126 Board deviat.ion from model [0/0] l1li First estimates k T,,:'!J Refined 30 20 10 o -10 -20 I ·.····· ·· ······ ·· ··· ·································...... ... ... ............... ... . ......... ·· SOUND ·B · ·- O·· l ·· RD ······ I ······ -30 ...... -:- ... .. .. -:-:- . . _ ... _ .. . _. '.= " := .. = . .. = . .3= .: .. ... ::...:" 30 20 10 o MO-2 MI-I MO-3 MO-4 MI-2 MO-S Ml-3 M O- 6 M2- 0 -1 0 I·· ·· .. ·· ················ ··············· 20 ................ . o ..J!lilI[£] == 30 .................. . -10 _ ............. .. __ : .:- 30 I ········ · ·· ·· ······ 20 ......... . 10 .... . ....... ...... . ... Ui = fBlSJ @j _ .. . ... u •••• •••••• -2 0 .................... SOUND u ·O · ··· .. · T)· T\···· 4 · ...... . -30 .. _ .. _ .. _ ._ .. _ . _ .. _. =: .D .= _. == ... =:: .... :.= ._ .. . MO-2 MI -l MO-3 MO-4 MI-2 MO-S MI-3 M2 -0 MO-6 32nd Czech Conference on Acoustics SPEECH - MUSIC - HEARING Prague, September 23 - 26, 1995 Formant positions of musical instruments and recommendations for ensemble scoring in orchestration treatises Christoph Reuter Musikwissenschaftliches Institut der Universitat zu Koln Albertus-Magnus-Platz, D-50923 Koln, Germany Abstract: This paper suggests that the preference for particular combinations of instruments in well-known treatises of orchestration could be attributed to individual instruments' form ant regions. Since instruments which have form ants (and corresponding spectral gaps) in the same positions of the spectrum should blend together especially well, combinations of instruments following such principles should correspondingly be found to be recommended often in orchestration treatises. This hypothesis is examined in the cases of the horn, the bassoon and the oboe. I. F ormant areas and partial masking Perception of instrumental timbre, as numerous investigation have shown, functions according to a pattern recognition process analog to that of speech in which formant areas play a primary role. Especially when various instruments play together, the ear recognizes and their timbres mostly by focusing on the spectral peak areas that are typical for each instrument. These peak areas are usually positioned in regions where another instrument has spectral gaps. Due to this partial masking (J ) as well as to our capacity of perceiving residuals, it is possible to hear the individual instruments playing in an ensemble and even to reconstruct their me\l'dic lines solely on the basis of the remaining partials, in spite of fundamental frequencies which partially mask each other. ',' Of course, it can be shown that there are pairs of instruments whose formant areas more or less coincide, such as the horn and the bassoon. If such instruments are combined, the resulting timbre will then be perceived as particularly homogenous. This relation between formant position and combinations of instruments will be examined further below using the horn, the bassoon and the oboe as examples. 2. Formant areas (Schumann's Laws of Timbre) versus sharpness and compactness. While the spectral dynamics of wind instrument timbres can be explained especially well by the four Laws of Timbre (2), concepts such as sharpness and compactness (3) do not adequately describe instrumental timbres. There are three reasons for this: I. The concept of sharpness only describes the main peak in a spectrum, without taking the other peaks, their form or their width into account. 2. Sharpness only gives a blunt approximation of perceived changes in dynamics by describing the increase and decrease in amplitude of higher partia\s. However, it can be shown that the perception of changes in dynamics is due to certain shifts in the positions of