Once again, the Futuresequence label has released a cracking compilation of experimental and ambient music for free. SEQUENCE7 contains 30 tracks that were whittled down from over 200 submissions through a selection process by label owner Michael Waring with the help of Pascal Savy, Ed Hamilton and Karl McGrath. This is the 7th in the series of SEQUENCE compilations, and I’m very pleased to say that it includes one of my tracks – the 12th in the series of Tintinnabuli Mathematica experiments. I’ve written elsewhere on this blog about that project in general; here I’ll explain a bit about this piece in particular.

Tintinnabuli Mathematica 12d is based on a melodic part (M-voice) constructed from a fractal integer sequence known as A194832 in the Online Encyclopedia of Integer Sequences (OEIS). I used the Mathematica code on that page to generate the first 657 numbers in the sequence. This is what it looks like when plotted as a graph:

A194832-658-plotThis sequence of numbers is converted to MIDI notes, mapping higher numbers to higher pitches. The reason for using the first 657 numbers is that the range of numbers in the sequence fits the scale I wanted to use: The 657th number in the sequence is 36 (that’s the point at the top right of the graph above), and there are 36 notes in a 5 octave scale. This piece uses the scale of A natural minor, from A2 (in scientific pitch notation) to A7. So, the first 10 numbers in the sequence are {1, 1, 2, 3, 1, 2, 3, 1, 4, 2}, which are converted to the MIDI notes {A2, A2, B2, C3, A2, B2, C3, A2, D3, B2}. The result of the conversion process for the M-voice sounds like this:

Once the M-voice has been created, the next step is to generate 6 T-voices using Arvo Pärt’s tintinnabuli method. I wrote a program to do this, which applies a transformation process to the M-voice, generating 6 MIDI files. In the final arrangement, the T-voices are staggered, so that the result is an arpeggiated pattern where the M-voice notes are followed by the descending T-1, T-2 and T-3 voices. The other T-voices (T+1,T+2, T+3) provide a bass part and higher-sounding voices that are interleaved with the other layers:

And here’s what it looks like as a spectrogram:


For those who might be interested in trying to use integer sequences such as this for musical purposes, the OEIS is a handy resource because it not only provides the algorithms to generate your own sequences, but also offers a sonification facility (by clicking on the ‘listen’ link below the main title for each sequence). This allows you to play a sequence and tweak the parameters, and also save the output as a MIDI file.

The previous 11 TM pieces will be released as an album – Tintinnabuli Mathematica vol. I – via Runningonair Music in the new year. These experiments are ongoing. Currently I’m exploring ways of extending the method – trying out new M-voice patterns, more complex variations of T-voices, and experimenting with new sounds. The aim is to release a second volume in due course.

This entry was posted in Audio, Music and tagged , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.