"Total Aural Dissonance" - the proper metric?

Cheever recommends a "figure of merit" -- Total Aural Dissonance -- achieved by a dynamic intermodulation measurement -- as being more consistent with what the ear actually hears (and creates due to the self-harmonics in the ear.)

I read Cheever's Master's thesis (linked as a 1 meg PDF here: http://w3.mit.edu/cheever/www/cheever_thesis.pdf and was wondering whether anyone on DIYAUDIO wants to offer a critique? Cheever lays the blame at high negative feedback, btw.
 
i guess that there was some discussion on RAHE (rec.audio.high.end), and I don't really pay that much attention to the high end audio magazines.

i know from my wife's work in molecular biology (getting her PhD at age 55) the work which goes into a thesis or peer-review journal article is astounding -- it was so much simpler 30 years ago when I got my masters. she's been getting home every night ~10:00 pm -- maybe I should check to see if she has a paramour! javascript:smilie(':bigeyes:')
 
Some people here can't read - cheever's thesis was a master’s thesis submitted to University of New Hampshire

it's still embarrassing to some of us that Sussman gave it any attention but the cheever thesis pdf is merely hosted on one of mit's machines, hardly an endorsement by the institute
 
I think there may be some merit in the theory that some distortion can be masked if the non-linearity that causes it is similar to the way that human hearing is non-linear. (Brain-wave: that would explain the seemingly ludicrous and drunken notion of there being audible differences when changing the "absolute polarity" of loudspeakers, etc....)

I've done a few subjective and rather unscientific experiments before on this using a modular soft-synth, and I compared:

-a distorted sine wave with harmonics that decay nearly exponentially as frequency increases, where the 2nd harmonic is at around -40dB

with

-a distorted sine wave where 2nd harmonic is still the loudest distortion component, but this time it's at around -58dB, and the higher harmonics decay more gradually, forming a flatter "distortion floor".

The first sine wave actually sounded cleaner. I could still hear the harmonics, but there wasn't any obvious un-sine-wave-like distortion. It sounded close to a pure sine wave, like a whistle tone approximates a sine wave.

The second sine wave sounded like a purer sine wave except that it was marred by a trumpet-like sound playing the same tone in the distance.

I wouldn't want an amplifier that produces either of those 2 distortions though, because IMD was still obvious when playing more than one note. I don't think we should go back to the days of valves amps either. My cheap-n-nasty sound card had easily enough resolution for the above experiments, so there!

After reading that thesis for hours and hours, I felt a bit ripped off at the end because there weren't any real ideas on how to improve the sound quality of amplifiers, just a supposedly improved method of critiqueing other people's designs. Plus, I'm not fully convinced about being able to use aural masking to hide distortion. Surely the distortion products would therefore form new harmonics in our ears that would then be audible?

CM
 
Prune said:
Can anyone comment on the proposal in the link I posted?

Played the sound files before... seems like the idea is that it's important for the gain to be smooth and completely free of sharp glitches, even if it is a curve rather than a straight line. The worst-sounding files appeared to have simulated crossover distortion due to reduced gain near the middle.
 
Musical Dissonance Index

hi, I had a thought and it seems relevant to this thread...


Amplifier Specs and Musical Dissonance Index (MDI)

Ok so amp specs are pretty rubbish at portraying how well an amp plays tunes and maybe an amp with great specs suggests the designer has been barking up the wrong tree? Not surprising since specs currently used have no acknowledgement or consideration of musical tone, pitch or harmonic integrity.
We need an indicator of how well an amp portrays music rather than just another electrical/mathematical parameter. The Musical Dissonance Index (MDI) may do just that.

Dissonance is how bad, wrong, unmusical or 'out of tune' a sound is. Prof. Sarah Bolton describes it in her Physics of Musical Instruments lecture on YouTube.

YouTube

Watch from 50:30 to 53:30 and refer to the illustration at 52:30. It shows each harmonic (number below each note) with an indicator of how dissonant it is with the fundamental (the number above the note). See that some harmonics are simple octaves of the fundamental (2, 4, 8 and 16 harmonics) so have no dissonance (no number) with fundamental. Some harmonics are a different note to the fundamental but are part of the relevant chord so are still quite musical, eg the 3rd harmonic is musical 5th, so for a C fundamental the 3rd harmonic is G, a totally different note but which goes well with C so its dissonance number is only 2.

Another explanation of musical dissonance...

