Tzolkin kymotrope

[MythMath]

I was motivated by the recent TwinStar thread to actually assemble
the 'tone lattice' of sinewaves based on the Tzolkin layout:

http://forums.abrahadabra.com/attachment.php?attachmentid=13&stc=1&d=1158648226

I've just finished videotaping a ruff clip so that I can examine
it later in the lounge, away from the 'workbench'...
_______________________________________

I would like to detail below the entire process...

By referring to the Tzolkin Freq Chart you'll find that it
has been directly adapted by multiplying each ordinal
number in the two sets (1-20 and 1-13) by 100...

This step converts the elements into the audible range
(now represented as Hertz) while preserving the ratio
relationships and without obscuring the original values...

I next generate the various sinewaves using Wavelab...

Each of the waves in the first set [100,200,...2000Hz] will be assigned
an overall length of 91 seconds, with a fade in of 2s. and a fade out 2s....

The tones in the second set [100,200,...1300Hz] each have an
overall length of 7s. (each with 2s. fades in and out as well)...
____________________________________

Now, using the chart I layout the tones...

Audio TRACK ONE (panned hard left):

The column shown running down the left on the chart [100,200,...2000], is
simply sequenced in numerical order; and since each of these 'longtones'
is 91 seconds in length, that makes the overall program length 30:20...

Audio TRACK TWO (panned hard right):

On the chart, to the right of 100, is the boxed row of numbers
[100,800,200,900,300,1000,...700Hz] representing
the first permutation of shorttones frequencies...

This first sequence will play concurrently with the first longtone [100Hz]...

Each shorttone, you'll recall, is 7 seconds in length (7x13=91)...

Similarly, 'under' the second longtone [200Hz] is the second run
of shorttones [200,900,...800Hz], and so on following the chart...
____________________________________________

So now TRACK ONE houses the 20 longtone frequencies, and on
TRACK TWO are the 260 shorttones [20 permutations of the 13]...

Now the next step is intuitive, and this is the
thing that revealed itself to us last year...

Think of TRACKS ONE & TWO as the 'single' stereo pair that they are...

If this L/R pair were to be cloned, then 'rotated' 180deg, and then
assigned to TRACK THREE and TRACK FOUR, it would feature all of the
tones in reverse order and panned opposite (from TRKS ONE & TWO)...

This cloning and rotation creates a wonderfully unfolding aural
palindrome when the four tracks are played simultaneously...

When the four tracks are mixed down to stereo, this new L/R is then fed into the
X/Y inputs of the phase scope and the display is videotaped as described earlier...

I'll put together a short excerpt and load it up on youtube in a few days for a demo...

All for now, but I'm eager to address any questions you may have...

MM

[m1thr0s]

this stuff is just too damn cool...

can't wait to see it dance!

m1thr0s

[Anibis]

That's wild. I'd love to see what you will do with this... I think M1thr0s mentioned it already, but it would be cool to see what the Twinstar looks like. On another topic, I was recently told about an Aphex twin track which if you play it backwards and examine the 'spectroscope' (sorry for not knowing all the right lingo; this is not my field), the artists FACE appears. This was achieve by taking a photograph, converting it into sound digitally, then manipulating that sound and embedding it in music. So can we take sigils for example, and code them into a piece of music?
-Ibisis-

[MythMath]

Ibisis,

The short answer to your question is, yes...!
________________________________

Here's a link to the Aphex spectrograph:

http://www.bastwood.com/aphex.php
________________________________

I've been looking over the various local pages
here discussing the TwinStar geometry...

But perhaps a list of pertinent numbers could be distilled
from which a kymotropic progression could be generated...

m1thr0s...?


MM

[m1thr0s]

m1thr0s...?well, there's got to be some way to do it but right now I am not clear as to what you need exactly. I could create a sequence of numbers corresponding to a 360° circle or any number of thngs I guess. What we need to ascertain is what arrangement of numbers best expresses the actual movement of energy through the Tetractys that results in the TwinStar "trail"...since this image is a consequence of leylines that emerge by counting through the points in a specific way. The more you can tell me regarding what you need exactly, the better I can assist you. There must be some way to do it though...it's just too cool a possibility to be impossible.

m1thr0s

[MythMath]

m1thr0s,

Well, I've never developed a kymotrope with another
person without being together in the same room,
but we shouldn't let mere physical distance dissuade us...

I've reviewed several of your concise graphsystems, so I'm becoming
more familiar with the various concepts and terms and layers...

As you mentioned, it may be best to have the tones progress along
a specific pathway that re-creates the process of your design...

If you were to design the tonal sequence and then describe it with
your (un)usual clarity, supported with a diagram or two, I'm sure
we could put together an appropriate kymotropic representation...

_______________________


The raw ingredients in any kymotropic design:


1. The scale or list or set or sequence of numbers.

If the number values fall in the range of 20 - 20,000, then
the numbers could be used directly as frequencies (as Hz)...

If not, then some type of conversion to the audible range
would be determined (by any of various means)...


