Review the advances of primes

[RuixiZhang42]

The horizontal advances of U+2032, U+2033, U+2034, and U+2057 are supposed to be in arithmetic progression; that is, ℎ, ℎ+𝑑, ℎ+2𝑑, and ℎ+3𝑑. The horizontal advances of U+2035, U+2036, and U+2037 should be identical with those of U+2032, U+2033, and U+2034, respectively.

The problematic glyphs I’ve found so far are:

1. uni2057 (raised and down-scaled). Purely metric-wise,

   • second can be reproduced with minute kern-156 minute and
   • uni2034 can be reproduced with minute kern-156 minute kern-156 minute.

   The quadruple prime uni2057 cannot be reproduced this way.

2. All .var variants (gigantic). Purely metric-wise,

   • second.var is minute.var kern-77 minute.var,
   • primetriple.var is minute.var kern-75 minute.var kern-75 minute.var, and
   • primequad.var is minute.var kern-75.333 minute.var kern-75.333 minute.var kern-75.333 minute.var.

   The reverse primes are in sync with the primes, so that’s a plus?

3. minute.ssty. This has an easy fix: uni2035.ssty has the correct horizontal advance, so minute.ssty should be mirroring uni2035.ssty. The implied inter-prime kern here is -131, for both primes and reverse primes.

On another plus side, all .ssty2 variants have correct horizontal advances, with an implied inter-prime kern of -171.

[RuixiZhang42]

The implied inter-prime kern of -156 of the pre-raised glyphs looks too tight. Is this because the glyphs (for both primes and reverse primes) are inherited from the Text font? Comparison with the .ssty glyphs is shown below:

[RuixiZhang42]

Yikes 😬! I just find out the existence of U+02B9 (Modifier Letter Prime) and U+02BA (Modifier Letter Double Prime). STIX Two Math has these two as well. Surprisingly, U+02BA is set metrically different from U+2033 🤔.

[RuixiZhang42]

[…] all .ssty2 variants have correct horizontal advances […]

Although the .ssty2 variants are metrically sound, they’re just too big to be used as second-level primes (e.g., in tensor notation):

• The pre-raised primes are 304 units tall.
• The .ssty variants, after down-scale to 70%, are 309.4 units tall—perfectly matching 304 units would be ideal, but 309.4 is close enough.
• The .ssty2 variants, after down-scale to 55%, are still 303.6 units tall! They look unreasonably large.

Compare with the x-height of the mathematical alphanumeric:

• The .ssty x-height, after down-scale to 70%, is 358.4 units.
• The .ssty2 x-height, after down-scale to 55%, is 300.85 units.

[RuixiZhang42]

Some visual experiments follow. The first-level scripts all use .ssty variants at 70% for both prime and alphanumeric. The second-level scripts use .ssty2 variants at 55% for alphanumeric and additionally down-scaled prime.

Proportion-wise, down-scale in the range 85%–90% (469–497 units tall) looks best. But note that the .ssty2 prime is down-scaled mechanically, without any optical adjustments (e.g., no thickening the stoke).