phase_accurate said:
Yes, it can change what the trafo will receive.
I think especially if you use Mains Earth (the third wire)
= Device GROUND.
If your setup of the power supply, trafo, rectifier, mains filtering
in a normal good manner, for audio use,
you will get close to DC output.
And surely such small effects that you here suggest
would be totally lost.
If your amplifier has got some PSRR, (power supply rejection ratio)
we are down maybe -40-80 dB further. ( 1/100 to 1/10.000 remains )
So the chances for anything else than some little ripple 100-120Hz
from the original mains signal to enter your amplifier
Is Extremely Small.
And if it does, you will have to have
Ears Like An Elephant
, or 24 carats Golden Ears ( what i know most 'golden ears' are only 15-16 carat GOLD )
to be able to hear any slightest, faintest thing of it.
After passing the magnetic field in a power (toroid) trafo
designed for to work as best at 50-60Hz.
(Audio trafos for 20-20.000 is something else, often used for input from microphones.
But also these are -3dB = damping at some frequency,just above 20kHz in best cases.)
If you are using such an transformer for Mains Power supply,
you are probably in for trouble.
If not dangers!
Besides what good is it with a power transformer
that will let higher frequency (above say 200 Hz) garbage pass
if your goal is to get good DC (0Hz) Output.
Will only make your
1. Rectifiers
2. LC or RC filtering
need to be more advanced.
lineup
Absolute polarity in the mains is a very interesting issue. I have not looked into it closely, but from some experience:
1. If you can measure an AC difference between the chassis of two equipment, reversing the mains polarity will allow you to find an arrangement to minimize this, and the results is slighlty more dynamics and cleaner sound.
2. Audible Illusions preamp I used do identify a preferred mains polarity on their power plug. Really don't know how they define ith though.
3. In transformers that have two or more non-center tapped outputs, using these in power amplifiers, the polarity between the two outputs do make a difference, very small though (unless your system has super good resolution). I suspect it's the flux modulation in the core when current is drawn that makes the difference.
1. If you can measure an AC difference between the chassis of two equipment, reversing the mains polarity will allow you to find an arrangement to minimize this, and the results is slighlty more dynamics and cleaner sound.
2. Audible Illusions preamp I used do identify a preferred mains polarity on their power plug. Really don't know how they define ith though.
3. In transformers that have two or more non-center tapped outputs, using these in power amplifiers, the polarity between the two outputs do make a difference, very small though (unless your system has super good resolution). I suspect it's the flux modulation in the core when current is drawn that makes the difference.
Most interesting discussion, where I must agree that there appears to be a case for absolute polarity. Only I am of the same opinion as rdf (and not being familiar with wiring in recording studios): I always thought that polarity out of your loudspeaker was absolute chance. Do we have any evidence that studios etc. actually care at all about this - though if microphones did indicate polarity they may have been wired the correct way simply out of ignorance (the installer might have thought they would blow up otherwise or such).
But I mainly wanted to enter just a few thoughts about (again) the role power supplies play. (And this is hi-jacking the thread somewhat, but as the door has been opened .....) Iwould rather refer to the position of mains plugs in wall outlets, as polarity where ac is concerned sounds a little strange. Yes, this could make a difference to "noise injection" as Phase_accurate explained, sometimes perceived as a sonic signal difference. This is fairly obvious depending on the internal wiring and transformer design and can easily be checked by injecting a noise source into the mains elsewhere. This is also a good check as to what degree one is getting rid of such interference. The way I found best is by having a screen between primary and secondaries, but judicious capacitor inclusion will also help - I think this is old hat to most here.
I do not quite understand what was meant by an "ac. difference between chasses". Are these not all connected together to the common "common"? Different earth leads earthed however can also create loops, but again this is probably old hat.
Regards
But I mainly wanted to enter just a few thoughts about (again) the role power supplies play. (And this is hi-jacking the thread somewhat, but as the door has been opened .....) Iwould rather refer to the position of mains plugs in wall outlets, as polarity where ac is concerned sounds a little strange. Yes, this could make a difference to "noise injection" as Phase_accurate explained, sometimes perceived as a sonic signal difference. This is fairly obvious depending on the internal wiring and transformer design and can easily be checked by injecting a noise source into the mains elsewhere. This is also a good check as to what degree one is getting rid of such interference. The way I found best is by having a screen between primary and secondaries, but judicious capacitor inclusion will also help - I think this is old hat to most here.
