As an example, a traditional way to harmonize a melody in top-down, close-position writing for 5 saxophones is the 1st alto plays the melody note, the 2nd alto plays the chord tone below the melody note, the 1st tenor plays the next chord tone (below that of the 2nd alto), the 2nd tenor plays the next chord tone, and finally the baritone doubles the 1st alto an octave lower. While there are 5 saxophones, the chord voicing is actually 4-part harmony.
Top-down, close-position 4-part harmony as described above for saxophones is also used for the brass section. The 4 trumpet parts are usually written first and then the 4 trombones double the trumpet parts an octave lower or with variations of this technique.
When the saxophones are joined with the brass in concerted ensemble passages, the 1st alto usually doubles one of the trumpet parts and the remaining saxes double either lower trumpet or trombone parts. Thus, there is a considerable amount of unison and octave doubling in traditional big band arranging.
Open or spread voicings can go beyond the 4-part harmony used in close-position writing. In spread vocings, the trombones and/or lower saxophones play basic chord tones (such as 1-7-3 or 1-3-7) and the trumpets and/or higher saxophones play remaining chord tones and, importantly, include tensions (natural or altered 9, 11, or 13) to give the voicings a richer sound. Here is an example of a 5-part spread voicing with an Ellington flavor on a C7 chord (from the bottom up): C, Bb, E, A (13), D# (#9). Spread voicings can use 5, 6, or 7-part harmony instead of being limited to 4-part. However, unison and octave doubling still occurs when even 7-part harmony is used in concerted saxophone & brass passages.
The simple reason why harmonic doubling is commonly used in big bands is there are more horn players in the band than the number of individual notes in the harmonic structures used by big band arrangers.
Given this perspective of harmonic doubling in big band music, I have an idea to offer to big bands: to try using my 6-horn ensemble scores with doubled players on a part. This is described in my Mid-Size Ensemble article. So far, big bands have been reluctant to try it. However, as I envision this approach, it can give a fresh sound to conventional big bands.
Bands are encouraged to experiment with this idea. For example, the horns can be used in different combinations at places in the score as well as playing together. Of prime importance is my concept of having 6 lines with distinct tone colors instead of the conventional sound of saxophone, trumpet, and trombone sections. This can be done by combining saxophones & woodwind doubles with the brass in various mutes (and playing open) to create an expanded palette of tone colors. With this approach, each wind instrument is used as an individual tone color -- and blended with other colors -- instead of as being part of a section.
Interested bands can write to me from the Contact page to discuss these ideas and to inquire about scores.