The fun starts at the 7th harmonic which is not in tune with any note, let alone the fundamental so its dissonance number is the highest so far at 31. Look at the 13th, 14th and 15th though! Erk! Musicians and instrument (eg piano) designers know to avoid or null out this musically destructive harmonic. You can see that whilst the 7th is highly dissonant at 31, the 8th is another octave above the fundamental and so is non-dissonant, hence its dissonance number is 0. Higher harmonics are statistically more likely to be dissonant but see that the 16th, a few octaves above, has a dissonance of 0 and is entirely musically consistent with the fundamental. Clearly each harmonic must be considered individually.

What we need is a weighting function (SPL values are already weighted, eg dB(A), to make them more relevant to how the ear/brain process sound). The function needs to multiply the amplitude of each harmonic of the distortion (from your distortion analyser fft) by its musical dissonance factor as shown on this illustration by Prof Sarah Bolton at 52:30. The sum of these products then gives the overall Musical Dissonance Index (MDI) as a quantitative indicator of how an amp preserves or corrupts musical tone.

More severe weighting than the linear MDI(lin) described above includes using the square of the dissonance factor. So MDI(sq) for say the 5th harmonic is its amplitude multiplied by 14 squared which is 196 times its amplitude. Note that, say, the 8th harmonic is still at 0 (amplitude times 0 squared), this is appropriate since it is the same musical note as the fundamental but a few octaves higher.

Given the low level of these distortion harmonics for an amp and the sensitivity of the ear/brain, a yet more severe weighting is to multiply the distortion harmonic amplitude by the dissonance factor in dB, MDI(dB). So the 4th harmonic amplitude is multiplied by 10 to the power 0, which is only 1(fair enough as its another musical octave), but the 7th is multiplied by 31dB which is 10 to the power 3.1 or a whopping 1259! This maybe seems excessive but the 7th must be seriously destructive to musical tone if all pianos are designed to null it out. Maybe amp designers should be doing the same?

Nothing magical here but maybe a spec relevant to how well your amp actually plays tunes? Maybe a useful tool for amp designers? What does an amp sound like when optimised for lowest MDI(lin/sq/dB)? Maybe this is what our grouping mechanisms have been waiting for?
 

PRR

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> fun starts at the 7th harmonic which is not in tune

This is far beyond the math ability of many folks here.

The overtones of a single string are one thing. The harmonics of a single sine-tone are another thing. Western music uses the Equal Tempered tuning which is a least-bad compromise for harmony in many keys (which are not an exact thing).

THEN consider that we never listen to single steady waves (which is kinda why we invented tempered tunings). Put two fundamentals through a nonlinearity and we get many-many "unrelated" partials all over the frequency spectrum (intermodulation). If you can put it to a display so you can use your eye's different analysis pattern it just looks like crabgrass. All of this can be mathed-out but it is pain in the pencil and doesn't immediately tell you anything useful like "put pixie-dust on Q5".

Yes, if you keep it simple and do single-tone Harmonic Distortion, you probably should weight the harmonics with a rising curve. What curve? And what if it makes our amp look bad next to others tested non-weighted? This ides is from before 1949 and has never caught-on.
 
fivekhz said:
Ok so amp specs are pretty rubbish at portraying how well an amp plays tunes and maybe an amp with great specs suggests the designer has been barking up the wrong tree?
A bold statement of a popular meme, with no evidence to support it.

We need an indicator of how well an amp portrays music rather than just another electrical/mathematical parameter. The Musical Dissonance Index (MDI) may do just that.
Any useful indicator will unavoidably be an electrical/mathematical parameter - unless, of course, the amplifier does not use any electronics. Such amplifiers are rare.

The fun starts at the 7th harmonic which is not in tune with any note
Yes, this is fairly well known. Any decent amplifier will have sufficiently low higher order harmonics. Achieving this does not necessarily require the presence of high levels of lower order harmonics, although some feedback haters will disagree.

Concentrating too much on particular harmonics can lead you astray. Harmonic distortion is almost inevitably accompanied by intermodulation distortion (the physics/maths requires this) and it is IM which often sounds worse.

This maybe seems excessive but the 7th must be seriously destructive to musical tone if all pianos are designed to null it out. Maybe amp designers should be doing the same?
You cannot null out a particular harmonic for all possible signal levels unless your amp includes an adaptive DSP. This is going in precisely the opposite direction from that advocated by the feedback haters! More complexity, more algorithms. Much simpler to simply ensure that all higher order distortions are suffciently low.
 
The Musical Dissonance Index (MDI) may do just that.

I have played (or tried to play) musical instruments since age 7. Anyone who has ever twiddled knobs on a music synthesizer, or taken a basis music theory class understands the relative consonance or dissonance of the harmonic series. With very few exceptions all IMD is dissonant. Power Chords heard in rock and metal guitar are chords designed such that the lower order IMD products are consonant, or nearly so.

So even with this new Index, why do two different amps with zero.nothing THD and IMD specs sound different, and why do tube amps with 1% or more 2H sound more pleasing than either to some listeners.

