sesquitertial
Definition
Adjective: - Mathematics: "Sesquitertial" describes a ratio or proportion of 4 to 3 (i.e., 4:3). The term is derived from Latin sesqui- meaning "one and a half" and tertius meaning "third," so it literally means "one and a third times," which equals 4/3.
- Music (historical): In ancient and medieval music theory, "sesquitertial" refers to the musical interval of a perfect fourth, where the frequencies of two notes are in a 4:3 ratio.
Usage Examples
Mathematics:
- The ancient Greeks used sesquitertial proportions in their geometric designs. (The ratio of 4:3 was employed.)
- A rectangle with sesquitertial sides has a length 1.33 times its width. (The sides are in a 4:3 ratio.)
Music:
- The perfect fourth, such as the interval from C to F, is a sesquitertial interval. (Its frequency ratio is 4:3.)
Advanced Usage
"Sesquitertial proportion": A specific mathematical relationship where one quantity is 4/3 of another.
- Architects of the Renaissance often employed sesquitertial proportions for harmony. (They used the 4:3 ratio.)
"Sesquitertial tone" (archaic): A tone whose frequency is 4/3 of a reference tone.
- In Pythagorean tuning, the sesquitertial tone corresponds to the subdominant. (The note a perfect fourth below the tonic.)
Variants and Related Words
Sesquitertia (noun, rare): The abstract quality or state of being in a 4:3 ratio.
- The interval of a fourth is based on sesquitertia. (The 4:3 ratio.)
Sesquialter (adj): A ratio of 3:2 (one and a half times), distinct from sesquitertial.
- A perfect fifth is a sesquialter interval, not sesquitertial. (3:2 ratio vs. 4:3.)
Synonyms
- 4:3 ratio: The specific numerical relationship.
- Perfect fourth (in music): The interval with a 4:3 frequency ratio.
Related Idioms
- None common. This is a highly technical term with no idiomatic usage in everyday language.