Sori refers to the type of curvature in a Japanese blade. The sori in a blade is found by determining the deepest point of the curve along the mune between the munemachi and the extreme tip of the kissaki (point section). Often the sori is very subtle and hard to classify but it is an important factor in kantei (appraisal).
'Koshi' means 'waist' and refers to the deepest point of the curve being near the waist of the sword just forward of the machi (the place where the blade meets the tang). It is also known as Bizen Sori because many of the Bizen schools used this form.
This form is named after the Torii or gateway to a Shinto shrine, bearing a resemblance to the curved crosspiece. The deepest point of torii sori coincides with the halfway point of the blade. Kyo is an alternative name for Yamashiro province, where many swords of this form were made.
Saki means 'tip' or 'upper' and refers to the deepest point of the curve being forward of the halfway point towards the kissaki. This sori form was popular during the Muromachi period. It is also the form most often seen in naginata.
Uchi means 'inner' and refers to the curve being on the inward portion of the blade. Usually refers to tanto blades. It is also known as Takenoko or 'bamboo-shoot' sori.
Mu means 'no' or 'none'. A blade with musori is therefore straight. This term is used for tanto blades with no sori. Straight sword blades were the Chokutô of the archaic period. However some musori sword blades were made in the Ôei period around 1400 CE, but the fashion soon passed. Chukan means 'middle', and refers to musori being between sori and uchisori.