Very practical, which is great. It is very easy to stay motivated when the tutorial is so focused on producing something that you like.
The only thing that I thought was missing was a discussion about micro and macro pulses in 4/4 versus 3/4 versus 6/8, because it is a simple concept that is easy to teach but offers the student much more variety of options in choosing a time signature. As a music teacher, I usually approach the issue by having students count 4/4 aloud ("1 2 3 4, noting that 1 and 3 are accented slightly) and 3/4 aloud (1 2 3, noting that beat 1 is accented). This teaches not just the structure of the time signatures but helps the student internalize them, which I've found speeds up learning and understanding without sacrificing the student's ability to understand what principles make rhythms work the way they do. (This would have made syncopation a lot easier to teach later in the article-- it can be defined as simply rhythms that don't conform to the usual micro/macro pulse of a time signature, i.e. 1 2 3 4, etc)
Also, one of the easiest ways to grok the time signature concept is to say the signature aloud like it's a fraction. i.e., 4/4 is "four fourths", 6/8 is "sixth eighths" etc. It really is that easy, and this approach combined with the understanding that the lower value gets one beat and there are x of them per measure usually makes time signatures one of the easiest sections of my theory courses.
Still, it's hard to criticize a tutorial that has you producing music so quickly.
Because the micro-pulse of 6/8 is different than 3/4. 3/4 is naturally emphasized as "1 2 3 1 2 3. In contrast, 6/8 is naturally emphasized with a micro pulse of 1 2 3 4 5 6, which produces a strong pulse on 1, a slightly weaker pulse on 4, and a macro pulse of "1 2. (Think 4/4 with triplets). You thus get a much different feeling from 6/8 than 3/4.
OK, my issue was with your statement that time signatures are simply fractions. If that were true than 6/8=3/4. But I understand you were presenting a simplified explanation.
Primarily for reasons of legibility, in my opinion.
Technically, any piece in duple meter could be written in any duple meter and any triple meter piece could be written in triple meter. In fact, you could even write a triple meter piece in duple meter if you are willing to notate everything as a triplet.
Also, as some of the answers below show, part of legibility is in supporting the speed or the feel of the piece.
(Also 2/2 is a fairly common time signature better known as cut-time. Many marches, for example, use this.)
Mostly to indicate tempo and style. A 3/4 measure and a 6/8 measure are the same length, but the 6/8 has twice as many beats at twice the rate. So a composer would use a 6/8 signature for a faster-moving piece with a lot of eighth notes. Similarly, a slow piece would have a 2/2 signature instead of 4/4.
alla breve, cut time: used for marches and fast orchestral music. Frequently occurs in musical theater. Sometimes called "in 2", but may be notated in 4.
That really isn't the case, that is the job of the tempo, a BPM speed set by the composer. The intended difference is purely that 3/4 groups quavers into groups of two, 6/8 into groups of three.
The only thing that I thought was missing was a discussion about micro and macro pulses in 4/4 versus 3/4 versus 6/8, because it is a simple concept that is easy to teach but offers the student much more variety of options in choosing a time signature. As a music teacher, I usually approach the issue by having students count 4/4 aloud ("1 2 3 4, noting that 1 and 3 are accented slightly) and 3/4 aloud (1 2 3, noting that beat 1 is accented). This teaches not just the structure of the time signatures but helps the student internalize them, which I've found speeds up learning and understanding without sacrificing the student's ability to understand what principles make rhythms work the way they do. (This would have made syncopation a lot easier to teach later in the article-- it can be defined as simply rhythms that don't conform to the usual micro/macro pulse of a time signature, i.e. 1 2 3 4, etc)
Also, one of the easiest ways to grok the time signature concept is to say the signature aloud like it's a fraction. i.e., 4/4 is "four fourths", 6/8 is "sixth eighths" etc. It really is that easy, and this approach combined with the understanding that the lower value gets one beat and there are x of them per measure usually makes time signatures one of the easiest sections of my theory courses.
Still, it's hard to criticize a tutorial that has you producing music so quickly.