Reconstruct a Recording of a Bach Fugue

Use pitch recognition to construct an approximation of a signal

Start with a recording of a Bach fugue:

In[1]:=

fugue=

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Data in Notebook

;

Track and visualize the pitch of the signal using a neural network-based method:

In[2]:=

pitch=PitchRecognizefugue,Method"CREPE",

opts

;ListLinePlot[pitch]

Out[2]=

Define a function that performs the recognition using the

"SoundNotePitch"

property in

PitchRecognize

, deletes the missing values, splits separate notes appropriately and finally outputs a

Sound

object containing the reconstruction:

In[3]:=

audioToSound[audio_,instr_:"Piano"]:=Module[{notMissing,boundaries},notMissing=DeleteCases[Normal[PitchRecognize[audio,"SoundNotePitch",Method"CREPE"]],{_,Missing[]}];boundaries=Map[{#〚1,2〛,{#〚1,1〛,#〚-1,1〛},instr}&,SplitBy[notMissing,#〚2〛&]];Sound[SoundNote@@@boundaries]]

Use the function to reconstruct a

Sound

object from the original recording:

In[4]:=

audioToSound[fugue]

Out[4]=

Since the pitch information computed by

PitchRecognize

is completely symbolic, you can reconstruct the melody using any instrument available through

SoundNote

In[5]:=

audioToSound[fugue,"Violin"]

Out[5]=

Force

PitchRecognize

to return a discretized set of frequencies:

In[6]:=

pitch=PitchRecognizefugue,"QuantizedFrequency",Method"CREPE",

opts

;ListLinePlot[pitch]

Out[6]=

Give the time series to

AudioGenerator

to control the oscillator frequency:

In[7]:=

recon=AudioGenerator[{"Sin",pitch}]

Out[7]=

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Improve the approximation by incorporating amplitude data from the original signal, using

AudioLocalMeasurements

to track the maximum sample values:

In[8]:=

amp=AudioGeneratorAudioLocalMeasurementsfugue,"Max",

granularity

;recon=recon*amp//AudioNormalize

Out[8]=

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Denoise the audio signal by eliminating all components with small amplitude:

In[9]:=

denoised=AudioSpectralMap[If[Abs@#Value<10,0.,#Value]&,recon]

Out[9]=

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Compare the spectrogram of the original and the reconstructed signal:

In[10]:=

Spectrogram#,

options

&/@{fugue,recon}

Out[10]=

For fun, generate the tonal response to the first statement of the theme. Translate the sequence up a fifth, except for the first note, which will be raised by a fourth:

In[11]:=

split=GroupBy[Normal[pitch],Last]

220.

1,1;first=TimeSeriesMap#

&,TimeSeriesWindow[pitch,{0,split}];rest=TimeSeriesMap#

&,TimeSeriesWindow[pitch,{split+.001,pitch["LastTime"]}];pitchTonal=TimeSeriesInsert[first,rest];ListLinePlot[pitchTonal]

Out[11]=

Repeat the generation:

In[12]:=

tonalResponse=AudioGenerator[{"Sin",pitchTonal}]*amp//AudioNormalize

Out[12]=

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In[13]:=

Spectrogram#,

options

&/@{tonalResponse,recon}

Out[13]=

Publisher Information

Contributed by: Wolfram Staff

Reconstruct a Recording of a Bach Fugue

Related Symbols

Publisher Information