This is a justly intoned arrangement of J. S. Bach's Fugue in C Sharp Major, the third Fugue 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 64 beats (4 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 Fugue in C Sharp Major - Chip Synth, Justly Intoned, Normalised Commas

most of the music is straight from tiktok.  the other music is from a friend

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!

a little bit of everything  including  Christmas  music 

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

David Ryan