The most logical system of musical note durations in contemporary practice, it
seems to me, is the one based on "whole notes" which are equal in duration to one
measure of common time. Common time is the same as "4/4" time, and thus a whole
note is equivalent to four beats or quarter notes.
Crotchets and quarter notes are two names for the same thing in our language. The
former is typical British terminology while the latter is far more common in
American English. In the context of 4/4 time, the American style seems to have
the force of common sense and logical simplicity on its side. Yet in 3/4 time,
this starts to break down. If the metrical sign is read as the fraction that it
very closely resembles, some sense is salvaged by saying that the length of a
measure is three quarters of a whole note, and thus each beat within the measure
is a quarter note. But the idea of the whole note has now lost its true native
meaning. I'd really like to speak of "third notes" in this meter.
In my own idealized metrical terminology, we shall take the terms "crotchet" and
"quaver" and modify them slightly to suit our ends. These terms have the perfect
amount of wiggle room, unlike the fractional terms that suggest a mathematically
precise relationship that ceases to make sense outside of duple meters. *Crotchet*
and *quaver* allow us to get back to the *natural sense* of the musical concepts,
if I may presume to speak of such a thing. We will use them in conjunction with
the *whole note*, which comes from a different naming convention but which suits
our purposes better than the "semibreve" which note inflation has rendered
misleading.
We presume that, *natively*, musical rhythm is based on a series of approximately
regular pulses called **beats** or *crotchets*. This is the fundamental unit of
rhythm, and it is compounded into groups of two to four to form **measures** aka
*bars* or *whole notes*. The crotchet can also be subdivided into groups of two
or three (duple or triple time) which are called **quavers**.
This idea is probably still a little half baked, but I'm working towards
something!
The observation that all of these systems of metrical notation try to capture is
that the lengths of musical events typically reflect a regular pulse length or
durations that are simple fractional multiples of this length.
These ratios are used:
1:1 a beat, a pulse, a "short note", a crotchet
2:1 a "long note", a minim, a half note, a measure of cut time (2/4)
3:1 alternate "long note", measure of waltz time (3/4)
4:1 a whole note, a measure of common time (4/4)
1:2 a quaver, and sub-pulse of duple time
1:3 a sub-pulse of triple time, a triplet eighth note
1:4 a semiquaver, sixteenth note
perhaps the only other ratio that is meaningful is
3:2 aka 1.5:1 this is typically represented by a dotted note
Rhythm is constructed in metrical space with the basic building blocks of long
and short pulses. The durations of these pulses, in the simple case, may be in
the ratio 2:1. Sometimes 3:1. But in many cases, as with odd meters, they
are in the ratio 3:2.
5/4 has a long pulse and a short pulse, where the ratio between the two is 3:2.
Likewise, 7/4 has a long pulse and two short pulses. 8/8 has two long pulses
and a short. 9/8 has one long and three shorts (if it does not have just three even pulses subdivided into triplets). 10/8 has two longs and two shorts. 11/8
has three longs and one short.