One reasonable and memorable approximation excluding any fine structure is:
see for example example: hydrogen 1-2 spectral line.
Equation 1. Hydrogen spectral series mnemonic.
Equation "Hydrogen spectral series mnemonic" gives for example from principal quantum number 1 to 2 a difference:
which with Planck-Einstein relation gives about 121.6 nm ( Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.
Kind of a synonym for hydrogen emission spectrum not very clear if fine structure is considered by this term or not.
A line set for hydrogen spectral line.
Formula discovered in 1885, was it the first set to have an empirical formula?