We can debate these kind of things forever, but the common theme that gets ignored is that most amplifier TESTING is done with a fixed load resistor and a static signal of one or more sine waves, or at most a periodic tone burst.

Most amplifier LISTENING is done with music having multiple signal sources (musical instruments) each with a wide range of amplitudes and frequencies.

The amplifier is loaded with a speaker that has a varying impedance which is TESTED and SPECIFIED with a signal having a single swept frequency at a constant amplitude. The result is given in an equivalent resistance, no phase angle info is given. Even when presented with single tone sine waves, the actual speaker impedance is a complex number (magnitude and phase angle) due to the inductive and capacitances associated with voice coils and crossover components.

This speaker will present a more complex and dynamically changing load when presented with complex music because the coil / magnet combination acts as a motor (coil moves cone) AND as a generator (cone moves coil). The speaker makes a good microphone too. Yes, it's listening to you...but it hears mostly it's own internal cabinet reflections, and sending this back to your amp. This counter EMF due to generator action (current from the speaker to the amp) is ALWAYS delayed in time due to the mechanics of the moving parts (finite reaction time) and internal reflection time.....Why do you think we stuff them?

The speaker's actual load impedance presented to the amp will not match its published specs when fed real music, and will change as the amplitude is increased (the more the voice coil moves, the more current it generates). The actual crossover frequencies will move with the music too. How the amp reacts to all this will depend on how it's feedback loop works, and how much feedback is used.

Obviously a zero feedback tube amp will not "react' to the counter EMF, but it's true frequency response will be dynamically changing due to the constantly varying load impedance.

A tube or solid state amp with a big bunch of feedback will present a near zero output impedance that effectively shunts the counter EMF, but the amp must still eat the associated current flow. Since this "reflected" current is not in phase with the "forward" current, a feedback term could still be generated, and will usually contain more higher order harmonics than the amp generates into a resistive load.

I am a (now retired) RF engineer who spent 41 years working at Motorola. We learned early on in the cellular world that a transmitter that measures near perfect on the test bench can (and DOES!) produce IMD products when installed on a tower with other transmitters. The RF energy from other transmitters on the same or nearby towers goes into the antenna, and backwards into the transmitter and it's feedback loop, causing IMD. Fortunately there are microwave devices called isolators that can stop the reverse RF. These unfortunately work only on a narrow frequency range and their size in inversely proportional to frequency.

We have RF test instruments called network analyzers that can measure the complex impedances of RF devices. They now exist for the audio frequency range, but unfortunately use a low level single tone test signal.

About 10 years ago I set out to find out just what the dynamic impedance of a "typical" speaker (my Yamaha NS-10M's) is, and what happens when you "turn it up." Unfortunately that rabbit hole got deeper and deeper with more and more diversions the further down the hole I traveled. After about a year of intermittent testing, I gave up with more questions than answers.

I made a setup to measure the voltage and current flow from and amp into the speaker using a DSO's two channels to capture info with real music test signals.

The NS-10's are nearly a pure resistance of about 24 ohms at woofer resonance of about 70 Hz. This explains the near perfect waveforms at 45 volts peak to peak that I was seeing across the speaker terminals from a single bass guitar note played through a 10 watt zero feedback single ended tube amp. 40 volts P-P into 8 ohms is 25 watts. 40 volts into 24 ohms is 10 watts, provided the amp does not clip.

On the other hand I believe their instantaneous impedance is very low, under 1 ohm, and possibly even negative (speaker is feeding the amp more that it receives) for the brief instant that a bass drum stomp tries to reverse the cone's motion during said bass guitar note. The bass guitar signal was recorded directly from the guitar, and the drum hit was pulled from a sample library in the DAW. I played with the relative timing of the two signals in the DAW.

I'm sure that there were many measurement errors especially in the dynamic tests, but the speaker DOES play a very big role in the amp's behavior, as does the music being played and it's volume level. The results were different with some DIY speakers.

I may revisit these tests at a later time....or I may not.....But....

Simple test. Hook up an amp to a resistive dummy load. Play a single sine wave into it. Connect a two channel scope (DSO preferred) to the amps input, and output, one channel on each. Drive the amp to a reasonable power level where you would play music. Adjust the scope so that the two sine waves lie on top of each other. This will obviously require reducing the gain a lot on the channel connected to the output.

If you scope has a math function, or the ability to invert one channel, then add them, you should be able to subtract the input from the scaled output leaving only the error signal on the screen. The gain of each channel can be increased in equal steps to magnify this error signal. The error should remain small for all valid input levels and frequencies.

