25 E+ 31 F+ 37 F#+ 43 G+
> > > 0 C 6 C# 12 D 18 Eb 24 E 30 F 36 F# 42 G
> > > 71 C- 5 C#- 11 D- 17 Eb- 23 E- 29 F- 35 F#- 41 G-
> > > 70 C< 4 C#< 10 D< 16 Eb< 22 E< 28 F< 34 F#< 40 G<
> > > 69 B^ 3 C^ 9 C#^ 15 D^ 21 Eb^ 27 E^ 33 F^ 39
F#^
> > >
> >
> > Well, this is great. Pretty much what Rick Tagawa was doing only
> > with, obviously, just ONE keyboard!
> >
> > Could be a new "generalized" keyboard for ALL of us... (??)
>
> Weeeell, I'm not sure that a 72-EDO instrument really deserves to
be
> classified as "MIRACLE". 72 notes per octave is just way too many.
> Most folks want more than one and a bit octaves on their instrument
> and to fit their fingers between frets.
>

This is, obviously, a problem.... How would it be possible to make a
keyboard based in 72-tET that would have more than ONE octave??

I think the original Microzone has several octaves... but it is very
pricey... (??)

_________ _______ ____ _____
Joseph Pehrson

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22430.html#22711

>
> Hmmm... I should give some thought to how the Miracle-31
> might be mapped onto a Ztar. Now *that* would be a fantastic
> instrument. But it's not as straightforward as Blackjack,
> since 31 is a prime and therefore won't reconcile with
> the Ztar layout easily.
>

Personally, I feel all the "futzing" around with different keyboard
layouts is going to be a problem, and is going to make scale learning
difficult.

What we need, in this view, is a STANDARDIZED 72-tET instrument, and
we may need to make it WIDER to accomodate more "octaves" of the 12-
tET "strands..."

Could be costly, but all the other "miracle" scales would be viewed
as SUBSETS of a generalized 72-tET. That's real musician stuff...

__________ _______ _______ _____
Joseph Pehrson