Ten-Tone Equal Temperament Nonuniform String

"Xenharmonic" music with alternative tuning (e.g. Just Intonation, Bohlen-Pierce, Wendy Carlos scales). Also some noise/concrete music, and a few otherwise typical pieces with a single odd aspect such as uneven rhythm.

ｘｅｎ / avant garde / experimental

electro-classical

Mohajira improv

J.S. Bach's fugue in C Sharp Minor from the Well Tempered Clavier book 1 reimagined in vocals using just intonation. Also new is legato and breathing. The only tools I used were csound, and vim.

Bach C# Minor Fugue in Just Intonation

This track was written to demonstrate the harmonic possibilities of using higher harmonics freely whenever the composer wishes, without the bounds of a traditional scale, but within the bounds of major/minor/seventh harmony. It is also quite funky!

Harmonics of 11ths, 13th, 23rds etc are prominent in this composition, without being overwhelming in their unusualness. The highest prime harmonic used was the 127th harmonic in the final melody! E#''' was also used (125th harmonic)

It was written using a new notation system which has been devised to make accessing higher harmonics as intuitive as possible (it still takes a bit of getting one's head around!). Please contact me if you would like to see the score written in this notation system, or for details about how this notation system enables interesting harmonic composition outside of the bounds of the Western 12-note scale to be realised.

It qualifies for chiptune since although it is (much to my shame) 16-bit 44100Hz audio instead of the pure 8-bit, the sounds were synthesised from scratch using modified sin/saw waves, with a bit of band-limited noise thrown in for good measure. The synth took as input CSV 6xN matrices as sequence files, and processed in Octave/MATLAB to give MP3 output which you hear here.
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update 10th Apr 2015:

Here is a brief description of how the MP3 track was generated:

Just Intonation Notes (1/1 4/3 7/4 etc) <-> New Notation System (C F `Bb~7 etc) which is easier to read than pure numbers and where the letter corresponds (roughly) to the position in the 12ET scale
-> Excel block of chords and melody notes for visual presentation to composer (.txt)
-> Excel long (~1700 columns) of calculated note letters, frequencies, note lengths, etc
-> Excel final sequence file with 6 columns: channel, start time, frequency, note length, loudness, stereo position (.csv)
-> Octave/MATLAB code to take the 6 columns and turn them into chiptune (.mp3 or .wav)
-> Sometimes extra post processing in Audacity for final .wav

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See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Sonata 1 'Cheery' - Chip Synth, Justly Intoned

From Rhythm and Xen (2015) by Sevish:
https://sevish.bandcamp.com/album/rhythm-and-xen

Desert Island Rain

A sketch in Superpyth[12], 6 steps down, on D. Tuned in 27edo.

Casey Hale's Album

More than three over two

10-tet Cadence (Nonuniform String)

This track has been created using an L-system, which is a type of fractal where large parts are comprised of smaller parts that look like reduced copies of the large parts.

As an example, a melody going up by a Just-Intonation perfect fifth (3/2 frequency ratio) could be comprised of three smaller copies going up 3/2, down 3/2, then up 3/2. This simple example would not be musically very interesting, however the idea is there.

In this particular track, the following mappings were used:

1 beat 1/1 --> 1/2 beat 4/3, then 1/8 beat 1/1, then 1/8 beat 9/8, then 1/4 beat 3/2 (inverted)
1 beat 3/2 --> 5/4, then 6/5 (both 1/2 beat)
1 beat 4/3 --> 10/9, then 6/5 (reversed)
1 beat 5/4 --> 9/8, then 10/9 (reversed)
1 beat 6/5 --> 4/3, then 10/9 (inverted)
1 beat 9/8 --> 1/1, then 9/8
1 beat 10/9 --> 1/1, then 10/9

Reversed means the smaller copy is played back in i) the reverse order and ii) the smaller copies are themselves reversed
Inverted means that the frequency shifts are inverted, e.g. f --> 1/f. So 10/9 inverted means ‘go down by 10/9’ or ‘shift by 9/10’

So an L-system melody has a set of melodies (in this case one each for 1/1, 3/2, 4/3, 5/4, 6/5, 9/8, 10/9) and each has its own set of ‘daughter’ melodies.

Each daughter has:
- an associated frequency shift
- a timescale, here they are all 1/2, 1/4 or 1/8 beat
- optional inversion and reversing operations, giving 4 possible orientations in total.

Rules include
- product of daughter frequency shifts must equal parent frequency shift
- sum of daughter timescales must equal parent timescale of 1 beat
- continue iterating until maximum timescale of (iterated) daughters is 1/2^n.

In this particular track, the three parts were:
Bass: reference freq 100 Hz, max timescale 1/32
Alto: ref freq 200 Hz, max timescale 1/64
Treble ref freq 400 Hz, max timescale 1/128

This gave a 3 part invention! Due to the fractal melody/harmony, the different parts were consonant with each other.

One extra option is pre-tuning or post-tuning.
- Pre-tuning means ‘take the note frequency to be from the start of the fractal block’
- Post-tuning means ‘take the note frequency to be from the end of the block’

In this track, post-tuning was used, which means that at the end of blocks the tuning tends to be in 1:2:4 (octaves) ratio. Pre-tuning could just as easily be used, meaning that blocks start off on octaves and change to other chords during each block.

Enjoy! Dave

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See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Example Just Intonation Fractal 3-part Invention

Tonality Flux Demo

Uses Kevin Hobby's ten-tet Piano sampler.
https://www.dropbox.com/sh/740uu4sfca82d11/AAAFKsTLL_6i4UTLzmCawq2ca?dl=0

10-tet Cadence (Nonuniform String)

pseudonym