Key Detection In Musical Signals Philip Brown, ’07 Advisor: Dr. Shane Cotter

Goals  Develop a Key Detection Algorithm  Implement Algorithm in Real Time  Create Stand-Alone Device to Perform Desired Calculations

Background  There are twelve musical notes  Each note is a frequency f and all other frequencies of 2f, 4f, 8f … 2^x*f  Keys are groups of musical notes that comprise most of the notes in a piece of music

Key Detection SignalWindow Spectrum Analysis Function Peak Finding Note Identification Data Storage Data Manipulation Data Summation Logic Statements Key Identification

Spectral Analysis  FFT vs. Constant Q  FFT: Spectral Data with uniform Frequency Resolution  Constant Q: Spectral Data with Exponential Frequency Resolution, Frequencies fall on Musical Notes

Problems With FFT 60 Hz Hz150Hz Intended Frequencies: Hz, 92.5 Hz, Hz FFT: 0.2s Window Samples/ second

Constant Q Intended Frequencies: Hz, 92.5 Hz, Hz Constant Q: b = 24 fo = 27.5 fmax = Samples/second 62.5Hz 92.5Hz146.83Hz

Problem!  Lower frequencies take longer amounts of time to calculate  In order to use Constant Q, these frequencies must be cut out  Key Detection Still possible in most cases

Key Detection SignalWindow Spectrum Analysis Function Peak Finding Note Identification Data Storage Data Manipulation Data Summation Logic Statements Key Identification

Peak Finding  Use for loops to find relative maxima of spectral content

Peak Find [frequency, amplitude] = Peakfind(signal,b,fk,minamp) Will find all peaks above minimum amplitude. For signal = constant q of 308.7, 617.4, and Hz sine waves. [frequency,amplitude] = Peakfind(signal,24,fk,minamp) outputs: frequency = [ ] amplitude = [ ] Which corresponds to the peak on the constant q plot.

Key Detection SignalWindow Spectrum Analysis Function Peak Finding Note Identification Data Storage Data Manipulation Data Summation Logic Statements Key Identification

Note Identification  Peak Finder outputs array of frequencies  Sorts through array of musical frequencies and find closest one  Takes amplitude of that note and add it to corresponding note in note matrix: [A Bb B C C# D Eb E F F# G G#]

Note Identification [notestrengths] = noteid(frequency,amplitude) Take previous example Will output: notestrengths = [ ]

Key Detection Music Signal Window Spectrum Analysis Function Peak Finding Note Identification Data Storage Data Manipulation Data Summation Logic Statements Key Identification

Data  Each Note Matrix stored Separately  Every time new matrix is added to data, oldest matrix is deleted  To calculate key, all Note Matrices in data are added  Logic Statements determine key by looking at notes with greatest amplitude

Key Detection Start with output of summation of note strengths: [ ] Set the 5 lowest to 0 [ ] Set the rest to 1 [ ] See if this matches any stored keys YES! Key is A.

Putting It All Together  MATLAB Program Implements All of these processes together to output Key vs. Time

Sample Data Key vs. Time Numbers Correspond to Different Keys Expected Keys: A, Key Change to Dm Keys Approximated: A,D,Dm

Problems  Key isn’t always correct  In some pop pieces, key is arguable  However, incorrect keys are generally 5ths of the expected key (as close as possible)  Some pieces have too many accidentals (notes outside of key)

Successes  Key changes are noticeable  Generally, one can determine the key from the output graph  In most cases, if the entire piece is examined, the findkey will output the correct overall key

Real Time  A 3 minute song takes 10 minutes to output key vs. time  Constant Q is very much like DFT  In order to process Constant Q in real time, need to relate it to FFT (possible future project)

More Accurate Key Approximation  Right now, key approximation takes into account 7 strongest notes, regardless of order  Attempts to account for fewer notes unsuccessful  More complicated logic statements could more accurately calculate key (possible future project)

What’s Next  Transfer code to C  Implement code on TI TMS320C6713 DSP Chipset  Tempo?

Acknowledgements and Questions  Thanks to Prof. Catravas for help on music theory  Any Questions?