According to the Jazz Education Network (JEN), a non-profit organization that supports jazz education and performance, the most common ratio between instruments in high school jazz bands is the standard big band instrumentation. This instrumentation typically consists of five saxophones, four trumpets, four trombones, piano, bass, and drums.
The saxophone section is composed of two altos, two tenors, and one baritone saxophone. The trumpet section typically includes two players on the first part and two on the second part. The trombone section includes two tenors and one bass trombone.
This instrumentation has become the standard for jazz big bands since the 1930s and has been used by many famous jazz bands, such as the Count Basie Orchestra and the Duke Ellington Orchestra.
While this instrumentation is the most common, it is important to note that jazz bands can vary in size and instrumentation depending on the specific needs of the music being played. Some bands may add additional instruments such as guitar or vibraphone, while others may have smaller ensembles consisting of only a rhythm section and a few soloists.
It is also worth mentioning that while the standard big band instrumentation is the most common in high school jazz bands, there are many other types of jazz ensembles that can be found in high schools. These can include small combos, vocal jazz ensembles, and Latin jazz bands, each with their own unique instrumentation and style.
In conclusion, the most common ratio between instruments in high school jazz bands is the standard big band instrumentation of five saxophones, four trumpets, four trombones, piano, bass, and drums. This information is supported by the Jazz Education Network, a respected authority in the field of jazz education and performance. However, it is important to remember that jazz ensembles can vary in size and instrumentation depending on the specific needs of the music being played, and that there are many different types of jazz ensembles that can be found in high schools.