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sounding third as the basis for interpretation, imagining the missing fifth of a chord, than to use a sounding fifth and imagine the third.127 In these cases, listeners will prefer to use the 03 or 04 interval as the root and third of a root-position triad. If the chord type contains neither a 3 nor a 4, listeners will use the 08 or 09 interval as the root and third of a first-inversion triad. If the chord type does not contain pitch classes 3, 4, 8, or 9, listeners will interpret the 07 interval as the root and fifth of a root-position triad. If the chord type does not contain pitch classes 3, 4, 7, 8, or 9, listeners will use the 05 interval as the fifth and root of a second-inversion triad. Finally, if the chord type does not contain pitch classes 3, 4, 5, 7, 8, or 9, listeners will interpret the bass as an added tone ornamenting a triad implied by the interval of a third or fifth between two of the remaining pitch classes.128 I represent added-tone sonority interpretations by a notation that specifies the quality (and root tone, if desired) of the underlying triad, the bass tone of the chord, and the specific pitch classes added to the underlying triad. The above interpretation of the 013578t chord type as an added-tone sonority, for example, would be represented using the notation m(1,5,8,t)/0. The lower-case âmâ specifies that the underlying triad is minor. Other options include âMâ for a major triad and âM/mâ for a triad with split third or no third; upper- and lower-case letter names may be used to specify a single transposition of 127 Auralizing the third would entail a greater degree of interpretation on the part of the listener, who must then decide whether the underlying triad is to be major or minor. Using the sounding third and imagining the fifth is thus simply less work than the alternative. In addition, the fifth of the chord is already present to some degree in the harmonic series of the root tone; thus, listeners may be able to imagine an absent fifth more easily than an absent third. 128 There are three possible combinations of pitch classes in which a third or fifth does not appear between the remaining tones. These three chord types (012, 01e, and 0te) are therefore not identifiable as addedtone sonorities via this system. One may note that the three non-analyzable chord types are the three possible âinversionsâ of a semitone cluster. 75