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update first and second chapters

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\section{Conclusions}
\label{sec:conclusions}

This paper has presented a novel experiment to investigate pitch accuracy and interaction in unaccompanied duet singing. 14 female participants sang two pieces of music in two test conditions (unison and duet) and three listening conditions (solo, simplex, duplex). 

According to the results, we determined that the following factors influence absolute pitch error: test condition, listening condition, vocal part, score harmonic interval.
1) In particular, singing in unison condition has 5 cents mean absolute pitch error less than duet condition and unison condition has 18 cents less mean absolute harmonic interval error less than duet condition. 
2) It was found that sing with a partner is more difficult to tune the individual pitch and interval, but easier to sing the interval between singers. Solo singers make less pitch error than singers who could hear their partner (8 cents). 
3) The factor of score interval has a significant effect on MAHIE. Perfect $5^{th}$ score melodic interval had the largest MAMIE and tritone score harmonic interval has the largest MAHIE. 

We tested the positive correlation relationship between pitch error of dependent singers and independent singers in simplex condition. MAPE of dependent singers adds 48 cents if MAPE of independent singers increase one semitone, while MAMIE of dependent singers growth 20 cents when MAMIE of independent singers gains one semitone.  

As for pitch stabilizability, it shows more stable in unison condition than duet condition, more stable in independent singers than dependent singers. 

Finally, we modeled pitch accuracy with multiple factors of influence in order to measure the effect size of each factor. The results indicate that pitch accuracy was influenced by various reasons. Many aspects of the experiment remain to be investigated, but we hope that current consequences take us one step closer to comprehend the interaction between duet singers.



\section{Data availability}
\label{sec:dataavailability}
The code and the data needed to reproduce our results (note annotations, questionnaire results, score information) are provided in an open repository at {\small{https://code.soundsoftware.ac.uk/projects/pitch-accuracy-and-interaction-in-unaccompanied-duet-singing/repository}}.