Some Work and Decisions

November 7th, 2011

Today I started working on this piece. I transcribed ratios 2,3,4,6 and 12 into notes and made some very interesting observations (s. next posts).

About the timbre and the pitch: I will not round into the next semitones. I say ‘welcome’ to the microtones. I will make an electronic version for each voice, then I will sing each with the electronic version as help for the microtones (through headphones), put chorus effect, expand short notes to long ones and put them all together.

I will write also a poem for it.

Real voices, electronic voices or electronic sounds?

November 10th, 2010

In the last days I make thoughts about the instrumentation of this piece.

  • If I write it for choir, then
    • either I should notate it exactly and supply electronic recordings for each part, so that the choir can study the non standard tuning. In this case, the rehearsal would be a difficult and expensive task, that is the work would get performed very rarely.
    • or I should adjust the non standard tuning to microtonal tuning of ¼ of a tone. Then it could be performed more frequently, but in this case not precisely.
  • If I write the piece for electronic voices, then I have precision, a choir, but a cheap imitation of the human voice.
  • If I write the piece for electronics, then I have to work hard in order to achieve a nice timbre. And nobody pays me for this… I.e. it could take months or years.

What should I do? I still don’t know.

Comment: The Model

November 9th, 2010

Which is the model behind this construction? Now, after Phase 2, it has become clear to me: before several years, while studying musicology, I had seen a mensuration canon of a Renaissance composer. IIRC It began with g’, was for 3 voices and the analogies were 1:2:3. If someone could tell me which piece it is, I would be grateful.

Phase 2: Create the data

November 9th, 2010

In order to stretch equidistant the Fibonacci sequences modulo m (m=2,…,12) to fit the same space, I just modified the previous Python script:

def my_zeros(n):
        result = []
        for i in range(n):
                result.append(0)
        return result

# print the numbers for the respective
# subdividion of the octave
def divide_oct(modulo):
        f = open('mod_'+str(modulo)+'.data', 'w')
        max = modulo**2
        fibonacci = my_zeros(max)
        fibonacci[0] = 0
        fibonacci[1] = 1
        j = 2
        for j in range(2, max):
                fibonacci[j] = (fibonacci[j-1] + fibonacci[j-2]) % modulo
                # the 2 last numbers x=F_(n-1) y=F_n of the period
                # must satisfy the following (for modulo m):
                # x + y = 0 mod m
                # y + 0 = 1 mod m
                # because 0 and 1 should be the next numbers.
                # Thus (x,y) = (m-1, 1).
                if fibonacci[j] == 1:
                        if fibonacci[j-1] == modulo - 1:
                                per = j + 1
                                break
        for i in range(per):
                #print float(i)/per, "\t", fibonacci[i]*1200/modulo
                f.write(str(float(i)/per)+"\t"+str(fibonacci[i]*1200/modulo)+'\n')
        f.close()

for i in range(2, 13):
        divide_oct(i)

The output is 11 data files: mod_2.data,…, mod_12.data (here are all). Then I wrote a gnuplot script, in order to visualise the results:

set terminal png
set grid
set yrange [0:1700]
set ytics ('c' 0, 'c#' 100, 'd' 200, 'd#' 300, 'e' 400, 'f' 500, \
        'f#' 600, 'g' 700, 'g#' 800, 'a' 900, 'ais' 1000, 'b' 1100, \
        'c' 1200);
set xlabel 'Duration'
set ylabel 'Pitch for c := 0'

set output "periods.png"

plot    'mod_2.data' u 1:2 w lp t 'mod  2', \
        'mod_3.data' u 1:2 w lp t 'mod  3', \
        'mod_4.data' u 1:2 w lp t 'mod  4', \
        'mod_5.data' u 1:2 w lp t 'mod  5', \
        'mod_6.data' u 1:2 w lp t 'mod  6', \
        'mod_7.data' u 1:2 w lp t 'mod  7', \
        'mod_8.data' u 1:2 w lp t 'mod  8', \
        'mod_9.data' u 1:2 w lp t 'mod  9', \
        'mod_10.data' u 1:2 w lp t 'mod 10', \
        'mod_11.data' u 1:2 w lp t 'mod 11', \
        'mod_12.data' u 1:2 w lp t 'mod 12'

And the output is:
periods

We see here some very interesting properties, which I will not analyse, because of lack of time. I just note, that it is not necessary, that all voices start at the same pitch, but I will adopt this idea, because it reminds me the beginning of some choir works of Josquin. But maybe I will change it later (however with small probability…).

