Actually it seems to me that this pattern is for ivory sets. This needs to be sorted out.
7) Plain sets
The majority of BC sets come without any decoration at all. Stems and basesUsually Barleycorn sets come with round or onion-shaped stems, threaded in the best sets. However, some exceptions exist.
A set with True Barleycorn decoration and ringed stems. The rings are repeated in every piece. Ringed stems are not particularily rare, although not common.
It is important to note that urn-like stems are characteristic to Washington pattern, NOT Barleycorn pattern.
The bases are usually plain. However, the edges of good set stems are often "cogged". The fanciest bases are called Van Dyke bases.
A Van Dyke base
English subpatterns
1) Cogged Crown
Kings: cogged crown finials and True Barleycorn or Plain ornamentation around barrel. In good sets, other sections have non-foliate ornamentation.
Queens: ball finials and True Barleycorn or Plain ornamentation. In good sets, other sections have non-foliate ornamentation.
Rooks: turreted towers. In good sets with flag finials and decorated ribbons around pieces.
Bishops: closed mitres, in good sets with non-foliate decoration.
Knights: horse heads, in good sets with non-foliate decoration.
Pawns: ball finials.
In good sets, all bases are cogged.
This is the classic and very common Barleycorn subpattern. Usually small to medium size sets (up to 11,4 cm). Made of bone.
2) Fountain Crown (Flower Crown)

Kings: Fountain Crown finials, True Barleycorn, Rope, Leaf or Plain decoration around barrel. In good sets, crowns with foliate decoration (Flower Crown) and other sections with non-foliate decoration.
Queens: tuft finials, True Barleycorn, Rope, Leaf or Plain decoration around barrel. In good sets, other sections with non-foliate decoration.
Rooks: turreted towers usually with flag finials, sometimes ball finials. In good sets with flag finials and decorated ribbons around pieces.
Bishops: closed mitres, in good sets with non-foliate decoration.
Knights: horse heads, in good sets with non-foliate decoration.
Pawns: ball finials.
In good sets, all bases are cogged.
This is the classic and very common Barleycorn subpattern for large size sets (up to 15,2 cm). Made of bone.
3) Stretched
Kings: Imperial Crown finials, Plain decoration, rarely downright ears.
Queens: tuft finials, Plain decoration, rarely downright ears.
Rooks: turreted towers usually with flag finials, sometimes with ball finials.
Bishops: very long round-topped open mitres.
Knights: horse heads.
Pawns: ball finials.
Another common pattern for larger sets (10-14 cm), easily recognizable for stretched Bishop finials. Usually without decoration. Made of bone.
4) Maltese Cross

Kings: Imperial Crown and Maltese cross finials, True Barleycorn, Leaved or Rope decoration around barrel. In the best sets, foliate decoration is repeated on the ball under the crown and other parts have non-foliate decoration.
Queens: ball or feather finials in good sets, True Barleycorn, Leaved or Rope decoration around barrel. In the best sets, foliate decoration is repeated on the ball under the crown and other parts have non-foliate decoration.
Rooks: turreted towers with cannon towers and flag finials, sometimes with decorative ribbons around the pieces.
Bishops: open mitres, sometimes with non-foliate decoration.
Knights: horse heads, sometimes with reigns.
Pawns: ball finials.
This is the pattern for high-end large (10-14 cm) bone sets. They are sometimes associated with the famous name of Charles Hastilow.
5) Acanthus

Kings: Imperial Crown and Maltese cross finials, usually Acanthus, sometimes other foliate decoration around barrel. Other parts have non-foliate decoration.
Queens: taft finials, usually Acanthus, sometimes other foliate decoration around barrel. Other parts have non-foliate decoration.
Rooks: turreted towers with cannon towers and flag finials, bricked bodies and decorative carvings on other parts.
Bishops: open mitres with non-foliate decoration.
Knights: well carved horse heads with spectacular manes.
Pawns: ball finials.
Van Dyke bases.
Another high-level pattern for larger bone sets, easily recognizable by Acanthus decoration and specific Knights.
6) Ivory

