Topic: All About Ambisonics

[Gutbucket]

^Mid/Side and ambisonics of any order.  Higher orders further extend the same basic relationship.  Mid/Side is sort of a sub-set of 1st order ambisonics, strongly constrained by the Mid pattern (W, and X channels are invariable, and no Z).

[Gutbucket]

In the dialog above there are two things I'd like to go over. Both concern the relationship between theory and practice / mathematics and perception.

Len posed this question to Kuba e-

With a single ambisonic mic decoded to XCY (again with hypercards), with the C mixed into both X and Y, what accounts for the directivity that we hear?

And with three traditional mono coincident hypercardioid mics pointed at +/- 65 and 0, with the 0 mic mixed into both left and right, what accounts for what we hear as left, right and center? What is that center mic doing?

Theoretically these are identical.  But in practice it depends on how well matched and behaved the patterns of the hypercardioids and how coincident they really are with each other.  A well calibrated ambisonics mic potentially allows for significantly greater accuracy in this regard than traditional mono mics.

Finally, move the right traditional mono hypercard to the right 17 cm. Mix them the same way as the coincident mics. What's the result? How does it differ from the coincident version of the array?

In this particular recording that Len is sharing with us, I slightly disagree with Gutbucket on one thing. It is a mistake to mix the left virtual microphone at 0 deg to the right channel. Comb filtering is created. It is much better to create a virtual microphone at 0 deg in the right microphone and mix it into the right channel. And if we do it this way, then we get back to that the resulting recording would be a near spaced pair of "supercardiods".

In the end the only thing that matters for music reproduction is how it sounds and connects with the listener, not easy clean math or the presence or absence of comb-filtering.  Its our own listening perception that provides final approval, not the academic position of Stanley Lipschitz.  The issue you describe might be problematic, but determining if it really is or not takes a subjective listening judgement. I'd need to go back and listen again, and ideally compare that against the alternate method you propose (which makes a lot of sense), to honestly determine which approach works best. 

In part of my recording array I regularly mix 3 supercardioids angled -45°, 0°, and +45° and spaced about 12-15" apart from each other down to two channels with very good perceptual results.  Even though mixing that 0° center channel in with the Left and Right is quite likely to produce some comb-filtering, and the virtual patterns generated in the L and R sums are not going to be simple, clean, well-behaved first-order patterns, it sounds good and does so in a repeatably way, making it all good as far as I'm concerned.

[Len Moskowitz (Core Sound)]

When we mix together any coincident virtual microphones at different angles in first-order ambisonics, we always get only one resulting microphone with a specific polar pattern (omni - fig.eight) in a certain direction.

That's true for mixing two orthogonally-placed first-order microphones, per M/S.

What happens when you have three or four, as in this case?

Previously I asked:

> With a single ambisonic mic decoded to XCY (again with hypercards), with the C mixed into both X and Y, what accounts for the directivity that we hear?
>
> And with three traditional mono coincident hypercardioid mics pointed at +/- 65 and 0, with the 0 mic mixed into both left and right, what accounts for what we hear as left, right and center? What is that center mic doing?
>
> Finally, move the right traditional mono hypercard to the right 17 cm. Mix them the same way as the coincident mics. What's the result? How does it differ from the coincident version of the array?

What do you think are the answers to these questions?

[kuba e]

Len, I'm sorry, I didn't mean my posts in a bad, confrontational way. Maybe the misunderstanding was caused by the translator, I only speak basic English. I really appreciate that we have a professional here on the forum, a manufacturer of amibsonic microphones. I really like ambisonics and I think it is very useful especially for people here who do on stage/ stage lip or ambience recordings. And why do I personally like ambisonic? I always liked to play with the recording and try different options. And since in most cases, I don't have the option of a rehearsal before recording and the microphone placement is limited, ambisonic is perfect for me.

