樂譜不只是由表面上的音符所構成，在音符中還包含了許多隱含的訊息，掌握這些訊息後，演奏家可以知曉展示一個生動且富有情感表演的方法。呈現一個好的表演是任何演奏者夢寐以求的。為此，在音樂表演前劃分樂句是一個基本且不可或缺的任務。懂得劃分樂句，就可以知道如何控制音樂的節奏、速度、力度…等等，這些物理因素直接的影響音樂表情以及音樂情緒的表達。在古典音樂中，樂句是曲式分析中基本的組織，想要在音樂中找到樂句的位置需要具有音樂理論的基礎，其中和聲、調性和終止式是判斷樂句的三大要素。因此，本文提出一個自動分析和聲、調性以及終止式的方法。
首先我們改進現有的和弦分析演算法，透過一個簡單的樣本匹配系統找出和弦標籤與其相關成本；接著藉由音樂中的音階與順階和弦的特徵來判斷每個小節的調性；最後結合前兩步驟的和弦與調性之結果，以及休止符與長音的特徵來偵測終止式的位置。
我們擷取了古典時期的作曲家貝多芬、莫札特、海頓以及克萊曼蒂的奏鳴曲作為資料庫。所有的樂譜皆是由兩個專業的音樂老師手動標記，系統的分析結果與老師標記的解答進行比對，藉此驗證系統在各個特徵的精確度。另外，我們也將本論文所提之方法使用在Kostka和Payne所撰寫的音樂理論教科書所摘錄的音樂片段，並將其結果與別人的演算法進行比較。其結果顯示，該系統還不足以良好的將樂句劃分出來。
未來我們計畫整合旋律以及和弦進行的時間序列分析，並使用機器學習的方法，如隱藏馬爾可夫模型或者遞歸神經網路，以達到提高辨識和弦、調以及終止式的準確度。此外，我們應用樂音合成系統，針對每個樂句賦予不同的音樂表情，使樂曲的表現更加豐富。

A Score is not just the aggregation of notes. It contains much implicit information to guide a musician how to play the piece. Phrasing is the basics for a good performance because musicians have to control factors such as tempo, velocity and so on. These physical factors do affect the making of expression and emotion in music. In classical music, phrasing is based on lots of music theory and the most important one is music form analysis. In this thesis, computer analysis of key, chord and cadence which are the three major factors of phrasing is presented.
The modification of an existing chord analysis method is first presented. We applied a simple template matching method for labeling chords associated with the costs. Then, we use the features calculated based on the diatonic chords and the scales to identify the key for every bar. Finally, we combine features of chords, keys, note length and rest to detect the cadence positions.
Piano sonatas composed by Mozart, Haydn, Clementi and Beethoven are used to test our system. All the scores are manually annotated by two professional pianists. The proposed system is compared to the above ground truth. Besides, the examples presented in the book, “Tonal Harmony” written by Kostka and Payne, are also used. Though it is compared favorably to some existing methods, the performance is still not enough to produce good phrasings.
In the future, we plan to incorporate time series analysis of melody and chord progression using machine learning techniques such as HMM and recurrent network in order to more accurately identify the chords, keys and cadences. Then, it is possible to use different phrasings to synthesize various touching expressions from a score automatically.

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