I do not quite understand what was meant by an "ac. difference between chasses". Are these not all connected together to the common "common"? Different earth leads earthed however can also create loops, but again this is probably old hat.
Regards
As soongsc noted this is not always tha case and not even always mandatory.
Edit: Forgot to mention that the worst culprit regarding the generation of mains interference is often sitting in the hi-fi rack: Beefy power amps ! I am not sure if every audiophile is aware of that !
Regards
Charles
Hi Soon and Charles (again),
I was not too clear on what I meant. If we are talking about different components of a hi-fi system, I would presume that all chasses are connected to the common of each component, and all of these are connected together via the screens of signal leads or otherwise. I recall vaguely that some equipment "earths" the chassis some other indirect way, but I never fancied the desirability of that. Earting the system as a whole properly is of course another matter - certainly not by running seperate (power cord) earths to wall plugs. But I was merely intrigued by "different" a.c. potentials between the chasses of components of the same system.
Regards.
I was not too clear on what I meant. If we are talking about different components of a hi-fi system, I would presume that all chasses are connected to the common of each component, and all of these are connected together via the screens of signal leads or otherwise. I recall vaguely that some equipment "earths" the chassis some other indirect way, but I never fancied the desirability of that. Earting the system as a whole properly is of course another matter - certainly not by running seperate (power cord) earths to wall plugs. But I was merely intrigued by "different" a.c. potentials between the chasses of components of the same system.
Regards.
cross posting from head-fi so I can attach the files
https://web.archive.org/web/20110101113016/http://www.ocf.berkeley.edu/~ashon/audio/primer1.htm does concentrate on phase coherence - some of the info supports absolute polarity discrimination - page down past the missing graphs
the 2nd harmonic relative phase shift test does amount to a test of polarity inversion audibility when the phase between the fundamental and the 2nd shift relatively by 180 degrees
don't confuse the 180 degree phase shift of symmetric waveform, 1/2 period delay with polarity inversion - polarity can only be seen with a asymmetric waveform - requires a specific harmonic structure
12 second 48k .wav of 200 + 400 Hz 1:1, with "alt" file alternating polaritiy every 3 seconds, 200 Hz + 400 Hz/90 degrees sines 1:1 amplitude
"same" is matched amplitude, frequencies, envelope but polarity doesn't change
haven't tried foobar2000 abx yet - because I can't hear a difference in "alt" sighted yet - but I'm somewhat distracted by the cliking in my left ear as my sinus intermittently blocks and clears
https://web.archive.org/web/20110101113016/http://www.ocf.berkeley.edu/~ashon/audio/primer1.htm does concentrate on phase coherence - some of the info supports absolute polarity discrimination - page down past the missing graphs
the 2nd harmonic relative phase shift test does amount to a test of polarity inversion audibility when the phase between the fundamental and the 2nd shift relatively by 180 degrees
don't confuse the 180 degree phase shift of symmetric waveform, 1/2 period delay with polarity inversion - polarity can only be seen with a asymmetric waveform - requires a specific harmonic structure
12 second 48k .wav of 200 + 400 Hz 1:1, with "alt" file alternating polaritiy every 3 seconds, 200 Hz + 400 Hz/90 degrees sines 1:1 amplitude
"same" is matched amplitude, frequencies, envelope but polarity doesn't change
haven't tried foobar2000 abx yet - because I can't hear a difference in "alt" sighted yet - but I'm somewhat distracted by the cliking in my left ear as my sinus intermittently blocks and clears
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back when my daughter still lived at home she played multiple instruments and played in the high school band. She always had her friends over, armed with a wide variety of musical waepons. I spent a lot of time recording their practice sessions with my PC and an early DAW (whatever version of Cakewalk was available in 1999). Most of the time I ran a mic directly into a 16 bit sound card.
I set up the system so that a positive pressure on the mic diaphram resulted in an outward movement of the speaker cone (Yamaha NS-10M Studio).
We experimented with all sorts of recording situations, and absolute polarity was usually not obvious as long as ALL of the mics were set up the same way. The only exception is the drums. The snare and the kick drum always sound better (more dynamic, or realistic) when the speaker cone moves toward the listener on the initial hit. Some listeners had a preference on the bass guitar if the player had a dynamic style, again the dynamics were percieved as more "in your face" if the cone moved toward the user as the strings were pushed toward the pickup.
If the dumb blonde one and a bunch of high school kids could figure this out, I would assume that a good studio engineer knows this stuff.
Most puzzling this.
