The sesquialterum in musical harmony is the ratio corresponding to the interval diapente.
In visual harmony, the sesquialter can be the ratio between the length and width of a rectangle. Most flags of the world's countries have a ratio of 3:2 between their length and width: this ratio is sesquialter. See, for example, the flag of Italy.
In rhythm, the plural sesquialtera refers to a group of three notes which are played in the same time usually occupied by two notes. Sesquialterum is also the ratio between the intervals of time occupied by a dotted note and its corresponding undotted note.
Manuscript Galileo 72 (http://www.mpiwg-berlin.mpg.de/Galileo_Prototype/HTML/F163_V/T1.HTM) (Textblock 1 of Folio Page 163v.) (Text in Latin.) The length of bc is twice the length of ab, therefore the ratio of ac to bc is a sesquialterum.
The sesquialterum in musical harmony is the ratio corresponding to the interval diapente.
Sesquialterum is also the ratio between the intervals of time occupied by a dotted note and its corresponding undotted note.
Manuscript Galileo 72 (Textblock 1 of Folio Page 163v.) (Text in Latin.) The length of bc is twice the length of ab, therefore the ratio of ac to bc is a sesquialterum.
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