Free Preview #3 of Chaos In Boxes "The Modal Brightness Stars"

Here is a .pdf of one of my favourite, proudest musical discoveries: The Modal Brightness Stars!

This is a chapter from the eBook versions of "Chaos In Boxes: twisted adventures in music theory."

http://seanluciw.com/pdfs/CIB_FreePreview_ModalBrightnessStars.pdf

Enjoy the pretty pictures... ever more symetry [sp] for the universal mind!

Björklund Plus Goldbach Equals Cool Rhythms...

Björklund Plus Goldbach Equals Cool Rhythms...

A few weeks ago I started reading about the Björklund algorithm, which is a method of distributing a certain number of items over a certain number of positions. I'll not describe that entire procedure here, as it is easily found elsewhere. The concept can be used to generate rhythms. For example, 5 accented notes over a length of 16 total semiquavers (1 = accented, 0 = unaccented) looks like this: 1001001001001000. As it turns out, this is a fairly common rhythm. Performing these accents with a kick drum (in conjunction with a standard rock beat with snare on 2 and 4) it would look like this:

Alternatively, you could spread the accent pattern over two bars of 4/4 by using a "quaver" grid instead of a "semiquaver" grid:

Alternatively, accents could be performed by snares and un-accents by kicks:

It could also be written like this:

It could also be described as "3 + 3 + 3 + 3 + 4." Shifting can also be applied without any compromise of integrity, and equates to the spinning of a necklace:

The above are all expressions of the Björklund rhythm E(5,16). E stands for Euclidian.

As an anecdotal aside, I remember once upon a party I had my djembe with me and I was trying to figure out how to evenly distribute 5 accents over a bar of 4/4 1/16th notes. I had no knowledge of the Björklund algorithm at that time, but it was pretty easy to figure out anyway. I chose to shift the necklace in such a way that none of the accents fell on beats 2 or 4 to avoid redundancy:

Lately I've been tending away from 4/4 time in favour of more obscure rhythmic adventures. So, when I started learning of the Björklund algorithm almost three weeks ago, it seemed like it would be extremely useful. I went ahead and crunched some numbers. For example, a rhythm in 13/8 time with 5 accents: E(5,13) = 1001001001010. Standard notation looks like this:

Here are a few more interesting examples:

E(6,15) = 100101001010010 (which could be written as 3 bars of 5/8 time),

E(5,13) = 1001010010100,

E(5,9) = 101010100, and

E(7,17) = 10010100101001010.

Next: Goldbach Conjectures. A few days later, I found myself reading about three Goldbach Conjectures:

1) The Strong Goldbach's Conjecture says that "every even integer greater than 2 can be expressed as the sum of two primes." I knew there must be some way to write rhythms with this idea. Furthermore, I wanted to combine Strong Goldbach with Björklund. It suddenly seemed obvious exactly how this should happen: I would use the The Strong Goldbach's Conjecture to "envelope" two different prime-number Björklund rhythms consecutively within an outer "even" rhythm. To help with this, I made a spreadsheet:

For a very "even" rhythm, I wanted to choose a sum that equates to good old 4/4 time, which would contain two of the more obscure prime-number time signatures. In the image above, I chose the number 32 (highlighted in yellow) because four bars of 4/4 time contain a total of 32 quavers - simple, common and even. From the table you can see that 32 is made up by adding the primes 13 and 19. Therefore, the associated Strong Goldbach-Björklund combination would consist of one bar of 13/8 time followed by one bar 19/8 time. The specific accent pattern, not yet established, requires deciding how many accents in each bar. Since I've been using the number 5 a lot, specifically for the next composition for my heavy metal band Volcano Calculator, I decided upon E(5,13) and E(5,19). The result is one bar of 1001010010100 followed by one bar of 1000100010001000100. Volcano Calculator decided our next composition would place snare drums in position 2 and 5, so here is what the standard notation looks like:

This combination of rhythms will sound very odd. However, this is where the idea of "enveloping" the prime rhythms within the "outer" even rhythm comes into play. In a multi-instrumental/band situation, some instruments can play the inner primes while other instruments play the outer even. So, the drums could play a straight 4/4 drumbeat while the guitar and bass play the 13+19 melody ...and/or vice-versa.