2. The design or arrangement or structure of the tones.

There are many variables here to be determined...

- Parameters of each frequency:
length, relative volume, fades in/out, modulations, panning, etc...

- Ultimately, the final audio mix that is fed into the phase scope
to create the kymotrope will be a stereo (L/R or X/Y) signal, so...

- When designing the tonal layout, it's best to think of placing the tone(s)
on the LEFT that will work in TANDEM with the tone(s) on the RIGHT.

- If just one tone is placed on each side a simple lissajous figure is formed.
If more than single tones are used, then the image will increase in complexity.

- It's often effective to position a long tone on one side,
and run a series/permutation of short tones on the other.

- Mirroring and/or rotations of number sequences lead to
palindromic layouts; think in various forms of symmetry...

___________________________________________

I'm sure if we bat it around a couple
of times all will be revealed...;)


Catch a wave,


MM

[Anibis]

Hmm. I wonder what the Key (http://forums.abrahadabra.com/showthread.php?t=167) would look like, too.
-Ibisis-

[MythMath]

Yeah, that seems perfect for kymotropisation...
[JOIN THE COIN-A-WORD-A-WEEK CLUB...!]
I'll start by absorbing the essence, and work from there...;)

I do recall scanning through this Key material
on my initial grokflights over this site/forum...

I recognized many common elements to our research....
___________________________

So, I'll head back to the forge for some anvil banging...


.M___Y___T___H.

.____Y___T____.

.____A___T____.

.M___A___T___H.


_____________________________

PS - Perhaps the future use of tri/hexagram patterns
to suggest the arrays of long and short tones...?

[Anibis]

This Kymotrope technology is very exciting. I had a look at your trailer, the patterns are very beautiful. I'm really interested to see the Tzolkin, and Twinstar kymotropes. The key would be cool too, but it looks like you have alot on your mythomatic plate, so to speak... If I can help elucidate anthing, let me know...
-Ibisis-

[MythMath]

m1thr0s,

I've reviewed several of your concise graphsystems, so I'm becoming
more familiar with the various concepts and terms and layers...

If you were to design the tonal sequence and then describe it with
your (un)usual clarity, supported with a diagram or two, I'm sure
we could put together an appropriate kymotropic representation...

I'm sure if we bat it around a couple
of times all will be revealed...;)

m1thr0s,

I've diligently been doing more reading (and re-reading) of
your Book of Mirrors and I'd like to humbly apologize
for my statements above...

To casually suggest that we could summarize all of the work you've done
over the past 3+ decades with a couple of brainstorming sessions,
is at best cheerfully ignorant, and at worst insulting to your efforts...

After reflecting on it,
I'm sure it's gonna require at least four brainstorming sessions...:o
___________________________________

Honestly though,
your discoveries are fascinating and they ring so purely...

As I read, it seems like things I've felt, and made mental notes of,
for years and years are now suddenly being clearly revealed...

Uhh, thanks,
.

[m1thr0s]

hang in there MythMath...we can get this puppy to dance yet!

though I admit...the math is a bit out of my area...it's in there someplace though...I can feel it...

and it looks awesome...reminds me of a quote from one of Crowleys more fictional rants..."Don't look at that star for Christ's sake!"...lol

Actually, I rather suspect Christ would be glued to the damn thing personally...but now I venture into the utmost speculation...

Perseverance Furthers,

edit: I am still not sure how to go about plotting something like this...something that moves already...could you just track it one degree at a time on a standard x/y grid and feed all that data in? It would take awhile to plot since it moves in two directions...now that Ibisis has got hold of it it even moves in two directions at once! My brains are still spinning from that little revelation...

m1thr0s

[Anibis]

Ambidexterity... the Juggler's friend...
-Ib-

[MythMath]

Here is the color adaptation of the frequency
chart link in the first post of this thread...

The color:number assignments were basically
arbitrary; I just used a spectral spread...

It's interesting to note the diagonal phasing that is
present in both the color and traditional graphs...

MM

[m1thr0s]

this stuff I really don't understand at all but I like the colors :)

m1thr0s

[MythMath]

The calendar's layout is essentially:

20 'months' with 13 'days' each...

The days run in a shuffled sequence...

And because each month starts on a different day,
this sequence permutates through all 20 months...

[m1thr0s]

ok...so how are the colors determined?

m1thr0s

[MythMath]

I just arbitrarily stretched a spectral spread
(ROYGBIV) to 'fit' my months (spaces 1-20)...

The days (1-13), correspondingly, used the same
portion of the spectrum that spanned spaces 1-13...
___________________________

Also featured in the color chart:

Each of the 20 horizontal rows
shows an upper solid segment...

This represents the month...

Under each of the solid segments appears the
'shuffled' sequence of 13 day segments for that month...

The number series along the top (01,08,02,...07) is
actually the sequence of days in the first month...

The sequence in the second month is the same,
but it starts on 02 (02,09,03,10,04,11,05,12,06,13,07,01,08)...

3rd month: 03,10,04,11,05,12,...09

Etc...



