Quantifying Tessitura in a Song
Ingo R. Titze · Journal of Singing · 2008
The term tessitura (Italian for texture) can be associated with a piece of music or with a singer. Often the concept of texture defaults to pitch, both range and average. Thus, the tessitura of a song tends to be associated with the distribution of pitches, measured in frequency of occurrence and duration of each occurrence. Similarly, the tessitura of a singer relates to the comfort level with a given distribution of pitches in a song. Recent investigations on vocal dosimetry conducted on teachers in public schools1 are based on four formal definitions of vocal doses: time dose, cycle dose, distance dose, and energy dose.2 These doses can be calculated from daily and weekly measurements made with a portable device.3 We have called the device the National Center for Voice and Speech (NCVS) dosimeter. Two of the doses calculated, the time dose and the cycle dose, appear to be useful for quantifying a singer's tessitura. We specify them here for each pitch in the song, Time dose = t^sub p^ , (1) Cycle dose = F^sub p^ t^sub p^ , (2) where t^sub p^ is the duration of time accumulated on each pitch over the entire song and F^sub p^ is the fundamental frequency of a given pitch in the song. The time dose can be measured in seconds of actual performance or in equivalent whole notes presented in the score. The cycle dose is measured in cycles of vibration of the vocal folds. Figure 1 shows a tessituragram for the aria Il mio tesoro intanto from Mozart's opera Don Giovanni, designated to be sung by a tenor in the role of Don Ottavio. It is notorious for its tessitura, hovering around the pitch F^sub 4^. The figure has five parts. At the bottom is a standard keyboard showing a range of pitches slightly larger than the typical tenor range. Above the keyboard is a voice range profile of a singer (the author in this case). In the middle is a distribution of the numbers of cycles of vocal fold vibration on each pitch. Second from the top is the equivalent number of whole notes sung on each pitch. The top shows the number of occurrences of each pitch. Unless there are embellishments in the form of additional (unwritten) notes produced by the singer, the distributions of occurrences, equivalent whole note durations, and vibration cycles can be obtained from the written music (without performance). If there are unwritten notes and fermatas, the distributions can be obtained only with a dosimeter during performance. In Figure 1, Mozart's written score was used. To give some specifics, this aria has 70 occurrences of the pitch C^sub 4^ (the supertonic in the key of B[musical flat]), 66 occurrences of the pitch B[musical flat]^sub 3^ (the tonic), and 49 occurrences of the pitch F^sub 4^ (the dominant). The supertonic leads in occurrences because of the frequent appoggiatura (leaning toward the tonic). There is only one occurrence of A^sub 4^, and one of E^sub 3^. There are two occurrences each of D^sub 3^, E[musical flat]^sub 3^, and D[musical flat]^sub 4^, and three occurrences of B^sub 3^. Other occurrences can be read off the scale to the left, which has a tic mark at 50 occurrences. Although C^sub 4^ has the greatest number of occurrences, F^sub 4^ (the dominant) has the greatest accumulated duration (time dose), the equivalent of 16 full notes, or 4 full measures. This does not include two fermatas on this pitch, which are not quantifiable from the score. The subdominant (E[musical flat]^sub 4^) has the second greatest accumulated duration (14 3/8 whole notes) and the tonic (B[musical flat]^sub 3^) has the third greatest accumulated duration (12 1/8 whole notes). By converting the 4/4 meter to a metronome marking, the actual durations in seconds could be computed. For example, at 96 beats per minute, F^sub 4^ would accumulate 64 full beats, which is 2/3 of a minute or 40 seconds. In terms of the cycle dose, the pitch F^sub 4^ encounters 5584 cycles of vibration, followed by 4471 cycles on E[musical flat]^sub 4^, 2825 cycles on B[musical flat]^sub 3^, and 2817 cycles on C^sub 4^. …