Key Detection In Musical Signals

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Key Detection In Musical Signals

• Philip Brown, 07
• Advisor Dr. Shane Cotter

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Goals

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

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Background

• There are twelve musical notes
• Each note is a frequency f and all other
  frequencies of 2f, 4f, 8f 2xf
• Keys are groups of musical notes that comprise
  most of the notes in a piece of music

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

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Problems With FFT
FFT 0.2s Window 44100 Samples/second
60 Hz
90-94.5 Hz
150Hz
Intended Frequencies 61.74 Hz, 92.5 Hz, 146.83Hz
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Constant Q
Constant Q b 24 fo 27.5 fmax 3520 44100
Samples/second
62.5Hz
92.5Hz
146.83Hz
Intended Frequencies 61.74 Hz, 92.5 Hz, 146.83Hz
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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

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

• Use for loops to find relative maxima of spectral
  content

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Peak Find
frequency, amplitude Peakfind(signal,b,fk,mina
mp) Will find all peaks above minimum
amplitude. For signal constant q of 308.7,
617.4, and 1648.1Hz sine waves. frequency,amplitu
de Peakfind(signal,24,fk,minamp)
outputs frequency 311.8 623.6
1664.9 amplitude 0.1229 0.1225
0.0742 Which corresponds to the peak on the
constant q plot.
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Key Detection
Spectrum Analysis Function
Peak Finding
Signal
Window
Data Storage
Data Summation
Note Identification
Data Manipulation
Logic Statements
Key Identification
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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

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Note Identification
notestrengths noteid(frequency,amplitude) Take
previous example Will output notestrengths
0 0 0 0 0 0 0.2455 0 0 0 0 0.0742
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Key Detection
Spectrum Analysis Function
Music Signal
Peak Finding
Window
Data Storage
Data Summation
Note Identification
Data Manipulation
Logic Statements
Key Identification
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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

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Key Detection
Start with output of summation of note
strengths 12 1 6 2 10 9 3 11 4 7 5
8 Set the 5 lowest to 0 12 0 6 0 10 9 0
11 0 7 0 8 Set the rest to 1 1 0 1 0
1 1 0 1 0 1 0 1 See if this matches
any stored keys YES! Key is A.
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Putting It All Together

• MATLAB Program Implements All of these processes
  together to output Key vs. Time

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

• Key isnt 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)

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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

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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)

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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)

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Whats Next

• Transfer code to C
• Implement code on TI TMS320C6713 DSP Chipset
• Tempo?

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Acknowledgements and Questions

• Thanks to Prof. Catravas for help on music theory
• Any Questions?