Main research focus: systematic and cognitive musicology (how music generates meaning in the sensorial, perceptive, cognitive, motoric and emotional domains); multimedia technology applied to the arts.

• In an experiment reported by Bharucha and Krumhansl (1983), psychological ratings based on the subjective responses from 16 subjects were determined for the 42 ordered pairs of diatonic triads in the major key.

• Werts's goal is to provide a musical rationale for these numbers. There are 6 musical properties (factors) which, when quantified and inserted into the regression formula below, leads to an extremely close approximation of the psychological data.

Explanation:

-Y is Krumhansl's data.

-Y(est) is approximated value for each chord progression.

-X1 through X6 are six musical properties (factors) chosen for Wert's formula after a long period of trial and error in which many factors, all of which seemed musically relevant, were tested.

• Description of the experiment. Playing IV-V-I cadence in C major and later in F# major. After listening to a cadence, the subjects stated how well a triad-pair "fits" after the cadence. Ratings: 1 (worst) -- 7 (best)

• Descriptions of "X" factors:

X1(Sum of Ideal Chord Weights) - most powerful factor, accounting for 54.1% of the explained variance in data. X1 = W1 + W2. W1 is the assumed psychological weight for the first chord in the progression, and W2 is the assumed psychological weight for the second chord.

X2 (Chord - Order Condition) – accounts for 13.9%. X2 can have two values: 1 (for progressions that meet the condition) and 0 (for those progression for all others)! Meeting the condition means that the pair of chords can be extracted from this model:

Am Em F Dm Bo G C

X3 (Subdominant-Dominant Condition) -- accounts for 8.4%. X3 can have two values: 1 (for progressions that meet the condition) and 0 (for those progression for all others)! Meeting the condition means that a chord pair has to contain at least one chord from S group and one from D group.

X4 (Root Movement By Upward Or Downward 5^th). 7.3%. Can be 1 (for 14 chord progression) or 0 (for remaining 28)! Condition: The root of the 2^nd chord has to be 5^th above or below that of the 1^st chord. (This has a positive effect on listeners' perception).

X5 (Problematic resoution of the leading tone). -- 7.8%. Negative factor. Can be 1 or 0. For 1 leading note cannot resolve to tonic because either 2^nd chord does not contain it (Em-G) or conventionally does not (Em-F).

X6 (Parallel Minor Condition). -- 8.5%. Negative factor. 1 or 0 again. Condition: progression must be part of, or lead smoothly to, a cadence in the parralel minor key, or otherwise create an impression of that key. This threatens the stability of the original key.

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