Trinaural decoding equations for 3 speaker stereo matrix ?

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The basic TriField equations are :
L' = 0.5[(sin(phi) + w)L + (sin(phi) - w)R],
R' correspondingly, and
C = sqrt(2)cos(phi)(L+R)

A certain selection of phi and w should yield the trinaural amplitude relationships but I haven't tried to solve the eq's
EDIT: Once I progress to try a 3-way full TriField matrix with the coeffs that Gerzon recommends, and with DSP linear phase, I'll know....

The variables, phi and w, what are they?

I am guessing they are weights (perhaps vectors and not constants) that are a function of something ?
 
Those are just scalar weight constants.

Phi is sort of a "projection blend control" angle and is used from 15° to 75°.
90° gives no center signal and pure L/R, while 0° gives an M/S-decoding.

W is the stereo width parameter and is nominally 1, allowing for fine tuning.

See UsPat#5594800, fig4 and description.
 
Looking at some of the articles quoted in the thread, I am not sure I understand: where do 1st order low/high filters come into play? I thought matrixing was done at all frequencies, or is Trifield different ?

Are there actually 3-speakers solutions that do NOT assume that the center speaker is identical to L and R ? The approach sounds promising and I would like to test it, but not if it means another bulky loudspeaker in the middle. How about if the center would only reproduce >100Hz, would the concept still work and would it change the matrixing ?

Interesting thread, btw.


In Trifield the audio band is divided in two parts and both parts have a matrix but the coefficients are a bit different for each band. The transition freq is somewhere in few kHz.

I think there is no benefit to use a matrix at bass freqs (since bass is mixed mostly mono anyway), so it would be feasible to matrix satellite speakers and keep bass separate. Or as you say put bass only in side speakers and play them ordinary stereo at low freqs.

At the moment in my experimental system the bass is not matrixed below about 100 Hz. I don't see any problems with that.


- Elias
 
Personally I was thinking about linear phase filters because 1st order analog, while summing linphase, has 90° phase between bands, and acoustic centers of same bands are far apart (speaker-2-speaker distance) so the there could be some off-axis ill effects that might be avoidable with round kneed, gentle slope linphase filters with compact, non-ringing FIR kernels.

I'm FIR based anyway and integrating the Trifield matrixing would not cause any computational resource penalties... still waiting for my new coax drivers (4pcs) but then I'll be eager to try TriField and find out if it significantly betters the simpler Trinaural.


On the other hand, by using linear phase filters do you think you could arrive in same perception as with original Trifield matrix ?

I believe Gerzon did not just put some numbers in his articles and patent but they were based on extensive listening tests. I also assume his filters were not linear phase.

So if you change the filters you'll get something else perhaps but not Trifield ?


- Elias
 
In Trifield the audio band is divided in two parts and both parts have a matrix but the coefficients are a bit different for each band. The transition freq is somewhere in few kHz.

Thanks ! I've checked the Gerzon article again and I see it's all there, missed it the first time.
So basically the split is done to "strech" the higher frequencies further apart (less power goes to center, more goes to L and R)

I wonder if one cannot get a similar effect "built-in" the loudspeakers themselves by boosting the highs on the L+R and rolling them off for the center ? The whole should still sum flat and it's not exactly tri-field, but it could still work.


I think there is no benefit to use a matrix at bass freqs (since bass is mixed mostly mono anyway), so it would be feasible to matrix satellite speakers and keep bass separate. Or as you say put bass only in side speakers and play them ordinary stereo at low freqs.

At the moment in my experimental system the bass is not matrixed below about 100 Hz. I don't see any problems with that.

I see. Checked the article and he also explicitly says that below ~150 Hz you can suit yourself depending on the bass capability of your speakers, as the phi angle is uncritical.
So I'll give it a try sometime.
 
T
I wonder if one cannot get a similar effect "built-in" the loudspeakers themselves by boosting the highs on the L+R and rolling them off for the center ? The whole should still sum flat and it's not exactly tri-field, but it could still work.

Did some quick maths based on the paper.