There is also the Weak Goldbach Conjecture, which says that "all odd numbers greater than 7 are the sum of three odd primes." This approach lacks the "even-ness" of the procedure above, but rather accentuates more "odd-ness" and supports the assembly of three consecutive sub-rhythms instead of only two. I plan on using this strategy as well... like so:

Booyah!

Q.E.D.

Sean A. Luciw

Book Launch Event today

Thank you to everybody who attended the "Chaos In Boxes" (re-)launch event today... I had a blast talking about all the nerdy number music stuff, I hope you did too! I intend to repeat the event in the spring when the weather's a little nicer. Here are a few photos taken at the gig:

eBook now available - a happy day !

YES !!! Fruition. The eBook Edition of "Chaos In Boxes: twisted adventures in music theory" is now available almost everywhere. It's a fun read, I swear! I've added some new Chapters & Appendices, and if you're doing the iBooks thing, you can enjoy the Enhanced Version with Audio.

Go here to my site, which has all the links:
http://seanluciw.com/Writing.php

Or, here are the links:

Nice looking all-in-one page:
http://my.bookbaby.com/book/chaos-in-boxes
http://my.bookbaby.com/book/chaos-in-boxes-(enhanced-with-audio)

iBooks eBook edition:
https://itunes.apple.com/us/book/chaos-in-boxes/id918313114

iBooks eBook (enhanced with audio)
https://itunes.apple.com/us/book/chaos-in-boxes-enhanced-audio/id918322676

Kindle:
http://www.amazon.com/dp/B00NT5GBGU/

GoodReads:
https://www.goodreads.com/book/show/13821509-chaos-in-boxes

and more:
http://www.barnesandnoble.com/w/chaos-in-boxes-sean-luciw/1120341082
http://store.kobobooks.com/en-CA/ebook/chaos-in-boxes
http://www.thecopia.com/catalog/details.html?catId=16425757
https://www.e-sentral.com/search/byid/43279/chaos-in-boxes--twisted-adventures-in-music-theory
(Malaysia)
http://www.scribd.com/book/239921198/Chaos-In-Boxes-twisted-adventures-in-music-theory
http://www.ciando.com/ebook/bid-1626838-chaos-in-boxes-twisted-adventures-in-music-theory/einblick/ (Germany)

Also available at Oyster and Gardners, available soon at Baker & Taylor, and FlipKart (India).

e-book available soon!

Whew! What a journey. Lots of html, css, epubcheck, mobi conversion and other various tech insanity have been happening in my world... In the last year or so I've managed to get all my e-ducks in a row for the new e-book version of "Chaos In Boxes," which should be seeping its way out to all the distributors in the next few days and weeks.

Quite a few things have been re-worded, several new Chapters and Appendices have been added, and the "enhanced" version (for iBooks only) features audio - that's right, 4 full-length songs have been added to the text! Yummy.

Here's a list of additions:

audio: Massive Solfeggio (enhanced version only)
audio: The Coin Song (enhanced version only)
audio: Fibonacci 21 (enhanced version only)
audio: Quasi-Palindromic Triangular Solfeggio Sequence (enhanced version only)
new Chapter: Audio Snippet Widget List (enhanced version only)
new Chapter: Solfeggio Beat Frequencies
new Chapter: Is Re The True Root of the Solfeggio?
new Chapter: Solfeggio Clef
new Chapter: The Modal Brightness Stars
new Chapter: Moon Modes
new Chapter: Related Material By The Authour
new Chapter: Colophon
new Appendix: BFF Beat Freqs Forever
new Appendix: The Coin Song

I'm gettin' anxious over here, can't wait for the e-book to drop! I actually think that, if you've read "Chaos In Boxes," you'll enjoy reading it even more the second time with this e-book version. Available soon.

Free Preview #1 .PDF of Chaos In Boxes

There was a .pdf here but then I deleted it for some reason... Here's a link to it again:

http://seanluciw.com/pdfs/ChaosInBoxesFreePreviewJuly2008.pdf

It includes two of my favourite chapters, The Times-Table Mirror and The Modal Mirror.