The Barleycorn world is generally made of bone. However, a certain number of ivory sets with similar foliate decorations exist. Ivory sets without foliate decorations are never called Barleycorn.
Ivory BC pieces have usually the following characteristics.
Kings: Imperial Crown and Maltese cross finials, True Barleycorn or Leaf decoration around the barrel. Other parts have non-foliate decoration.
Queens: ball, taft or feather finials, True Barleycorn or Leaf decoration around the barrel. Other parts have non-foliate decoration.
Rooks: turreted towers with stems and flag finials.
Bishops: mitres with non-foliate decoration.
Knights: horse heads, sometimes with reigns.
Pawns: ball finials.
Non-English subpatterns1) Plain Nurenberg (Plain German)
Barleycorn design was used in the continental Europe as well. The design believed to have been originated from Germany has clearly different proportions than English sets. The round sectionsand Rooks look shorter. Another different feature is the sawed-out Knight which appears in many Continental designs, including Selenus. Rook Flag finials are not used.
Plain German (Nurenberg Barleycorn) chess set
The design varies greatly. It was also made in wood.
2) German Skirted Barleycorn

Kings: Spiked coronet finial, plain decoration around the barrel and "skirted" carvings on it's lower edge.
Queens: pointed finials, plain decoration around the barrel and "skirted" carvings on it's lower edge.
Rooks: turreted towers with ball finials.
Bishops: short mitres and urn-like stems.
Knights: horse heads and ringed stems.
Pawns: pointed finials and urn-like stems.
This is a quite well established pattern and both urn-like and ringed stems are correct for this sort of a set. They were produced in early 19th century and do not need an ornamental lathe to make.
3) Pierced

Kings: Imperial crown and Maltese cross finials, pierced barrel.
Queens: Imperial crown finials, pierced barrel.
Rooks: turreted towers with Maltese cross finials.
Bishops: short and flat-ended mitres.
Knights: sawed-out horse heads.
Pawns: pointed finials.
All pieces with plain bases and urn-like stems.
Another well-established German pattern. Does not need an ornamental lathe as well.
4) Little Faces

Kings: Royal face finials, Leaf decorations around barrel, non-foliate carvings around other parts.
Queens: Royal face finials, Leaf decorations around barrel, non-foliate carvings around other parts.
Rooks: turreted towers with cannon tower and halfmoon finials.
Bishops: flower finials with non-foliate decorations around other parts.
Knights: well-carved horse heads with non-foliate decorations around other parts.
Pawns: pointed finials.
A Barleycorn version of German "Little faces" high-end design, also used with other patterns.
Conclusion
'Barleycorn' term has been applied to a variety of chess sets and has lost it's original meaning long ago. The royal pieces are decorated with ears, barley leaves, acanthus leaves, general leaves, rope twist, ragged bricks or just ringed. German sets might be even pierced. I am sure that there are some rare decorations left out from the list provided above.
There seems to exist a wide consensus that chess sets should be labeled Barleycorn by the general shape of the pieces, not by some particular way to decorate a ribbon around barrel of some royal piece.
The barrel should be considerably stouter than the neck and finials. Slim ringed sets as the following example are often listed as 'Barleycorn' by auction houses. I think that is not right because no slim bone sets with any foliate decoration exist (there are some with Rope decoration, though). If there were slim sets with foliate decorations, then in my opinion only these should be called 'Barleycorn' as in the case of ivory sets.
Slim English playing set. Evolved from Captain Cook pattern?
I think that following characteristics should be common to and required from the whole family:
1) existence of base, stem, barrel, upper stem and finials in Royal pieces;
2) massive cylindrical barrels, stouter than finials, about as wide as bases;
3) stout Rooks without stems in bone sets;
4) foliate decoration around barrels of ivory royal pieces.