Still unclear about this whole sesquialtera situation? Not even sure what it is, let alone when it applies?
In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In pitch, hemiola refers to the interval of a perfect fifth. In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats.
The word hemiola comes from the Greek adjective ἡμιόλιος, hemiolios, meaning "containing one and a half," "half as much again," "in the ratio of one and a half to one (3:2), as in musical sounds."[1] The words "hemiola" and "sesquialtera" both signify the ratio 3:2, and in music were first used to describe relations of pitch. Dividing the string of a monochord in this ratio produces the interval of a perfect fifth. Beginning in the 15th century, both words were also used to describe rhythmic relationships, specifically the substitution (usually through the use of coloration—red notes in place of black ones, or black in place of "white", hollow noteheads) of three imperfect notes (divided into two parts) for two perfect ones (divided into three parts) in tempus perfectum or in prolatio maior.[2][3]
Hemiola can be used to describe the ratio of the lengths of two strings as three-to-two (3:2), that together sound a perfect fifth.[2] The early Pythagoreans, such as Hippasus and Philolaus, used this term in a music-theoretic context to mean a perfect fifth.[4]
In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera . In pitch, hemiola refers to the interval of a perfect fifth. In rhythm, hemiola refers to three beats of equal value in the time normally occupied by two beats.
What does “sesquialtera” really mean? This Early Music Monday we dive in to one of the most confusing and contentious topics in early music: Tactus and Proportions, with the help of our friends over at Early Music Sources!