The Saxophone by Model and Measurement

X(z) = Z0U(z) z −N λN(z) TB(z) YB(z) This work presents an extension to a measurement technique used to estimate the reflection and transmission functions of musical instrument bells within the context of parametric waveguide models. In the original technique, several measurements are taken of a system—a 2-meter long cylindrical tube with a speaker and co-located microphone at one end and incrementally varying termination conditions at the other. Each measured impulse response yields a sequence of multiple evenly spaced arrivals from which estimates of waveguide element transfer functions, including the bell reflection and transmission, may be formed. Use of this technique to measure a complete saxophone presents a number of difficulties stemming from the fact that the bell is not easily separated from the bore for an isolated measurement. The alternative of appending the complete saxophone yields a measured impulse response where 1) echos overlap in time and are not easily windowed and 2) the presence of a junction between measurement tube and saxophone cause spectral artifacts. In this work we present an alternate post-signal-processing technique to overcome these difficulties, while keeping the hardware the same. The result is a measurement of the saxophone’s round-trip reflection function from which its transfer function, or its inverse—the impulse response, may be constructed. 1

Automatic phrase continuation from guitar and bass guitar melodies

A framework is proposed for generating interesting, musically similar variations of a given monophonic melody. The focus is on pop/rock guitar and bass guitar melodies with the aim of eventual extensions to other instruments and musical styles. It is demonstrated here how learning musical style from segmented audio data can be formulated as an unsupervised learning problem to generate a symbolic representation. A melody is first segmented into a sequence of notes using onset detection and pitch estimation. A set of hierarchical, coarse-to-fine symbolic representations of the melody is generated by clustering pitch values at multiple similarity thresholds. The variance ratio criterion is then used to select the appropriate clustering levels in the hierarchy. Note onsets are aligned with beats, considering the estimated meter of the melody, to create a sequence of symbols that represent the rhythm in terms of onsets/rests and the metrical locations of their occurrence. A joint representation based on the cross-product of the pitch cluster indices and metrical locations is used to train the prediction model, a variable-length Markov chain. The melodies generated by the model were evaluated through a questionnaire by a group of experts, and received an overall positive response