## 4 Experimental Setup
### Analysis Parameters  
The parameter estimation for the SM follows [20] with a Hann window for analysis, and phase interpolation across frames via cubic splines followed by additive resynthesis. The estimation of parameters for EDS uses ESPRIT with a rectangular window for analysis and OLA resynthesis [36]. Parameter estimation in eaQHM used a Hann window for analysis and additive resynthesis following Equation (11). In all experiments, \(\varepsilon\) in Equation (12) is set to 0.01 and \(f_{s}=16\) kHz for all sounds. The step size for analysis (and OLA synthesis) was \(H=16\) samples for all algorithms, corresponding  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Family** & **Musical Instrument Sounds** \\ \hline \multirow{5}{*}{**Brass**} & Bass Trombone (C3 f nv na), Bass Trombone (C3 f stac), Bass Trumpet (C3 f na vib), Cimbasso (C3 f nv na), Cimbasso (C3 f stac), _Contrabass Trombone_* (C2\(\sharp\) f stac), Contrabass Tuba (C3 f na), Contrabass Tuba (C3 f stac), Cornet (C4 f), French Horn (C3 f nv na), **French Horn** (C3 f stac), Piccolo Trumpet (C5 f nv na), Piccolo Trumpet (C5 f stac), Tenor Trombone (C3 f na vib), **Tenor Trombone** (C3 f nv sa), Tenor Trombone (C3 f stac), **C Trumpet** (C4 f nv na), C Trumpet (C4 f stac), Tuba (C3 f vib na), Tuba (C3 f stac), Wagner Tuba (C3 f na), Wagner Tuba (C3 f stac) \\ \hline \multirow{5}{*}{**Woodwinds**} & Alto Flute (C4 f vib na), Bass Clarinet (C3 f na), Bass **Clarinet** (C3 f storz), Bass **Clarinet** (C3 f stac), Bass (C3 f na), Bass (C3 f stac), Clarinet (C4 f na), Clarinet (C4 f sta), _Contra Bassoon_* (C2 f stac), _Contra Bassoon_* (C2 f storz), English Horn (C4 f na), English Horn (C4 f stac), **Flute** (C4 f v n na), Flute (C4 f vib na), **Oboe 1** (C4 f vac), **Oboe 2** (C4 f nv na), Oboe (C4 f pa), Piccolo Flute (C6\(\sharp\) f vib forz), Piccolo Flute (C6 f nv ha ff) \\ \hline \multirow{2}{*}{**Plucked**} & Cello (C3 f pz vib), **Harp** (C3 f), Harp (C3 f pdlt), Harp (C3 f mu), Viola (C3 f pz vib), Violin (C4 f pz mu) \\ \hline \multirow{2}{*}{**Bowed**} & **Cello** (C3 f vib), Cello (C3 f stac), **Viola** (C3 f vib), Viola (C4 f stac), Violin (C4 f), Violin (C4\(\sharp\) f vib), Violin (C4 f stac) \\ \hline \multirow{5}{*}{**Struck**} & **Glockenspiel** (C4 f), Glockenspiel (C6 f wo), Glockenspiel (C6 f p l), Glockenspiel (C6 f met), Marimba (C4 f), Vibraphone (C4 f ha 0), Vibraphone (C4 f ha fa), Vibraphone (C4 f ha sl), Vibraphone (C4 f med 0), Vibraphone (C4 f med fa), Vibraphone (C4 f med 0 mu), **Vibraphone** (C4 f shed sl), Vibraphone (C4 f so 0), Vibraphone (C4 f so fa), Xylophone (C5 f GA L), Xylophone (C5 met), Xylophone (C5 f HO L), Xylophone (C5 f mP L) \\ \hline \multirow{2}{*}{**Bowed**} & \multirow{2}{*}{Vibraphone (C4 f sh vib), Vibraphone (C4 f sh nv), Vibraphone (C4 f lg nv)} \\  & **Accordion** (C3\(\sharp\) f), **Acoustic Guitar** (C3 f), Baritone Sax (C3 f), **Bass Harmonica** (C3\(\sharp\) f), Chromatic Harmonica (C4 f), Classic Guitar (C3 f), Mandolin (C4 f), **Pan Flute** (C5 f), **Tenor Sax** (C3\(\sharp\) f), **Ukulele** (C4 f) \\ \hline \multirow{2}{*}{**Keyboard**} & **Celesta** (C3 f na nv), Celesta (C3 f stac), Clavinet (C3 f), **Piano** (C3 f) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Musical instrument sounds used in all experiments. See text in Section 4.1 for a description of the terms in brackets. Sounds **in bold** were used in the listening test described in Section 6. The quasi-harmonic model (QHM) failed for the sounds _in italics_ marked *.  
to 1 ms. The frame size is \(L=qT_{0}f_{s}\) samples with \(q\) an integer. The size of the FFT for the SM is kept constant at \(N=4096\) samples with zero padding.