Are there any casstettes with that kind of progression available for universal use (close ratio for high speeds and wide for climbing). All I see is MTB cassettes with close ratio granny gears and wide gear steps at upper range or road cassettes with tight overall spacing. Only campagnolo ekar is the the most similar currently, but comes with otherworldly price.

custom cassette

custom cassette 2

No mtb cassette, but 12s road cassette with the same spread. Like shimano 12s 11-34 or 11-34, or SRAM 12s 10-33 to name a few.

I don’t see anything linear about that gearing.

These examples are not really linear, but they're close. When the number of teeth between steps increases by first 1, then 2, 3, and at the largest cogs by up to 13 teeth, the difference in drive ratio is not as far from linear as it might seem. That's because as a percentage, the increasing number of teeth is nearly the same at each step.

If we look at a table showing gear inches for every ratio in a [pick your favorite chain ring] x 13-46 drivetrain, we see that each step up increases by about 8 to 18%.

What are you looking for? Smaller steps all the way up the range? Small steps in the little cogs and bigger ones in big cogs? Are there cassettes with the numbers in your examples, or did you put in some hypotheticals? Are you saying this is what you'd like but it isn't available?

Those gear train examples in the o.p. don't look right to me. I'm a gear inch fossil and I'm not about to put every tooth of a custom cassette into a gear inch calculator but: 42 x 13 as a top gear is impractical, even for MTB. That's 80" with a typical MTB wheelset. Is the o.p. MTB or Road? We can't discuss this intelligently until we know what they need. But ... as I understand it, a Rohloff IGH hub has 14sp with exactly 14% steps between each one! Only $1500USD. Maybe?

...and linear in what respect? Half-step gearing does fine at keeping the increase from gear to gear at roughly the same percentage of gear inches/ development/ gear ratios. But at different times I think I'd want, for example, a linear increase in perceived effort or calorie burn (although I can't imagine how to measure that reliably) or heart rate going from gear to gear? That's just to name a few possibilities.

Most people, or at least I, want the 1 tooth spacing to be from the 11 tooth cog to about the middle of the stack. That's the cogs I'm using the most when riding with groups and it lets me find a comfortable combo for the cadence I wish to use at the speed the group is riding at.

And that seems to be the way most cassettes have always been made for.

You might be after a unicorn.

There are only a few cassette manufacturers. The range and # of cogs will further limit your choices. You may be looking at only 10-15 available cassettes. 30 minutes of Google will give you the specs you need.

Could combine riveted cluster from MTB cassette with a road cassette as seen in some videos, etc,
but it seems like it always results in a huge gap in the middle.

When I was looking at Ekar I did note that it had closer ratios at the higher end of the cassette and wider ratios at the lower end than either Shimano or SRAM equivalents in total range.

What you’re describing is a geometric progression. There’s nothing linear about it.

Dura Ace 11-30 12 Speed comes closest. I'd love to have that cassette and a 53/36 up front although my 10-28 SRAM with 48/35 isn't unbearable.

11-12-13-14-15-16-17-19*-21*-24*-27*-30*T

We called that a “ straight block” BITD. With fewer gears back then, the cassette almost looked like all the cogs were the same size. An old friend of mine had one on his Raleigh. He mostly rode around town and never did any appreciable climbing.

With a 1 X, 44t front, I just went from an 11-34 11 speed to an 11-34 12 speed. I am using bar ends in friction mode, only had to change the cassette and chain, and adjust the limit screws on the rear dr. The main reason was pure curiosity, but also, I did not like the jump from 21t to 24t on the cassette. I bought a cheaper Sunshine cassette, now no 4 tooth gaps, and the first 3 tooth gap is 25 to 28: 11,12,13,15,17,19,21,23,25,28,31,34. I really like that progression, as I am kind of particular about being in the gear that is right for me. I have only done a short ride to make sure it is operating properly, and will be doing a normal 25 to35 mile ride, shortly. My investment in dollars was only $63, the removed 11 speed cassette and chain will be used on a different bike. Don't know that this helps the OP, but thought I would share my experience. In my search, it seems going to a wider range 12 speed cassette, one is limited as to choice of biggest cog.

If you linear you mean approximately the same percentage of change as sprockets go from small to large, then you won't find any made for modern drivetrains. It's also undesirable except where road gradients don't change much.

There's also the mathematical fact that as sprockets get larger 1T changes become smaller percentages. A 10-11 is an 11% reduction. A 16-17 is only a 6% reduction, but a 16-18 is back to an 11% reduction. I have a 13-15 jump that's almost a 13% jump. It feels too large compared to the same percentage with much larger sprockets. In my experience riding many thousands of miles in the mountains, larger percentage changes are not as troublesome in the larger sprockets. My 10-36 has 21-24-28-32-36 sprockets. The 21-24 is 14%, while the 32-36 is down to 11%. I wouldn't want any smaller percentage changes.

SRAM makes a 10-33 cassette to get a 1/1 ratio with a 33T little ring. The 28-33 jump is 15%.

The forces against you are not all linear. At "higher" speeds, wind resistance dictates small gaps between gears whereas going slowly, the forces are linear and the gearing gaps should be larger. To double your speed, the wind resistance is 8 times higher or more realistically, a 10% increase in speed when riding "fast" requires about 30% more power. On a steep hill, 10% increase in speed only requires a 10% increase in power. So, a corn cob at one end and big gear jumps at the other. SRAM's 10-33 or Shimano 11-30 12 speed pared to the right chain rings for your preference would be about as close to "linear" as you can get.

^^^Astonishing that Shimano, SRAM, Campy etc might have some understanding of proper gearing. Who knew?

Astonishing that 12 speed cassettes were not around for decades.

Shimano and Campy have it right, SRAM's 10T is a stupid waste of watts. It "feels" awful when pedaling and is measurably a waste of energy.

pr
I have only one 1x 42t proprietary
chainring, could have went for 38t but decided to go for 42t to keep the chainline straighter on the most used sprockets.

Linear would be straight upwards line. In this case logarithmic would be more appropriate. Have read a lot of discussions about cassettes but never stumbled upon exactly this kind of aspect. Seems like loaded touring bikes are still compelled to use MTB cassettes mostly.

Normal range cassettes are somewhat made this way. Wide range cassettes seem to be made with closer steps in lower gears and wider at higher gears.

Campy has a 9-36 and 9-42 available. I marginally agree with you and use their 10-44.

For those of us who are 2X and preferential to 12x28 cassettes - road rides/light gravel + hills = Does this progression of cogs (assuming 10spd) have much real-world relevance beyond minor variations in cadence?

Not linear. Not logarithmic.

Nope, but folks read about something and love to chew on it. Many threads on BF have begun with "I'd have hung with the pack if only I'd had a 16t cog."