Some examples of waveforms with the same power spectrum, different phases

[Mike Sulzer]

Thanks. I did learn Python some years ago, but made little use of it, and have forgotten much of it. But, I should be able to decode this anyway. The math syntax seems to resemble MatLab.

As for the various AIFF files, maybe others can use them as well. If so, if they aren't huge, it might be best to post them. Later, I can use them to cross-check my programming.

Mathematica can accept AIFF, but not MP3 just yet, though they say they will add this. (Mathematica does just about every scientific file format known.)

I tried to post the aiff files in the first post, but the forum does not accept them, nor any other lossless audio format, or so it appears. It does take zip archives according to the file list. I have not tried this yet, but will attempt to pack all of the aiff files into an archive and post that later today, time and forum permitting.

As said before, you are making too big an issue out of the mp3 format. The time and spectra plots of the mp3 files converted back to aiff show that the harmonics are there and in at least very close to the correct phase relationships. How could this hide potential differences due to phase? It is still a valid test even if the signals were not exactly what I intended.

[David King]

DropBox?

[Mike Sulzer]

Here are the aiff files in a .zip archive.

aiffFiles.zip

I tried to post the aiff files in the first post, but the forum does not accept them, nor any other lossless audio format, or so it appears. It does take zip archives according to the file list. I have not tried this yet, but will attempt to pack all of the aiff files into an archive and post that later today, time and forum permitting.

As said before, you are making too big an issue out of the mp3 format. The time and spectra plots of the mp3 files converted back to aiff show that the harmonics are there and in at least very close to the correct phase relationships. How could this hide potential differences due to phase? It is still a valid test even if the signals were not exactly what I intended.

[Joe Gwinn]

As said before, you are making too big an issue out of the mp3 format. The time and spectra plots of the mp3 files converted back to aiff show that the harmonics are there and in at least very close to the correct phase relationships. How could this hide potential differences due to phase? It is still a valid test even if the signals were not exactly what I intended.

Perhaps you are right, perhaps not. The issue is to reduce the areas of exposure. Said another way, the more complicated the path, the greater the number of possible critiques.

Although we are by down a few gears in the path, we still have the glories of a computer sound system.

[Mike Sulzer]

Perhaps you are right, perhaps not. The issue is to reduce the areas of exposure. Said another way, the more complicated the path, the greater the number of possible critiques.

Although we are by down a few gears in the path, we still have the glories of a computer sound system.

The issue is not whether there is some possibility that my test might have a flaw. Instead, it is whether you can find any test that shows that the phases of the harmonics in a musical type of waveform matter. Every moment you spent criticizing my test is time away from showing that.

[Joe Gwinn]

The issue is not whether there is some possibility that my test might have a flaw. Instead, it is whether you can find any test that shows that the phases of the harmonics in a musical type of waveform matter. Every moment you spent criticizing my test is time away from showing that.

Well, I wanted to listen, but I hope you are not expecting that these impromptu listening tests will settle a debate that has been around for decades, long before modern computer sound was invented.

[Mike Sulzer]

Well, I wanted to listen, but I hope you are not expecting that these impromptu listening tests will settle a debate that has been around for decades, long before modern computer sound was invented.

The matter is settled by default unless someone comes up with a pair of waveforms that meet the criteria as musical waveforms, with the claim that they differ in sound as a result of differences in phase. Then the testing begins.

Why? You cannot prove a negative. Nobody can prove that there is no such pair of waveforms. But it is easy to show that there is no significant difference in cases where there "ought" to be if phase matters. That is where the matter sits until someone makes a claim.

[Joe Gwinn]

The matter is settled by default unless someone comes up with a pair of waveforms that meet the criteria as musical waveforms, with the claim that they differ in sound as a result of differences in phase. Then the testing begins.

Why? You cannot prove a negative. Nobody can prove that there is no such pair of waveforms. But it is easy to show that there is no significant difference in cases where there "ought" to be if phase matters. That is where the matter sits until someone makes a claim.

Not so fast there. See "More on the world above 20 KHz - a reference" thread. There are references, from long before.

[Mike Sulzer]

Not so fast there. See "More on the world above 20 KHz - a reference" thread. There are references, from long before.

The important reference would be the one containing a description of a pair of music-like waveforms that claim to demonstrate the sensitivity of the ear/brain to phase. I did not see that in the references you refer to.

[Joe Gwinn]

The important reference would be the one containing a description of a pair of music-like waveforms that claim to demonstrate the sensitivity of the ear/brain to phase. I did not see that in the references you refer to.

Please define "music-like waveform" in mathematical terms.

[Mike Sulzer]

Please define "music-like waveform" in mathematical terms.

Included in "music-like waveform" are those which have a fundamental and harmonics in a frequency range useful for music. Such a waveform has a reasonably steady period, possibly after some transient behavior, during which the amplitudes and phases of the different harmonics do not change or change slowly. Excluded from this definition are waveforms in which the spectral content has huge changes in time on a scale similar to the the chirped waveforms posted earlier. Such waveforms can be made from other waveforms by changes in phase as a function of frequency. Such changes also can be clearly identified as time changes where different frequencies in the spectrum come and go at different times. On the other hand, the "music-like waveform" has all the harmonics present together, possibly decaying slowly at different rates, though. In this case, it makes no sense to talk about different time delays since the fundamental and harmonics emerge from the initial transient together, and it is necessary to describe the relationships between the fundamental and harmonics and among the harmonics as "phase". If you try to describe such a waveform by relative time delays, you have to pick an arbitrary reference. On the other hand, the chirped waveform has unambiguous delays between different parts of the spectrum.

