Today, I'll show you the origin of the divisibility of the modern note values and the time signature. Have you ever wondered why the symbol of C means 4/4 time or "alla breve" means "2/2" time? You'll find out now.
This is a continuation of the previous essay "Thinking about Tempo, Part 1 - Note Values".
If you haven't read it yet, please take a quick browse.
[Divisibility of note values in modern notation]
The chart above shows the divisibility of the modern notes values. A semibreve (whole note) is divisible by two minims (1/2 notes), a minim (1/2 note) is divisible by two crotchets (1/4 notes), and so on. Though the use of the breve (double whole note) is rare nowadays, the same rules apply; a breve (double note) is divisible into two semibreves (whole notes). This system is based on a division by two (binary) and has been used after 1600 till now.
[Note values in mensural notation]
Before 1600, in mensural notation, note values were divisible by either two or three depending on the "mensuration" signs. Such signs were located at the beginning of a composition, indicating what kind of divisibilities had to be used. And this is the ancestor of the modern "time signature".
The mensuration sign "O (full circle)" symbolises the Trinity, a perfect whole made of three elements. The mensuration "C" represents an imperfect whole because it is made of only two elements.
The sign "O" and "C" were used in combination with one or two numbers and a dot resulting a variety of mensurations.
The table on the left is showing a part of the table above.
The numbers in yellow represent the ratio of semibrevis (today's semibreve/whole note) to the note in qustion, e.g. when the mensuration is "O3", the value of the "brevis" is equal to the value of "3" semibreves. In the same way, the value of the "maxima" is equal to the value of "27" semibreves.
The numbers in cyan represent the divisibility of the note value, e.g. the first "2" shows that the "semibrevis" is divisible by "two" (a semibrevis = two minimae). In the same way, the "longa" is divisible by "3" (a longa = three breves).
For example, the sign of "O2" indicates that the "longa" is divisible by three "breves".
The sign of "O" indicates that the "longa" is divisible by two "breves", and the "brevis" is divisible by three "minimae".
[Note] If you're in a hurry, click here to skip to the next section "Diminished variants of the mensuration signs", if you'd like to find out more about this, please keep reading.
So, now let's have a look at the table above again.
Note values from the maxima through the semibrevis were divisible by either two or three. Divisibility by three was called "perfectum (perfect)", while divisibility by two was named "imperfectum (imperfect)". The smaller note values were divisible only by two.
The division of the "maxima" into "longae", the "longa" into the "breves", the "brevis" into "semibreves", and the "semibrevis" into "minimae" were called successively "maximodus", "modus", "tempus", and "prolatio".
Have a look at the following pages from "Plaine and Easie Introduction to Practicall Musicke (1597)" by Thomas Morley. Morley was an English composer, theorist, editor and organist of the Renaissance, and the foremost member of the English Madrigal School.
[Diminished variants of the mensuration signs]
Each of the mensuration signs had a diminished (diminutum) variant, indicated by a vertical stroke through the sign. These signs represent a reduction of all temporal values by two (twice as fast).
It's possible to say that this was the very first appearance of the concept of notated "tempo changes" in the history of music.
[The origin of the time signature "C" as 4/4 time]
Morley expalins the divisibility of notes of each mensuration on his book. The chart below shows the note value when "mensuration" sign is "C".
Does this chart remind you something familiar? Yes, this is the origin of the modern note value system (compare with the first chart on the top of this blog), and the modern practice of using the sign "C" for the "4/4" time! Today, the "C" is also known as "common time".
Additionaly, the diminished version of the mensuration "C", is the ancestor of today's 2/2, also called "alla breve", "cut time", or "cut common time".