Unusual musical scales
Click here to go to the page for the Tumbling Dekany (a polytope music generator).
In my paper Harmonic errors in equal tempered musical scales, I have investigated equal divisions of the octave other than 12 (equal tempered) and have rated their usefulness based on the quality of the available harmonies and the number of divisions required (the fewer the better). This paper may also serve as an introduction to microtonalism.
Here's a start at explaining An algorithm for dynamically choosing the best 12 notes from an extended meantone.
Prompted by a challenge issued by Paul Erlich, and
inspired by Margo Schulter's meantone spectrum chart,
I produced these visualisations of the
Harmonic errors in single-chain-of-fifths tunings
Harmonic errors in double-chain-of-fifths tunings
That is, the errors in the intervals of those octave-based tunings whose notes are generated by chains of uniform fifths, whether the chain be closed (equal tempered) or open (e.g. meantone).
First, here's a coloured 9-limit lattice for the ordinary diatonic scale so you get the idea.
Here are the results of my computer search for generators of 7-limit MOS scales. I have since added triple chains 1/3 octave apart to the search and found no new generators.
A chart classifying all the tetrachords available in 72-ET (a Ms Word document).
Here's a variation on the above dekany graph to reduce clutter.
An Excel spreadsheet for calculating the size of MOS scales (those with Myhill's property).
Keyboard mapping spreadsheet. It gives an ideal generalised-keyboard mapping for any linear temperament.
The Noble Mediant: Complex ratios and metastable musical intervals coauthored with Margo Schulter.
The Conundrum of the Bent Tuning Forks on combination-tone chords.