173Richtcharakteristiken

Directivities of Musical Instruments

Room simulation software needs the directivities of sound sources to describe their radiation properties. It states differences of sound pressure level at selected angle sectors, resulting from a randomly chosen main radiation direction. The main radiation direction is not always as clear as for example in case of the trumpet. In this case the main radiation direction is usefully defined along the symmetrical axis of the mouth because here the sound radiation is at its maximum for all frequencies. The choice for a reference direction with other instruments can be determined by the symmetrical properties of sound radiation. This allows an easy handling of room simulation software.

To specify the characteristical data for a certain instrument, the declaration of a spherical coordinate system and a reference direction is needed first. In the following the specification is made according to the format of a common room simulation program (CATT-Format SD1). Here the reference direction is described as "front" and the spatial changes of the relative sound pressure level are specified along semicircle slices that are distorted against each other by 10° a time. The data of each of these slices begin at the reference direction (0°) and are stated in 10° steps on an angle sector of 180°. This results in 19 level readings in dB noting that the first has to be 0 dB as reference point. In this format 36 semicircle slices are to specify for spatial presentation. They all have to cut not only at the reference point "front", but also at the opposite point "back" showing the same level readings. The count direction of these 36 semicircle slices begins vertically above the sound source ("Top") and looking in reference direction continues counterclockwise by 10° steps (mathematically positive).

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The practical importance of the reference direction shows also at auralisation. That is when reflexion free recorded sounds of the musical instrument concerned are played back in a virtual computer model. The directivity is correctly applied only when the recording microphone was positioned in a reflexion free surrounding exactly in the main radiation direction and pointed at the center of the instrument. This can lead to unusual recording positions with some instruments that don't seem optimal regarding the sound. For example the reference direction of the transverse flute is along the longitudinal axis towards the flutes end because the directivity is rotationsymmetrical around this axis. For auralisation the recording microphone has to be positioned at the open end of the flute.

This example shows clearly the problems of directivities: To simulate correctly the properties responsible for the dipole kind of radiation behaviour of traverse flutes the reference direction has to be selected along the lengthening of the two radiating holes (mouthhole and first open key). With each different selection of the reference direction a suitable transformation of the directivity has to be realized. It has to meet all mentioned conditions. That is all angle dependent level graphs have to show a reference level of 0 dB at "front" and a constant level at "back" (-180°). Inevitably each graph has to distinguish itself from the neighbouring graphs. This can only be managed by a transformation computer program and is contrary to the relatively simple intuitive input by using the rotation symmetry. Meanwhile this transformation has been carried out using the CATT SD2-module. Now (7th November 2001) it is possible to give a directivity of the flute with the reference direction corresponding to the line of vision of the player. This way recordings for auralisations can be used, that were taped with the usual microphone positioning in front of the player in a reflexion free chamber.

By applying our directivities in room simulation programs it has to be taken in consideration wether data were gained together with a musician covering inevitably a part of the radiated sound, or the measurement of the instrument was done by using an artificial excitator and the influence of a musician can be neglected. For each instrument two data versions are provided: One CATT produced .SD1 file and derived out of this one software independend .txt file containing the relative levels in 6 octave bands as described above.

Every line corresponds to the 19 levels of a semicircular graph (illustrated on the left-hand side, "Arc"). The first level reading is always 0 and correspondents to the reference point at front. The last level reading is the rear cutting point of all graphs and has to be constant at all frequencies. The 36 lines correspond to the spatial angles around the reference direction in 10° steps ( illustrated on the right-hand side, "Rot"). The header at the beginning of the .txt file contains further information about the properties of sound sources.

Please consider that the data show mean values relating to the played sound material as well as to the frequency bands in octave size. The latter is similar to the approach to calculate room simulations because reflection properties of surfaces to consider are available only in octave or third bands.

Details to measurements are written in the book "Akustik und Musikalische Aufführungspraxis" by Jürgen Meyer, 3rd edition, Fachbuchreihe das Musikinstrument, published by Bochinsky, Frankfurt 1995. See also the references noted in this book.

Specified directivities:

Violin | Viola | Violoncello | Double Bass

Grand Piano | Singing Voice | Guitar

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