High and Low Melodies

Author

Joey Stanley

There’s a bell curve, and that’s always going to be true based on stats.

Highest “average” notes

Okay, but the highest note isn’t everything. A melody may pop up to a high note once in the song but be relatively low for the rest. Or, a hymn may “feel” high because it’s consistently in an upper register, even if the highest note isn’t record-breaking. We quantify how high a hymn “feels” by taking the “average” note in the melody.

Technical details for nerds :)

To calculate the average note, I converted each note to its MIDI value, which is a number between 0 and 127 that is assigned to each pitch. Middle C has a MIDI value of 60. The C\(\sharp\) above it has a value of 61. The D above that has a value of 62. And so on. There’s nothing special about MIDI values but it’s a convenient way to turn notes into numeric values.

So, let’s take a simple C arpeggio, starting with Middle C. The notes would have the values 60, 64, 67, 72. The average of those four notes is 65.5, which would be halfway between the F and F\(\sharp\). The average note may not be as easy to intuit as a set of numbers because major and minor scales contain a mixture of whole steps and half steps, which are represented visually equidistant on a staff but are acoustically different sizes.

However, I can’t just take the average of the pitches because duration plays an important part. As mentioned already, Lean on My Ample Arm (120) sits on its highest note for a dotted half note and a fermata. Meanwhile, The Morning Breaks (1) goes up to an F\(5\), but it’s only for an eighth note. That dotted half note should be weighted differently than an eighth note when calculating average pitches.

So, what I’ve done is I’ve taken a weighted average, with longer notes carrying more weight than shorter notes, within the context of a single hymn. So if we take that same C arpeggio of note values 60, 64, 67, and 72, but we hold the last note out for three times as long, the average note should be higher. The way I’ve calculated this by multiplying each note’s midi value by how many beats that note’s duration is. So quarter notes are unaffected, eighth notes get the MIDI value cut in half, half notes get it doubled, etc. Then for each hymn, I take the average of those weighted note values. I then divide it by the average duration of notes.

So, for the C arpeggio, here’s the step-by-step process:

Multiply each note’s MIDI value by its duration. If we’re assuming I have three quarter notes and a dotted half note, then it’ll be \(60\times 1=60\), \(64\times 1=64\), \(67\times 1=67\), \(72\times 3=216\).
Take the average of those values. \(\frac{60+64+67+216}{4} = 101.75\)
Find the average duration: \(\frac{1 + 1 + 1 + 3}{4} = 1.5\)
Divide the average value by the average duration: \(\frac{101.75}{1.5} = 67.833\)

So, the average value would be five-sixths of the way between note 67 (G\(4\)) and 68 (G\(\sharp4\)). Compare that to the unweighted mean of 65.5. So the held high note did indeed bring the average note up a bit.

This was a simple example, but it can be easily extended to entire melody lines. And, as we’ll see in later blog posts, to harmony lines as well.

So, what hymn has the highest average note in the soprano line?

Fun Fact

The melody with the highest average note is True to the Faith 254.

The melody to True to the Faith 254 is consistently rather high. The average note is a little higher than a B4. As we’ll see later, there are hymns that don’t even reach the middle of the treble clef, so it’s surprising that there’s this one that averages higher than that.

It’s average was a 71.324, which is about quarter of of the way between B4 and C5

There is only one other hymn that averages higher than a B4, and that’s the soprano line of What Was Witnessed in the Heavens? (11). If you consider the part where the men sing without the women as the melody, the number changes, but we’re strictly speaking looking at soprano parts.

Its average is 71.14, or 14% of the way between B4 and C5.

Another nine hymns have average notes somewhere between B4 and B\(\flat4\). The following table lists them, along with the two hymns previously mentioned.

Hymns with soprano lines that average at a B\(\flat4\) or higher. Note that B\(\flat4\) is 70 and B\(4\) is 71.
Hymn Name	Hymn Number	Average Note
True to the Faith	254	71.24
What Was Witnessed in the Heavens?	11	71.14
Awake, Ye Saints of God, Awake!	17	70.64
The Lord Is My Shepherd	108	70.59
Come, Ye Children of the Lord	58	70.53
The Morning Breaks	1	70.51
Jehovah, Lord of Heaven and Earth	269	70.44
How Wondrous and Great	267	70.38
The Happy Day at Last Has Come	32	70.27
Jesus, Savior, Pilot Me	104	70.24
As the Dew from Heaven Distilling	149	70.15

So what does this mean? Well, it means that if you’re singing the melody to any of these hymns, you’re going to feel like the hymn is pretty high. It may not have the highest notes in the hymnal (note that Lean on My Ample Arm (120) isn’t on this list!), but you go high and stay there pretty consistently without much of a break.

Conclusion

I’m not saying that all hymns need to be restricted to the same range of notes, or that we need to sing everything lower. But, in this post, I’ve highlighted a few hymns that might benefit from being transposed down a bit, either permanently in the next hymnal, or as needed by the organist.

Recommendation for the next hymnal

Lower these hymns a key or two so that they don’t feel as high for people who sing the melody.

Recommendation for organists

If there is an easy way to transpose the hymns, whether it be on the organ itself or through the church’s website, turn these hymns down a key or two.