I'm an amateur taper and unfortunately I've hardly been recording now. Since I only record as a hobby, I'd rather leave this great discussion to Gutbucket and you. I hope Gutbucket will join. For me, this discussions is very inspiring. It is an opportunity for me to understand ambisonic in depth. Thank you and Gutbucket.

[Gutbucket]

I'll take this up for Kuba e..

When we mix together any coincident virtual microphones at different angles in first-order ambisonics, we always get only one resulting microphone with a specific polar pattern (omni - fig.eight) in a certain direction.

That's true for mixing two orthogonally-placed first-order microphones, per M/S.

What happens when you have three or four, as in this case?

Essentially the same thing.  Assuming perfect coincidence, the specific first-order pattern produced and its orientation depends on the patterns, vector angles, signal levels, and polarities of the signals being mixed.  The two microphones needn't be orthogonal, and neither do more than two. We do need to know the vector angles but the microphones needn't be oriented 90-degrees to each other. Take the A-format to B-format translation as a four channel example.  Physically, A-Format is four cardioid patterns from which we can use relatively simple sum difference processing to produce B-format consisting of three orthogonal virtual bi-directional patterns and and omni (X,Y,Z, and W).. or any other combination of first order patterns that can be pointed in any direction.

Previously I asked:

> With a single ambisonic mic decoded to XCY (again with hypercards), with the C mixed into both X and Y, what accounts for the directivity that we hear?

Level differences in the Left and Right channels resulting from a virtual 1st order L/R coincident microphone pair.  The virtual polar pattern of the left channel is the result of the sum of the Left angled hypercard and the Center forward-pointed hypercard.  The angle between them is specified as 65 degrees, but their relative levels are not.  We know that the result will be a first order pattern somewhere toward the more cardioid side of hypercardioid, but to be more precise we'd need to know their relative levels. Assuming the L and R angled virtual hypercards have equal level, the Right channel will be a mirror image of the Left channel, except angled rightward rather than leftward.

> And with three traditional mono coincident hypercardioid mics pointed at +/- 65 and 0, with the 0 mic mixed into both left and right, what accounts for what we hear as left, right and center? What is that center mic doing?

Theoretically the same as the previous answer.  However because in the real word the three microphones cannot be arranged so as to be fully coincident, pattern consistency breaks down above a certain frequency corresponding to wavelength and the actual spacing between the capsules. Technically the same problem occurs in real world ambisonic microphone, yet because the capsules are arranged so as to be closer together, the threshold frequency at which this occurs is higher, and the errors (as messy as they are) manifest in a more symmetrically due to the geometrically-regular arrangement of the cardioid capsules on the faces of a tetrahedron.
 

> Finally, move the right traditional mono hypercard to the right 17 cm. Mix them the same way as the coincident mics. What's the result? How does it differ from the coincident version of the array?

The resulting directivity pattern will vary with frequency.  At low frequencies where the wavelength is long in comparison the the spacing between the microphones, the pattern will be similar to the rightward facing virtual pattern generated in the previous two examples.  At some midrange frequency where the relationship between wavlength and the spacing between microphones begins to become significant we'll begin see the virtual pattern begin to change shape.  As the frequency increases further we will begin to form deeper cancellation notches, then comb filtering with the teeth of the comb multiplying rapidly with increasing frequency.

This is exactly the same phenomena which occurs in both previous examples.  The important difference is that the spacing between microphone capsules in the third example has been made significantly larger, which causes the comb filtering to begin at a lower frequency where it is perceptually much more significant.  We can never escape this problem entirely, but we can seek to push it higher in frequency to where it is no longer perceptually significant.

This is why getting the microphone diaphragms as close together as possible is important for any coincident microphone technique, and why ambisonic microphones which have a tighter spacing between the four cardioid capsules are capable of generating well-defined virtual patterns the shapes of which remain accurate up to a higher frequency than one which uses a less tight spacing between microphone capsules.  Your Tetramic is superior to other ambisonic microphones by this measure.

[kuba e]

Thank you Gutbucket for the very nice explanation!