Enjoy :)

Eureka! Modal Mirror Tetrachord Symetry [sp] Found

Eureka!

I'd previously thought that the Melodic Major Scale was equivalent to the bottom half of the Major Scale combined with the top half of the Minor Scale. In other words, Ionian bottom with Aeolian top. However, while pondering tetrachords, it just occurred to me... The Modal Mirror suggests that the Melodic Major's upper half comes from Phrygian, not Aeolian. The difference is not apparent in the interval spelling, of course, since both of their top halves are the same and the bottom half is being covered by Ionian. By extension, Melodic Major could also be seen as Mixolydian bottom, Aeolian top.

A natural extension of this observation is the following procedure: Here it is: From the Modal Mirror, combine the bottom half of each pair with the top half of its partner, and vice-versa. Yes! Another bona-fide legit musical structure unearthed for the benefit of all.

Eureka encore!

Details for each combo are here:

1,3 Ionian,Phrygian: R 2 3 4 5 b6 b7 8ve = WWHWHWW, a.k.a. Melodic Major
3,1 Phrygian,Ionian: R b2 b3 4 5 6 7 8ve = HWWWWWH, same as 7,4

4,7 Lydian,Locrian: R 2 3 #4/b5 b6 b7 8ve = WWWWWW, a.k.a. Whole-Tone Scale
7,4 Locrian,Lydian: R b2 b3 4 5 6 7 8ve = HWWWWWH, same as 3,1

5,6 Mixolydian,Aeolian R 2 3 4 5 b6 b7 8ve = WWHWHWW, a.k.a. Melodic Major
6,5 Aeolian,Mixolydian R 2 b3 4 5 6 b7 8ve = WHWWWHW, same as Dorian

2,2 Dorian,Dorian R 2 b3 4 5 6 b7 8ve = WHWWWHW, unchanged as Mirror surface

Some interesting developments indeed. There a couple of double occurrences, and a Wholetone scale appeared out of nowhere! The combination of Aeolian bottom with Mixolydian top, to become the same interval spelling as Dorian, harkens back to a prior notion from "Chaos In Boxes" that Mixolydian and Aeolian are the most closely related to Dorian by virtue of only one interval difference. Furthermore, this strengthened association hints toward the development of an expanded version of the Modal Mirror, one which positions each bottom-top mode combo in appropriate order, emanating from Dorian which is of course the center of the entire symetry. Of course, combo 6,5 is closest to 2,2 on the list, which looks like this:

2,2 - 6,5 - 5,6 - 1,3 - 3,1 - 7,4 - 4,7

and whose elements have the following quantities of interval difference from Dorian:

0 - 0 - 2 - 2 - 2 - 2 - 4

In this ordering system, wherever two Mode pairs have the same interval spelling (and therefore the same amount of interval difference from Dorian or "distance from centre"), the deciding factor becomes the interval contents of each constituent mode in its entirety as opposed to only the top or bottom half that got used in the combo. For example, 3 bottom, 1 top is the same as 7 bottom, 4 top; but modes 7 and 4 are each 3 intervals different from Dorian, whereas modes 1 and 3 each differ from Dorian by only 2 intervals, therefore 7,4 is further down the list than 3,1.

Notice that, since interval pairs appear consecutively on the combo list (ie, 6,5 is followed by 5,6, etcetera), it seems feasible and appropriate to re-order the original Modal Mirror according to each distance from Mode 2. The Modal Mirror has the Mode numbers 1 through 7 in consecutive order, arbitrarily clockwise, around the outside of the circle. The new ordering of the Modal Mirror would have Modes 5 and 6 closest to Mode 2, then Modes 1 and 3 further away, and then Modes 4 and 7 at the far side of the circle away from Dorian. Since the Modal Mirror itself does not distinguish or specify which element from each of its pairs takes precedence over the other in any way (that I can currently recall), the new combo list loses a dimension when interpolated or regressed back to the Modal Mirror. That is, the Modal Mirror does not provide a means of accommodating both 6,5 and 5,6. This could be accommodated by making further enhancement to the Modal Mirror. For example, turn the Dorian mirror line to become horizontal and specify that whichever Mode's bottom appears first in the combo list should be shown above the horizontal, and the other below.