For low freq (phi = 35 deg) you get:
C3 ~ 0.58(L+R) L3 ~ 0.78L - 0.21R (similar for R3)

For highs ((phi = 55 deg)) you get:
C3 ~ 0.40(L+R) L3 ~ 0.90L - 0.09R (similar for R3)

So you can't achieve exactly the same effect by rolling off the high freq on the center, because the phi also controls the "mix" in the L and R, but one might get away with rolling off the center ~3dB down above 5kHz and still getting a good effect, while avoiding additional high/low pass filtering in the matrix circuit.
 
If the conclusion is 3 channels/speakers is better than 2 speaker stereo, then yes. This was 80 years ago :eek:

Their conclusion was five speakers up front is optimal for mapping a frontal soundstage, three was the minium, and two was unacceptable.

This conclusion was the basis for movie theaters installing 5 speakers behind the screen - though it was shrunk to three in the early eighties.
 
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If the conclusion is 3 channels/speakers is better than 2 speaker stereo, then yes. This was 80 years ago :eek:

Their conclusion was five speakers up front is optimal for mapping a frontal soundstage, three was the minium, and two was unacceptable.

This conclusion was the basis for movie theaters installing 5 speakers behind the screen - though it was shrunk to three in the early eighties.
 
Must be weird kinds of music you are listening to. :eek:
I prefer music were - by and large - the harmonics roll off with rising frequency.

Rudolf


Sounds like a constructed case. Any specific recording that would contain such signals?


A metal plate hit by a wooden stick ;) In some music there is two metal plates hitting each others in a consecutive on-off manner ;)
 
A metal plate hit by a wooden stick ;) In some music there is two metal plates hitting each others in a consecutive on-off manner ;)

Then why is it that cymbals are amongst the instruments that generally can be localized best? They are not "split into the speakers".
The "instrument" you are talking about with "less signal energy at 1 kHz and more energy above 6kHz" is probably a steady-state test signal that doesn't resemble any real instrument.
 
A metal plate hit by a wooden stick ;) In some music there is two metal plates hitting each others in a consecutive on-off manner ;)
Those small metal plates at the top end of a vibraphone or marimbaphone are at f³ (english F6), which is nearly 1.4 kHz. Even if they were f4 (which is the highest f on a standard piano), it would be 2.8 kHz only. People often grossly mistake the frequency of high notes.

Rudolf
 
Elias was probably talking about a hihat. "two metal plates hitting each others in a consecutive on-off manner" would fit the description :)

Anyway, while Tri-something is interesting, the real question is what such an upmixing approach is supposed to do. Stereo unfortunately presents the listener with ambiguous cues and I don't think there's a benefit in presenting even more ambiguous cues over 3 speakers instead of two ;)
 
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Did some quick maths based on the paper.

For low freq (phi = 35 deg) you get:
C3 ~ 0.58(L+R) L3 ~ 0.78L - 0.21R (similar for R3)

For highs ((phi = 55 deg)) you get:
C3 ~ 0.40(L+R) L3 ~ 0.90L - 0.09R (similar for R3)

So you can't achieve exactly the same effect by rolling off the high freq on the center, because the phi also controls the "mix" in the L and R, but one might get away with rolling off the center ~3dB down above 5kHz and still getting a good effect, while avoiding additional high/low pass filtering in the matrix circuit.

Sooo, I gave a try to trinaural decoding, more or less as per Gerzon paper, with a phi around 45 degrees. My "implementation":
- main L and R speakers are dipoles using 6xFRS8 + Neo3PDR, crossover to bass is active
- In the crossover, I added a switchable simple circuit that does the matrixing as per Gerzon paper something like L-0.19R / R-0.19L
- for the center, I simply built another dipole panel with 4xFRS8. 2xFRS are connected in parallel and fed from L channel, the other 2xFRS8 fed from the R channel - they sum acoustically. Overall, given the different series/parallel connections of the FRS8 in the L/R/C, the center gives the acoustic sum of around 0.55(L+R), which is what the decoder should give. I measured the output to be sure. The center has no tweeter and slightly rolls off about 3dB above 5kHz, emulating the frequency dependent effect described in the paper.