Now feed the amp some real music, but leave the resistive load attached. Many amps will display a larger error when fed real music, not all amps are equal. You are now staring down the entrance to the rabbit hole.....

Remove restive load, attach speakers, repeat......try different speakers....Why is this happening? Welcome to the rabbit hole. There are many paths to choose, but.....there is no way out!
 
Author of thesis under "discussion" here. Quick rebuttal after 30 years

Oddly I never saw this. But maybe a good thing. Its now 30 years after i wrote this, and 15 years since the ugly posts.

1st...Making fun of the validity of work from UNH in general is plain ignorant. Maybe the intent was rather to make fun of "cow hampshire" as I now call it...I live in the Boston suburbs now. Principal EE CT front end electronics (read...all analog attoamp resolution circuits)

2nd there is an OBVIOUS hi-end trend toward more linear open loop amplifier circuits (read...low or at least lower negative feedback) because THEY SOUND BETTER. Fle power or supid high power. BTW I communicate with Nelson Pass and he always enjoyed my thesis. I’ve built zero feedback SS amps with his SIT fets...but never was able to cure DC stability at higher powers. I ended up with a 100uF series film cap the size of a small cat. But I would get runaway infront of the cap. An OPT does not help.

3rd…I’m busy right now and seemingly forever…need to write at least something. This this is not a thorough new post addressing every word of the previous posts.

Ok...here goes

In 30 years as an audio hobbyist I’m now still believing in this business of the ratio of HD3 to HD2 needs to be correct if the HD3 is above even 0.2%. Am I saying the ear-brain systems needs HD2 to mask the HD3? Who knows?

I now make a commercial product, if you call it that as I’ve sold only 3….I keep fiddling. It’s a 1.2W headphone amplifier that has an adjustment knob of the single ended triode grid bias on the front panel. On can adjust the harmonic content from very little (-60db of fundamental) to measurable at -25dB HD2…without negative feedback trickery. At AXPONA I won best in show. Herb Reichert of Stereophile was impressed. No one says its warm or bloated. Everyone seems to enjoy the dynamics and low fatigue.
Like my thesis DUT, my output is a single ended directly heated triode, a cheap version of a 45, whose transfer function makes HD3 at levels 3-10x below HD2, depending on where you are ‘riding the curve” ..thus that 3-10x user adjustable from the front panel.

Into speakers of >92 dB/w with a benign reactance the thing sounds ultr hi end. Dynamic. Natural cymbal wash. Holographic imaging. Muddy bass when pushed to mid volume.

So I built a speaker amp on the same topology with 4 parallel connected DHT. 0.75ohm output impedance and 6W. Sounds better than anything ive passed thru my lab…and I service a hi-end shops’ amplifiers. McIntosh, Krell, D’Agostino, Jadis. They dont sell 300B SE amps…so these are push-pull big amps. None as spatially exciting and fatigue free.

So sure people have made fun of my math for 30 years. Even the whole basis of the ear-brain systems of removing the natural HD of the ear being related at all to subjective sound quality. Duh is say.

No long rebuttals needed…I’ve got lots on my plate…but for sure ill get annoyed at another stream of words from someone who has not had a Passlabs amp or a SE amp in their system.

-Dan
 
Hi Dan,

I am not familiar with your work, but based on what I've read here it is in line with the work that we did many years ago. Both seem to indicate that high levels of feedback can be problematic. High feedback can cause the higher harmins to rise even while lowering the lower one (I mean it is all relative, but you get the picture.) I first learned this in Active Noise Control where we found that the system would do a great job of cancelling the fundamentals, but it often raised the harmonics. Subjectively this would null the effect since we tend to be more sensitive to harmonics further from the fundamental because of masking.

When I looked at amps using a unique test that would detect the harmonics below the noise floor I found many differences in amps. But the specs only show the levels of Signal plus noise, thus nulling out what I suspect are the actual problem areas.

And yes, I found the critiques to be unprofessional.
 
If you scope has a math function, or the ability to invert one channel, then add them, you should be able to subtract the input from the scaled output leaving only the error signal on the screen. The gain of each channel can be increased in equal steps to magnify this error signal. The error should remain small for all valid input levels and frequencies.

Now feed the amp some real music, but leave the resistive load attached. Many amps will display a larger error when fed real music, not all amps are equal. You are now staring down the entrance to the rabbit hole.....

Remove restive load, attach speakers, repeat......try different speakers....Why is this happening? Welcome to the rabbit hole. There are many paths to choose, but.....there is no way out!

Another test along these lines, but for speakers, is to look at the current and voltage in a Lissajou pattern. Theoretically what should result has to be an ellipse (a line and circle being ellipses.) What you get is anything but. The deviations from elliptical are due to the loudspeakers nonlinearity.