About Harmonious


For Students, Composers, Songwriters, Arrangers & Working Musicians

What if you could learn music theory from a mentor that had all the answers? Start with what you know and follow your curiosity, confident that you have all musical options at your disposal, since Harmonious is the most complete chord and scale map.* Harmonious is a map of all chromatic-cluster-free hexatonic, heptatonic, and octotonic scales and modes and their compatible chords (Levine 1995) in twelve-tone equal temperament. Find extensions, substitutions and chromatic flavors that lie at the edge of the familiar and the exotic. See connections through the dual lens of chords and scales, linking harmony and melody.

Copyright © 2008–2018 Jared Updike.

To report bugs or errors, or to suggest improvements, feel free to email the public support forum at support@harmoniousapp.net. (The contents of your email will be public but not your email address.)

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Jared Updike is a software engineer, UI/UX developer, and graphic designer based out of Los Angeles. He started playing guitar around 1995 and began building software to help understand music theory soon after that. He played electric bass in a rock band in high school, sang in choirs, and performed in the collegiate pop a cappella group Out of Context (bass and vocal percussion) while studying Computer Science at Caltech, graduating in 2005 with a Bachelor of Science. He currently lives in California with his wife, son, and two guitars.

The aim is for Harmonious to be a complete, authoritative, and practical reference on everything harmony-related in twelve-tone equal temperament (and nearby tunings). Harmonious combines elements of musical set theory and atonal theory (Forte 1977) and jazz theory (Levine 1995) with harmony and music theory in the extended common practice, as outlined by Tymoczko (2011). Along with Quinn, Callender, and others, Professor Tymoczko* Tymoczko’s work feels, in spirit, like Richard Feynman’s lecture on Algebra (Feynman 1964) where he ends up connecting algebra to geometry and derving trigonometry from first principles in the space of an hour. Feynman shows that you can abstract and generalize simple rules (counting, addition, multiplication, exponents, and their inverse operations: subtraction, division, roots and logarithms), until at a certain point, shockingly, you stop inventing new number objects (negative numbers, rationals, irrational reals) and you hit the limit (of new types of mathematical objects you need to solve algebraic equations) when you hit complex numbers. And on top of that, a single equation ties all of these things together (Euler’s formula). Reading Tymoczko's work was the first time music theory started to circle back on itself and feel rich but complete, instead of esoteric and arbitrarily open-ended. builds off work by Forte, Lewin, Clough, Douthett, Guerino Mazzola, and many more theorists who sought to explore the edges of tonality and discover its underlying structure.

Common approaches to music theory present an arbitrary subset of possible chords, scales, functions, or progressions (without explaining why they are favored) or present long (but incomplete!) lists of notation, jargon, and formulae to memorize, with no end in sight. There are in fact bounds to the number of meaningful relationships between musical objects, at least if we stick to 12-TET, and we can enumerate those relationships from first principles without fear of arbitrarily leaving something out, using the underlying mathematical structure to guide us through the space of possibilities. In addition to attempting to be as complete a reference as possible, Harmonious attempts to map out the richness and ambiguity inherent in harmony as precisely as possible.

For a longer Bibliography, see the references in Tymoczko 2011.

Callender, Clifton, Ian Quinn, and Dmitri Tymoczko (2008). “Generalized Voice-Leading Spaces,” Science, 320: pp. 346–348.

Clough, John and Jack Douthett (1991). “Maximally Even Sets,” Journal of Music Theory, 35: pp. 93–173.

Edwards, Bill (1989). Fretboard Logic I & II, Edwards Publishing, Temple Terrace, Florida.

Feynman, Richard, Robert B. Leighton, and Matthew Sands (1964). The Feynman Lectures on Physics, Volume I, Ch. 22, p. 22-8. (Read online.)

Forte, Allen (1977). The Structure of Atonal Music. Yale University Press, Second Edition.

Leinberger, Charles Francis (2011). “Chord Functions for Musical Analysis,” University of Texas at El Paso website, http://utminers.utep.edu/​charlesl/chords.html. Retrieved March 2, 2018.

Levine, Mark (1990). The Jazz Piano Book, Sher Music/Advance Music, Petaluma, California.

Levine, Mark (1995). The Jazz Theory Book, Sher Music/Advance Music, Petaluma, California.

Lewin, David (1959). “Re: Intervallic relations between two collections of notes.” Journal of Music Theory, 3: pp. 298–301.

Lewin, David (1987). Generalized Musical Intervals and Transformations, Yale University Press. Second edition by Oxford University Press, 2007.

Quinn, Ian (2004). A Unified Theory of Chord Quality in Equal Temperaments, Department of Music Theory, Eastman School of Music, University of Rochester. Rochester, New York.

Tymoczko, Dmitri (2006). “The Geometry of Musical Chords,” Science, 313: pp. 72–74.

Tymoczko, Dmitri (2009). “Three Conceptions of Musical Distance,” Bridges 2009: Mathematics, Music, Art, Architecture, Culture: pp. 29–38.

Tymoczko, Dmitri (2011). A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, Oxford University Press, New York.

Harmonious is powered by Node.js and the following packages: immutable, connect, finalhandler, serve-static, synchronize, uglifyjs, typescript, and livescript. It shows off what you can do with preprocessors such as TSVG, Less.js, and Handlebars. Harmonious ships with code from Vexflow, Vexflow-JSON, Underscore.js, jQuery, iScroll, Base-64, JSHash (MD5), sorttable, and on iOS, SSZipArchive, TUSafariActivity, and MBProgressHUD. Typography is greatly enhanced by the lovely open-licensed font families Fira Sans and Bitstream Charter.

Harmonious is protected by copyright and any reproduction beyond fair use is prohibited. If you wish to share the information in the app, please share a link to Harmonious on the web. Each page can be shared individually.

Thank you for supporting Harmonious. Purchases of the app support its continued development and improvement, helping bring this resource to the level of accuracy and completeness it deserves.

Harmonious on the web is free for non-commercial use and is provided as a service to the community (especially students) but it is not free; it is subsidized through the support of app purchasers. If you use Harmonious in a professional setting (as a teacher, as a working musician), the author requests your support through the purchase of the app in the iOS App Store. There are many plans for improvements and upgrades to bring this resource to the level of accuracy and completeness it deserves, but it is hard to justify the time commitment without the financial support of the portion of the community who benefits from its continued development.

Every effort has been made to supply information that is accurate and exhaustive, and suggested corrections and amendments are always welcome (see contact section above), but it is impossible to guarantee that there are no problems with the supplied information. the author offers this resource as-is and makes no representations or warranties of any kind concerning this work, express, implied, statutory or otherwise, including without limitation fitness for a particular purpose, or the absence of latent or other defects, accuracy, or the presence or absence of errors, whether or not discoverable, all to the greatest extent permissible under applicable law.

Harmonious on the web may collect anonymous usage data (IP address of website visitors, etc.), but the offline (iOS) app does not collect any data on the device, so no data is returned to any server. Anonymous usage data is never shared with anyone.

If you are helping to test the beta, no information is collected other than your email address, which is not shared with anyone, and communications with the public support forum (Harmonious Google Group and/or emails to/from support@harmoniousapp.net) related to the application will be publicly available. (The contents of your email will be public but not your email address.)

harmonious adj.
1. having components pleasingly or appropriately combined; symmetrical
2. constituting a consistent or an aesthetically pleasing whole
3. exhibiting equivalence or correspondence among constituents
4. exhibiting harmony or being in harmony
5. congruous; suitable and fitting; concordant; consonant; symphonious; melodious; dulcet; tuneful





© 2008–2018 Jared Updike.
All rights reserved.


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