One cannot doubt the conclusions of several experimenters even though it might be classed as anecdotal - and I do not do so now. The reporters are mostly well-known on this forum. (Micrphones 'set up the same way' - what is meant by that - surely there were distance differences from instruments to mic, thus phase differences?)
But: That would then mean that realism is set up during the first half cycle. What about some time afterward as any form of tone/timbre is only set up after a full cycle, probably several - by which time the information of a compression/rarefaction during the first half cycle is long lost. For a drum, one must also take into accout a delay between the initial movement of the side being hit and the other side (finite air velocity and delay, in terms of the wavelength) - not applicable for a kettle drum though. Thus physiologically quite puzzling. I can recall when Graham Maynard accentuated the importance of the first cycle here some years ago; equally puzzling.
Thus though the perception is accepted, the explanation is certainly not obvious. Anybody to expound on the physiological side of things?
One cannot doubt the conclusions of several experimenters even though it might be classed as anecdotal - and I do not do so now. The reporters are mostly well-known on this forum. (Micrphones 'set up the same way' - what is meant by that - surely there were distance differences from instruments to mic, thus phase differences?)
But: That would then mean that realism is set up during the first half cycle. What about some time afterward as any form of tone/timbre is only set up after a full cycle, probably several - by which time the information of a compression/rarefaction during the first half cycle is long lost. For a drum, one must also take into accout a delay between the initial movement of the side being hit and the other side (finite air velocity and delay, in terms of the wavelength) - not applicable for a kettle drum though. Thus physiologically quite puzzling. I can recall when Graham Maynard accentuated the importance of the first cycle here some years ago; equally puzzling.
Thus though the perception is accepted, the explanation is certainly not obvious. Anybody to expound on the physiological side of things?
look at the waveform in my recent post - even harmonics give asymmetry to even a continuous tone type waveform - descriptions indicate there can be a change in perceived timbre with this type waveform's polarity
a careful selection of Linkwitz-Riley XO and test frequency could cause substantial phase shift between fundamental and 2nd harmonic, amounting to inverting the polarity
but simply delaying, phase shifting the waveform as a whole can't change the polarity
a careful selection of Linkwitz-Riley XO and test frequency could cause substantial phase shift between fundamental and 2nd harmonic, amounting to inverting the polarity
but simply delaying, phase shifting the waveform as a whole can't change the polarity
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Granted there were differences worse than phase shift. There were different brands of mics of varying quality from good to Radio Shack junk. I tried to use a decent Shure mic for the drum experiments.....until I tried one experiment too many.....don't put the mic INSIDE the kick drum.
I had two identical Shure SM57's that I use for the snare and kick drum, or for micing guitar amps.
I spent a lot of time with drums, because my daughter was the captain of the marching band drum line, and most of the kids that hung out here were drummers. If you have been out on the field with the marching band surrounded by drummers, you know what real live percussion sounds like. It is hard to realistically duplicate that experience with speakers.
The polarity experiment was done two ways. In one test we swapped the speaker polarity, and in the other test, we swapped the wires inside the XLR connector on the mic cable. Some people claimed the results were not the same. This was predominant when using a SE tube amp. In this case the best results were obtained when the plate of the output tube was being pulled down on the initial attack.
These experiments all took place about 15 years ago. Looking back I am sure they were quite crude, and most definitely uncontrolled. There was one adult and 3 to 10 high school age musicians all learning about digital audio workstation recording and playback. My equipment at the time was crude compared to today. I don't remember if I had 2 or 4 record channels, but it was 16 bit 48 KHz.....and a Teac 3340.
If you want to do experiments on absolute phase audibility than an SE amp will introduce spurious results. This is because the dominant second harmonic generated by the amp does not invert when the signal is inverted. If this is of a similar order of magnitude to the second harmonic already present in the music signal then you will get noticeable enhancement or partial cancellation - which is likely to be audible but has nothing whatsoever to do with absolute phase audibility.
I'm sure you know this, but others may not. We don't want to have silly claims from others that apparent phase audibility from SE means that SE is 'more discriminating' when in fact the reason is that SE is 'more second-order distorting'.
I'm sure you know this, but others may not. We don't want to have silly claims from others that apparent phase audibility from SE means that SE is 'more discriminating' when in fact the reason is that SE is 'more second-order distorting'.
Also a SE amp typically has a different slew rate in each direction.
I have not figured out a way to reliably measure this, but you can sense the current in the output tube's cathode with a small resistor and a scope, and put a small resistor between the OPT and the load, connected to a scope.
