Waveform analysis/Doh ray me

Analyse a given section of monophonic audio waveform, for average pitch and output one of the sol-fa trigraphs (like these, except each has three letters) corresponding to average pitch level: Doh, Ray, Mee, Fah, Soh, Lah, Tee, doh.

Optionally, follow the trigraph with a plus or minus symbol, to indicate whether the note falls above or below the solfa. Extend the scale to cover 21 notes: DOH, RAY, MEE, FAH, SOH, LAH, TEE, Doh, Ray, Mee, Fah, Soh, Lah, Tee, doh, ray, mee, fah, soh, lah, tee.

A calibration parameter can be provided to suit different voices. This can be provided as a variable defined within the code.

Go

Clearly, this task is only feasible if you know how frequencies are encoded as bytes in the waveform and even then there are mathematical difficulties in reversing the procedure which mean that the eventual result is unlikely to be exact.

As an example, we analyze the .wav file (notes.wav) created by the [Musical Scale] task. As we know that the same frequency was used to generate each sample (44100 bytes), it is only necessary to examine a small number of bytes for each sample to determine the average frequency for the file as a whole (8 samples).

However, as each calculation was of necessity rounded to the nearer byte, it seems sensible to use more than one byte per sample (but not so many that the multi-valued arcsine function will be applied to a value outside its principal range) to try and reduce the effect of rounding. 20 bytes per sample is used here though curiously using only 3 bytes per sample would have produced a more accurate result (384.9 Hz).

Some optional aspects of the task have been ignored as they are not relevant to this particular example. <lang go>package main

import (

   "encoding/binary"
   "fmt"
   "log"
   "math"
   "os"

)

var (

   freqs = []float64{261.6, 293.6, 329.6, 349.2, 392.0, 440.0, 493.9, 523.3}
   notes = []string{"Doh", "Ray", "Mee", "Fah", "Soh", "Lah", "Tee", "doh"}

)

func getNote(freq float64) string {

   index := len(freqs)
   for i := 0; i < len(freqs); i++ {
       if freq <= freqs[i] {
           index = i
           break
       }
   }
   switch index {
   case 0:
       return "Doh-"
   case len(freqs):
       return "doh+"
   default:
       if freqs[index]-freq <= freq-freqs[index-1] {
           return notes[index] + "-"
       }
       return notes[index-1] + "+"
   }

}

func check(err error) {

   if err != nil {
       log.Fatal(err)
   }

}

func main() {

   file, err := os.Open("notes.wav")
   check(err)
   defer file.Close()    
   hdr := make([]byte, 44)
   _, err = file.Read(hdr)
   check(err)
   // check header parameters
   sampleRate := int(binary.LittleEndian.Uint32(hdr[24:28]))
   fmt.Println("Sample Rate    :", sampleRate)
   dataLength := int(binary.LittleEndian.Uint32(hdr[40:]))
   duration := dataLength / sampleRate
   fmt.Println("Duration       :", duration)

   sum := 0.0
   sampleRateF := float64(sampleRate)
   data := make([]byte, sampleRate)
   nbytes := 20
   fmt.Println("Bytes examined :", nbytes, "per sample") 
   for j := 0; j < duration; j++ {
       _, err := file.Read(data)
       check(err)
       for i := 1; i <= nbytes; i++ {
           bf := float64(data[i]) / 32
           freq := math.Asin(bf) * sampleRateF / (float64(i) * math.Pi * 2)
           sum += freq
       }
   }
   cav := sum / (float64(duration) * float64(nbytes))
   fmt.Printf("\nComputed average frequency = %.1f Hz (%s)\n", cav, getNote(cav))

   sum = 0.0
   for i := 0; i < len(freqs); i++ {
       sum += freqs[i]
   }
   aav := sum / float64(len(freqs))
   fmt.Printf("Actual average frequency   = %.1f Hz (%s)\n", aav, getNote(aav))

}</lang>

Output:

Sample Rate    : 44100
Duration       : 8
Bytes examined : 20 per sample

Computed average frequency = 387.1 Hz (Soh-)
Actual average frequency   = 385.4 Hz (Soh-)

Julia

Uses the LibSndFile library for WAV file reading and the DSP module's implementation of the ESPRIT algorithm to analyze the sound for its fundamental frequency. <lang julia>using DSP, FileIO, LibSndFile

const soundfilename = "Cscale3octaves.wav" const freq_to_solfa = Dict([ 130.81 => "DOH" 146.83 => "RAY" 164.81 => "MEE" 174.61 => "FAH" 196.0 => "SOH" 220.0 => "LAH" 246.94 => "TEE" 261.63 => "Doh" 293.66 => "Ray" 329.63 => "Mee" 349.23 => "Fah" 392.0 => "Soh" 440.0 => "Lah" 493.88 => "Tee" 523.25 => "doh" 587.33 => "ray" 659.25 => "mee" 698.46 => "fah" 783.99 => "soh" 880.0 => "lah" 987.77 => "tee" ]) const sfreqs = sort(collect(keys(freq_to_solfa)))

function closestfreqs(samples, fs=44100.0)

   pfreqs = Float64[]
   for sample in samples
       M = div(length(sample) + 1, 3)
       arr = [Complex{Float64}(x) for x in sample]
       narr = filter(x -> x > 0, esprit(arr, M, 4, fs))
       idx = argmin([abs(f - narr[end]) for f in sfreqs])
       push!(pfreqs, sfreqs[idx])
   end
   return pfreqs

end

function getchunks(soundfile, channel=1, timespan=0.1)

   sv = load(soundfile)
   fs = LibSndFile.samplerate(sv)
   samplespan, data = Int(round(timespan * fs)), view(sv, :, channel)
   return (fs, [data[i:i+samplespan-1] for i in 1:samplespan:length(data)-samplespan-1])

end

function makenotelist(soundfile, repetitionsneeded=2)

   changelist = String[]
   fs, samples = getchunks(soundfile)
   freqs = closestfreqs(samples, fs)
   reps, prev = 0, ""
   for freq in freqs
       note = freq_to_solfa[freq]
       if note != prev
           prev = note
           reps = 0
       else
           reps += 1
           if reps == repetitionsneeded
              push!(changelist, note)
           end
       end
   end
   return changelist

end

println(makenotelist(soundfilename))

