Doubling a note means 2 parts produce the same note either an octave above, below, or in unison.
GENERAL RULE: The root note of the chord is preferably doubled.
While doubling the fifth has a good effect, it sometimes results in difficulties when realizing the next chord.
As for the third, double it as little as possible and only when forced to do so in order to avoid breaking certain rules concerning realization contained in later chapters.
This rule is subject to taste and experience, and the intentions of each author. Its modification is sometimes required due to melodic interest of the parts, but also by the tonal influences. Therefore, it often better to double the root note.
For example, doubling the third of the submediant chord (sixth), as its the tonic note, has a good effect. In other cases, the dominant or subdominant note is preferably doubled, as these two notes have the greatest tonal strength after the tonic. This latter consideration must influence the choice of note to be doubled.
The tonic, dominant, and subdominant are categorized as GOOD NOTES of the tone (see 3.2). On the contrary, the leading tone always plays a delicate part in harmony and must never be double because it becomes too preponderant.
Suppressing a note occurs when a chord note is not realized as part of the harmony. This often happens when less than four-part realization, and sometimes happens in four or more part realization.
GENERAL RULE: The fifth of the chord is preferably suppressed.
The third is rarely suppressed, as it generally contributes the most to the character of the kind of chord and mode. Suppressing the third causes a vague sensation which results in pungent effects, none of which are allowed in study or the rigorous style.
The dominant chord (fifth) in both modes is the chord best suited for suppressing the third, because the chord implied by this degree is the same in both modes (major and minor), thus leaves no room for doubt in its sensation:
The suppression of the root will be discussed later.
Old Music Theory 