When the tube's grid is hit with a large positive going transient the output tube is switched full on. This puts the power supply across the OPT primary (in series with the tube's Rp and the OPT's DCR). The (current) slew rate will be determined by the power supply's ability to charge the damped inductance of the OPT. When going the other way the tube is cut off, and the energy stored in the OPT discharges through the load.
The dynamics of an amp operating into a real speaker is a totally different matter that doesn't get much discussion.
By now most readers know that an "8 ohm" speaker isn't 8 ohms. Most speakers have a published curve of impedance VS frequency so we can look up the impedance at a particular frequency. This is good information, but these are steady state measurements with a swept sine wave.....I don't know too many people who listen to those.
Again, I have not figured out how to reliably measure this, but one scope probe across the voice coil, and the other across the small resistor in series with the voice coil will give you the E, and the I readings. Since we are dealing with reactive loads and AC there is a phase component. The voltage and the current are almost never in phase. It is possible to see AMPS of current while there is ZERO voltage across the voice coil and vice versa. The instantaneous speaker load is therefore a complex number. We are not only dealing with a complex impedance (R,L, and C all at once), but we are dealing with a load that can, and does generate energy of it's own. There is a coil of wire moving in a strong magnetic field....the speaker is a motor/generator.
Consider this case:
There are only two instruments, a drummer and a bass guitar player. Both instruments are recorded and later played back through a monitor system using typical HiFi speakers at high volume. The amplifier is a typical solid state design with near zero output impedance and can source all the current the speakers can eat. The bass guitar player hits a low "D" note at about 73 Hz and lets it ring out. The speakers are receiving a near sine wave at 73 Hz, which is near the resonance of the woofer and the speakers impedance is quite high, while cone movement is near Xmax. As the speaker cone is moving in one direction through the linear part of it's excursion, the drummer whacks the rim of the snare drum with his stick. This impulse can be in such phase as to act to instantaneously reverse the speaker cones direction, and loud enough to nearly clip the amp. The amp forces maximum current into the speaker in an attempt to reverse its cone travel in an instant.
What is the instantaneous impedance of the speaker at this point? This is one of those situations where you can see amps of current flowing into the speaker with near zero voltage across it.
The graph on my Yamahas says 18 ohms. I know there is some error in my measurement system, but I see about 16 ohms on the steady state looped bass guitar, but less than 2 ohms during the transient peak. I think this number is limited by the current limiting in the amp and the speaker mechanics. I believe I have seen instances of negative impedance...the speakers are feeding the amp. Try sine wave bursts near woofer resonance, the speaker is feeding the amp for several mS after the tone ceases.
Of course different amps handle this situation differently. I am using a cheap Chinese class D board which employs a TI TPA3116D2 chip. The non zero (and often reactive) output impedance of a tube amp adds more variables to the equation that I am trying to minimize. I run the 50 WPC amp well below clipping and try to avoid current limiting.
The situation varies with the phase relationship between the two instruments, and of course this will vary in a live music situation, and also varies in recording, mixdown, or sound reinforcement situations. I am experimenting with sound samples in a DAW where I can tweak the phase, and make what I want.
Note DAW = Digital Audio Workstation. Cakewalk Sonar, Ableton Live, and FL Studio are examples.
I have not figured out a way to reliably measure this, but you can sense the current in the output tube's cathode with a small resistor and a scope, and put a small resistor between the OPT and the load, connected to a scope.
When the tube's grid is hit with a large positive going transient the output tube is switched full on. This puts the power supply across the OPT primary (in series with the tube's Rp and the OPT's DCR). The (current) slew rate will be determined by the power supply's ability to charge the damped inductance of the OPT. When going the other way the tube is cut off, and the energy stored in the OPT discharges through the load.
The dynamics of an amp operating into a real speaker is a totally different matter that doesn't get much discussion.
By now most readers know that an "8 ohm" speaker isn't 8 ohms. Most speakers have a published curve of impedance VS frequency so we can look up the impedance at a particular frequency. This is good information, but these are steady state measurements with a swept sine wave.....I don't know too many people who listen to those.
Again, I have not figured out how to reliably measure this, but one scope probe across the voice coil, and the other across the small resistor in series with the voice coil will give you the E, and the I readings. Since we are dealing with reactive loads and AC there is a phase component. The voltage and the current are almost never in phase. It is possible to see AMPS of current while there is ZERO voltage across the voice coil and vice versa. The instantaneous speaker load is therefore a complex number. We are not only dealing with a complex impedance (R,L, and C all at once), but we are dealing with a load that can, and does generate energy of it's own. There is a coil of wire moving in a strong magnetic field....the speaker is a motor/generator.