</lang>

Output:

["DOH", "RAY", "MEE", "FAH", "SOH", "LAH", "TEE", "Doh", "Ray", "Mee", "Fah", "Soh", "Lah", "Lah", "Tee", "doh", "ray", "mee", "fah", "soh", "lah", "tee"]

Phix

Translation of: Go

Likewise analyses the output file of Musical_scale#Phix <lang Phix>constant freqs = {261.6, 293.6, 329.6, 349.2, 392.0, 440.0, 493.9, 523.3},

        notes = {"Doh", "Ray", "Mee", "Fah", "Soh", "Lah", "Tee", "doh"}

function getNote(atom freq)

   integer idx = length(freqs)+1
   for i=1 to length(freqs) do
       if freq<=freqs[i] then
           idx = i
           exit
       end if
   end for
   string res
   if idx=1 then
       res =  "Doh-"
   elsif idx>length(freqs) then
       res = "doh+"
   elsif freqs[idx]-freq <= freq-freqs[idx-1] then
       res = notes[idx] & "-"
   else
       res = notes[idx-1] & "+"
   end if
   return res

end function

object data = get_text("notes.wav") if data=-1 then crash("error opening notes.wav") end if integer sampleRate = bytes_to_int(data[25..28]),

       dataLength = bytes_to_int(data[41..44]),
       nbytes = 20, offset = 45

atom duration = dataLength/sampleRate,

    tot = 0

printf(1,"Sample Rate : %d\n", sampleRate) printf(1,"Duration : %s\n", elapsed(duration)) printf(1,"Bytes examined : %d per sample\n\n", nbytes) for j=1 to duration do

   for i=1 to nbytes do
       atom bf = data[offset+i]/32,
            freq = arcsin(bf) * sampleRate / (i*PI*2)
       tot += freq
   end for
   offset += sampleRate

end for atom cav = tot / (duration * nbytes),

    aav = sum(freqs) / length(freqs)

printf(1,"Computed average frequency = %.1f Hz (%s)\n", {cav, getNote(cav)}) printf(1,"Actual average frequency = %.1f Hz (%s)\n", {aav, getNote(aav)})</lang>

Output:

Sample Rate    : 44100
Duration       : 8s
Bytes examined : 20 per sample

Computed average frequency = 387.1 Hz (Soh-)
Actual average frequency   = 385.4 Hz (Soh-)

Raku

The input .wav file (notes.wav) is created by the [Musical Scale#Go] entry.

Translation of: Go

<lang perl6># 20200721 Raku programming solution

my \freqs = < 261.6 293.6 329.6 349.2 392.0 440.0 493.9 523.3 >; my \notes = < Doh Ray Mee Fah Soh Lah Tee doh >;

sub getNote (\freq) {

  my $index = +freqs;
  for (0..^$index) { if freq ≤ freqs[$_] { $index = $_ ; last } }
  given $index {
     when 0      { "Doh-" }
     when +freqs { "doh+" }
     default     { freqs[$index] - freq ≤ freq - freqs[$index-1]
                      ?? notes[$index] ~ "-" !! notes[$index-1] ~ "+" }
  }

}

my $file = slurp "./notes.wav", :bin or die;

my $sampleRate = Blob.new(@$file[24..27]).read-uint32(0,LittleEndian);

self-ref: [+] @$file[24..27].pairs.map: {$_.value*256**$_.key};

say "Sample Rate : ", $sampleRate;

my $dataLength = Blob.new(@$file[40..43]).read-uint32(0,LittleEndian);

self-ref: [+] @$file[40..43].pairs.map: {$_.value*256**$_.key};

my $duration = $dataLength / $sampleRate; say "Duration : ", $duration;

my Num ( $sum , $sampleRateF ) = ( 0e0 , $sampleRate.Num ) ; my $nbytes = 20;

say "Bytes examined : ", $nbytes, " per sample";

for @$file[44..*].rotor($sampleRate) -> $data {

  for (1..$nbytes) -> $k {
     my Num $bf = @$data[$k].Num / 32e0;
     my Num $freq = $bf.asin * $sampleRateF / ( 2e0 * π * $k.Num );
     $sum += $freq;
  }

}

my Num $cav = $sum / ( $duration.Num * $nbytes.Num ); say "Computed average frequency = ",$cav.fmt("%.1f")," Hz (",getNote($cav),")";

$sum = 0e0; $sum += freqs[$_] for 0..^+freqs; my Num $aav = $sum / +freqs.Num; say "Actual average frequency = ",$aav.fmt("%.1f")," Hz (",getNote($aav),")"</lang>

Output:

go run Musical_scale.go
file notes.wav
notes.wav: RIFF (little-endian) data, WAVE audio, Microsoft PCM, 8 bit, mono 44100 Hz
./Doh_ray_me.raku
Sample Rate    : 44100
Duration       : 8
Bytes examined : 20 per sample
Computed average frequency = 387.1 Hz (Soh-)
Actual   average frequency = 385.4 Hz (Soh-)