The usual rarity scale found in coin catalogs is the scale of 1 to 10, where 1 is exceedingly rare and 10 is exceedingly common.Various catalogs have explained this scale in different ways. In the Qing Dynasty cash variety catalog, Ch'ing Cash until 1735, by Dr. Werner Burger, there is a statistic on what the rarity scale means in terms of actual numbers of pieces. I am reproducing it below (click on the image to zoom), 
but I am not sure if it is applicable across the whole spectrum of cash coins. If I were to use my own statistical analysis of bulk quantities of Northern Song cash, I might want to revise some of the rarity numbers of some varieties. I think I must agree with something that was written by O. D. 
Cresswell in his catalog Chinese Cash. "I have resisted the temptation to make facile estimates of rarity as it has been my experience that one collector may have several specimens of a coin which to another has remained unobtainable." If you collect by sorting through hoards and bulk lots of cash, it all depends on just what happens to be in that particular hoard.
The rarity scale used in Liang Song Tie Qian is one that I have encountered nowhere else, and it is only by the kind advice of HKMAL, a collector friend in Hong Kong, that I now understand it. It is based on a scale of 1 to 5, but each number is divided into an 上 above and a 下 below. It can be compared to the scale of 1 to 10 in this way:
but I am not sure if it is applicable across the whole spectrum of cash coins. If I were to use my own statistical analysis of bulk quantities of Northern Song cash, I might want to revise some of the rarity numbers of some varieties. I think I must agree with something that was written by O. D. 
Cresswell in his catalog Chinese Cash. "I have resisted the temptation to make facile estimates of rarity as it has been my experience that one collector may have several specimens of a coin which to another has remained unobtainable." If you collect by sorting through hoards and bulk lots of cash, it all depends on just what happens to be in that particular hoard.
The rarity scale used in Liang Song Tie Qian is one that I have encountered nowhere else, and it is only by the kind advice of HKMAL, a collector friend in Hong Kong, that I now understand it. It is based on a scale of 1 to 5, but each number is divided into an 上 above and a 下 below. It can be compared to the scale of 1 to 10 in this way:
一上 = 1a = 1
一下 = 1b = 2
二上 = 2a = 3
二下 = 2b = 4
三上 = 3a = 5
三下 = 3b = 6
四上 = 4a = 7
四下 = 4b = 8
五上 = 5a = 9
五下 = 5b = 10
In the example rubbing, LSTQ-147 has a rarity of 4a / 7.
This is how rarity will be expressed in this blog for iron cash referenced to Liang Song Tie Qian.
Back to the topic of the Chinese cash rarity scale, I am again indebted to HKMAL for what I believe is a very good schedule of what rarity means in terms of the actual number of extant specimens.
His schedule is put together with not a little humor, and I recommend that you view it at this link. The table to the right summarises his conclusions and can be downloaded and printed out by left clicking the image to zoom and then right clicking and selecting "Save Picture As" to download it to your computer for viewing or printing.
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