Violin Timbre Analysis withMel-Frequency Cepstral Coefficients

Victor Ronchetti

ECE 272 Final Projectvronchet@u.rochester.edu

Abstract

Timbre Analysis serves to quantify the subtle color changes that make for an effective musical performance.What the human ear distinguishes easily requires some manipulation in the digital world. This paperexamines the abilities of the Mel-Frequency Cepstral Coefficient (MFCC) to distinguish between the timbreof different instruments, different violins, and three different types of violin playing. K means clusteringis used to sort the resulting data.

I. Introduction

The objective of this project is threefold. First,to verify that MFCC as capable of distinguish-ing different instruments by timbre. Second,to show the same ability is possible for twodifferent violins. Finally, to explore the effectof different types of violin playing on MFCCtimbre calculations to see if poor technique canreflect in a consistent MFCC grouping for amusical scale as compared with correct tech-nique.

The MFCC is based upon the raw Cepstrummathematical approach:

X[q] = IFFT(log|abs(FFT[x[n]])|) (1)

The MFCC involves filtering the magnitudespectrum through a set of overlapping triangu-lar filters based upon the mel scale:

Figure 1: Mel Filterbank

The general form for coverting between thefrequency and mel scale:

The magnitude spectrum in filtered, con-verted to the logarithmic scale, and, finally, con-verted to Mel-frequency Cepstral Coefficientsthrough the Discrete Cosine Transform. TheMel filter bank more realistically resembles thereal-life filtering of the human ear than the fullCepstrum spectrum.1 For this reason, MFCCis used in cutting-edge speech processing and

1Walker, J, The Use of Mel-frequency Cepstral Coefficients in Musical Instrument Identification. University of Limerick,Ireland. 2013. pg 2

1

mailto:vronchet@u.rochestere.edu

voice recognition applications. An instrumentwithin the range of the human voice, the violinshould be a good candidate for MFCC analysis.

II. Method

This project used parameters widely believedto be optimal for MFCC analysis: Hammingwindowed, frame length less than 100ms, sam-pled at 44,100kHz, around 14 coefficients cal-culated.2

Three tests were prepared. First, threedifferent instruments were compared usingMFCC analysis: a trumpet, a clarinet and aflute. A wide range scale was used for eachinstrument. Second, two different violins werecompared. Scales were recorded with vibratoand a tenuto bowing approach. Finally, oneviolin was recorded playing on three differentlocations on the string- the middle, towards thefingerboard, and towards the bridge.

Figure 2: Correct approach

Figure 3: Towards Bridge

Figure 4: Towards Fingerboard

2Lukasik, E. Long Term Cepstral Coefficients for violin identification. Poznan University of Technology, Institute ofComputing Science, Poznan. 2010. pg 1

2

III. Results

Figure 5: 2nd vs. 3rd MFCC: Blue - Trumpet,Yellow - Clarinet, Red - Flute

Figure 6: 15 MFCC blue- Violin 1, red - Violin 2

Figure 7: K means clustering MFCC 1st blue-Violin 1, red - Violin 2

Figure 8: 15 MFCC blue- middle, red - towardsbridge, cyan - towards fingerboard

3

Figure 9: K means clustering MFCC 1st blue-middle red - towards bridge yellow - away frombridge

IV. Discussion

The MFCC was a useful tool when comparingdifferent instruments by timbre. As Figure 5shows, the three instruments occupy almosttheir own area of the plot. It was expected thatmeasurements of the same type of instrument(two different violins) would be less distinctthan the first test. However, certain character-istics consistently occurred. Figure 6 showseach of the 15 MFCC coefficients for every noterecorded on the two violins. At the coefficientindex gets higher, the two values blend, butthe first seven coefficients indicate distinct dif-ferences - particularly the first coefficient. Kmeans clustering partitions data into distinctgroups, called clusters. When a two-cluster, kmeans cluster algorithm is performed on the

2-violin 1st MFCC data (Figure 7), the two in-struments partition virtually cleanly. Only 1data point is incorrectly grouped.

Analyzing the timbre differences of differ-ent technique on one violin proved even moresubtle than Test 2. As Figure 8 demonstrates,the MFCCs of the 3 playing techniques exhibitsignificant overlap. However, the first few CC’sappear to show some distinction. Once againK means clustering confirms this. Figure 9shows three bands of a data with three cen-troids marking the mean of the clusters. Here,4 data points (out of 18) have been incorrectlyclustered.

Producing good tone in scales is an integralpart of a musicians practice. Post-Analysis ofa recorded scale against a database of Profes-sionally recorded and processed scales couldhelp the beginner student when his teacher isnot around. Future work could include a realtime MFCC analysis so the playing would nothave to be post-processed.

References

[1] Jacqueline Walker, The Use of Mel-frequencyCepstral Coefficients in Musical InstrumentIdentification, Science Federation Ireland,2013.

[2] Ewa Lukasik, Long Term Cepstral Coefficientsfor violin identification, Poznan University ofTechnology, 2010.

[3] Jane Charles, Playing Technique and ViolinTimbre:Detecting Bad Playing, Dublin Insti-tute of Technology, 2010.

[4] William Brent, Cepstral Analysis Tools forPercussive Timbre Identification, Universityof California, San Diego 2010.

4

IntroductionMethodResultsDiscussion