Let me take a stab at giving this the 5 year old makeover.
Mr. Scavone is a very smart man who used fancy arithmetic to compare a skinny mouthpiece to a fat one where if the big open part was taped shut they would both hold the same amount of milk. His fancy arithmetic says that the skinny mouthpiece will have more high notes in its tone than the fat one. But, Mr. Scavone didn't find out if when you blow across the tops of the taped mouthpieces whether they make the same note or not. Mr. Scavone didn't even check to see if a cone without any ice cream in it that holds the same amount of milk when you blow across it would make the same note either. Silly Mr. Scavone. Now we know skinny and fat mouthpieces sound different, but we don't know if they both play in tune on all the notes of the scale. That's why we have to play with skinny and fat mouthpiece ourselves.
The theory goes like this: There are only two musically useful shapes for wind instruments that want to play more than one octave, and those are a cylinder and a cone. Only those two shapes have impedances (points of resonance) that are in integer relationships. So why is that important? I'll keep it as simple as I can.
When we play a note, there is a strong resonance point (impedance maximum)at the end of the horn, and then a series of other impedance maxima at points along the tube. What we want is for those points to be in integer relationships with each other. If we have a cone, the first partial (resonance point) is the length of the tube, because that is the easiest point for the horn to resonate (I'm simplifying JBT). For a harmonic series, we want the second one at half the length of the tube, the third at 1/3 the length, the fourth at 1/4 the length, etc. That is important. If the shape is wrong, then the impedance points in the tube will be in the wrong places. Now as long as the first resonance point is strong, it will force all the rest of the partials to be in harmonic ratio, even if they are pulled off their own resonance points. There is what is called a "regime of oscillation", where all the partials give or take depending on their energy, so that the note can sound with all the partials in line.
Now let's say we have a poor tube shape, and all the resonances are "out of line". The strong first resonance will always be at the end of the tube--or the first open tone hole, and it will pull all the rest into the correct integer relationships whether they like it or not. So generally speaking, no matter how much the tube shape is off, it won't affect the tuning of the first register: as long as the tone holes are in the right places it will play in tume.
But now let's hit the octave key , and break up that strong first partial so that the second partial becomes king of the hill. Once that happens, #2 will immediately shift to its point of strongest resonance, and if that is not in integer relationship with the fundamental (first partial), then the octave will not be in tune.
So if the shape is wrong, the most obvious thing that will happen is that the second register will be out of tune with the first. But something else happens as well. It takes energy for the strongest partial to hold the others in line, and if they are pulled off their impedance maxima, they become weaker, and there is a tug-of-war going on. The sound gets duller, the note is unstable, and the response is not good--the horn feels resistant.
So how do we make sure that the shape is correct? We can't. The ideal applies only to a full cone, and on a full cone there is no place to put a mouthpiece. We have to cut off the top of the cone, and once we do that, we throw all the partials out of line, and to different degrees. The first partial, comprising the whole cone, is the least affected, since the truncation (part cut off) is a smaller proportion of the length of that wave than for any other. The second partial is halfway up the cone, so the truncation becomes twice the proportion of the wavelength for that partial, and 3x the proportion for the third partial, etc. The partials get spread. What that means is that as the upper partials are pulled into line, they lose more and more of their energy.
But all is not lost! The closer we get the mpc to "appear" to the wave as the missing part of the cone, the more we get the partials back into line, so that they can contribute, rather than sucking energy from the sounding note. This all has to do with the wave timing. The math is nasty, but basically the wave travels faster as the diameter narrows. Now since the sax is quite a bit shorter without the missing apex of the cone, we have to make the mouthpiece wider than the neck. That way, when the wave leaves the neck and enters the mpc, it slows down, and we want to slow it down just enough that it will hit the reed tip at just the same time as it would if it were traveling right to the tip of the missing conic apex at full speed.
We want the mpc to mimic the missing conic apex. The first way to satisfy that condition is to have the volume of the mpc equal that of the missing conic apex. That makes the strong first partial very happy, as the timing is just right. But the higher we go up the tube, the less satisfactory that first condition becomes. The upper partials are better than if the volume were wrong, but the shape is still wrong, and the change in shape becomes more critical the shorter the wavelength. Now no way are we ever going to get the shape right, but there is a second condition that we can shoot to satisfy, and that is for the resonance of the mpc to match that of the missing tip.
If you were to take that cut off tip, and blow across the open end like blowing across a bottle, you would get it sounding a note. That is the Helmholtz resonance. I'm not going to get deep into it, but Helmholtz resonances can be changed for the same volume by varying the size of the opening as compared to the size of the inner chamber. For instance, if you blow across the top of a bottle, you can change the note depending on how much of the hole you cover with your lip. So by varying the size of the chamber as compared to that of the throat, you can change the Helmholtz resonance of a mouthpiece.
Just making the volume right (not easy for many reasons) will be pretty good until the upper half of the second octave, after that the Helmholtz resonance of the mpc comes into play. If the resonance is low, it will tend to make the high notes flat; if it is high it will make them sharp. If we are in the ballpark, then we should be pretty well in tune across the range of the instrument.
Here is where we get to the point in question: about mpc length. It's clear that we can have a longer mpc that has the same volume as a shorter mpc--we just have to make the inner diameter commensurately thinner. Theory says that in the first octave and a half or so, those two mpcs should play intonationally the same. But if the Helmholts resonance is different (which it will be, because the throat diameter is determined by the neck diameter), then above that they will not be intonationally the same.
What Scavone did was to model a short, fat mouthpiece and a long, thin mouthpiece. He did not match the Helmholtz resonances, because he wasn't interested in checking the intonation in the second octave. He wanted to know what it did to the tone quality. What he found was that the long mpc was brighter--had more high partials, than the short mpc. He attributed that to the fact that it more closely mimicked the shape of the missing conic tip, which meant that the timing for the higher partials was not off so much. By making the upper tube resonances more in integer relationships to the longer tube resonances, the higher partials we not so attenuated by being pulled off their centers.
So forget Scavone in terms of intonation. And the problem with checking Helmholtz resonance is that we have to blow across our mpcs at the point where the neck begins, and with the end the same diameter as the neck. If anyone is so inclined, I suggest this: take the end of an old neck or make something to resemble it, but make it very short: only long enough to allow a mpc to be put on it and removed. Now take the mpcs in question and put them on a functioning saxophone and record how deeply they neck is inserted for them to play in tune on the horn. Then insert the neck stub that same amount, seal the reed, blow across the end of the neck stub (or do a pop frequency test--better) and see if they have the same Helmholtz resonance frequency.
That won't be the actual Helmholtz frequency, but it will show if there is a differential between the Helmholtz frequencies of different mpcs. Theory says that all else being equal (which it never is), the lower the pop frequency, the flatter the high notes will be.
Was that somewhat clear? Questions?