電吉他弦訊號傅立葉變換音頻 與音色的量化之研究

Abstract

本論文嘗試以不同於聆聽和演奏者的角度，透過傅立葉變換量化電吉他訊號，溫暖之於明亮，沉悶之於尖銳，客觀地分析量化不同音色的差別。本文依據十二平均律律法中幾何平均數演算，並經不同演算工具量化音源之頻率，更換不同材質及不同物理表面特性及材質的電吉他弦，錄音取樣後作傅立葉變換分析，數據顯示音頻裡的主要頻率及其諧頻的波形對照標準音頻波形的相似度，決定了樂器音色的主要穩定性與動態表現，分析波形的主頻率及諧頻與標準音頻波形面積形狀越接近，代表其音色越穩定;再者從主頻率及其諧頻的振福表現，可得知不同弦的音頻表現在高音頻的諧頻振幅越大，聲音特性趨於明亮，反之音頻表現在中低音頻的諧頻振幅越大，聲音特性趨於溫暖，音頻特性圖結果顯示不同表面特性的弦對音色和音頻有著極大的差異性，表面越是平滑的弦頻率和諧頻具有穩定的動態波形表現和較多的中低頻表現，反之不平滑弦其頻率和諧頻的動態波形表現極不穩定和擁有較多的高頻表現。

The thesis is designed to make differences between player and listener by fourier transformation. Warm tone is opposite of the bright tone. It could be defined as stuffy tone is opposite of the intense tone as well, and we should stay objective in the process of analysis. As per equal temperament, we use the 12th root of 2 to calculate and quantize the frequency of signal with different tools. Import the samples to perform fourier transformation. By replacing the string with different quality of material and surface, the data show up the similarity between wave form of main frequency and standard define the dynamic of music instrument. The tone will be more stable if the area of 1st harmonic and higher harmonics are similar to the standard harmonics. The tone tend towards being bright tone if the performance of harmonics in higher frequency is significant with different string. Otherwise the tone will be warm if the performance of harmonics in middle and low frequency is significant. The results of frequency characteristic diagram demonstrate the frequency and tone is statistically significant toward the strings with characteristic surface. The harmonics of flatwound string have stable wave form and higher performance in middle and low frequency. Otherwise the harmonics of roundwound string have unstable wave form and higher performance in high frequency. .