In many early American churches—and some churches today—congregational singing consisted of either a preacher lining out a melody, with the congregation responding, or a cappella singing using words-only hymnals.  In either case, most folks learned the melody by ear.  Over generations and in the absence of notated music, each local church community would develop its own version of a hymn tune.  These versions form a tune family—that is, a collection of tunes that are regional or denominational variants of the same melody.  Unless we know the original melody, however, it is not always clear which tunes belong in the same family.  Another wrinkle in the story is that melodies can vary through oral transmission and also by the conscious act of an arranger or editor.  In the American folk hymn tradition, the tune and the text are rarely “married” to one another; one text can be substituted for another when they share the same poetic meter.  Therefore, I will disregard the text for the moment.

BOURBON (page 13t) and its variants CONFLICT (260t), DISMISSION, MEDITATION, etc. belong to the same tune family.  In my discussion of BOURBON, I mentioned that I consider it to be more distantly related to THO’ DARK BE MY WAY (305), which Hauser originally titled BEGONE UNBELIEF.

Here are my questions on tune families…

1. I’ve described a tune family as a collection of tunes that “seem to be” variations of a single, original melody, which may be unknown.  Can we make this more precise?  How different can two melodies be, while belonging to the same tune family?
2. Can we quantify some sort of “melodic distance” so that any two melodies that are in the same tune family are “close” according to this distance?
3. Supposing we have a way of calculating distance between two melodies.  Can we use that to identify melodies that are more distantly related, but still descended from a common ancestor—that is, to find melodic cousins, in addition to siblings.
4. Can we make a “tune family tree” and recover the original, ancestral melody?

I’m certainly not the first person to ask these questions.  Question 1 is difficult to answer. Students of American folk hymns such as George Pullen Jackson and Nikos Pappas have relied on their own intuitions—good though those intuitions are—rather than giving precise instructions for identifying a tune family.  Question 2 interests me greatly, and may help us answer Question 1.  There have been several theoretical measures of melodic similarity developed that seem reasonable in this context and have withstood empirical testing.  However, I think we can do better, in this case, because the category of American folk hymns is quite narrow.  In this repertoire, we have extra information—the poetic meter of the hymn text—that parses each melody into phrases (most commonly, into four or eight phrases).  The poetic meter also tells us which musical notes correspond to accented syllables in the text.  Question 3 is especially relevant to large databases of hymn tunes such as Temperley’s Hymn Tune Index and Pappas’ SWASMIS.  At the moment, these are searchable by exact melodic matches, but not by near matches.  The answer to Question 4 is probably “no,” but why not try?  There are some tunes, like Billings’ SAVANNAH, that crossed into the folk hymn repertoire, so we can even get a sense of how fast melodies “mutate”—perhaps we can tell how old a tune family is by the amount of variation it has?

Here are some thoughts on identifying tune families and quantifying musical distance in general.  Please understand that I am not claiming that any of these songs are “the same,” any more than I would think that two siblings are the same person.  Moreover, my concept of relatedness is based on notes of the melody, and ignores aspects such as text, harmonization, history, etc.

CONTOUR SIMILARITY.  I’m going to start with a simplified case: suppose we have a four-line hymn, where there are four iambic feet per line.  Poetry that follows this pattern, including all the texts for the BOURBON tune family, is said to be in long meter (L. M.).  Common meter (C. M.) songs like “Amazing grace, how sweet the sound” have four lines, alternating four and three iambs per line.

My first thought is to reduce each tune to a “skeleton” representing the notes that fall on syllables of poetry.  Here’s a reduction of Lewis’ BOURBON, using open notes for accented syllables and filled notes for unaccented syllables.  The small notes to the left of the key signature are the ambitus, representing the span of the highest and lowest notes in the song.

This reduction has the advantage that we no longer have to worry about the rhythmic irregularities of a particular setting of the song (those are interesting, but we’re doing a reduction here).  So the fact that Davisson added rests in the middle of his setting from c.1822 doesn’t change the basic skeleton of the melody.

Here’s DISMISSION.  You can see how similar they are at this level.

