Does 5/8 = 5/4 = 5/2 ? The Definitive Guide.

Does 5/8 = 5/4 = 5/2 ? The Definitive Guide.

Not! First let me state that this is in no way a definitive, nor even an authoritative statement on the differences between 5/8 and 5/4, they are my interpenetration of the differences and my use of them in my compositions.

On the surface one can say that they are mathematically equivalent. By this we mean that by setting the eight note in 5/8 time and the quarter note in 5/4 time to the same BPM (metronome mark) both bars would move through time at the same rate. Thus one could argue that they are equivalent and that there no real difference between them. But ask your self this is a there a difference between 6/8 and ¾ time? We can set their eight note BPM to the same value, and both bars would move through time at the same rate; but would they have the same feel? How about 6/8 and 6/4 ?

Part of the issue is how do we define rhythm?

So what is the difference (from my perspective)? It is one of “pulse”. In 5/4 time one would “feel” five pulses in the bar, no matter the BPM. In 4/4 time one feels four pulses in each bar. (I feel a lot of 4/4 music might be better notated as 2/2, but that is another discussion.) In 5/4 there might be an emphasis on particular pulses (beats), but there would be five even beats to the bar. In 4/4 there are 4/4 even pules (beats) to the bar with perhaps (given the gene of music) bit more emphasis on the first and third beats, or as some have explained; a pattern of a Strong, Weak, Strong, Weak emphasis in the bar with the third beat a little less strong than the first beat. In 5/4 time we might have a pattern of Strong, Weak, Weak, (Less) Strong, Weak.

So let us go back and examine 6/8, ¾ and 2/4. In 6/8 and ¾ we have the same number of eight notes but one is “felt” in two and one is felt in three. In 6/8 time one has two even “pulses”, where the ¾ time has three pulses. [Yes at extreme tempos, the ¾ could turn into more of a single pulse]. Are you familiar with Bernstein's “America” from West Side story? It is in alternating 6/8 and ¾ bars. The “tempo” of the eight notes remain constant, but the pulse, or beat, changes from one bar to another. So what is the difference between 6/8 and 2/4? They both are felt in two, but one has a base sub-division of three eight note and one has a basic sub-division of two notes. But in both the pulse remains constant.

Now onto 5/8 (and by extension 7/8, 9/8 divided asymmetrically, 11/8, 13/8, 14/8, et cetera). My approach to 5/8 is that (when divided 3+2 or 2+3) it has TWO pulses or beats per bar. But unlike 6/8 or 2/4 that also have two pulses per bar, the two pulses in 5/8 are uneven in length; asymmetrical! In a 3+2 division the first pulse of the bar would be 50 percent longer than the second pulse. If you where to tap your toes to the pulse in 5/8 the tapping would be asymmetrical, Does 5/8 = 5/4 = 5/2 ? The Definitive Guide.

Not! First let me state that this is in no way a definitive, nor even an authoritative statement on the differences between 5/8 and 5/4, they are my interpenetration of the differences and my use of them in my compositions.

On the surface one can say that they are mathematically equivalent. By this we mean that by setting the eight note in 5/8 time and the quarter note in 5/4 time to the same BPM (metronome mark) both bars would move through time at the same rate. Thus one could argue that they are equivalent and that there no real difference between them. But ask your self this is a there a difference between 6/8 and ¾ time? We can set their eight note BPM to the same value, and both bars would move through time at the same rate; but would they have the same feel? How about 6/8 and 6/4 ?

Part of the issue is how do we define rhythm?

So what is the difference (from my perspective)? It is one of “pulse”. In 5/4 time one would “feel” five pulses in the bar, no matter the BPM. In 4/4 time one feels four pulses in each bar. (I feel a lot of 4/4 music might be better notated as 2/2, but that is another discussion.) In 5/4 there might be an emphasis on particular pulses (beats), but there would be five even beats to the bar. In 4/4 there are 4/4 even pules (beats) to the bar with perhaps (given the gene of music) bit more emphasis on the first and third beats, or as some have explained; a pattern of a Strong, Weak, Strong, Weak emphasis in the bar with the third beat a little less strong than the first beat. In 5/4 time we might have a pattern of Strong, Weak, Weak, (Less) Strong, Weak.

So let us go back and examine 6/8, ¾ and 2/4. In 6/8 and ¾ we have the same number of eight notes but one is “felt” in two and one is felt in three. In 6/8 time one has two even “pulses”, where the ¾ time has three pulses. [Yes at extreme tempos, the ¾ could turn into more of a single pulse]. Are you familiar with Bernstein's “America” from West Side story? It is in alternating 6/8 and ¾ bars. The “tempo” of the eight notes remain constant, but the pulse, or beat, changes from one bar to another. So what is the difference between 6/8 and 2/4? They both are felt in two, but one has a base sub-division of three eight note and one has a basic sub-division of two notes. But in both the pulse remains constant.

Now onto 5/8 (and by extension 7/8, 9/8 divided asymmetrically, 11/8, 13/8, 14/8, et cetera). My approach to 5/8 is that (when divided 3+2 or 2+3) it has TWO pulses or beats per bar. But unlike 6/8 or 2/4 that also have two pulses per bar, the two pulses in 5/8 are uneven in length; asymmetrical! In a 3+2 division the first pulse of the bar would be 50 percent longer than the second pulse. If you where to tap your toes to the pulse in 5/8 the tapping would be asymmetrical, uneven, but not random. The underlying eight note “rate” (temp) would remain constant, but the pulse would fluctuate (in a precise manner). In 5/4 time the pulse would remain “constant”; id est two eight notes for every beat/pulse. 10/8 time and 5/4 time that both had the same BPM would be mathematically equivalent, but each would be felt differently. In 10/8 time we would normally have four (un-even) pulses to the bar (3+3+2+2 for example) where in 5/4 we would have five even pulses (2+2+2+2+2). 7/8 time would have three pulses, 9/8 (divided 2+2+2+3) would have four pulses, 11/8 (3+3+3+2) would be four pulses (Don Ellis once called it 3 and 2/3 time). Et cetra.

At extreme tempos these feelings of pulse can break down or blur, and I am sure there are examples in the literature that do not follow these guild-lines; as I stated this is my working model on the use of 5/8 vs 5/4 in my music.

Questions?

Ursus Demens