The short answer is planetary gear sets are constrained by the tooth count of the sun gear, ring gear, and planet gears as well as an additional constraint driven by the number of planet gears. The 8L90 uses 4 planetary gear sets with two linked mechanically or referred to as compound planetary gear sets. The four gear sets are used to make 8 forward gears and one reverse gear which means multiple sets are used for several gears. In the end, the constrained combination of gear teeth of each planetary gear set multiplied by the constrained combination of gear teeth in another planetary gear set determines the gear ratio in each gear which sometimes results in an unfavorable RPM drop between some gears...in the 8L90, that would be 4th and 5th gears. Keep following for the long answer but be warned it takes some spatial imagination, geometric progression recognition, intuitive math skills, and a warped mind.

First, we'll start with the GM patent for the 8L90:
http://pdfpiw.uspto.gov/.piw?PageNum...O%2Fpatimg.htm

The first drawing in the patent has all of the elements of the transmission for power flow and followed by 16 pages of text. The drawing in the patent is as follows:



The four gear sets are 16, 18, 20, and 22. It's a pretty difficult image/text to follow so let's simplify a little with a stick drawing:



The output shaft of the torque converter is the input shaft.
From the stick diagram, there are 4 simple planetary gear sets. The shift elements function as follows:
1) Brake A activation grounds the sun gears of gear sets 2 and 3.
2) Brake B activation grounds the ring gear of gear set 3.
3) Clutch C activation ties the input shaft to the sun gear of gear set 4.
4) Clutch D activation ties the ring gear of gear set 1 to the sun gear of gear set 4.
5) Clutch E activation ties the ring gear of gear set 2 and the sun gear of gear set 1 to the sun gear of gear set 4.

Additionally, the following rigid links exist:
1) The input shaft is rigidly connected to the planetary carrier of gear set 2.
2) The sun gear of gear set 1 and the ring gear of gear set 2 are connected together.
3) The sun gears of gear sets 2 and 3 are connected together.
4) The planetary carriers of gear sets 1 and 4 are tied together which in turn is the output shaft of the transmission.
5) The planetary carrier of gear set 3 is tied to the ring gear of gear set 4.

For 1st gear:
First gear is achieved by engaging both brakes A and B and clutch C. Engagement of brakes A and B locks the sun gear and the ring gear of gear set 3 to ground, which means the planetary carrier of gear set 3 is tied to ground as well. Since this planetary carrier is rigidly tied to the ring gear of gear set 4, this means the ring gear of gear set 4 is stationary. The engagement of clutch C ties the input shaft to the sun gear of gear set 4. This sets up an underdrive gear with a ratio of:

1st = (S4+R4)/S4 = 4.56
(S4 would be the sun gear in gear set 4 and R4 would be the ring gear in gear set 4.)

We know the gear ratio is ~4.56:1, and also that given the torque capacity requirements GM is using four planetary pinions for higher torque rating, therefore (S4+R4) has to be divisible by 4. Also (R4-S4) has to be an even number. A candidate tooth count is S4=29 and R4=103, which leads to a feasible arrangement with four 37 tooth planetary pinions and a first gear ratio of 4.5517:1, which is quite close to the known ratio. Since S4+R4 = 132 is divisible both by 4 and 3, for the lighter duty versions of the 8L family it is possible for GM to reduce the number of planetary pinions to 3 for applications that don’t quite require the 1000 Nm the 8L90 is capable of.

For 2nd gear:
To shift up to second gear, both brakes A and B stay locked, clutch C is disengaged, and E is engaged. Doing so connects the sun gear of gear set 4 to the ring gear of gear set 2. The sun gear of gear set 1 is grounded and the planetary carrier of gear set 2 is connected to the input. Therefore this sets up an overdrive cascaded with an underdrive.
Knowing the gear ratio, and methods similar to the 1st gear estimation, an estimate for tooth counts is S2=42, R2=78 with an 18 tooth planetary pinion. The ratio is:

2nd = (S4+R4)R2/S4(R2+S2) = 2.9586
Close to the known ratio of 2.97:1.

Since S2+R2 = 120, it is possible to put in 3 or 4 pinions.

For 3rd gear:
The shift up to third gear is accomplished by releasing brake A, and engaging clutch C. Therefore shift elements B, C, and E are engaged. By doing so, the ring gear and the planetary carrier of gear set 2 turn at the same speed as the input, and therefore the sun gear of gear set 2 also turns at the input speed. Since this sun gear is linked to the sun gear of gear set 3, and the ring gear of gear set 3 is grounded by brake B, the carrier of gear set 3 is under driven with respect to the input. Therefore gear set 4 acts as a mixer module, with the sun gear rotating at the input speed, the ring gear turning slower than the input, forcing the carrier to turn at a speed that is slower than the input. Knowing the gear ratio and methods similar to the 1st gear estimation, an estimate for tooth counts is S3=39, R3=77 with an 19 tooth planetary pinion. The ratio is:

3rd = (S3+R3)(S4+R4)/(S4R3+S3S4+S3R4) = 2.0745
Close to the known ratio of 3rd gear 2.08:1.

Since S3+R4 = 116, it is possible to put in 4 pinions.

For 4th gear:
The 4th gear up shift is achieved by releasing clutch C and engaging clutch D, i.e. shift elements B, D, and E are engaged. Engaging B and D at the same time means the ring gear and sun gear of gear set 1 spin together with the sun gear of gear set 4. Since the planetary carriers of gear set 1 and 4 are linked together, all 3 members of gear sets 1 and 4 spin together at the output speed along with the ring gear of gear set 2 and the planetary carrier of gear set 3. Since the ring gear of gear set 3 is grounded, this causes the sun gears of gear sets 2 and 3 to be overdriven with respect to the output by a factor of approximately 3. This causes gear set 2 to act as a mixer module, with the planetary carrier as the input and sets up an underdrive gear. The ratio is:

4th = 1 + [(S2R3)/S3(R2+S2)] = 1.6910
Actual 4th gear ratio is 1.69:1.

