Papers by Paul Erlich

Paul Erlich, the innovative musical theorist, has written several papers including:

the Middle Path between Just Intonations and equal temperaments which describes a variety of two-dimensional musical systems,

a generalization of diatonic scales with special focus on 22-tone equal temperament,

the Forms of Tonality, which illustrates the concepts of tone-lattices, scales, periodicity and notational systems for 5-limit and 7-limit music,

In addition, Paul developed the notion of harmonic entropy, which is described in some detail in an Appendix of Tuning Timbre Spectrum Scale as well as here.