As this graph contains rhythmical and pitch information, I would like to visualize only the rhythmical aspect, in order to have an overview of the resulting rhythmical grid. The new gnuplot script is:

set terminal png
set grid
set yrange [1:13]
set xlabel 'Duration'
set ylabel 'Modulo'

flat(a,x)=a

set output "periods_flat.png"

plot    'mod_2.data' u 1:(flat(2, $2)) w lp t '', \
        'mod_3.data' u 1:(flat(3, $2)) w lp t '', \
        'mod_4.data' u 1:(flat(4, $2)) w lp t '', \
        'mod_5.data' u 1:(flat(5, $2)) w lp t '', \
        'mod_6.data' u 1:(flat(6, $2)) w lp t '', \
        'mod_7.data' u 1:(flat(7, $2)) w lp t '', \
        'mod_8.data' u 1:(flat(8, $2)) w lp t '', \
        'mod_9.data' u 1:(flat(9, $2)) w lp t '', \
        'mod_10.data' u 1:(flat(10, $2)) w lp t '', \
        'mod_11.data' u 1:(flat(11, $2)) w lp t '', \
        'mod_12.data' u 1:(flat(12, $2)) w lp t ''

and the result:
periods

Now, the next step is: select 5 voices out of the grid.

Phase 1: Fibonacci Sequence modulo m

November 9th, 2010

Before applying the 24:17:13:7:3 sequence of the previous post, I though, that I could check all Fibonacci sequences modulo 2 to 12 (period(12)=24) and see if some are interesting for my goal.

The period of a Fibonacci sequence is called Pisano period and —to my knowledge— there is not a formula with ()+-*/^ that could give them as a function of the modulo m. Thus I wrote a small Python script that does this:

def my_zeros(n):
        result = []
        for i in range(n):
                result.append(0)
        return result

for modulo in range(2,13):
        print "modulo =",modulo
        max = modulo**2
        fibonacci = my_zeros(max)
        fibonacci[0] = 0
        fibonacci[1] = 1
        j = 2
        for j in range(2, max):
                fibonacci[j] = (fibonacci[j-1] + fibonacci[j-2]) % modulo
		# the 2 last numbers x=F_(n-1) y=F_n of the period
		# must satisfy the following (for modulo m):
		# x + y = 0 mod m
		# y + 0 = 1 mod m
		# because 0 and 1 should be the next numbers.
		# Thus (x,y) = (m-1, 1).
                if fibonacci[j] == 1:
                        if fibonacci[j-1] == modulo - 1:
                                per = j + 1
                                break
        print fibonacci[0:per]
        print "period =", per
        print

The output is very interesting:

modulo = 2
[0, 1, 1]
period = 3

modulo = 3
[0, 1, 1, 2, 0, 2, 2, 1]
period = 8

modulo = 4
[0, 1, 1, 2, 3, 1]
period = 6

modulo = 5
[0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1]
period = 20

modulo = 6
[0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1]
period = 24

modulo = 7
[0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1]
period = 16

modulo = 8
[0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1]
period = 12

modulo = 9
[0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1]
period = 24

modulo = 10
[0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5,
3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4,
9, 3, 2, 5, 7, 2, 9, 1]
period = 60

modulo = 11
[0, 1, 1, 2, 3, 5, 8, 2, 10, 1]
period = 10

modulo = 12
[0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1]
period = 24

Now the idea is the following: let all sequences represent divisions of the octave by the respective modulo (e.g. m=12: semitones, m=11: 1/11 of the octave etc) and stretch them equidistant in order to fill the same duration. Then select the ones that are going to sound at the given position (filtering). Allow rhythmical and pitch deviations. The whole piece is in forte.

About the words: I decided not to use a poem. I think 2 arts at the same time is a bit too much for my taste. Music alone should suffice.

