Why don't we have third notes? [duplicate]

Question

why isn't there a third note It could be use in 3/2 or 3/4,and others that divide the measure with 3,what more of a question it can be formed too. If there was a third not it would work well in 3/2 or 3/4 time

Answer 1

Actually we did have "third notes", sort of, back in the medieval period, but they dropped out of use because the medieval system for notating rhythm was rather complicated compared with the modern system, and also because of technology: the medieval notation used two colors, black for "halved notes" and red for what the OP calls "third notes," which was fine when all music was written and copied by hand using pen and ink, but beyond the capability of the first attempts at printing sheet music, round about 1600.

The medieval theory of rhythm, as described by Philippe de Vitry in about 1320 in his book "Ars Nova" ("New Art") the longest note (the "long") could be divided into either two or three shorter notes ("breves"). These rhythms were called "modus imperfectus" and "modus perfectus" - division into three was considered "perfect" by analogy with the Christian doctrine of the Holy Trinity.

Similarly a breve could be divided into either two or three semibreves - these rhythms were called, similarly, "tempus imperfectum" and "tempus perfectum"

Finally, a semibreve could be divided into either two or three minims, called "prolatio imperfectus" and prolatio perfectus."

Combining these three options gave eight possible basic rhythms, i.e. divisions into 2/2/2, 2/2/3, 2/3/2, etc up to 3/3/3. Some of these correspond to common modern rhythms like 3/4, 4/4, 6/8, etc, but some have completely fallen out of use - for example the "most perfect rhythm" in the system, corresponding to modern 9/8 time with each 8th-note divided into a triplet of 16th-notes.

The final innovation in this system was the use of a sign at the start of the piece showing which subdivisions were used - equivalent to a modern time signature.

In fact one of his signs is still in use: "tempus perfectum" was indicated by a (perfect) circle, and "tempus imperfectum" by a broken (imperfect) circle. The broken circle, and one of its variations in de Vitry's system, remain in use as the modern "C" sign for common time, and the C with a vertical stroke through it for "cut time". The explanation in English-speaking countries that "C" is an abbreviation for "common" is incorrect folk etymology!

All this was fine until composers wanted to change the rhythmic divisions within the course of a piece - which is where the use of different colored notes came in. When printing could only be done efficiently in monochrome, an alternative was tried using white and black note heads, but that had the disadvantage that some of the symbols (e.g the modern half and quarter notes, i.e. a black or white note head with a stem) could have two different meanings depending on the context! Eventually, this was replaced by the modern notation for triplets - a figure "3" over or under the notes.

Answer 2

First, let's remember what time signatures like 3/2 and 3/4 indicate: that each measure comprises three of the denominator's note values. In other words, a measure of 3/2 comprises three half notes, since the denominator "2" signifies half notes.

As such, any time signature with a 3 in the numerator already "divide[s] the measure [by] 3," since that's the very definition of these time signatures. (One could make an argument that 3/8 is really "in one" as opposed to "in three," but that doesn't alter this main point.)

Second, there actually are "third notes" already, assuming you mean pitches that are worth one-third of some value. We simply call them triplets. In a triplet construction, three instances of a particular note value are crammed into the space of two of these pitches. Put another way, a note value within the triplet is worth one-third of two of those pitches.

In the above example, the first three pitches are triplet eighth notes. This means that those three pitches together use the duration of two normal eighth notes (i.e., a quarter note). This means that a single eighth-note triplet lasts precisely one-third of a quarter note in this measure.

The quarter-note triplets are each worth two-thirds of a beat, since these three quarter notes take up the span of two quarter notes (i.e., two beats).

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By and large, you can use triplets in any simple time signature. But in compound meters (those with an 8 on the bottom of the key signature), the beats are actually already split into 3.

In the above 6/8 example, each beat is itself worth 3 eighth notes. This means that a measure of 6/8 is split up into two dotted-quarter beats, meaning that the notated eighth notes in a compound meter are also worth one-third of a beat.

See also Why is meter divided into simple and compound types?