Paper Number 71, Proceedings of ACOUSTICS 2011 2-4 November 2011, Gold Coast, Australia Acoustics 2011 1 Linearity in the loudness envelope of the messa di voce Densil Cabrera (1), Manuj Yadav (1) and Dianna T. Kenny (2) (1) Faculty of Architecture, Design and Planning, The University of Sydney, NSW 2006, Australia (2) Faculty of Arts, The University of Sydney, NSW 2006, Australia ABSTRACT The messa di voce (MDV) is a vocal exercise used by singers, consisting of a crescendo and decrescendo on a single sustained note. In this study we analysed recorded MDVs sung by tertiary singing students to examine the extent to which MDVs have a linear crescendo and linear decrescendo. The MDVs studied were recorded over a 3-year period, as a cohort of classical singing students progressed through their tertiary education and training. Previous studies of MDV envelopes have examined the envelopes in decibels, but in the present study we use envelopes derived from a dynamic loudness model. We did not find an overall tendency for increased linearity as students mature. INTRODUCTION Classical singing at a professional level typically requires many years of training, so that the singer has the ability to project their voice appropriately, and control their voice pre- cisely. There are many singing exercises that can be used to help a student refine their voice control, and the messa di voce (Italian for ‘placing the voice’, and abbreviated here to MDV) is one such exercise. The MDV is very simple in con- cept, consisting of a crescendo and decrescendo on a single sustained note (while simple in concept, the MDV is not simple for a singer to execute). The simplicity of the MDV makes it an interesting candidate for acoustic analysis of voice production, exemplified by several previous studies (e.g., Titze 1992, Titze et al. 1999, Bretos and Sundberg 2003, Collyer et al. 2007, Collyer et al. 2009, Mitchell and Kenny 2010). Such analysis can examine both coarse and fine features of MDVs – such as envelope symmetry, the linearity of the growth and decay functions, the voice spec- trum (e.g., how it changes with sound pressure level and pitch), vibrato, and so on. In this study we analyse a set of recorded MDVs to examine the extent to which their loud- ness envelopes exhibit linear growth and decay functions. Two previous studies have focussed on the envelope structure of MDVs. Titze et al. (1999) studied MDVs from six singers in relation to physiological features (such as lung volume), finding that greater temporal symmetry in the MDV sound pressure level was evident in participants who had a smaller dynamic range. They suggest that this could be because the high dynamic range participants expend more of their lung volume, giving them less control. The high dynamic range MDVs tended to be characterised by a delayed rise in sound pressure level, followed by a sudden fall after the peak. Titze et al. (1999) also observed that some MDVs have a plateau- like sound pressure level envelope (i.e., the maximum level is sustained for some time), and they speculated that even though the level did not vary much during this period, the loudness of the MDV might still be changing due to the ef- fects of vibrato or spectrum (i.e. changes in the strengths of formants). This observation is relevant to the present study, in which we examine the MDV envelope using a computa- tional loudness model. The other major study of MDV envelope structure is by Col- lyer et al. (2007), using five singers. Their study had a stronger focus on the shape of the crescendo and decrescendo envelope, that is, the extent to which it is linear. Unlike Titze et al., they did not observe a relationship between dynamic range and linearity. They examined the relationship between sound pressure level and spectral balance (expressed as the ratio of power in the 0-2 kHz band to that in the 2-4 kHz band), finding a linear correspondence. According to Titze et al. (1999), the ideal MDV has a sym- metric triangular envelope – and this ideal was taught to the singers involved in the present study. However, one of the difficulties with previous acoustical studies of MDV enve- lopes is that the envelopes are represented in decibels. The identification of linearity in crescendo and decrescendo is somewhat problematic using the decibel scale, since the scale has no true zero and is not linearly related to loudness. It seems unlikely that singers would aim to perform in relation to the decibel scale – especially as most singers would be unfamiliar with it. The ‘plateau’ mentioned by Titze et al. might be partly due to the compressive effect that a logarith- mic scale has on high underlying values. This raises the ques- tion, then, of what might we mean by ‘linear’. There are many possibilities – for example, we could consider the pres- sure envelope or the pressure squared envelope, both of which are common ways of representing physical sound quantity without using decibels. Another possibility is to raise the pressure envelope to the power of 0.6, which is the exponent found by Stevens (1955) relating the pressure of mid-frequency pure tones to loudness. A reasonable assump- tion is that in aiming for a linear crescendo and decrescendo, singers attempt to control the loudness of their voice linearly (as suggested by Titze et al.). If that is the case, then some type of loudness model should be effective for analysing the MDV envelope, and there are more sophisticated approaches to this than raising the pressure envelope to a power. Time-varying loudness can be modelled in various ways, and we have previously used the models of Glasberg and Moore (2002) and Chalupper and Fastl (2002), obtaining similar results from the two models (Lee and Cabrera 2010). Such models include the effects of the outer and middle ear trans- fer functions, auditory filtering in the inner ear, functions relating excitation to specific loudness, temporal integration, and loudness summation. Differences between these two models are examined by Rennies et al. (2010). For the sake of succinctness, rather than focusing on detailed issues in loudness modelling, in this paper we present results derived from Glasberg and Moore’s (2002) model.