在執行106年科技部計畫時，我們成功的使用了5個FZ-ARMA(4,6)模型去合成曾侯乙編鐘的鐘音，並使用Simulink 發聲，去測試較低不和諧度的新音階，並與原曾鐘的音階做比較。鑒於Simulink的操作本身是無法即時互動演奏的，所以我們需嘗試使用互動式電腦音樂軟體Max/Msp來發聲。因Max/Msp只有單一二階的Biquad Patch，並無更高階的IIR filter可用，且受限於演算的精度，之前的FZ-ARMA(4,6)模型在Max/Msp的環境下，會形成不穩定的系統而無法執行。因此我們提出了全新的名為直接弦波生成法，使用多個類似電話撥號音DTMF產生器的二階IIR濾波器並聯加總而合成。我們能以Msp完成在同一版面上可彈奏七個音的環境，此系統可達到Real-time操作與多音同時發聲，有效的提供新音階於彈奏樂曲的比較與分析之用。此合成演算法可較FZ-ARMA(4,6)法省一半的計算時間，且具模組化與可擴縮性(scalable)，很適合互動音樂的發展，並可應用在任一非和諧式樂器的合成與自然音效的模擬，以提供電腦音樂界作曲創意的發展工具。
This project is a followed up project of our project of last year. While synthesized the ancient Chinese chime-bells instrument from the Tomb of Marquis Yi of the Zeng State we had successfully used 5 FZ-ARMA(4,6) to complete the Bell tone by Simulink; however, we are not able to let the synthesis work right in Max/Msp environment. In Max/Msp there is only a biquad patch that can be used to represent a second order system. Our system model of 4 zeros, 6 poles system cannot be applied to Max/Msp directly. Therefore, similar procedure as we had done in last project that uses a tf2sos (transfer function to second order system) in Matlab to transform the ARMA(4,6) to three cascaded second order systems was applied. Unfortunately, even with this transform, it is still not possible running correctly in Max/Msp due to the Java sound precision limit has caused a critical stable system to become unstable. To resolve the long system order problem we are apt to parallel system model. This comes to a novel designed synthesis model called the DSG (Direct Sinusoid Generation) that uses parallel second order systems. The second order system was frequently used in DTMF (Dual Tone Multiple Frequency) for dial tone generation. Our preliminary test showed good resemblance of the bell tone and is executable in Max/Msp. It is real-time and can be polyphonic. For ease of interactive playing of the virtual instrument set we also need to design an interface system that allows us to play ‘keys’ on a paper sheet. A microcontroller using Arduino can easily be applied for this task together with some conducting paper pads. Our design strategy can be extended to any inharmonic instrument or nature sound effect synthesis which can be beneficial to computer music composers.
