By Any Name It Sure is a Beautiful Scale

Here is some work I've done with the Miracle Tuning using the
following ratios - 2/72,58/72, 65/72 then 44/72, 58/72 and 65/72. I
think that is 5-9-11 paired with 3-9-11 (from the toad eikosany) but
please educate me if I'm off the mark ( I think today my creativity
can handle it :-)). The scale is really nice because it keeps
revealing more and more subtlety (and I still have 18 more to go).
In response to suggestions I have posted a really short snippet (
424kb) and a longer one (2.5mb). Enjoy, and let me know what you
think.

http://www.elucida.com/Nada.html

Mary

Hello Mary!

Just a very public "thank you" for the music that is both lovely and
intriguing, as I've enjoyed all the samples I've downloaded. I will
ask you more in detail about some of your piece's "inner workings" at
a later time, but for now I am having a good time.

One little note, and I hope this is considered a positive and
constructive comment. I used the link:

--- In tuning@y..., nanom3@h... wrote:
> http://www.elucida.com/Nada.html

...and downloaded (I thought) the 'long' version -- but it came over
the 56k modem real fast! I check the file size and it was the small
one! I checked back and you have a mangled link for the Long Style,
which splits in the middle on the "5-3-9-11" -- clicking on that part
links to the short version, while The_Unknown_,Long_Style and the end
of the link point to the actual long version.

Would be a simple fix...

But, yowie, nice stuff!

Cheers,
Jon

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

/tuning/topicId_22906.html#22914

> Hello Mary!
>
> Just a very public "thank you" for the music that is both
> lovely and intriguing, as I've enjoyed all the samples
> I've downloaded. I will ask you more in detail about some
> of your piece's "inner workings" at a later time, but for
> now I am having a good time.

Wow, Mary - this is *really* fantastic!!!!!

http://www.elucida.com/resources/The_Unknown_Long_Style.mp3

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

--- In tuning@y..., nanom3@h... wrote:
> Here is some work I've done with the Miracle Tuning using the
> following ratios - 2/72,58/72, 65/72 then 44/72, 58/72 and 65/72.

I hope you mean you've used degrees 2,44,58,65 of 72-EDO. i.e. not
frequency ratios but fractions of an octave.

So only the four notes (plus octaves)?

> I
> think that is 5-9-11 paired with 3-9-11 (from the toad eikosany) but
> please educate me if I'm off the mark ( I think today my creativity
> can handle it :-)).

Ok. These are all within M-10, the 10 note strictly proper MIRACLE
MOS. We have steps of 42,14,7,9 (1/72nds of an octave). Here are the
available harmonies.

dyads
notes freq ratio
2-44 2:3
2-58 7:6
2-65 6:11
44-58 7:4
44-65 9:11
58-65 15:8 (not as accurate as the others, -5c)

a low number triad
2-44-65 6:9:11

>The scale is really nice because it keeps
> revealing more and more subtlety (and I still have 18 more to go).
> In response to suggestions I have posted a really short snippet (
> 424kb) and a longer one (2.5mb). Enjoy, and let me know what you
> think.
>
> http://www.elucida.com/Nada.html
>
> Mary

Thanks! Very interesting.

-- Dave Keenan

clicking on that part
> links to the short version, while The_Unknown_,Long_Style and the
end
> of the link point to the actual long version.
>
> Would be a simple fix...
>
Thank you Jon for your kind words and for pointing out the link
problem. I am using AdobeGoLIve (Mac) which I wish I could just
throw out a window. Its artsiness makes doing simple things very
complicated while complicated stuff like layering pictures
that "float" is very easy. Is anyone using a better program on the
Mac. Unfortunately Adobe PageMill which was quite simple no longer
works on my system - planned obselescence.

> But, yowie, nice stuff!

Thanks. It is so much fun to make the stuff and be able to share it.
>
> Cheers,
> Jon

Hi Dave

I think I am beginning to understand a little of what you are talking
about, and that is exciting!

I hope you mean you've used degrees 2,44,58,65 of 72-EDO. i.e. not
frequency ratios but fractions of an octave.