Consider this case:
There are only two instruments, a drummer and a bass guitar player. Both instruments are recorded and later played back through a monitor system using typical HiFi speakers at high volume. The amplifier is a typical solid state design with near zero output impedance and can source all the current the speakers can eat. The bass guitar player hits a low "D" note at about 73 Hz and lets it ring out. The speakers are receiving a near sine wave at 73 Hz, which is near the resonance of the woofer and the speakers impedance is quite high, while cone movement is near Xmax. As the speaker cone is moving in one direction through the linear part of it's excursion, the drummer whacks the rim of the snare drum with his stick. This impulse can be in such phase as to act to instantaneously reverse the speaker cones direction, and loud enough to nearly clip the amp. The amp forces maximum current into the speaker in an attempt to reverse its cone travel in an instant.
What is the instantaneous impedance of the speaker at this point? This is one of those situations where you can see amps of current flowing into the speaker with near zero voltage across it.
The graph on my Yamahas says 18 ohms. I know there is some error in my measurement system, but I see about 16 ohms on the steady state looped bass guitar, but less than 2 ohms during the transient peak. I think this number is limited by the current limiting in the amp and the speaker mechanics. I believe I have seen instances of negative impedance...the speakers are feeding the amp. Try sine wave bursts near woofer resonance, the speaker is feeding the amp for several mS after the tone ceases.
Of course different amps handle this situation differently. I am using a cheap Chinese class D board which employs a TI TPA3116D2 chip. The non zero (and often reactive) output impedance of a tube amp adds more variables to the equation that I am trying to minimize. I run the 50 WPC amp well below clipping and try to avoid current limiting.
The situation varies with the phase relationship between the two instruments, and of course this will vary in a live music situation, and also varies in recording, mixdown, or sound reinforcement situations. I am experimenting with sound samples in a DAW where I can tweak the phase, and make what I want.
Note DAW = Digital Audio Workstation. Cakewalk Sonar, Ableton Live, and FL Studio are examples.
'Instantaneous impedance' is not a useful concept. You may see amps of current and near zero voltage (or vice versa) whenever inductance or capacitance dominates, so there is nothing strange about this.
Any resonator can temporarily 'feed' its source; this is not "negative impedance", but simply energy storage. The fact that a speaker is an electromechanical system does not introduce anything new. What is different is that a speaker is less linear than typical electronic components, and it is a bidirectional transducer so sound in the room can get back to the amp. Fortunately, most speakers are quite inefficient so they don't feed back very much.
Any resonator can temporarily 'feed' its source; this is not "negative impedance", but simply energy storage. The fact that a speaker is an electromechanical system does not introduce anything new. What is different is that a speaker is less linear than typical electronic components, and it is a bidirectional transducer so sound in the room can get back to the amp. Fortunately, most speakers are quite inefficient so they don't feed back very much.
I understand that you will have peak current with zero voltage or vice versa when operating into a pure capacitance, or inductance, but others may not.
Yes, a resonator can feed its source, and a speaker cone at resonance does qualify. This is why you can see the woofer's steady state impedance rise around its mechanical resonance point. The energy fed into the voice coil is in phase with the movement of the coil in the magnetic field. If the amplifier attempts to instantaneously reverse that motion, the momentum of the moving mass will fight that reversal. While technically not "negative impedance" the amplifier can be asked to supply more current than it will see into a short, or more voltage than it will see into an open for an "instant" if the timing is right.
A JBL D130 guitar speaker can generate about 1 volt peak to peak into an 8 ohm load when it's cone is pushed in and out a few mm. This is a significant amount when the source is a tube amp with an output impedance above 1 ohm. Many SE amps, including some of mine are in the 1 to 2 ohm range, and some pentode based P-P guitar amps with the "presence" control in the feedback path can go higher than that over a portion of the audio band.
The point that I was trying to make is that the phase, both absolute, and relative (instrument to instrument) can make audible differences in what the listener hears. I have tried to simplify my explanation for the average DIYer to the best of my ability without screwing up the technical details to much.
I am an RF engineer, I work with complex impedances daily, Or at least my computer does. I think that the actual impedance that a speaker imparts to the amp while playing real dynamic music at a high volume level and the interaction of that impedance with a real amp, requires math and physics far beyond my level.
