1 An enhanced model of a bowed string is developed, 2 incorporating several new features: realistic damping, 3 detailed coupling of body modes to both polarisations 4 of string motion, coupling to transverse and longitu-5 dinal bow-hair motion, and coupling to vibration of 6 the bow stick. The influence of these factors is then 7 explored via simulations of the Schelleng diagram, 8 to reveal trends of behaviour. The biggest influence 9 on behaviour is found to come from the choice of 10 model to describe the friction force at the bow, but 11 the other factors all produce effects that may be of 12 musical significance under certain circumstances. 13 14 PACS numbers: 43.40.Cw, 43.75.De 15 1 Introduction and historical 16 background 17In an earlier paper [1], a review was presented of 18 the physical ingredients necessary to give an accurate 19 travelling-wave model of the motion of a stretched 20 string in the linear range, for example as required to 21 synthesise the motion of a plucked string. That model 22 and classifying the possible regimes of vibration for a 75 bowed string. Raman was also the first to point out 76 the existence of a minimum bow force [5] as well as 77 the geometrical incompatibility of the ideal Helmholtz 78 motion with uniform velocity across a finite-width 79 bow during episodes of sticking [4], both of which were 80 confirmed later and are still topics of active research 81 [6]. 82 Using Raman's simplified dynamical model, Fried-83 lander [7] and Keller [8] published two independent 84 but similar studies. Their results indicated that if 85 dissipation is not taken into account, all periodic mo-86 tions are unstable, including the Helmholtz motion. 87 As explained later, [9, 10, 11] any small perturbation 88 to the Helmholtz motion produces unstable subhar-89 monic modulation of the Helmholtz motion. In re-90 ality, because of the energy losses in the system this 91 instability is usually suppressed, but under certain cir-92 cumstances these subharmonics can be heard, or seen 93 in measurements of bowed-string motion [9]. 94 The next major development in modelling bowed 95 string dynamics was introduced by Cremer and 96 Lazarus in 1968. Acknowledging the fact that sharp97 corners are unlikely to occur on any real string due to 98 dissipation and dispersion, they proposed a modifica-99 tion of the Helmholtz motion by "rounding" the trav-100 elling corner [12]. Cremer then developed a model of 101 periodic Helmholtz-like motion, which revealed that 102 when the normal force exerted by the bow on the 103 string is high the corner becomes quite sharp, but 104 as bow force is reduced, the corner becomes progres-105 sively more rounded [13, 14, 15]. Ideal Helmholtz mo-106 tion is completely independent of the player's actions, 107 except that its amplitude is determined by the bow 108 speed and position. Thus, this mechanism gave a first 109 indication of how the player can exercise some control 110 over the timbre of a steady bowed note. 111 In 1979, McIntyre and Woodhouse presented a com...