以雷射測距儀量測古典吉他之音色

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姓名

林韋志(Wei-Chih Lin) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

以雷射測距儀量測古典吉他之音色
(Timbre measurement of classical guitars using laser displacement sensor)

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摘要(中)

吉他產生的音色主要取決於其腔體的振動特性（也就是吉他腔體的自然頻率和模態形狀），藉由激發琴弦的振動傳遞至琴橋，最後帶動整個腔體的振動，並由音孔發出聲音。從上述吉他發出聲音的過程中可以發現不論是弦的材質、張力，或是面板使用的木頭種類、面板厚度、力木結構等等，都會對吉他的音色造成影響，因此，在本研究中，我們將針對吉他腔體的共振頻率、不同張力的吉他弦對於音色的影響、不同位置撥弦對於音色的影響這三大主軸進行討論。
本研究最終的目標是以客觀的方式建立了一套古典吉他音色定義的方法。我們利用雷射測距儀測量吉他面板的振動，建立一套安全的非接觸式量測。首先透過氣球爆破實驗瞭解到每把吉他的自然頻率，並且設計了撥弦裝置，結合推拉力計和電控移動平台，建立了一套可重複且具定量性的撥弦系統。我們分析了撥弦位置和琴弦張力對音色特徵的影響，結果顯示，靠近下弦枕的撥弦位置會產生較強的Air resonance，和較低的弦音與Air resonance強度比例。另外，不同張力的琴弦對音色特徵的影響也會因吉他而有所不同。由於弦音、air resonance是古典吉他最強的兩個發音頻率，我們因此以Air resonance的頻率、Air resonance的品質因子、弦音與Air resonance強度比例為三個主要參數，構建了古典吉他音色空間的三維模型。透過計算兩點間的歐氏距離，我們能夠量化音色的相似性，並客觀評估和比較不同吉他的音色差異。本研究的結果為古典吉他音色的提供了一個量化的方法。

摘要(英)

The tone produced by the guitar primarily depends on the vibration characteristics of its soundboard, which includes the natural frequencies and mode shapes of the guitar cavity. Through the excitation of string vibrations, these vibrations are transmitted to the bridge, subsequently driving the overall cavity vibration and resulting in sound emission from the sound hole. It can be observed from the guitar sound production process that various parameters such as string material, tension, wood species used for the soundboard, soundboard thickness, and bracing structure, have an impact on the guitar′s tone. Therefore, in this study, three main aspects are investigated the resonant frequencies of the guitar cavity, the influence of guitar strings with different tensions on the tone, and the impact of plucking positions on the tone.
The main goal of this study is to establish an objective method for defining the timbre of classical guitars. We employ a laser displacement sensor to measure the vibrations of the guitar soundboard. This approach provides a safe and non-contact measurement setup.
Through the balloon burst experiments, we obtain the spectrum of the natural frequencies of each guitar. Furthermore, we design a plucking device that integrates a tension gauge and an electronically controlled moving platform, creating a reproducible and quantitative measurement system.
Moreover, we analyze the influence of the plucking positions and string tension on timbre characteristics. The results indicate that plucking positions near the bridge generate stronger air resonances and lower ratios of string tone to air resonance intensity. Additionally, the impact of different string tensions on timbre characteristics may vary among guitars.
Since the intensity of string tone and the air resonance are the two strongest peaks in the spectrum of eh guitar, we construct a three-dimensional model of the classical guitar timbre space based on air resonance amplitude, quality factor of air resonance, and the amplitude ratio of the string tone to the air resonance . By calculating the Euclidean distance between two coordinates in the three-dimensional model, we can quantify the similarity of tones and compare the timbral differences among different guitars. The findings of this study provide a quantitative approach for investigating classical guitar timbre.

關鍵字(中)

★ 古典吉他
★ 音色
★ 空氣共振
★ 聲響頻譜
★ 雷射測距儀

關鍵字(英)

★ Classical Guitar
★ Timbre
★ Air resonance
★ Acoustic Spectrum
★ Laser Displacement Sensor

論文目次

摘要 ii
誌謝 v
目錄 vii
圖目錄 ix
表目錄 xii
第一章、緒論 1
1-1 前言 1
1-2 樂器音色 3
1-2-1 音調和諧性（Tonal Consonance） 3
1-2-2 多維感知音色空間(Multidimensional Perceptual Scaling of Musical Timbres) 3
1-2-3 三刺激音色模型(Tristimulus timbre model) 5
1-3 吉他聲響時域上表現 7
1-3-1 頻譜包絡（Spectral envelope） 8
1-3-2 瞬態（Transient） 9
1-3-3 衰減（Decay） 9
1-4 吉他的聲響頻譜 10
1-4-1 諧波 11
1-4-2 腔體振動 13
1-5 結論 15
第二章、吉他結構與聲學 17
2-1 吉他基本構造 18
2-1-1 吉他各部位簡介 18
2-1-2 吉他力木(bracing)結構 21
2-1-3 吉他琴弦 23
2-2 吉他的聲學原理 25
2-2-1 吉他的發聲原理 25
2-2-2 基音與泛音 25
2-3 結論 28
第三章、古典吉他面板振動之量測 29
3-1 實驗架構 29
3-2 撥弦裝置介紹 32
3-3 實驗步驟 34
3-3-1 量測點與激發點 34
3-3-2 求施力原點並決定各條件下之位移、施力及作功 34
3-4 結論 37
第四章、實驗結果分析 38
4-1 撥弦實驗結果分析 38
4-1-1 吉他腔體的自然頻率 38
4-1-2 狼音 40
4-1-3 音孔共振 41
4-1-4 拍頻 43
4-2 利用Air resonance定義音色 48
4-2-1 撥弦位置對共振強度的影響 49
4-2-2 古典吉他音色空間 56
4-3 結論 60
第五章、結論與未來展望 62
5-1 結論 62
5-2 未來展望 63
附錄1：A吉他撥一～六弦頻譜 65
附錄2：B吉他撥一～六弦頻譜 67
附錄3：撥弦時的位移、施力及作功 69
參考文獻 73

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指導教授

陳啟昌(Chii-Chang Chen)

審核日期

2023-8-7

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