For 5th gear:
Fifth gear is achieved by releasing clutch E and engaging clutch C, i.e. shift elements B, C, and D are engaged. The fifth gear power flow is quite challenging to understand, bring your spatial imagination to the game. Since C and D are engaged, the following members turn at the input speed:
1.The ring gear of gear set 1
2.The planetary carrier of gear set 2
3.The sun gear of gear set 4

The planetary carriers for gear sets 1 and 4 are rigidly linked together and turn at the output speed. Ring gear of gear set 3 is grounded because brake B is engaged. This sets up the following kinematic states:
1) The sun gears of gear sets 2 and 3 are rotating at 2.16 times the input speed.
2) Since the ring gear of gear set 3 is grounded, the planetary carrier of gear set 3 is therefore spinning at 0.73 times the input speed.
3) Since the ring gear of gear set 4 is connected to the planetary carrier of gear set 3, gear set 4 becomes a mixer module with the sun gear spinning at input speed, the ring gear spinning at 0.73 times the input speed, and the planetary carrier being the output. Knowing the gear ratios, it is possible to back calculate feasible gear parameters for gear set 1. After a little bit of work, S1 = 39, and R1 = 77 with 19 teeth planetary pinions. The 5th gear ratio is therefore:

5th = [S1S3(R2+S2)(R4+S4) + S3R2(R4R1-S4S1) + R3S2S1(S4+R4)]/[S1S3(R2+S2)(R4+S4) + S3R2(R4R1-S4S1) + R3S2S1S4] = 1.2682
Actual 5th gear ratio is 1.27:1.

Gear sets 1 and 3 appear to be identical in terms of number of gear teeth.

For 6th gear:
Sixth gear is achieved by releasing brake B and engaging clutch E, i.e. the 3 rotating clutches C, D, and E are all engaged but both brakes A and B are open. This means all members of all 4 gear sets turn at the same speed as the input. The ratio is therefore quite simply

6th = 1.00:1

Since all planetary gear sets have "locked" gears, there is no relative motion between gears. With no power flowing through any gears, there is zero HP loss to gears meaning being in 6th gear is the most efficient gear to perform a chassis dyno assuming the dyno has a high enough speed capacity.

For 7th gear:
Upshift to seventh gear is accomplished by releasing clutch E and engaging brake A. The engagement of brake A grounds the sun gear of gear set 2, while the engagement of clutches C and D connects the ring gear of gear set 1 to the input shaft. The ring gear of gear set 2 spins approximately 1.5 times faster than the input because the sun gear is grounded, the planetary carrier is the input, and the ring gear is the output. Therefore gear set 1 acts like a mixer module, with the sun gear rotating at approximately 1.5 times the input speed (due to the rigid connection to the ring gear of gear set 1), the ring gear turning at the input speed, and the planetary carrier being the output. The ratio is therefore decided by the ratios of gears sets 1 and 2 alone

7th = R2(S1+R1)/[R2(S1+R1)+S1S2] = 0.8467
Actual 7th gear ratio is 0.85:1.

For 8th gear:
Eight gear is achieved by disengaging clutch C and engaging clutch E, i.e. shift elements A, D, and E are engaged. Engaging clutches E and D at the same time causes all 3 members of gear set 1 to rotate at the same speed, and since the planetary carrier of gear set 1 is also the output shaft, this means that the ratio is decided strictly by the gear teeth count of gear set 2. The sun gear of gear set 2 is grounded, the planetary carrier is the input and the ring gear is the output. The ratio is therefore:

8th = R2/(R2+S2) = 0.6500
Actual 8th gear ratio is 0.65:1.

For Reverse:
Reverse gear is achieved by locking both brakes A and B, and engaging clutch D. The sun gear of gears set 2 and the ring gear of gear set 4 are therefore grounded, the sun gear of gear set 1 spins at approximately 1.5 times the input speed (just as it does in 7th and 8th gears). The kinematic constraints imposed by the rigid link between the planetary carriers of gear sets 1 and 4, along with the actuation of clutch D which locks the ring gear of gear set 1 with the sun gear of gear set 4 causes the sun gear of gear set 4 to spin backwards at approximately 1.17 times the input speed, which means that the transmission output spins backwards but 3.908 times slower than the output

Reverse = [R2(S1S4-R1R4)]/[S1S4(S2+R2)] = -3.9080
Actual reverse gear ratio is 3.82:1.

Based on the available information, likely gear parameters for the 8L90 are:
Gear set 1: Sun gear S1 = 39, Ring gear R1 = 77, Planetary pinion gears P1 = 19
Gear set 2: Sun gear S2 = 42, Ring gear R2 = 78, Planetary pinion gears P2 = 18
Gear set 3: Sun gear S3 = 39, Ring gear R3 = 77, Planetary pinion gears P3 = 19
Gear set 4: Sun gear S4 = 29, Ring gear R4 = 103, Planetary pinion gears P4 = 37


To reiterate what I said in the short answer above: as constraints for one gear set are chosen and combined with other gear set constraints plus compound planetary gear sets, you're limited in what gear ratios you can have and sometimes you have to make compromises to come up with the best combination of gear ratios for all gears. Having only one gear in the 8L90 with a less than optimal ratio isn't too bad all things considered. Hopefully this explanation answers your question and doesn't make things more confusing...