Which hymns cluster with each other?

Some hymns tend to be sung during the same meeting as other hymns; they co-occur. This is most apparent in holiday hymns. For example, if He Is Risen! (#199) is sung, there’s a decent chance that Christ the Lord Is Risen Today (#200) is also sung. What other pairs like this exist and do groups of hymns form clusters? In this post, I explore the the co-occurrence of hymns primarily through network analysis.

1 Methods

Since this is a somewhat technical post, let me take a moment to explain my methods. First, I start off with my entire dataset, which contains data from over 95,000 sacrament meetings.

To check co-occurrence of all hymns, here’s my procedure. I started with The Morning Breaks (#1) and found how many times it occurred in my dataset (662 times). I then looked at The Spirit of God (#2) and looked at how many times it occurred (1,886 times). I then looked at those two lists of meetings and identified any where both of them occurred (17 times). I can now get some interesting numbers. Of the meetings that The Morning Breaks (#1) occured, \(17 \div 662 = 2.57%\) of them also contained The Spirit of God (#2). Similarly, of the meetings that The Spirit of God (#2) is sung in, \(17 \div 1886 = 0.90%\) of them also contained The Morning Breaks (#1).

I then repeated this procedure for every pair of hymns, all the way until Little Baby in a Manger (#1209) and Long Ago, Within a Garden (#1210). That’s something like 138,000 unique combinations of hymns.

Most combinations—100,007 or 72.1% of them—were actually not attested in my dataset. Some of these include pairs of sacrament hymns, such as As Now We Take the Sacrament (#169) and There Is a Green Hill Far Away (#194). That makes sense since we usually don’t see two sacrament hymns in the same meeting. Others were between hymns from two different holidays, like Joy to the World (#201) and America the Beautiful (#338). Still others were between holiday hymns and certain non-holiday hymns, like Oh, Come, All Ye Faithful (#202) and How Firm a Foundation (#85). Some pairs of common enough non-holiday hymns that didn’t occur in the same meeting in my dataset, purely due to chance, include Now Let Us Rejoice (#3) and Come, Sing to the Lord (#10), On This Day of Joy and Gladness (#64) and Did You Think to Pray? (#140), and They, the Builders of the Nation (#36) and Testimony (#137). Of course the list goes on and on for other pairs that weren’t attested in my dataset.

But that means I did see 38,594 different combinations, which is a lot. It’s obviously way too large of a task to try and go through or explain all those pairs. So, I needed to find some sort of cutoff point between the most strongly paired hymns and others that happened to occur together.

2 Distribution of co-occurrences

Figure 1 shows the distribution of these 38,594 pairs of hymns and how often they occur in the same meeting.

Figure 1: Distribution of co-occurrence frequencies

The x-axis in this plot is log10 transformed because there were many pairs that didn’t occur in very many meetings and a few pairs that occurred in a lot; transforming it like this makes it easier to see the distribution. For example, on the far left of the plot, we see some very short bars. This means that a few pairs of hymns rarely occurred together. In this case, all of of these very short bars were combinations of two sacrament hymns. It is pretty rare for a sacrament hymn to be sung during a different slot in the meeting, so to divide that small number by the very large number of times that those sacrament hymns are otherwise sung results in a small co-occurrence rate.

The middle of the plot shows where the majority of the data lies. The most frequent co-occurrences by sheer number of meetings were actually not very interesting because they usually involve a sacrament hymn. In some cases, the pairs are between somewhat less frequent hymns like Guide Me to Thee (#101) (which is only sung about every 8.3 years) and sacrament hymns like God, Our Father, Hear Us Pray (#170). So, while there’s no inherent connection between the two, the sheer fact that one of them isn’t sung very often just means that whatever it happens to show up with will seem like a lot. In other cases, they’re between a sacrament hymn and a common hymn, like O God, the Eternal Father (#175) and Be Thou Humble (#130). Again, not very interesting because there doesn’t seem to be a clear connection between the hymns.

But then we get to the far right of Figure 1. There were a few pairs of hymns that maybe didn’t occur in too many meetings, but when one of them did the other one tended to as well. This is what I’m most interested in. As mentioned above, the strongest pair was He Is Risen! (#199) and Christ the Lord Is Risen Today (#200). If you sing one of those in church, there’s a 57% chance you’ll sing the other. The next two most tightly paired hymns are between those two and That Easter Morn (#198)! So, there’s certainly something up with the three Easter hymns! I’ll talk more about that below. Other pairs that were strongly connected were between other holiday hymns like Thanksgiving hymns, New Year’s hymns, patriotic hymns, and some Christmas hymns.

Let’s further explore these pairs in a little more detail and in a way that’s a little more interesting to look at.

3 Clusters

Figure 2 is a network visualization of the most commonly co-occurring pairs of hymns. There are lots of decisions that go into creating a plot like this, so don’t take it as the absolute truth. For one, I couldn’t show every pair of hymns because it would be far too cluttered. So I had to decide on a cutoff point. Based on Figure 1, I knew that a cutoff of roughly 10% co-occurred would likely be a good starting point since pairs above that point were what I expected to see and many pairs below that were not. After toying around with it, I eventually settled on pairs of hymns that occurred with each other 7% of the time.

Figure 2: Most frequently co-occurring pairs of hymns. Large version here