Tempo, and why it is not the same thing as groove
The speed of the pulse, written in Italian words or in beats per minute, and the difference between playing fast and playing with the right groove.
The time signature says how many pulses there are and which note value is worth one. It does not say how fast the pulse goes by. That is tempo, and it is a choice separate from everything else: the same score, with the same note values, exists slow and exists fast.
Beats per minute
The exact way to write tempo is to say how many pulses fit in a minute. A marking like "crotchet equals 60" means sixty crotchets a minute, one per second. At 120, two per second, and the music runs twice as fast.
That bar lasts four seconds at 60 and two seconds at 120. The note values did not change; the ruler did. That is why "a crotchet lasts one beat" is right and "a crotchet lasts one second" is not: the beat is a relative unit, and tempo is what converts it into seconds.
The number refers to the note value representing the pulse, and in compound time that value is dotted: in six-eight, the tempo is written over the dotted crotchet, because there are two pulses per bar, not six.
6/8The Italian words
Before the metronome, tempo was written in words, and the words stayed. The commonest, from slowest to fastest:
- Largo — broad, very slow, around 40 to 60.
- Adagio — slow, at ease, around 66 to 76.
- Andante — walking, at a walker's pace, around 76 to 108.
- Moderato — moderate, around 108 to 120.
- Allegro — cheerful, fast, around 120 to 168.
- Presto — very fast, above 168.
The ranges are approximate and always were. A word says as much about character as about speed: andante is a way of walking, not only a number, and a score commonly carries both, the word for the character and the number to settle the doubt.
Changing tempo
Music does not always stay at one tempo. Ritardando asks you to slow down gradually; accelerando, to speed up; a tempo restores the tempo from before. A fermata over a note holds it beyond its written value, outside the count. All of them are instructions about the ruler, not about the note values: the notes still last what they last, and it is the pulse that stretches or shrinks.
Tempo is not groove
Two rhythms at a hundred beats per minute may sound nothing alike. A samba at a hundred and a baião at a hundred have the same pulse and completely different sensations, because what distinguishes them is not the speed: it is where the accents fall and how the subdivisions are laid out. That is the groove, and it belongs to syncopation and to each genre's rhythms, not to tempo.
The two bars last the same at any tempo; the second has a dotted value in place of two equal quavers, and it is that, not the speed, that changes the swing. Confusing the two is how a piece gets played "at the right tempo" and still sounds wrong.
What to take from here
Tempo is the speed of the pulse, written in beats per minute or in a word that says the character, and it is independent of the note values: the same score exists at any tempo. It changes with ritardando, accelerando and fermata, which stretch or shrink the ruler without touching the notes. And it is not the groove: two rhythms at the same speed can be different music, and what distinguishes them comes next.