MM

[m1thr0s]

cool...looks great.

m1thr0s

[Anibis]

It does look great. An update on the logic of the thing. There is a sequence of 20 special days. You can count them on your fingers and toes. They are grouped into four different color groups (Yellow, Yed, White, and Blue,) and five different 'number classes' (So red 1-5, blue 1-5, yellow, 1-5 etc). They permute in a regular sequence. This is the basic ordering logic. The Tzolkin grid itself is a 13 across and 20 down, so it is basically the numbers 1-20 run 13 times side by side. What MythMath says is true that there are 20 day months and 13 day weeks. This means that it take a total of 260 days for the days and months to mesh. Since every 13 day period is essentially like the Initiation through Discharge of an energy, and each has a unique sequence depending on which 'day' starts it (tone one), each of the 20, 13-day periods is considered appropriate for developing one particular sort of faculty. So the 'wavespell' which starts with SUN (0/20) will explicate the energy of divine fire, while the one starting with MONKEY (13) will explicate the energy of playfullness and illusion.

The two important things to remember is that there are two sequences running silmutaneously (without mixing them up, or 'confusing the planes'). There is a 1-13 repeating sequence and a 1-20 repeating sequence. These run parrallel to one another.

The 1-13 can be considered 'tones' or stages of manifestation, while the 1-20 are specific energies which get articulated through the thirteen tones. In other words each 'Day sign' has 13 possible variants.

So the tzolkin grid would look like this: (in this case (0) is counted as 20)

1:1
2:2
3:3
4:4
5:5
6:6
7:7
8:8
9:9
10:10
11:11
12:12
13:13
14:1
15:2
16:3
17:4
18:5
19:6
20:7

This would be the first column of the Tzolkin with the first number being the day sign, and the second being the tone. This logic extends through twenty sde-by-side columns, and therefore 260 days in total. (it can also be divided into 5 52 day segment), as I will try to show later.

Okay. That's the basic logic. This becomes interesting when you know what the day signs and the tones actually mean. The whole thing is a sort of social energy weave out of which lots and lots of cool stuff can be teased. News at Eleven, or should I say, 13...

-Ibisis-

[MythMath]

Yeah, I did use our generic terms month and day as examples,
but the accurate Tzolkin terms are Day and Tone, respectively...

Eschew Obfuscation...;)

[Anibis]

Alright, here is a bit of a symbolic interpretive key to the aformentioned numbers.

First the tones (more or less as I understand them):

1:Unifying
2:Polarizing
3:Activating
4:Formalizing
5:Commanding
6:Rythmic
7:Resonating
8:Modeling
9:Pulsing Intention
10:Manifesting
11:Dissolving
12:Crystalizing
13:Transcending

And the signs:
1: Dragon, Birthing
2: Wind, Communicating
3: Night, Dreaming
4: Seed, Targeting
5: Serpen, Life Force
6: Death, Crossing
7: Hand, Healing
8:Star, Beautifying
9:Moon, Purification
10:Dog, Loyalty
11:Monkey, Illusionism
12:Human, Free Will
13:Reed ('Skywalker') Exploration
14:Wizard, Enchantment
15: Eagle, Vision
16:Warrior, Courage
17: Earth, Navigation
18: Mirror, Endlessness
19: Storm, Catylization
0/20: Sun, Divine fire

So you understand that each of the 20 signs develops in a 13 fold wave, and the Tzolkin itself is 20 such waves interwoven with the progression of the signs forming a self contained 260 unit matrix.

Alright. I'll supply some of the actual glyphs next, and the mayan notation system for numbers. Then, when it comes to the TwinStar, it's really just a matter of assigning the tones to the 'points' and the daysigns to the paths. Then, any day in the tzolkin count will be one point combined with one path. Every combination of points and paths can be exhausted in 260 days.
-Ibisis-

[Anibis]

Arg. Those smileys. Well, they're sortof amusing...
:D
-Ib-

[m1thr0s]

lol...I rarely use them myself but it is nice to have a few choices when you do want to use them...so I have a few more on the way...just ignore them if they bug you I guess...

I know a member on another board that absolutely hates the little buggers with a passion...kind of amusing actually...

here you go Ibisis...this one's for you... :juggle:

m1thr0s

[Naomi]

So I watched the kymotropes with the kids tonight, it was fucking weird, they were on the edge of their seat, you know and for graphic animation that doesn't involve anything more than moving geometry I thought it was pretty funny...

Anyways so they were trying to see stuff in the shapes and were exclaiming what they were seeing and i'm just laying back listening to their weird observations, and then David blurts out

"ALIENS ATTACKING THE PLANET AND CUTTING OFF THE POWER BECAUSE THEY'RE INVADING!"

I think it was on the Jeopardy one...

rofl

So MM showed me how these things are created, I have to admit it's very fucking cool...I was all spaced out when we were making one so it was amusing, and there's definately a lot of tricks to it, I have to wonder where the technology could go if it wern't for the limitations of the technology itself, it does look intimidating to be honest...

I do understand it a lot more now than I did before I went to visit...