The first post had two pairs of waveforms that are music-like by this definition, but have different phases between the members in the pair. It also had one of the other kind that can clearly be identified as time changes, even if created by changing the phase with frequency. The chirped waveforms presented later also can be created by shifting the phase of some other waveform, but the changes are best described as changes in the spectrum with time.

[Joe Gwinn]

Included in "music-like waveform" are those which have a fundamental and harmonics in a frequency range useful for music. Such a waveform has a reasonably steady period, possibly after some transient behavior, during which the amplitudes and phases of the different harmonics do not change or change slowly. Excluded from this definition are waveforms in which the spectral content has huge changes in time on a scale similar to the the chirped waveforms posted earlier. Such waveforms can be made from other waveforms by changes in phase as a function of frequency. Such changes also can be clearly identified as time changes where different frequencies in the spectrum come and go at different times. On the other hand, the "music-like waveform" has all the harmonics present together, possibly decaying slowly at different rates, though. In this case, it makes no sense to talk about different time delays since the fundamental and harmonics emerge from the initial transient together, and it is necessary to describe the relationships between the fundamental and harmonics and among the harmonics as "phase". If you try to describe such a waveform by relative time delays, you have to pick an arbitrary reference. On the other hand, the chirped waveform has unambiguous delays between different parts of the spectrum.

The argument is over what "a frequency range useful for music" might be, so it's circular to assume that one knows this in advance.

Nor is it given that all music is steady. Xylophones and gongs and triangles come to mind. Or even anvils and cannons. Or a snare drum.

[Mike Sulzer]

The argument is over what "a frequency range useful for music" might be, so it's circular to assume that one knows this in advance.

Nor is it given that all music is steady. Xylophones and gongs and triangles come to mind. Or even anvils and cannons. Or a snare drum.

It is a bad phrase that I chose. Can you suggest a better one for the definition that I made?

[Joe Gwinn]

It is a bad phrase that I chose. Can you suggest a better one for the definition that I made?

I cannot, and that's the point.

We instinctively know what does and does not sound musical, and over the millennia humans have collected and codified these observations into Music Theory. But Music Theory reads like a cookbook, and nobody has a clue why any of these rules work. But they do work, music is made, and life goes on.

And scientists remain puzzled.

[bbsailor]

I cannot, and that's the point.

We instinctively know what does and does not sound musical, and over the millennia humans have collected and codified these observations into Music Theory. But Music Theory reads like a cookbook, and nobody has a clue why any of these rules work. But they do work, music is made, and life goes on.

And scientists remain puzzled.

Joe and Mike

When I put my communication theory research hat on it appears that humans have evolved to separate the random nature of noise from the more harmonically unified nature of music which is more pleasing. This is complicated by the fact that a cannon shot can be considered noise but when well timed in a musical sequence, it can enhance a musical phrase and be considered musical.

Guitars were initially located in the rhythm section of big bands where only the initial quick attack of chords could be heard integrated into the rhythm patterns and add a subtle flavor to the sound. Over time guitars were amplified to allow guitars to be heard over the other instruments and even become featured lead players.

Almost everyone can tell the difference between an acoustic guitar sound and an electric guitar sound. The key research issue is what part of the guitar sound make the most difference in telling what type of guitar created the sound. I believe that the initial attack of the note or chord reveals the fingerprint of the sound source, acoustic or electric.

One test to confirm this would be to record the same sounds made by both acoustic and electric guitars and shorten the sample until it is difficult to tell the difference between acoustic or elecrtric sound sources. This will help confirm that the initial attack of a musical sound helps fingerprint the identity of the sound source.

As electric guitars evolved, adding clipping and distortion allowed guitars to sound like other instruments where the initial attack is less important, such as a sounding like a violin or a saxaphone or even a pleasing modulated sound wave.

High impedance guitar pickups have some interesting characteristics that may help to explain why the initial attack as it is harmonically related to the more immediate sustain is critical to accurately identify a sound source.

Early guitars were plugged into early PA amplifiers combined with a speaker in the same cabnet. This required the pickup to put out about 100mv to 200mv to adequately drive the input stage. The consequences of 5,000 to 6,000 turns of wire creates a pickup in the 2H to 4H range with coil winding capacitance and a guitar cable coax capacitance forming a resonance in the hearing range where the human ear is most sensitive.


Another consequence of this design is that the pickup coil is very low Q with DCR in the 5,000 ohm to 7,000 ohm range and a time constant (TC) defined by the coil inductance divided by the DCR. I believe that how the attack TC stays harmonically related to the sustain/decay sound also helps fingerprint the sound source (acoustic or electric) and also helps define what we perceive as pleasing.

This would be ideal graduate level research topic for a research thesis.

Thanks for bringing up an interesting topic.

Joseph Rogowski