Yes I meant fractions of an octave and I can see why that is
confusing between mathematicians and musicians. I am creating these
tonalitites in LISP and think that if I write create tonality
toad '(2/72, 58/72, 2/72, 65/72, 2/72, 35/72, 44/72, 58/72, 65/72,
35/72) that it gives me a scale with the following cents values
(apprx) 33 cents, 968.6 cents, 1079 cents, 583.3 cents, 733.4 cents.
But you have raised a bit of doubt in my mind so I am going to go
back, input the degrees as cents and check the sysex output of both
to see if that is what I am getting.

Actually in this notation discussion going on my sympathies lie with
the mathematicians in wanting just one universal language that means
the same thing.

Ok so now going on to the dyads 2-44 is a freq ratio of 2:3. I
realize I don't follow. I can see on my colored chart this is a
ratio of 3 (ie red) with a value of 7, which I see you could get by
subtracting .33 from 7.33 but could you explain the math behind that
calculation? If I see one example I should be able to figure out the
rest.

Again thank you for your patience and tutoring, and I hope you don't
mind me just teasing you once in a while:-)

Mary

--- In tuning@y..., nanom3@h... wrote:

/tuning/topicId_22906.html#22946

> Ok so now going on to the dyads 2-44 is a freq ratio of 2:3.
> I realize I don't follow. I can see on my colored chart this
> is a ratio of 3 (ie red) with a value of 7, which I see you
> could get by subtracting .33 from 7.33 but could you explain
> the math behind that calculation? If I see one example I should
> be able to figure out the rest.

Hopefully Dave won't mind if I jump in here.

The interval you're talking about is given in the
colored interval matrix table by me and Paul Erlich,
on my Blackjack webpage
<http://www.ixpres.com/interval/monzo/blackjack/blackjack.htm>
as being between the 13th and 1st degrees of the Blackjack
scale.

If you scroll down and look at my Ztar mapping of the entire
72-EDO with the Blackjack scale in orange, you'll see that
these Blackjack degrees translate into what you're calling
2/72 and 44/72, respectively.

This notation is really an unfortunate shorthand. I say
unfortunate because it's so easily confused with ratios,
which are very common here on the tuning list.

In mathematical terms, the proper way to describe these
72-EDO intervals is: 2^(2/72) and 2^(44/72), where the
caret ^ means "to the power of". These fractional exponents
are simply another way of notating roots, as in "the 72nd
root of 2 to the 2nd power" and "the 72nd root of 2 to the
44th power". ASCII limitations force us to use the former
notation.

If you do the calculations, you'll find that the ratios
and cents values of these pitches are:

2^(2/72) ~1.019440644 33&1/3
2^(44/72) ~1.527435131 733&1/3

The tilde ~ means "approximately", and I give fractional
cents instead of decimals whenever the value is an exact
fraction but a repeating decimal.

The formula to calculate cents is:
LOG(ratio)*(1200/LOG(2))

(logs are base-10)

So you can see that the interval in question has a width
of 733&1/3 - 33&1/3 = 700 cents, our familiar old 12-EDO
"perfect 5th".

Hope that helps.

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

> In mathematical terms, the proper way to describe these
> 72-EDO intervals is: 2^(2/72) and 2^(44/72), where the
> caret ^ means "to the power of". These fractional exponents
> are simply another way of notating roots, as in "the 72nd
> root of 2 to the 2nd power" and "the 72nd root of 2 to the
> 44th power". ASCII limitations force us to use the former
> notation.
>
> If you do the calculations, you'll find that the ratios
> and cents values of these pitches are:
>
> 2^(2/72) ~1.019440644 33&1/3
> 2^(44/72) ~1.527435131 733&1/3

OK I do understand that. I had just been using the EDO step of
16.667 cents (2^91/72) and multiplying by the degree
>
> So you can see that the interval in question has a width
> of 733&1/3 - 33&1/3 = 700 cents, our familiar old 12-EDO
> "perfect 5th".

OK that is easy enough to get from the colored chart. The two
degrees intersect on a red square which says 7, meaning 700 cents,
and that comes from the difference.

