奈米精密度雷射測距儀量測與比較吉他音色與音量之研究

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蘇冠丞(Kuan-Cheng Su) 查詢紙本館藏

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光電科學與工程學系

論文名稱

奈米精密度雷射測距儀量測與比較吉他音色與音量之研究
(Measurement and comparison of timbre and sound level of guitars using displacement sensor with nanometer precision)

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摘要(中)

樂器大多是以基音與泛音組合的聲音作為不同樂器音色的區分。每個樂器例如：吉他，都有自己的基音和泛音組合，造成吉他獨一無二的音色。
在本研究中，我們以古典吉他為標的，探討古典吉他Apoyando與Tirando的彈奏法的音色不同的原因。本研究由文獻得知，Apoyando的彈奏法較會引起垂直於吉他面板的絃的振動型態。Tirando的彈奏法較會引起水平於吉他面板的絃的振動型態。我們透過雷射測距儀，其位移量測精密度為30nm，取樣頻率為20kHz，量測吉他面板所產生的振動，並獲得其振動頻譜，可分析此兩種激發絃音方法在音色上的不同。我們發現，垂直於吉他面板的絃的振動型態(Apoyando)可引起基頻音的較大的振幅。水平於吉他面板的絃的振動型態(Tirando)，會引起較大的諧振音的振幅。如此造成兩種彈奏法音色上的不同。
吉他的結構是由音箱的形狀、木板種類、木板厚度、力木形狀等因素所影響。這些由音箱結構所決定的音色，是吉他音色的另一個來源。本論文提出於吉他音箱內部產生聲音脈衝的方法，用於量測在無絃狀態的吉他的基本音色。當演奏吉他時，吉他音箱的音色，與上述垂直或水平於面板的撥絃所生成的絃的音色的合唱，形成了吉他的音色。因此本論文的量測法，可分別獨立地針對音箱與完整的吉他分別分析其振動頻譜。
在本論文中，我們使用雷射測距儀對兩把吉他進行量測。其中一把為本實驗室自製之手工吉他，面板為Sitka Spruce雲杉，側板以及背板使用香絲焦檀。另一把吉他為1997年製西班牙 José Ramirez 3E，面板是Cedar，側板與背板是使用Rosewood。分別分析兩把古典吉他，以垂直或水平於面板的撥絃的吉他頻譜。也分析在無絃的狀態，音箱內聲音脈衝所造成的吉他振動頻譜。我們使用兩把吉他的頻譜，進行頻譜相似度與聲能比的計算。可以得到兩把吉他在音色上的相似度，與音量的倍率。這些數據可以給製琴師力
木與音箱結構修改的依據、樂器販售公司與吉他彈奏者性價比估計的依據。對於樂器的定價將可能有具體的幫助。
本論文所提出所使用的雷射測距儀與聲音脈衝量測法，均為非接觸式的方法。對於樂器的不會造成任何損傷。比過去文獻所提出的敲擊與加速規的量測法，提高了許多量測的安全性。本研究所提出的量測法的量測結果，可定量的比較各樂器的音色與音量。

摘要(英)

The combination of harmonics with different characteristics of the formants forms the timbre of the instruments. For the classical guitars, the timbre may be determined by the types of woods, the bracing and the shape of the body as well as the material of the string and the plucking condition to the strings, etc. The basic plucking methods of the classical guitars are Apoyando and Tirando which induce the perpendicular and parallel vibration of the strings to the soundboard. In this work, the timbres of the plucking method Apoyando and Tirando are investigated by the laser displacement sensor. The vibration spectrum of the soundboard can be obtained with a resolution of displacement of 30nm. The sampling frequency of the laser displacement sensor is 20kHz. The results show that the intensity of the fundamental notes for the perpendicular plucking is stronger than that for the parallel plucking. However, the harmonics for the perpendicular plucking is lower and that for the parallel plucking. This effet induces the timbre difference between Apoyando and Tirando.
The vibration of the soundboard for the guitar without sting is measured using the pulsed acoustic source positioned inside the body. The acoustic spectrum corresponding to the timbre of the pure body without sting can be acquired. As one plays the guitar, the chorus of the timbre of the pure body and that induced by stings forms the timbre of the guitar. In this study, we will independently study the timbres.
One home-made classical guitar and a 1997 Spanish José Ramirez 3E guitar are measured and compared in this work. We analyze the spectra of the two guitars for the perpendicular and parallel sting plucking to the soundboard. The similarity of timbre is calculated by the cross-correlation of the spectra for the two guitars. The sound energy of the two guitars is also compared.