Joining the re-ordered Mode numbers in numerical order generates an interesting-looking symmetrical curve.

(refer to culmination diagram)

Q.E.D.

Brainfart Gem Discovered While Editing

An e-book version of "Chaos In Boxes" is currently in the editing phase. While I was editing, a footnoted brainfart got a bit of exploration, and an exciting new observation is the result.

Ready?
Here it is:

QUESTION: What do you get when you subtract the Major Scale from the Chromatic Scale?

PROCEDURE: The C Major Scale contains the notes C, D, E, F, G, A, B. The Chromatic scale contains all of these, plus C#, D#, F#, G#, A#. Those notes make up the F# Major Pentatonic Scale.

ANSWER: the Chromatic Scale minus any chosen Major Scale results in the Major Pentatonic Scale whose root is a tritone away from the root of the chosen Major Scale.

At the risk of attracting ridicule from the establishment, I'm sticking my chest out real far while putting a big old "Quod Erat Demonstrandum" on this document.

Q.E.D.
Booyah, baby!

Sean Luciw,
authour, "Chaos In Boxes: twisted adventures in music theory"

Ancient Solfeggio Synth VSTi

I've created a VSTi synthesizer which specializes in

producing the Ancient Solfeggio frequencies. It's

available for download here:

http://seanluciw.com/VSTis.php

The synth is FREEWARE, but if you feel inspired

to do so, you can click the Donation button, submit

a testimonial, or check out some of my musical

projects.

On a related topic, I have Ancient Solfeggio Tone

music available for purchase at:

http://seanluciw.com/ULCD-020.php

Happy music making everyone!

Sean

Ancient Solfeggio Tones Volume 1

In Section V of my book "Chaos In Boxes" I explore
the Ancient Solfeggio Tones at great length, using
various diagrams and a healthy mixture of vertical
thinking (ie. cold logic) and lateral thinking (ie. creativity)...
where I discovered, for example, the presence of
The Golden Mean. These are ideas presented on a
printed page.

I am now pleased to announce the availability of
real Solfeggio music, available for download and on
hardcopy. Each tone is presented in a multilayered,
multi-octave texture, generated electronically
in a style which is aesthetically similar to didjeridoos or
crystal bowls for a lush meditative experience. Enjoyable
at low or high volume, in the background or as part of
an immersive experience.

Go to the page on my website which includes a list of
links, or go directly to iTunes.

365 degrees, not 100

The temperature range from water's freezing point to
its boiling point should be sectioned into some
number of degrees other than 100.  I say this because
the Celcius equivalent of 0 degrees Kelvin is -273.15,
which seems like a meaningless number, lacking beauty
and symmetry, like maybe there's a smoother fit to be
found - some number that reflects the underlying
numerical perfection of the universe. I thought the
number of days in a year might be a good place to
start. So, 365.256363004 (the number of days in Earth's
year), multiplied by 2.7315 (absolute zero's
proportionate temperature below freezing compared
to boiling), results in a new value of -997.6977555454
degrees for absolute zero. This may not look any more
elegant or symmetrical than 273.15, until you notice
that it's quite close to 999.999, or 1000.

Why bring a time-related number into a question of
temperature, you ask? Okay, I admit - proclaim, even -
lateral thinking may have snuck into my idea here, as
it often does.

Well, there it is, my latest product of so-called
insomnia.

(for entertainment purposes only?)

SydLeicx?

Am I dyslexic? I recently took a survey which said so, and it's been suggested that I am. Not like it really matters much. Anyway, there was a comment form at the end of the survey and this is what I wrote:

"I was always talented at math; usually top-of-the-class. However, the mistakes that I did make were usually adding errors, getting adding mixed up with multiplication, or getting my fractions upside-down. This last example is oddly relevant considering that, in music theory, a musical interval is determined by the ratio of two frequencies and that a chord is considered to retain its integrity when inverted (ie. when the fraction is turned upside-down). I'm a musician.