Thanks - I realize I was attempting to get the ratio without using
the logs. I hope that if I just keep working this stuff out with
pencil and paper it will eventually become "intuitive".

Sent off the letter about the ZTar, it really does look like a fun
toy and I hope it gets made. If I bought a ZTar now at the current
price, would it come already to use for Blackjack. Or would I have
to retune, reprogram etc.

Mary>
> Hope that helps.
>
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"

--- In tuning@y..., nanom3@h... wrote:

/tuning/topicId_22906.html#22948

> OK I do understand that. I had just been using the EDO step of
> 16.667 cents (2^91/72) and multiplying by the degree

I recognize that there's a typo here: 16&2/3 cents is the
width of 2^(1/72). I guess you meant to add another set
of parentheses but accidentally hit the "9" instead.

> >
> > So you can see that the interval in question has a width
> > of 733&1/3 - 33&1/3 = 700 cents, our familiar old 12-EDO
> > "perfect 5th".
>
> OK that is easy enough to get from the colored chart. The two
> degrees intersect on a red square which says 7, meaning 700 cents,
> and that comes from the difference.
>
> Thanks - I realize I was attempting to get the ratio without using
> the logs. I hope that if I just keep working this stuff out with
> pencil and paper it will eventually become "intuitive".
>
> Sent off the letter about the ZTar, it really does look like a fun
> toy and I hope it gets made. If I bought a ZTar now at the current
> price, would it come already to use for Blackjack. Or would I have
> to retune, reprogram etc.

The Starr Labs instruments are strictly MIDI-controllers,
without any sound source - you supply that yourself. So
they can be programmed to any tuning as long as you use a
sound-source that uses "tuning tables" (as opposed to
12-EDO-with-MIDI-pitch-bend).

You can do the programming yourself if you wish. But since
I'm at Starr Labs now, it's no problem for me to set up
the tuning for any instrument anyone buys. Note, however,
that I really recommend using the Ztar for Canastra rather
than Blackjack, because that scale is much more versatile
and can be easily accomodated on the Ztar.

Paul presented Blackjack as a suggestion for those with
more limited keyboarding facilities, such as adapting the
regular Halberstadt, etc. With the Ztar there's no reason
to not use Canasta instead.

I hope to be able to create a Canasta page similar to my
Blackjack page sometime this week, so there will be another
web resource with some good info on it. Right now the
best place to look is Graham's site
(<http://x31eq.com/decimal_lattice.htm#mos>,
right after the Blackjack lattice), and the archives from
list list since April 29.

-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..., nanom3@h... wrote:

/tuning/topicId_22906.html#22948

> Thanks - I realize I was attempting to get the ratio without
> using the logs. I hope that if I just keep working this stuff
> out with pencil and paper it will eventually become "intuitive".

Mary, I meant to add a comment about this.

Logs are only necessary to compute cents or EDO scale degrees
(cents are simply 1200-EDO).

To calculate a ratio *from* an EDO-scale degree logs are
not used. One simply performs the calculation specified
in the notation I used.

So, for example, to calculate the ratio for 2^(2/72), you
simply raise 2 to the (2/72) power, which gives a ratio of
~1.019440644.

Spreadsheet programs like Microsoft Excel will do this as
notated; you simply put an equal sign = before the formula.

To do it on a hand calculator, calculate the fractional
exponent first, then store it in memory, then enter "2"
and hit the "y^x" key, then recall the stored memory value,
hit the equal key and there's your answer. You generally
need a "scientific" calculator to have the "y^x" key provided.
(Windows provides one on-screen.)

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

Hi Mary,

Did you know you can do this in FTS too?

Just type out the scale using the usual notation:

e.g. 2^(5/72), or you can use shorthand n(5/72) for that one as it
is so frequently used that a shorthand seemed useful.

You need to make sure each formula has no spaces in it as that is how
the program tells where one note ends and the other begins.
(you can have spaces within brackets as it can tell by the brackets
that it is all one expression).

