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When I first began teaching myself music theory in late 2003, I was thrilled to discover that a perfect fifth, added to a perfect fourth, yielded an octave! How cool! What little I have learned in the two years since then I can attribute to the kind and generous assistance of a few individuals, whom I would like to name here – keeping in mind that they should gain the credit for that which is correct, whereas the blame for errors is mine. Please note that my acknowledging the contributions of the people named below should not be construed as an endorsement by them of the ThumMusic System. Prof. William Sethares' excellent book “Tuning, Timbre, Spectrum, Scale” was my first introduction to music theory, and his continuing willingness to correspond with a wild and crazy guy from Western Australia was very encouraging. Dr. Sam Leong, then Director of Music Education at the University of Western Australia, played a critical role in providing an early letter of support for the ThumMusic System, without which the interest of subsequent contributors might not have been gained. Similarly, Ron Gorow's “Hearing and Writing Music” gave me a deep respect for the Harmonic Series, and his correspondence on music notation kept me from making a number of errors I surely would have made otherwise. His extension of ThumLine to sequencer (“piano roll”) notation was also a significant contribution. Thomas Reed, author of the Music Notation Modernization Association's “Directory of Music Notation Proposals,” was also instrumental in helping me understand the trade-offs involved in the design of a new musical staff, and helped verify the novelty of ThumLine's approach. W.A. Mathieu's “Harmonic Experience” was remarkably illuminating; without it I doubt that I would have understood of the role of commas in the structure and affect of tonal music. Michael Good, creator of the MusicXML music notation interchange format, provided excellent feedback on the design of ThumLine, its integration into computer-based notation programs, the structure of the music publishing industry, and the importance of distinguishing, in notation, the difference between augmented and diminished intervals (even if they are the same width in 12-tet). Andy Milne, musician and music theorist, also emphasized the importance of this distinction. More importantly, however, he was the first to recognize the relationship between the structure of isomorphic note layouts (such as the ThumField) and meantone tuning systems – a significant insight for which I suggest he deserves widespread recognition. Bill Miles came up with the content I've tried to capture in Figure 10, and with other insights into the application of the ThumMusic System to music education which are too numerous to mention. His enthusiasm and encouragement have been of great moral support. Acknowledgement should also go to the investors in Thumtronics Ltd., whose confidence in the market potential of the Thummer™, the ThumMusic™ System, and Thumtronics' related innovations has been unswerving. Finally, I would like to acknowledge the patience of my wife and family, who have tolerated two years – so far! – of my complete obsession with the challenge of making it easier to understand, perform, and explore new realms in music. Thank you all. J Previous - Join Us! Next - Appendix: Isomorphic Keyboard Layouts |