The power of tempo in music cannot be overemphasized. Before a thing is called “the influencer,” it must be a big deal. It must have a lot to do with the subject. That is why; it’s quite barbaric to start reading the rhythm of a piece of music without paying attention to the tempo mark.
This is true because in music, rhythm is governed or regulated by meter (time signature), and highly influenced by tempo. If the tempo is fast, the rhythm will also be fast. If the tempo is low, the rhythm will also be slow. If the tempo is moderate, the rhythm is bound to be moderate. Simply put, rhythm cannot be faster or slower than tempo.
Tempo can make a crochet (a quarter note) to sound like a quaver (an eighth note). It can also make the crotchet to sound like a minim. It can make a dotted crotchet to sound like a dotted minim. It can also make a dotted minim to sound like a dotted crotchet, and so forth.
Put differently, tempo influences meter such that a 3|4 meter can behave like either 6|8 or 3|2. A 3|4 meter with a fast tempo mark behaves like a 6|8. A 3|4 meter with a slow tempo mark behaves like a 3|2. These and many more are made possible by tempo.
In the same vein, we can put it that 12|8 meter is a variant of 4|4. If too many triplets in 4|4 meter are to be avoided, 12|8 is a good option. 9|8 meter is a variant of 3|4. If too many triplets in 3|4 meter are to be avoided, 9|8 is a good option. 6|8 meter is a variant of 2|4. If too many triplets in 2|4 meter are to be avoided, 6|8 is a good option. Tempo has a lot to do in these.
Tempo mark, just as the name implies, is a mark placed on the score by the composer, describing the speed at which the piece of music and sometimes, passage should be played or sung. The art of indicating the tempo of a piece of music is known as tempo marking. The two concepts are closely related and somehow synonymous.
Paying less or no attention to the tempo mark is a mark of rascality. To be accurate in the rhythm reading, you must pay keen attention to the given tempo mark. If the tempo has not been marked, the default tempo mark is moderato. Your musicality should let you determine whether the moderato is okay or not. You can increase or decrease the tempo to suite the music.
From whatever perspective you would love to approach, you would still conclude that tempo influences rhythm. You can approach it from any of the following perspectives: the rudiment of music, the philosophy of music, the psychology of music, the physics of music and so forth. Music is broad, music is deep, and music is unfathomable.