Just put all the formulae for the scale on one line, paste into
any of the FTS windows that accept scales, then go to File | Number
options and tick Show cents, and it will convert them all to cents.

Or Show cents and small ratios, and it will show the ones that are
exact ratios (or very very close to exact) as ratios, and all the
others as cents. You can also set a value to the Tolerance in cents
to show the nearest close ratios to the scale to within that tolerance
and it shows them followed by a ~ to show it is approcimante
(though I'm working on this last option and there will be more
to it in the next beta upload).

I often tick Use SCALA notation, decimal point = cents in the same
window, because that makes the scale use less room. When ticked,
if you enter anything with a decimal point in it, it is taken to
be in cents, and anything shown with a decimal point in it is in
cents.

Just thought, may poss. save you some calculations.

Rather than type the scale straight into an edit box, can
be useful to type it in a word processing program and use
copy and paste to paste it into the box to convert it to
cents or whatever.

Robert

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

/tuning/topicId_22906.html#22950

> The Starr Labs instruments are strictly MIDI-controllers,
> without any sound source - you supply that yourself. So
> they can be programmed to any tuning as long as you use a
> sound-source that uses "tuning tables" (as opposed to
> 12-EDO-with-MIDI-pitch-bend).

I believe I was in error there and that that's not entirely
true.

Harvey is revamping the Ztar software. I'm not real clear
on the details, but it will be able to send out any
MIDI-note and controller data individually from each key.

So I do believe that it will also do 12-EDO MIDI with pitch-bend.
I'll report better info as I learn more.

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

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

/tuning/topicId_22906.html#22983

> Harvey is revamping the Ztar software. I'm not real clear
> on the details, but it will be able to send out any
> MIDI-note and controller data individually from each key.
>
> So I do believe that it will also do 12-EDO MIDI with pitch-bend.
> I'll report better info as I learn more.
>

Of course, keep in mind that there's still the restriction
of only 16 MIDI channels.

Damn... can't the MIDI powers-that-be simply add another
byte to the protocol, and make it 4096 channels? Then
we'd have all the room we could possibly want for adding
all that pitch-bend.

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

Hi Monz

> Damn... can't the MIDI powers-that-be simply add another
> byte to the protocol, and make it 4096 channels? Then
> we'd have all the room we could possibly want for adding
> all that pitch-bend.

Now that's a thought!!

One extra byte - would have been a lot when MIDI was invented
I suppose, but nowadays one is hardly waiting for the MIDI
files to stream because of the number of bytes involved!

Robert

--- In tuning@y..., robertinventor@h... wrote:

/tuning/topicId_22906.html#22988

> Hi Monz
>
> > Damn... can't the MIDI powers-that-be simply add another
> > byte to the protocol, and make it 4096 channels? Then
> > we'd have all the room we could possibly want for adding
> > all that pitch-bend.
>
> Now that's a thought!!
>
> One extra byte - would have been a lot when MIDI was invented
> I suppose, but nowadays one is hardly waiting for the MIDI
> files to stream because of the number of bytes involved!
>
> Robert

That's the crux of what I was saying: the MIDI spec was
established around 1983 and hasn't changed since. Remember
what kind of computers we were running back in '83?
Heck, I didn't even have one yet.

I saw a serious proposal about 7 years ago for ZIDI, which
was a good idea for an update to the MIDI spec. What ever
happened to it?

I'd say that MIDI is the aspect of modern music-making that
is furthest behind the times... which is really too bad for
me, because it's the method I use about 99% of the time.
(Finale being the other 1%... but that's really MIDI too).

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

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

/tuning/topicId_22906.html#22950

> I hope to be able to create a Canasta page similar to my
> Blackjack page sometime this week, so there will be another
> web resource with some good info on it. Right now the
> best place to look is Graham's site
> (<http://x31eq.com/decimal_lattice.htm#mos>,
> right after the Blackjack lattice), and the archives from
> list list since April 29.
>

Thank you so much, Joe! These resources will be very valuable for
many of us! Maybe you've already done this... I'm still behind.

____________ _________ ______
Joseph Pehrson