Concept for a more useful measure of musicality.

I've been thinking that the existing tests are too simple and don't emulate the complexity of real world music. It's my hypothesis that maintaining linearity across a complex signal with different amplitude signals at different frequencies is what is required for instruments to sound "real" since it will maintain the relationship between an instrument's fundamental tone and its harmonics.



I've created two sample files one minute long to demonstrate what I would like to see tested. They're all 24 bit 48kHz 2 channels.



Here are the two files:

http://ck.kolivas.org/LinearityTests/harmonic.flac

http://ck.kolivas.org/LinearityTests/nonharmonic.flac



The first I called "harmonic" is a set of summated sine waves of halving amplitude with a doubling of frequency at each step, starting at 25Hz. It is designed to emulate the fact that instruments have harmonics at various multiples of their fundamental frequency. Additionally distortion also tends to fall at exactly these frequencies in amplification and so on.



It has the following make up:

25Hz -6dB

50Hz -12dB

100Hz -18 dB

etc. till 12800Hz.

The following spectrum plot demonstrates the relative amplitude and discrete frequencies.

harmonic.png

Its waveform looks like this:

harmonicwave.png



The second file I called "nonharmonic" is a set of sine waves of halving amplitude at ever increasing frequencies that do not fall at multiples of the original, starting at 25Hz. This is designed to emulate the presence of multiple fundamental frequencies from different instruments at differing volume, and as distortion tends to fall at multiples of frequencies, it would be testing a different aspect to that of the first file.

Nonharmonic is more complicated with the following tones:

25Hz -6dB

48Hz -12dB

91Hz

173Hz

329Hz

626Hz

1189Hz

2258Hz

4291Hz

8152Hz

15489Hz



nonharmonic.png

Its waveform looks like this:

nonharmonicwave.png



What I envision is these two files could be used to determine a number of things.

One is the distortion of the two different synthesised sounds at different output levels from an amplifier (or other piece of equipment).

The second is the one I'm more interested in seeing and that is getting an accurate plot of the amplitudes of the various output frequencies and how it compares to the original, and seeing if that relationship is maintained at different output levels.



It's my theory that the relationship between the amplitudes of the various frequencies relative to the original input is what will determine if instruments sound real in the harmonic example, and the nonharmonic example will be measuring the underlying linearity without the effect of distortion which normally falls at harmonics. I'm not sure which of these would be more useful but I'd also like to believe they may reveal something about the character of preferred distortion by comparing the former to the latter.



Unfortunately, performing these tests is way beyond my means and expertise but I needed to put in writing what my thoughts were in the hope it stimulated thought - or even better - development in other ways of testing hi-fi.