1. Coordinated Start: When you say that dancers count 5678, one way to interpret this question is that you are referring to the count down given by musicians / dancers before they start their steps/music. If this is true, then dancers count down the music as 5678 so that there is coordination of feet with the next beat of music on 1. Musicians on the other hand (since they don’t count in terms of 8’s, rather only 4’s) count down as 1234 so that there is a coordinated start on the next beat of music on 1. As mentioned by Peter J Saleh and others, this count down does the following:

– set the tempo of the piece

-a coordinated start (in a band the drummers usually strike their drumsticks together and count of 1234… and then the guitarist/ vocalist all jump in together on the next bar on 1. For dancers, the 5678 helps all dancers in the group to start coordinated on the next beat i.e. 1.

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2. Start on the Correct Foot: Another way to interpret your question is that dancers count 5678 (or 1234) so that they know which foot to start as mentioned in answers by User-12575220831194166050 and Leonid S. Knyshov.

By saying “5678” I am saying to my dancers “Here are the last 4 beats of the intro or right foot measure and the timing. Get ready to start on 1 with your left foot”. If I am rehearsing a figure and I need my dancers to start on their right foot, I would actually count “1234” and they would know that the next count is 5. This is done very often when practicing but rarely when performing.

The first half of the 8 is done with one foot and the second with another. Different dances start with different feet.

For instance take the following 3 dance forms from a dancers POV-

a) Salsa (this is a 4 count dance) – Forward basic (starts with left leg) is starts on 1, whereas back basic (starts with right leg) and starts on 5

b) Waltz (this is a 3 count dance) – Forward basic (starts with left leg) is starts on 1, whereas back basic (starts with right leg) and starts on 4

c) ChaCha (this is a 4 count dance) -Forward basic (starts with left leg) is starts on 1, whereas back basic (starts with right leg) and starts on 1 also

Musician counting: In all the above, the musician simply counts it as 1234+1234 (Salsa), 123+123(Waltz) and 123chacha+123chacha (Chacha). If I tell a musician to only play note 6 (in salsa) he would not know which is the 5th note because he has never learnt the piece that way (a random note of music) (see more on this below in point 3)

Dancer counting: In all the above, the dancer simply counts it as 1234+5678 (Salsa), 123+456(Waltz) and 123chacha+123chacha (Chacha TBH I’ve never heard of anyone counting Chacha as 123chacha+567chacha). If I tell a dancer to only dance on note 6 (in salsa) he would know that is his left foot since he learns dancing this way (which foot on which count of music) (again see explanation in point 3 below)

If a dance instructor, says 5678 (in salsa), then we know that we have to start on 1 on our left foot going forward for the next beat. But if he says 1234 (salsa), then we know we have to start with our right foot on count 5 going backwards for the next beat

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3. Easier to remember steps: The last way to interpret this question (which I haven’t found on this discussion yet) is in counting of the BMP. Peter J Saleh, Ramandeep Trehan and David Fung have somewhat hit the nail on the head with their explanation but I’ll try to elaborate:

a) Musicians can do 2 things – read + hear music (later on they will memorize the piece if they want to play it by rote/by heart), dancers also do 2 things viz. hear music+memorize steps (they never get a chance to read the music, since they dont have sheet music in front of them). What does this mean?

As Peter J Saleh mentioend

Musicians use 4, possibly to allow for “chunking” while keeping it easier for the eye to take in while reading music. This is similar to how two 4-digit numbers are easier to quickly read and recite than a single 8-digit number

In 4/4 timing, this helps musicians since the music is broken up into smaller segments and during practice if a musician feels he needs practice in some bars, he can simply repeat them again (in the below image I’ve highlighted bars 10–15 in red). So here, the smaller bars help him in counting bars & breaking up the large sheet of music into smaller bars (each of 4 beats). The musician gets to see + hear the music.

In the above piece it says 105 beats per minute, (not bars per minute as discussed later in this post) so in 60 seconds there would be 105 notes played.

Another related point is that in the above piece it says 105 beats per minute, (not bars per minute as discussed later in this post) so in 60 seconds there would be 105 notes played.

Compare this to a dancer who counts in 8’s because he has to hear music & memorize steps. For instance in a Salsa choreography, I’ll have the following

A dancer counts in 8’s because he has to hear music & memorize steps.

Here a dancer has finished 3 sets of 8 beats i.e. 24 beats across 3 sets. Now because the dancer memorizes steps according to 8’s if the teacher requested him to dance the 2nd set (incorrectly called the 2nd bar since a bar is usually 4 beats, not 8), he would dance the orange highlighted steps. If the instructor told him to dance the 1st half of the 1st“bar” and the 2nd half of the 3rd “bar”, because he has memorized it, he will dance 1234 of the yellow & 5678 of the green.

But contrast this with a musician, he will count this as 6 bars each of 4 beats (here ‘bar is correctly used since a bar is of 4 beats – in most cases) i.e. 24 beats across 6 sets/bars. But because the musician doesn’t memorize like the dancer if the instructor tells him to play the 1st“bar” and the 6th “bar”, he would be confused since off the top of his head he will not know what is the music in the 6th bar (he can read the notes if he had sheet music in front of him though) because he isn’t trained to memorized subparts like dancers are

Check out the below video – I want you to count the number of bars (not beats) firstly in 4’s and then in sets of 8’s. Look at the YT timer & stop when you hit 1 minute. You’ll notice that you counted as follows:

4 bars sets – 6 sets until 60 seconds (note the title of the song also calls this out as 24 BPM. Note dancers count BARS PER MINUTE, rather than as explained above BEATS PER MINUTE which musicians count. Here total beats = 6 sets*4 bars in each set*4 beats in each bar=96 beats

8 bar sets- 3 sets. Here total beats = 3 sets * 8 bars in each set * 4 beats in each bar = 96 beats

https://www.youtube.com/watch?v=0HEoEEZCaRw

Hope this helps!