Finding intensities and temporal characteristics in piano music

Wai Man Szeto, Kin Hong Wong, Chi Hang Wong
Department of Computer Science and Engineering
The Chinese University of Hong Kong
Shatin, N.T., Hong Kong
{wmszeto, khwong, chwong1}@cse.cuhk.edu.hk

Abstract

Timing and dynamics are two important factors in music performance. Research on dynamics-related issues is comparatively rare because data on dynamics is difficult to obtain from music performance. Nevertheless, research of this kind is vital to the understanding of music performance and here we are investigating ways to identify the intensities of individual notes in a mixture of simultaneous notes. The approach to this problem is divided into two stages. The first stage consists of obtaining the magnitude of the fundamental frequency of an individual note to determine its intensity out of a mixture of simultaneous notes, on condition that the corresponding pitches of which are given. Two simultaneous notes an octave apart are also included in this study. The second stage consists of generating, artificially, a mixture of notes from a recorded single-note database, subsequently referred to as "estimated mixture". The time lag between individual notes in the estimated mixture is adjusted, so that the residual between which and the input comes to a minimum. The proposed method is verified with real data and the result is satisfactory.

1  Error map

Error map
(Click here for a full-size image.)

The full-colour error map of t1 and t2 of a C2-A2 mixture (Figure 4 in the paper). A white line connects a starting point and its corresponding local minimum. [^x]p1,[^v]*1 is C2 at MIDI velocity 70 and [^x]p2,[^v]*2 is A2 at MIDI velocity 70. The periods of these C2 and A2 are 676 and 401 samples respectively. The variables s1 and s2 are equal to 3 so along each axis, adjacent starting points are separated by one third of the period. The period is the period of C2 for the x-axis and is the period of A2 for the y-axis. The residue-to-signal ratio at the global minimum (133, 63) is 0.0159.

2  Demonstrations

Some audio files of the overall performance (first testing condition) including all the 7 cases of misclassified MIDI velocity can be downloaded below. To increase support for audio players, the 24-bit wave files are amplified linearly by 5 and are converted to 16-bit waves files. The sampling frequency 44.1 kHz remains unchanged.

Pitch Original Estimated Residue
MIDI velocity mixture y MIDI velocity mixture [^y] Residue-to-signal ratio RSR signal y-[^y]
C2-E2 70-70 wav 70-70 wav 0.0107 wav
C2-F#2 70-70 wav 70-70 wav 0.0152 wav
C2-G2 70-70 wav 70-70 wav 0.0198 wav
C2-C3 70-70 wav 70-70 wav 0.0341 wav
C2-C4 70-70 wav 70-80 wav 0.1601 wav
C3-C#3 70-70 wav 80-70 wav 0.0863 wav
C3-D3 70-70 wav 80-70 wav 0.0525 wav
C3-E3 70-70 wav 70-70 wav 0.0046 wav
C3-F#3 70-70 wav 70-70 wav 0.0039 wav
C3-G3 70-70 wav 70-70 wav 0.0031 wav
C3-C4 70-70 wav 70-60 wav 0.1029 wav
C3-C5 70-70 wav 70-70 wav 0.0137 wav
C4-E4 70-70 wav 70-70 wav 0.0069 wav
C4-F#4 70-70 wav 70-70 wav 0.0098 wav
C4-G4 70-70 wav 70-70 wav 0.0174 wav
C4-C5 70-70 wav 70-70 wav 0.0489 wav
C4-C6 70-70 wav 70-90 wav 0.3096 wav
C5-D#5 70-70 wav 70-80 wav 0.1415 wav
C5-E5 70-70 wav 70-70 wav 0.0120 wav
C5-F#5 70-70 wav 70-70 wav 0.0053 wav
C5-G5 70-70 wav 70-70 wav 0.0169 wav
C5-C6 70-70 wav 70-90 wav 0.3722 wav


With the help of TEX by TTH, version 3.67.
On 13 Apr 2005.