There may be some small issues from room reverberation and speaker non-linearity, but the main issue is amplifier output impedance and its non-linearity and frequency dependence and how that interacts with the speaker impedance. I suspect that sometimes people get excited about the small issues before they have properly taken account of the main issue. Hence all the loose talk (which comes and goes, following the usual fashion cycle) about 'back emf' and feedback loops, when they are really just talking about output impedance.
When non-linearity is included you get into the world of Volterra series. Fortunately non-linearity is usually sufficiently small that it can be handled as a perturbation on a linear model.
Getting back to the subject of this thread, I think we need to carefully distinguish between 'absolute phase' (inverting the entire signal) and 'relative phase' (inverting some components, such as even harmonics). For some percussive sounds the audible difference may depend on whether you are in front or behind the instrument.
When non-linearity is included you get into the world of Volterra series. Fortunately non-linearity is usually sufficiently small that it can be handled as a perturbation on a linear model.
Getting back to the subject of this thread, I think we need to carefully distinguish between 'absolute phase' (inverting the entire signal) and 'relative phase' (inverting some components, such as even harmonics). For some percussive sounds the audible difference may depend on whether you are in front or behind the instrument.
still no activity re my polarity test fies? - admittedly I just put the files here because I couldn't link them to the discussion on head-fi
but as the discussion developed I did install foobar2000 and its ABX plugin and it turns out that I can hear the difference, just can't articulate it clealry - foobar2000 abx, motherboard Realtek HD sound, HD600 direct from computer headphone connector
I seemed to confuse some by citing phase distortion audibility papers - which oddly seems less controversial than audibility of absolute phase
so I prepared visual for showing how polarity of a 1:1 fundamental and 2d harmonic asymmetric test tone depends on relative phase of the components
I add a phase dependent offset (magneta) to the dynamic sum (sum in blue, magenta is "0" line for blue) to show the +/-90 plots mirrored about the x axis so polarity should be clear by eyeball
I move both the fundamental and the 2nd phase to center the +/-90 sum's peaks on the y axis - "48" in the algebra pane is just the value of alpha when I did the screenshot
the varying vertical offset is just a visual aid I hoped would make the sine harmonic addition picture easier to read - less lines crossing over to keep track of - our eyes are really happier looking at a mirrored figure/seeing the inverse symmetry when the "fold" doesn't have overlap, is based off the mirroring line
green, red should be very easily seen to be mirrored about the x axis == inverses, inverted in polarity waveforms just from shifting a sine and its 2nd harmonic
direct link to animated gif in case diyAudio "pickles" the image http://img.photobucket.com/albums/v252/f5r5e5d/polarity_zps3af73b48.gif
obviously the audio doesn't want the offset - see my earlier Spice sim waveform picture - which didn't seem to convince everyone
I did get one taker for a listening test over there so far
Testing audiophile claims and myths - Page 167
but as the discussion developed I did install foobar2000 and its ABX plugin and it turns out that I can hear the difference, just can't articulate it clealry - foobar2000 abx, motherboard Realtek HD sound, HD600 direct from computer headphone connector
I seemed to confuse some by citing phase distortion audibility papers - which oddly seems less controversial than audibility of absolute phase
so I prepared visual for showing how polarity of a 1:1 fundamental and 2d harmonic asymmetric test tone depends on relative phase of the components
I add a phase dependent offset (magneta) to the dynamic sum (sum in blue, magenta is "0" line for blue) to show the +/-90 plots mirrored about the x axis so polarity should be clear by eyeball
I move both the fundamental and the 2nd phase to center the +/-90 sum's peaks on the y axis - "48" in the algebra pane is just the value of alpha when I did the screenshot
the varying vertical offset is just a visual aid I hoped would make the sine harmonic addition picture easier to read - less lines crossing over to keep track of - our eyes are really happier looking at a mirrored figure/seeing the inverse symmetry when the "fold" doesn't have overlap, is based off the mirroring line
green, red should be very easily seen to be mirrored about the x axis == inverses, inverted in polarity waveforms just from shifting a sine and its 2nd harmonic
direct link to animated gif in case diyAudio "pickles" the image http://img.photobucket.com/albums/v252/f5r5e5d/polarity_zps3af73b48.gif
obviously the audio doesn't want the offset - see my earlier Spice sim waveform picture - which didn't seem to convince everyone
I did get one taker for a listening test over there so far
Testing audiophile claims and myths - Page 167
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I think these are too many issues which may effect the audibility of absolute polarity and phase of music. If other design performances are not addressed, it is hard to figure out what is right even when you do hear a difference. And as mentioned before, the polarity and phase of the recording process is equally important, but we have no control over.
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