Music recognition.

IONS OCCURRING IN MUSIC RECOGNITION Simultaneous Interval Recognition and Transposition The unit of the musical scale as conventionally defined is the semitone. When two tones are played simultaneously we are able to tell how many semitones they are apart independently of the absolute pitch of the component tones. Thus, two tones three semitones apart constitute a minor third, four semitones apart constitute a major third, and seven semitones constitute a fifth. In physical terms, since the musical scale of pitch stands in logarithmic relationship to the frequency scale, intervals appear identical if they stand in the same physical ratios to each other. An octave is produced by the physical ratio 1 : 2, a fifth by the ratio 2 : 3, and so on. Thus equal frequency ratios appear as equal intervals. Chord Recognition and Transposition Just as with intervals, we are able to classify simultaneous combinations of more than two tones, independently of their component frequencies. For instance a combination of three tones of which the lowest and middle are four semitones apart, and the middle and the highest three semitones apart is known as the root form of the major triad. It might be thought that chord recognition follows logically from interval recognition; however, it can be shown that abstraction of all the intervals involved in a chord does not uniquely define the chord. Consider, for instance, the root forms of the major and minor triads. As shown in Figure 1 they are both composed of a major third, a minor third, and a fifth. However, they sound quite different. Thus the problem of how we abstract chords is not solved by the knowledge of how we abstract intervals. Tune Recognition and Transposition A tune is a series of successive intervals. When two tones are played successively, we are able to tell how far apart they are from each other on the musical scale, independently of their absolute pitch (in physical terms, we abstract their ratios independently of their absolute frequencies). This process of abstraction is so fundamental that it is easier for us to remember a tune than it is to remember the absolute pitch of the component tones. We transpose tunes so readily that it is extremely difficult for us not to do so. Tune recognition is more complicated than simultaneous interval abstraction because it involves recognition of the time order in which the two components of the interval occurred. For instance all three intervals in Figure 2 sound different although their component frequencies are identical. Recognition and Transposition of Sequences of Chords It follows from the transposability of harmonic sequences that we abstract successive relationships not only between tones played separately, but also between simultaneous combinations of tones. Such successive relationships may however be defined by specifying all the abstracted successive intervals involved. For illustra-