Page  295 ï~~EXPERIENCE WITH A HARMON' Suzanne Haig, Gershon Horowitz, Computer Science Department, t Warren Weaver Hall, New Yoi ABSTRACT This paper describes a series of experime The input to the program is a set of melodies a the program learns these harmonies by adjustir program to learn musically significantA styles, styles, is discussed. 1. Introduction In a previous paper [Harrison, Haig, Horowitz 1 harmony to a melody. The algorithm uses an evaluatioi harmonization, along the traditional lines suggested in

Page  296 ï~~For each piece we provide the "correct" harmoni performer), and compute the goodness value accordins This value is of the form xHiT,, where the Tj are tab] We compute the Ht, melody and the harmonization. "positive" example). Our algorithm then generates the and computes its H values, say H',. The values of the tab Ti +ac(Ha-) where c is a parameter which can be chosen to adjust thc correct harmonzation is picked as best (we say that the seems unlikely. Since the Hi values for any harmonization are indc cess generates a single positive example and a finite nu that, as in the classical case, resolution, if possible, is ass For many pieces, we construct a single large p pieces, with a marker between pieces which suppresses resolves, this means that all the constituent pieces resolvW 3. Initial Experiments Early results suggested that the harmonies used by different tables, and such tables could regenerate arnrox

Page  297 ï~~5. Multi-chord Sequences It is widely accepted that sequences of three orrr important role. Our algorithm does not account for these late three-chord sequences to some extent in the followii rename each middle chord to be unique. Enter these chc result is that these sequences can have their table val chords not used in the sequences. The main disadvanta much flexibility, since these new chords are free to bu chords, so results are difficult to interpret. For example four-chord sequences to be recognized as two overlappi recognize five-chord sequences). 6. Results At the time of writing we have tested the lean chorales, each regarded as a single phrase. For 167 no adjust the tables so that 116 chords were correctly chose cedure was applied, 31 chords needed to be forced to ge from one force out of 15 to six forces out of 21 0 We also of the chorales, and when we broke the pieces into phras( same chord positions. We have also tested two roUns of 7 Bach chnrale;