One dotted quarter note

One beat

One dotted quarter note rest

One beat

Three eighth notes

1/3 of a beat,
1/3 of a beat,
1/3 of a beat 

Ternary music covers all what the binary has left aside, or about 6%.
Humans seem to be fundamentally binary beings.
The ternary division is misunderstood. Very often, it is written as binary.
It represents close to a quarter of classical music.

The
ternary
division

Part of the incomprehension surrounding ternary rhythms comes from triplets.
Triplets are occasional ternary beats encountered in binary music.

They are grouped with brackets and crowned with a 3.
It is important to understand that triplets are exceptions.
One cannot say that a piece of music is in tripet rhythm.
This is either wrongly identified ternary music or a ternary passage in a binary piece.

One has to admit that that the way ternary rhythm is written is lame, since the basic organization of rhythmic values is binary.

Rhythmic values were conceived for binary music

The system had to be adapted for ternary music and uses dotted figures for durations of one beat and more.

Rhythmic values adapted for ternary music

Waltzes are representative of the confusion around ternary music.
All waltzes are ternary.
Most of them have four beats per bar.
The popular saying goes that waltzes have three beats and it is wrong.
When people count 1, 2, 3, 1, 2, 3, ..., they are doing the ternary division since they place their foot on each 1.
The mix-up comes from the fact that waltzes are traditionally badly notated.
They are written in 3/4 time with the mention "Tempo di valse" placed at the top of the sheet music. This tells the musicians to consider each bar as a single beat.

A: Count 1, 2, 3, 1, 2, 3, aloud, making sure you space the numbers equally, be curt and precise.

B: Beat your foot on number 1 only.

C: Say Ta, Ta, Ta, instead of 1, 2, 3.