Results: not to dismiss the whole thing yet, but am _not_ convinced. Having tried Ambiophonics at some point in time with the same speakers, I must say Ambiophonics did a better job.

Details:
- yes, the center image is there, stable and carved in stone no matter how you turn the head. But unfortunately there's a big "who cares" factor about this: the center image has been always dead sharp stable also without the center with my speakers ! Maybe in contrast to what some people might say about dipoles, mine have an excellent "phantom center".

- it might be that the sound stage is marginally more stable when listening off-center compared to standard stereo, but OTOH it is flatter, narrower and unconvincing(artificial) no matter where you sit compared to listening to normal stereo from the central listening point. So the trade-off is either a "rich" spatial perception in one single listening position(standard stereo setup) or a flat and weak one overall with trinaural, not a fortunate choice :( Spatial perception is an illusion and if the illusion is bad, then it's not really worth it IMHO.

- something weird seems to happen with the tonal balance, might be related to the combing of the rear radiation. It actually should be better with a center, but it's not, the sound is somewhat colored.

I'll do some more listening tests, including some stereo test tones. Maybe I got it wrong, maybe in needs more tweaking or maybe it simply does not work well with dipoles.

I wonder if the paper authors also used music for testing - did not find it explicitly mentioned. Because, you know, people don't listen to test tones..
 
Sooo, I gave a try to trinaural decoding, more or less as per Gerzon paper, with a phi around 45 degrees. My "implementation":
- main L and R speakers are dipoles using 6xFRS8 + Neo3PDR, crossover to bass is active
- In the crossover, I added a switchable simple circuit that does the matrixing as per Gerzon paper something like L-0.19R / R-0.19L
- for the center, I simply built another dipole panel with 4xFRS8. 2xFRS are connected in parallel and fed from L channel, the other 2xFRS8 fed from the R channel - they sum acoustically. Overall, given the different series/parallel connections of the FRS8 in the L/R/C, the center gives the acoustic sum of around 0.55(L+R), which is what the decoder should give. I measured the output to be sure. The center has no tweeter and slightly rolls off about 3dB above 5kHz, emulating the frequency dependent effect described in the paper.

Results: not to dismiss the whole thing yet, but am _not_ convinced. Having tried Ambiophonics at some point in time with the same speakers, I must say Ambiophonics did a better job.

Details:
- yes, the center image is there, stable and carved in stone no matter how you turn the head. But unfortunately there's a big "who cares" factor about this: the center image has been always dead sharp stable also without the center with my speakers ! Maybe in contrast to what some people might say about dipoles, mine have an excellent "phantom center".

- it might be that the sound stage is marginally more stable when listening off-center compared to standard stereo, but OTOH it is flatter, narrower and unconvincing(artificial) no matter where you sit compared to listening to normal stereo from the central listening point. So the trade-off is either a "rich" spatial perception in one single listening position(standard stereo setup) or a flat and weak one overall with trinaural, not a fortunate choice :( Spatial perception is an illusion and if the illusion is bad, then it's not really worth it IMHO.

- something weird seems to happen with the tonal balance, might be related to the combing of the rear radiation. It actually should be better with a center, but it's not, the sound is somewhat colored.

I'll do some more listening tests, including some stereo test tones. Maybe I got it wrong, maybe in needs more tweaking or maybe it simply does not work well with dipoles.

I wonder if the paper authors also used music for testing - did not find it explicitly mentioned. Because, you know, people don't listen to test tones..


Interesting results. So you tried Trifield, not Trinaural ;)

Ambiophonics is propably hard to beat by any method, if you are willing to remain sitting in the sweet spot all the time.

Would you try Trinaural next ? ;)

You can wire three speakers Trinaurally in a very simple way to form a matrix (abandon the input resistors in this case)

Ls = L - 0.5*R
Rs = R - 0.5*L
Cs = 0.5*L + 0.5*R

An externally hosted image should be here but it was not working when we last tested it.



- Elias
 
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Or the Dynaco method from the early 1960s
 

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