過去樂器多使用三色法(Tristimulus)來分析其音色。此方法使用了基頻與各階泛音的強度加成後的比例來定義音色的座標。此座標法在文獻中已用來分類音色對人的感覺。在本研究中，我們發現絃的基頻的振動在不同的量測中，有些基頻聲波封包隨時間呈現指數型衰減，有些卻呈現非指數型衰減。因此我們發現基頻本身的聲音亦會對音色造成影響，然而在許多絃樂器中，基頻的強度常是比泛音強了許多，因此一個絃樂器聲音的基頻音色可以是決定聲音音色的重要關鍵。故本研究針對古典吉他絃的基頻與音色關係進行探討。我們使用了有限元素分析法，模擬古典吉他第一絃的振動，我們使用的不同施力激發條件。我們假設了指甲的不平滑造成激發時施力隨時間的不均勻。計算出絃在施力激發後隨時間的振動。使用短時距傅立葉轉換發現，不平滑的指甲引所起的絃振動(基頻與所有泛音所引起的振動)，其振動隨時間波型封包為非指數型衰減。然而基頻的振盪僅觀察到頻率隨時間的飄移。在基頻隨時間的振動封包中，並沒有非指數型下降的現象。我們針對古典吉他第一絃、第二絃、第三絃實驗使用人造手指與馬達撥絃，錄下的聲音使用短時距傅立葉轉換，我們發現基頻並沒有明顯的飄移。但觀察絃的基頻隨時間振動的封包，卻有指數型衰減以及非指數型衰減的情形。本研究的結果，在假設指甲磨擦不均勻施力的條件範圍內，排除了非指數型衰減的情形是由於指甲磨擦所造成的。;In the past, the tristimulus was used for the timbre analysis of musical instruments. The intensity ratio between the fundamental oscillating mode and the overtones are used to define the coordinates in the tristimulus. The timbre can be approximately classified by the coordinates. In this study, we found that the different types of the vibration decay of the string at the fundamental frequency could significantly result in the different timbres. In our experiment by exciting the first, second and third strings of the classical guitar, at the fundamental frequencies, two types of decay, exponential decay and non-exponential decay, can be observed in the recorded sound. Different timbres can be sensed. Therefore, this study is aimed to understand the physical origins to excite the non-exponential decay of sound of the string of the classical guitar at the fundamental frequency. We suppose that the different types of string vibration decay result from the non-uniform force as the string slices on the rough surface of the nail. We use the finite element analysis method to simulate the vibration of the first string of the classical guitar under the different non-uniform excitation forces. The short-time Fourier transform (STFT) of the vibration is applied to analyze the vibration decay at the fundamental frequency. The significant frequency shift is observed. In this work, the sound of strings of a home-made classical guitar is recorded using an artificial finger controlled by a motor to pluck the strings. The exponential and non-exponential decay of the recorded sound can is observed. The origins of the non-exponential decay are exempted from the non-uniform forces induced by the nail supposed in the simulation of this study.
