XronoMorph: Loop generator

XronoMorph is a free macOS and Windows app for creating multilayered rhythmic and melodic loops (hockets). Each rhythmic layer is visualized as a polygon inscribed in a circle, and each polygon can be constructed according to two different mathematical principles: perfect balance and well-formedness (aka MOS). These principles generalize polyrhythms, additive, and Euclidean rhythms. Furthermore, rhythms can be smoothly morphed between, and irrational rhythms with no regular pulse can also be easily constructed.

XronoMorph subsumes the earlier MeanTimes app described in Milne, A. J. and Dean, R. T. (2016).

Each polygon can play an independent sound, and XronoMorph comes with a useful selection of samples to play the rhythms. Alternatively, you can load your own VST or AU plugins, or send MIDI to an external software or hardware synth. The rhythmic loops can be saved as presets within XronoMorph; they can also be saved as Scala scale tuning files, which means XronoMorph can be used as a tool for designing well-formed (MOS) and perfectly balanced microtonal scales.

The video below gives an overview of what XronoMorph is and what it does. More videos are available on the XronoMorph YouTube channel—please leave a comment or a like if you enjoy what you see!

Perfectly balanced and well-formed rhythms

The mathematical principles utilized by XronoMorph are perfect balance and well-formedness (MOS).

Perfect balance is a generalization of the polyrhythms found in many African and jazz musical traditions. A rhythm is perfectly balanced when the mean position (centre of gravity) of all its rhythmic events, when arranged on a circle, is the centre of that circle.

Well-formedness is a generalization of the additive rhythms found in aksak (Balkan), sub-Saharan African, and progressive rock musical traditions. Well-formed rhythms contain no more than two interonset intervals, arranged as evenly as possible. WF rhythm are typically nested by faster WF rhythms, which in combination form complex interlocking rhythmic hierarchies.

More detailed explanations of the two principles are provided in the videos on the XronoMorph YouTube channel and in this article in The Conversation. The following peer reviewed papers describe the app, well-formedness and perfect balance in extensive detail:

Milne, A. J., Bulger, D., and Herff, S. A. (2017). Exploring the space of perfectly balanced rhythms and scales. Journal of Mathematics and Music, 11(2).

Milne, A. J., Herff, S. A., Bulger, D., Sethares, W. A., and Dean, R. (2016). XronoMorph: Algorithmic generation of perfectly balanced and well-formed rhythms. In Proceedings of the 2016 International Conference on New Interfaces for Musical Expression. Brisbane, Australia.

Milne, A. J. and Dean, R. T. (2016). Computational creation and morphing of multilevel rhythms by control of evenness. Computer Music Journal, 40(1):35–53.

Milne, A. J., Bulger, D., Herff, S., and Sethares, W. A. (2015). Perfect balance: A novel principle for the construction of musical scales and meters. In T. Collins, D. Meredith, and A. Volk (Eds.), Mathematics and Computation in Music—MCM 2015, volume 9110 of LNAI, pages 97–108, Heidelberg. Springer.


XronoMorph is a portable standalone application distributed in a zip file. No installation is required—when you have downloaded the file, unzip it and double click to run.

Possible issues on OS X/macOS:

  • On first run, you may need to right-click (control-click) the app and select 'Open'.

Possible issues on Windows:

  • If you get a message complaining of missing dlls you will need to install the Visual C++ Redistributable Package for Visual Studio 2013 from Microsoft's Download Center. For the 32-bit version of XronoMorph, download the vcredist_x86.exe version of the above package; for the 64-bit version of XronoMorph, download the vcredist_x64.exe version of the above package.

Known bugs:

  • VST/AU plugins are not stored in presets (this should be fixed very soon).

We uploaded the latest versions of XronoMorph, 1.5.0 for Windows, on Jan 30, 2017, and 1.5.1 for macOS, on Jan 18, 2018.

  • Download XronoMorph for Windows 32 bit
  • Download XronoMorph for Windows 64 bit
  • Download XronoMorph for macOS
  • Although XronoMorph is available free of charge, we would greatly appreciate a small donation to help us continue to provide updates and develop new software.

    To send feedback or report a bug, please send an e-mail to andymilne [ a t ] dynamictonality [ d o t ] com.

    XronoMorph uses the excellent HISSTools Impulse Response Toolbox, hence the following copyright notice and conditions:

    HISSTools Impulse Response Toolbox
    Copyright (c) 2012 Alex Harker and Pierre Alexandre Tremblay
    All rights reserved.
    Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
    * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
    * Neither the name of the University of Huddersfield nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

    XronoMorph also uses the remarkable bach package for Max—bach is licensed under the Creative Common BY-NC-SA 3.0.

    Site design by Anthony Prechtl