Piece for choir

November 7th, 2010

After writing some stuff on Small Thoughts about the Fibonacci numbers, I decided to write a piece for choir based on this series.

Here I will write my plans and daily remarks about my thoughts on the piece.

Goals:

  • A small piece for choir, 2 Alto, Tenor, Baritone, Bass. Low register.
  • It should be ready by the end of November.
  • The lyrics will be a poem of mine (which one? a new one?).
  • The piece should have a rather dark colour.
  • It should last about 5 min.
  • The higher the voice, the smaller duration values it will use.
  • Each voice will make use of a different octave and rhythmic division.

About the last postulate: let the highest voice have a potential of 24 values. Then consider the following division:

VoiceA1A2TBaB
Primary Division24181284
Deviated Division24171373

The octave division will be analogous (:24, :17, :13 etc).

Each voice will posses a predefined grid of tones and time positions according to its division (like the prior filter technique, but much more flexible).

pd and random walk 1

July 17th, 2009

Today I had a look at pd. This is a great piece of software! I am thrilled!

I experimented a while with it and designed a simple random walk. I decided to do many versions of it by making it more interesting in each vesion.

Here is the first version:

And here is the sound of a finite trajectory.

In the 2nd version I did the addition more elegantly (with respect to the operation sequence):

Many versions will follow!…

New Compositions

July 6th, 2009

[I will stop the guitar project for a while because of other priorities.]

In the last year (or years) I was thinking of composing music in a totally different style than I did before. Five years long I did not compose music, I was engaged in composing poems, but I made many thoughts about composition. Unfortunately I did not have the time (among other necessities) to work on the ideas that I had. The study of mathematics and other reasons prevented me from doing so.

Now the situation is much more worse. I work (earning money) and parallel I work on my dissertation which has to be given in September. This is exactly the situation for me to seek a way out for the body and the mind.

For the latter, composing is here again! The ones that liked my music before 2002 will be possibly disappointed; for my new style there are no scores and the music may seem too simple or too… I don’t know. I do not mind, because —as always— I only care, if the art I create satisfies me.

The new pieces (5 small poems) are available at the composition section “Second Berlin Period“.

The Goal

October 21st, 2008

SInce January I learn to play the guitar. I am a beginner; I can play any chords but very slowly, and all major and minor scales. I like in this instrument its gentle and quiet sound.

The goal of this project will be a piece for solo guitar. It should be so difficult, that it should possible to be played by myself. It should use the trivial melodic material of the chromatic scale. The rhythm should also be simple. The piece should prefer homogeneity rather than contrast. Contrast should exist in the middle form, in the manner of (self) dialogue, it should not occur as two opposite aspects.

These were some general axioms, but they say nothing about the long form. The piece should have the form of a great chromatic scale, which has its local peaks and lows and generally begins around a and ends in the high register of the instruments. It should present in this manner the whole range of the guitar. It will not be a great crescendo. The many local ups and downs should be unpredictable in contrast to the general trend (upwards).

The middle trend should not be monotone increasing (from the bottom, to the top), but it should have its peaks and lows as well. This scope is the key structure that will make the piece interesting; it will balance between the unpredictability of the local motion and the simplicity of the general one.

The unpredictability of the local motion will be determined by selected randomness, using discrete trajectories of stochastic processes. I will use mathematics and computer programming. But I do not want to risk producing great masses. Programming can be great instrument in producing large amount of data, but I am a lover of small structures and detail.

The duration of the piece should be ≈10 minutes.

About this blog

October 20th, 2008

Composing is an adventure. You draw plans, you go for it, change direction, take decisions, and one day you reach a point. This point may not be the one that you wanted to reach. It could be disappointing or much more better than that you had dreamed of. But in any case, the adventure is of great interest as the goal itself.

Of course the above statement holds not only for composing music, but for every task that lasts, and therefore demands good planning: proving of mathematical theorems, writing poems, constructing a machine etc. But here, as a composer, I am going to talk about composing.

In the next posts, I will set the goal, and plan the ways to get there. I will describe my thoughts and explain my decisions. I will document every step in the composition process. I hope that I will find the time and the power for this quite demanding attempt.