In this work, we propose a novel and non-contact measurement method using the laser displacement sensor and pulsed acoustic source. The process prevents from the damage that might be induced by tapping and contact measurement using accelerometer. Our results can be used to compare quantitatively the timbre and the sound level of the guitars. This quantitative analysis might be helpful for luthiers to undertand the relation between the bracing and the timbres, for the guitar shop to price of the guitars, and for the comstomers to evaluate the price quality ratio of the guitars.

關鍵字(中)

★ 古典吉他
★ 雷射測距儀
★ 聲音頻譜
★ 振動頻譜分析
★ 音色
★ 音量
★ 止絃法
★ 跳絃法

關鍵字(英)

★ classical guitar
★ laser displacement sensor
★ acoustic spectrum
★ timbre
★ apoyando
★ tirando
★ sound level

論文目次

目錄
摘要 i
ABSTRACT iii
誌謝 v
目錄 vi
圖目錄 ix
表目錄 xiii
第一章、緒論 1
1-1前言與動機 1
1-2文獻探討 3
1-2-1音色的特性 3
1-2-2樂器音色分析的方法 6
1-2-3吉他振動量測方法 11
1-2-4有限元素分析 11
1-3研究方法 12
1-4結論 14
第二章、吉他理論背景 16
2-1聲音原理 16
2-1-1響亮度和分貝標度 16
2-1-2 聲音的頻率 18
2-1-3人耳對聲音的反應 18
2-1-4 聲音的傳播 19
2-1-5 聲波的波形與頻率 20
2-2吉他構造與性質 24
2-2-1 吉他各部名稱 24
2-2-2 吉他各部位木材材質 25
2-2-3 吉他音樑 27
2-2-4 吉他琴絃的構成 28
2-3吉他的聲學原理 30
2-3-1吉他的發聲與頻率 30
2-3-2十二平均律 31
2-3-3吉他觸絃方式 31
2-4物理力學 37
2-4-1應力 37
2-4-2應變 37
2-4-3應力與應變之關係 38
2-4-4吉他絃張力、絃重與波速、頻率間關係 40
2-5結論 42
第三章、吉他絃振動與模擬 43
3-1 振動頻率與阻尼 43
3-1-1吉他絃振動的頻率 43
3-1-2吉他絃振動的阻尼 43
3-2 COMSOL有限元素分析 47
3-2-1有限元素分析 47
3-2-2 COMSOL Multiphysics聲學模組 47
3-2-3軸向力彈簧元素分析 48
3-3振動模擬的物理參數 50
3-4不同有效絃長模擬 51
3-4-1水平面板撥絃 51
3-4-2垂直面板撥絃 52
3-5模擬結果分析 53
3-6結論 58
第四章、吉他絃振動實驗與頻譜分析 60
4-1實驗設備 60
4-2撥絃裝置設計 62
4-3實驗量測與頻譜資料 66
4-3-1 環境噪音量測 66
4-4實驗結果分析 67
4-4-1 吉他撥絃量測結果分析方式 67
4-4-2吉他撥絃量測結果分析比較 69
4-4-3水平、垂直撥絃與泛音分析 85
4-4-4不同吉他的聲能倍數與音色相似度分析探討 86
4-5結論 88
第五章、結論與未來展望 90
5-1結論 90
5-2未來展望 92
參考文獻 93

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指導教授

陳啟昌(Chii-Chang Chen)

審核日期

2021-8-20

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