Also: when given driving instructions, I've found difficulty (slowness) in visualizing a response to "turn left" or "turn right", or any description involving left and right. However, this problem diminished with care and attention. I've put some effort into trying to become ambidextrous but with not much success. I'm a very good speller but most of my typing errors involve pressing keys in the wrong order. When handwriting, I often leave off the last letter of a word (unintentionally of course). Also, my middle name is Alexander and I've use that as a source for one of my musical pseudonyms, Lex Plexus. Am I dyslexic? I don't know. I usually avoid labels as they can become limiting."

Root 2 connections

The brainfart on page 47 of my book "Chaos In Boxes" describes a hairy scenario involving the Square Root of 2; it was the first irrational number to be discovered by Hippasus* and resulted in his assassination by his fellow Pythagoreans, who believed all numbers to be expressible as the ratio of two integers!

(This came about during the Chapter "Quincunx And The Legend Of The Chromatic Transformation Matrix Starflower", wherein I was inspired to compare a semitone to a fifth.)

Since then, I've noticed a few connections concerning Root 2.

A musical interval between two notes can be described by dividing their frequencies; it so happens that Root 2 (which equals 1.414213...) is exactly the ratio for the infamous Tritone in Equal Temperament. This seems somehow suitable or ironic, considering that:

a) the Tritone was once condemned as "evil" by some religions - echoing in my mind the Pythagorean's rejection of Hippasus

b) the Tritone ultimately holds the key to undeniably powerful harmony through the resolution of a dominant chord towards its parent tonic chord - echoing in my mind the importance of Hippasus' discovery of irrational numbers

I was quite thrilled to notice this.

But wait, there's more...

As I was sitting at a friend's living room jamming along with cable radio, I switched to the jazz station. It was channel 414. I had to wonder if someone at the radio station chose channel 414 as their station number because of the significance of the number 1.414. After all, a very common technique in jazz is Tritone substitution, a.k.a. the "Sub V". This is based on the fact that a dominant 7th chord is extremely similar to the same type of chord a Tritone away, sharing most of the same tones.

Just today I learned that ISO paper sizes (A0, A1, A2, A3, A4, etc.) all have an aspect of Root 2! (The big advantage of this proportion is that you can cut or fold such a rectangle in half and it will still have the same aspect ratio, enabling scaling without cutoffs or margins.)

I feel inspired to find more Root 2 connections; I thought I would find something in astronomy but haven't found anything yet. I guess I'll just have to wait for the next brainfart to dawn on me; that's just the way it goes sometimes.

* note: The Hippasus scenario happened in the 5th century B.C., but there exists a Babylonian clay tablet depicting Root 2 which is 1100 years older. Others may have probably discovered irrational numbers at various points in history.

Moon Modes

I've devised a sensible correlation between the 7 modes of the Major Scale and the phases of the moon. The brightest mode (Lydian, mode IV, with the most sharps) corresponds to the Full Moon (the brightest phase). Observe the complete system below:

Chaos In Boxes: twisted adventures in music theory

Sean Luciw: guitarist, producer, recording artist, multi-instrumentalist, artist, record company owner, authour.

"Chaos In Boxes: twisted adventures in music theory" is a 190-page, handmade limited edition book documenting some of my travels thru the universe of music and numbers, written in a quirky, down-to-earth style.

go here to purchase either a handmade limited edition or a print-on-demand edition: http://seanluciw.com/Writing.php


Music is the context for most of my life's passions. I like knowing how things work, so I ponder music theory quite a bit. (I've been playing guitar and producing music for over 20 years, as well as any other various artistic creativities to satisfy my short attention span). It's amazing how so many things in the universe can be explained by, or likened to, musical concepts. I wrote the book "Chaos In Boxes" as a method for making abstract ponderings real. The book spans the gamut from philosophical head-scratchers to absolute silliness, but my favourite parts - the real juicy bits - are my new contributions to music theory. There's stuff in here for musicians and non-musicians alike, but if you're familiar with the 7 modes and the chromatic scale and whatnot, there's definitely some stuff in "Chaos In Boxes" for you to sink your teeth into.