Bringing Flute Pipes To Sonic Field

For this piece I really wanted a very sweet sounding flute pipe:

I found the sound I wanted in the strangest place. Sawtooth waves sound harsh; they can be tamed, but they are never sweet in the way I imagined the flutes to be. Nevertheless, by adding an extra parameter to a simple additive sawtooth generator flutes and strings suddenly appeared! 

In a sawtooth each overtone (harmonic) is scaled down as 1/n where n is the frequency ratio of the overtone. So, the 1st harmonic at 2 times the frequency has 1/2 the volume; the second harmonic at 3 times the frequency is 1/3 the volume. Now, raise that ratio of a power, say 0.5 or 2.0 and so forth. Low powers increase the harmonic content and a string sound appears, how powers decrease it and bright or sweet (even lower content) flutes appear. Here is the code:

def makeSimpleBase(length,frequency,z):

    p=random.random()

    if frequency>4000:

        sig=sf.Mix(

            sf.PhasedSineWave(length,frequency,p),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*2.0,p),(1.0/2.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*3.0,p),(1.0/3.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*4.0,p),(1.0/4.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*5.0,p),(1.0/5.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*6.0,p),(1.0/6.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*7.0,p),(1.0/7.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*8.0,p),(1.0/8.0)**z)

            )

    else:

        sig=sf.Mix(

            sf.PhasedSineWave(length,frequency,p),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*2.0,p),(1.0/2.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*3.0,p),(1.0/3.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*4.0,p),(1.0/4.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*5.0,p),(1.0/5.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*6.0,p),(1.0/6.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*7.0,p),(1.0/7.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*8.0,p),(1.0/8.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*9.0,p),(1.0/9.0)**z),

            sf.NumericVolume(sf.PhasedSineWave(length,frequency*10.0,p),(1.0/10.0)**z)

        )

    return sf.FixSize(sig)

def niceSaw(length,frequency):

    return makeSimpleBase(length,frequency,1.0)

def violaBase(length,frequency):

    return makeSimpleBase(length,frequency,0.5)

def sweetFluteBase(length,frequency):

    return makeSimpleBase(length,frequency,8.0)

    

def brightFluteBase(length,frequency):

    return makeSimpleBase(length,frequency,3.5)

def celestFlute(length,freq):

    sig=sf.Mix(

        sf.Pcnt50(sweetFluteBase(length,freq)),

        sf.Pcnt50(sweetFluteBase(length,freq+1.0)),

        sf.Multiply(

            cleanNoise(length,freq*0.5),

            sf.SimpleShape((0,-60),(64,-28),(128,-40),(length,-40))

        )

    )

    return pitchMove(sig)

def sweetFlute(length,freq):

    sig=sf.Mix(

        sweetFluteBase(length,freq),

        sf.Multiply(

            cleanNoise(length,freq*0.5),

            sf.SimpleShape((0,-60),(64,-30),(128,-40),(length,-40))

        )

    )

    sig=sf.FixSize(polish(sig,freq))

    return pitchMove(sig)

def brightFlute(length,freq):

    sig=sf.Mix(

        brightFluteBase(length,freq),

        sf.Multiply(

            cleanNoise(length,freq*0.5),

            sf.SimpleShape((0,-60),(64,-28),(128,-40),(length,-40))

        )

    )

    sig=sf.FixSize(polish(sig,freq))

    return pitchMove(sig)