Just Intonation (JI) is music created using frequencies where all the intervals are rational numbers (a/b with a, b both positive whole numbers; e.g. 1/1, 3/2, 100/7, etc).

JI sounds more interesting than music created on the twelve-note piano scale (12-EDO) since JI has pure harmonics, and 12-EDO does not. The only pure harmonic in 12-EDO is the octave.

This playlist contains all my JI compositions or arrangements.

Just Intonation music composed or arranged by David Ryan

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

This is a justly intoned arrangement of J. S. Bach's Prelude in C Major, the first Prelude of the 48 Preludes and Fugues, a body of work by Bach which demonstrated that with tempered tunings every major and minor key was usable.

As well as being one of my favourite pieces of music, I thought it would be worthwhile to demonstrate that this music sounds just as interesting (maybe more interesting!) in Just Intonation (JI), where exclusively rationally-spaced intervals are used. JI is the natural way of tuning intervals. It derived from harmonic series, which are produced by string and wind instruments.

Due to the 'wrap-around' nature of tempered tunings, some transitions (e.g. D minor to G major) are good transitions in tempered tunings, but sound 'further away' or less harmonious in JI. Also, transitions from ,D' to `D (10/9 to 9/8) and from C to `C~7 (1/1 to 63/64) are noticeably microtonal shifts. Some people might like them, some might not. Personally, I like them. The major advantage is the purity of all the triads and seventh chords, which in my opinion outweigh the 'disadvantages' of having noticeable microtonality.

As always, I've slipped in an 11th and 13th harmonic (the 11th is obvious, the 13th less so). I refuse to write any new music which does not contain both 11th and 13th harmonics.

Another interesting feature was Bach's usage of diminished chords. My favourite justly intoned diminished chord is the sequence 10:12:14:17:20:24:28:34:40 etc. Hence, some 17th harmonics have been used, wherever there is a diminished chord, in both 17/1 and 1/17 formats (and 5/17).

Hence, this track contains all the harmonics 2, 3, 5, 7, 11, 13 and 17. I will attempt to remedy the lack of 19, 23, ..., 127th harmonics in my next upload.

Enjoy!

Dave

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Bach number of this track: BWV846 or BWV 846

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

Bach BWV846 Prelude in C major - Chip Synth, Justly Intoned

This is a justly intoned arrangement of Chopin's Etude in C Major (Opus 10, No. 1), the first Etude of his series of Etudes which demonstrated his new piano performance techniques.

Although Etudes are usually technical exercises, Chopin's are special since they are immensely listenable with intricate harmonies.

I have retuned Chopin's harmony to have much more than 12 notes to the scale. More to come (hopefully soon!) about the notes which have been used. Concisely, the major and minor triads and sevenths have almost everywhere been preserved, and Chopin's use of sequences leads the harmony down very interesting and long paths in the 7-limit tonal lattice. A couple of jarring transitions are where the harmony jumps up by a syntonic comma (or 7-limit comma). As always, 11th and 13th harmonics are smuggled in, in some of the diminished chords near the end.

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

Chopin Etude in C Major - Op. 10, No. 1 - Chip Synth, Justly Intoned

Stevie Wonder has written a great song - You Are The Sunshine Of My Life. But those amazing harmonies are crying out for something - Just Intonation!

By using my new notation system to convert his piano scale harmonies to natural harmonics, a purer and more interesting harmonic structure is revealed.

As always, the underused 11th and 13th harmonics are hidden in this retuning (in the intro section using neutral thirds)

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

Stevie Wonder - You Are The Sunshine Of My Life - Chip Synth, Justly Intoned

This is a justly intoned arrangement of J. S. Bach's Prelude in C Sharp Major, the third Prelude of the 48 Preludes and Fugues, a body of work by Bach which demonstrated that with tempered tunings every major and minor key was usable. It was made using a custom sequencer in Excel+Octave which allowed exact frequencies to be specified.

'Normalised commas' mean that the piece was composed in simple Just Intonation by specifying local frequency ratios, the most important of which are major (4:5:6) and minor (10:12:15) triads locally. However, between different sections they may be out of tune by microtonal commas (e.g. 81/80) and to fix this the different sections need to be stitched together by multiplying the later section by an accumulation of commas. This means that we get 'comma travel' so the piece moves sharp or flat in frequency. To fix this second issue, the commas can be normalised by dividing out by a local moving average of the accumulated commas.

By comparing this normalised version to the 'comma travel' version, it is easy to detect this movement in pitch. The commas on this track were normalised over 48 beats (8 bars).

Accumulation of commas, normalised or unnormalised, will be explained further in my second JI maths/music paper - pending! The theme of it is how to take any sheet music and retune it into JI using comma alterations, mainly of 5th and 7th harmonics. However, as always, in this track I've snuk in some 11th and 13th harmonics which you might be able to locate by ear or by examining the code blocks in Github (upload pending as of 9th Nov 2015).

Enjoy!

Dave

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Bach number of this track: BWV848 or BWV 848

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

Bach BWV848 Prelude in C Sharp Major - Chip Synth, Justly Intoned, Normalised Commas

This track is an example of where the melody in each bar alternately takes utonal and otonal values, that is, uses alternately subharmonics (of a very high note) and harmonics (of a very low note).

The bass and backing was devised first, using a repeating series of 12 chords which were alternately utonal and otonal.

After that, the melody was chosen from the subharmonic or harmonic spectrum for that chord in each bar.

Its in three parts - a melody, a 2 part harmony, then all 3 parts superimposed.

Harmony is supposed to be a bit tricky and captivatingly strange at times! Enjoy the 11ths, 13ths and 29ths - 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 of alternating undertone and overtone melody and harmony

I'm into Just Intonation (JI), which is using harmonics (or undertones) to generate music. Over time, my profile will fill up with wonderful and melodious New Harmony, fresh from the infinite vaults of the original and best source of harmony, Just Intonation.

I’ve written some papers on the music theory of Just Intonation. You can check them out via the arXiv link below. Topics include the mathematical analysis of harmony (in Just Intonation), and a notation system to cover all of Just Intonation.

Enjoy listening!