BORE RECONSTRUCTION BY PULSE REFLECTOMETRY AND ITS POTENTIAL FOR THE TAXONOMY OF BRASS INSTRUMENTS David Sharp, Arnold Myers, Raymond Parks and Murray Campbell Department of Physics and Astronomy, University of Edinburgh, Edinburgh, UK. SUMMARY The character of a brass musical instrument is primarily dependent on its bore profile. Many historic brass instruments are so constructed that substantial parts of the air column are inaccessible to direct measure- ment. This paper discusses the factors involved and reports recent advances in the use of pulse reflectometry for bore reconstruction, in particular compensation for losses and allowance for multiple reflections. Mea- surements of historic musical instruments are presented and their significance evaluated. TAXONOMIC OBJECTIVES By a ‘brass instrument’ we mean a lip-vibrated aerophone consisting of a tube narrow in relation to its length, with or without a mechanism for changing the sounding length. Here we limit ourselves to unper- forated tubes, i.e. instruments without finger-holes. The bore profiles which have proved to be viable for brass instruments have at one end a mouthpiece, which may be cupped or funnel-shaped, followed by the narrowest part of the windway, the ‘mouthpiece throat’. From the throat, the windway passes through the mouthpiece backbore, the mouthpipe or leadpipe, any tuning-slide or valves, finally coupling with the free air at the widest part of the tube, the bell. The area of cross-section in most cases increases monotonically; in some cases there is a localised narrowing (e.g. at slides and at valves, or due to some slight damage). The traditional bore cross-section is circular; where (rarely) a deliberately elliptical cross-section is introduced, or in the slight deformation at bends in the tube, the bore profile can for most purposes be considered to be equivalent to that of a cylindrical tube of the same cross-sectional area. Few classification systems go beyond a division of brass instrument types into ‘conical’ and ‘cylindrical’: both concepts have intuitive meaning, but are not capable of rigorous definition. In order to approach an acoustically-based system of taxonomy, it is helpful to look separately at the beginning, middle, and the end of a brass instrument. The choice of a mouthpiece can affect the character of an instrument, though not com- pletely determine it (Myers and Campbell 1993). The design of the bell flare is of critical importance in the sound radiation properties and in the relative intonation of the resonating modes (Benade and Jansson 1974; Jansson and Benade 1974). However, it does not appear that the mouthpiece and the bell flare even consid- ered together can account for the more subtle distinctions between instrument types, or between earlier and later historical models of the same instrument type. It is therefore necessary to examine the complete bore of an instrument. A mouthpiece, where present, can be physically measured, as can the tapered mouthpiece receiver on the body of the instrument. The bell can also be physically measured, or at least enough of it to allow calculation of the horn function in the region of its peak value (in the case of flaring bells). Much of the sounding length of the instrument can, however, pose severe problems for direct physical measurement, particularly in instruments with many coils.