Matt Bower (The Revenant Sea & Wizards Tell Lies) and myself (Amonism) put together a series of dark ambient / experiment modern classical tracks after a series of conversations that arose from being label mates on First Fold Records. Thee covered music, philosophy and art amongst other things and that discourse is expressed in a new release (and sadly one of the final releases) from the excellent J&C Tapes label. There are four tracks that comprise cello, piano, field recording and sonic manipulation. The material is dark and introverted but also rich, layered, beautiful and meditative. Also there is excellent cover art courtesy of Craig Earp.
Matt Bower of Revenant Sea and myself put together some tracks for our cassette album ‘The Hidden’ released on J & C Tapes.
The last track ‘Vulture Path’ you can have a listen to here
We had a great review of this on textura
This is quite a personal release, made from a series of improvisations that are reaction to an image sent to me by the lads at Arell
This time I resorted to pen and paper to find out if 1/17ths and 1/19ths have recurring sequences when described as decimals. I’m not sure I could have kept a long sequence in my head, and the calculator apps I have do not run to enough decimal places to spot the pattern, in fact it is much easier to ‘see the pattern coming’ working manually for reasons I stated in my last post.
1/17 = 0.058823529417647058823529417647……
with a 16 digit long sequence
1/19 = 0.052631578947368421052631578947368421
with an 18 digit long sequence
So far my hunch is right, though it would be good to have a deductive rather than inductive method of proof. Another pattern that seems to be emerging for these vulgar fractions with prime number denominators is that the recurring sequences are 1 less than the denominator. n/7ths have a 6 number sequence and n/13ths have two sequences of 6 numbers (6+6=12).
n/11ths (0.09090909…., 0.18181818…., etc), n/3rds, n/5ths (which have a simple relationship to the decimal system) fall outside this pattern. Though it could be argued that there 10 separate recurring number sequences.
Next steps would be to look at n/23rds, n/39ths, n/31sts. Working in different bases. My other hunch is that this is something akin to addition of oscillating waves, a result between the interaction of two base systems; that of the denominator and that of the system within which it is described.
From my time many years ago as a mathematic student writing a piece of software in Fortran to calculate the area under the graph of a particularly complex equation I discovered how difficult it is for binary to describe fractions that decimal does easily, for example
1/5 in base 2 = 0.00110011…….
The version of Fortran we were using had a fixed point rather than a floating point number system and initial coding led to wild results.
Another thing I have noticed (though this should be obvious but nine the less interesting) is the sequence remains intact in integer multiplication, or when added to themselves except the result is an integer. As a sequence they almost have a DNA like predilection for self replication.
Anyway this may seem all rather tedious to some of you on this day after a General Election but the conundrums of numbers will last on into the future much longer than present woes and help me keep some perspective on it all.
More to follow.
Occasionally when I can’t sleep I do complex arithmetic in my head, just to see if I can keep all those numbers in my short term memory and distract myself from what ever is worrying me. Long division is especially good for this purpose. A couple of nights ago I got to 1032 divided 14 and came across an interesting recurring fraction (when described in base 10) ; 73.714285714285……
10/14 or 5/7 gives the 0.714285714285…… You know when you’re going to get a recurring sequence when carrying over (in long division) when you come across a number that has carried over before; in this case it was carrying over 10 to get 100/14, which gives 7 remainder 2.
It got me thinking. All sevenths have the recurring sequence 714285 shifted along to the left of right.
1/7 = 0.142857142857…..
2/7 = 0.285714285714…..
3/7 = 0.428571428571……
4/7 = 0.571428571428…….
5/7 = 0.714285714285……
6/7 = 0.857142857142……
which is a tad more interesting than thirds (0.3333333….), sixths(0.1666666…..) & ninths (0.111111111…….)
I wondered if any other fractions described in decimal would create interesting sequences apart from sevenths and its family (1/14ths, 1/21sts, 1/28ths etc).
I guessed prime numbers would be good candidates for denominators.
1/13ths were interesting as they have two sequences of numbers that recur
1/13 = 0.07692307692307………
3/13 = 0.230769230769……
4/13 = 0.307692307692……..
9/13 = 0.692307692307……
10/13 = 0.769230769230……
12/13 = 0.923076923076……..
and 153846 in
2/13 = 0.153846153846….
5/13 = 0.384615384615…..
6/13 = 0.461538461538….
7/13 = 0.538461538461……
8/13 = 0.615384615384….
11/13 = 0.846153846153…..
which is pretty funky too
1/17th & 1/19ths seemed to give sequences that did not repeat
Though maybe I need to carry on further as there are only a finite number of numbers that can carry over (the remainder left over after a division to describe one decimal place) and returning to the same means the sequence will start again. But my instinct could be wrong.
I wonder if a vulgar fraction has to end up with a finite number of decimal places or a recurring pattern?
Of course this is all dependent on which number system you are describing the vulgar fractions, I wonder what would happen if 1/10ths where described in base 13 ? Or rather in base 13 speak – 1/Aths ?
Anyway the mathematicians amongst you will know better.
Just finished working on ‘Boi Boi Is Dead’ by writer Zodwa Nyoni. Real pleasure working with Composer Michael Henry and Director Lucian Msamati.
Some stunning music written by Michael Henry mixing Afro Jazz, vocal soundscape and Miles Davis style Trumpet solos for Actor/Musician Jack Benjamin. My job, apart from writing additional underscores, involved mixing and producing the recorded and live music.
This is the pre show music mixing some of the music written by Michael Henry from the show with soundscape using cello, celesta, chimes and other processed sound.
An experiment with meaning. Using time-lapse, train journeys and a window with a view out on to the world.
Sort of a music video to my track “Second Light”
I’ve been working on music for choreographer Julia Cheng’s (Kolesk Dance) contribution to the CAS (Chinese Arts Space) New Moon Project. The music is four parts and has mostly been written with the possibility of live performance in mind, though the performances at Rich Mix on the 20th February and The Albany on the 21st February will be pre recorded.
Here is a sketch of the first two sections using Marimbas, Celesta, Xylophones, Small Gongs, Wood Blocks and some processing on the Marimbas
The third section is for Cello and Piano
A teaser trailer with superb dancers Hannah Anderson-Ricketts, Maria Fonseca, Ffion Campbell-Davies
Been a bit mental over here over the last bit.
Currently working on sound design for “Little Red Riding Hood“, a Rock n Roll panto that’s going to be on at the Liverpool Everyman. It’s going to be an extravaganza and tickets are selling quick.
My work seems to be turning in this direction at present. Stripping back down to my main instrument and a handful of effects. Let’s see where it takes me.