George Pullen Jackson indexed songs by their first few notes, as he explained on page 132 of his White Spirituals of the Southern Uplands (1933).  Among his “eighty most popular tunes, ” pages 133-150, he lists SUPPLICATION, BOURBON, and CONSOLATION as one tune and  DISMISSION as another.  For reference, here is SUPPLICATION

and here’s CONSOLATION

A good case can be made that these two tunes are closely related to each other, though SUPPLICATION is long meter and CONSOLATION is common meter.  Note the similar ambitus and contour.  Clearly, though, BOURBON is closer to DISMISSION than it is to either of these.  To be fair, Jackson comments,  ”Tune indexing is still an infant endeavor,” (page 132) and he remarks elsewhere on the similarity of BOURBON and DISMISSION.

Let’s revisit BEGONE UNBELIEF (305) and also look at RESTORATION (312b or 268t in The Sacred Harp, depending on which revision you use).  Although neither song is in long meter, both consist of four lines with four accented syllables each.  RESTORATION is in the “8s & 7s” meter, meaning alternating eight- and seven-syllable lines, usually with this accent pattern:

RESTORATION.  8, 7.

COME thou FOUNT of EVE-ry BLESS-ing
TUNE my HEART to SING thy PRAISE

There are exotic meters, like 10s, 11s, or even 12s, that follow the same pattern of four accented syllables per line.

BEGONE UNBELIEF.  10, 10, 11, 11.

Be-GONE un-be-LIEF my SAV-ior is NEAR …
By PRAY’R let me WREST-le and HE will per-FORM

In these cases, it’s harder to “map” one tune to another because the unaccented syllables are associated with the accented ones in different ways.  A naive fix for this would be to just look at accented syllables.  Here are BOURBON, DISMISSION, BEGONE UNBELIEF, and RESTORATION.

BOURBON. L. M.  (ShH 13t)

DISMISSION. L. M. (MH 145)

BEGONE UNBELIEF.  10, 10, 11, 11.  (ShH 305)
Tho’ Dark Be My Way

RESTORATION.  8, 7. (SH 312b, CB 268t)

The resemblance is not nearly as close as between BOURBON and DISMISSION, but there does seem to be a relationship, and it also seems reasonable to attempt to quantify how close the skeletal melodies are to each other.  The simplest measure is to count the number of places where the melodic reductions differ, so that the “distance” between BOURBON and DISMISSION is 2, while the distance between BEGONE UNBELIEF and RESTORATION is 8—half the maximum distance of 16.  A natural refinement is to count the number of scale-steps difference, rather than just treating any difference equally.  This approach favors similarities of contour without requiring actual pitch matching.  Of course, we can throw  other information into our calculations–the ambitus, perhaps.

Here is another group of tunes that have similar melodic contours, this time alternating 4 and 3 accented syllables per line.

NEW BRITAIN / HARMONY GROVE.  C. M. (SH 45t, ShH 300t)

PRIMROSE.  C. M. (SH 47t)

YE OBJECTS OF SENSE.  11, 8.  (ShH 444t)

CARRADOC PLAINS.  11, 8. (Olive Leaf; also arr. J.P. Karlsberg)

OTHER SIMILARITIES. Contour seems, to me, the most promising way to study tune similarities.  However, there are other approaches.  For example, notice that all the members of the BOURBON family end with “fa-sol-la” (3-4-5) at the end of the second phrase of the melody.  Is it possible that all or most tunes with this motif are related?   IDUMEA (SH 47b) is an example, as is TENDER THOUGHT (ShH 21) and HUMBLE PENITENT (ShH 399).  Another consideration is phrase structure—see the comments here.

If contour is the main marker of tune family, perhaps a tune family can contain both minor and major melodies…. Here’s a thought—does anyone else think of IDUMEA (SH 47b) and PSALM 30 (ShH 22b) as variants of each other?  Of course, the fact that they share a text helps.  Again, phrase structure is telling.  I would describe both songs as ABB-A, where B- is a prolongation of the B phrase.

MORE COMMENTS.  I’ve received several thoughtful responses to this post on fasola-discussions and Facebook.  Jason’s comment about developing a generative theory of hymn tune melodies reminded me of George Pullen Jackson’s overlay of the melodies of PISGAH (SH 58) with Ruth Crawford Seeger’s transcription of the singing of Jesse Allison and his group, recorded here.*  Here’s a reduction of PISGAH as in the Sacred Harp, plus my reduction of the Allison recording.  I’ve kept in the unaccented syllables, but of course you can ignore them.

PISGAH.  C. M. (SH 58)

AMAZING GRACE.  C. M. (transcr. R. C. Seeger from Jesse Allison)

*George Pullen Jackson, White and Negro Spirituals, New York: J. J. Augustin, 1943, p. 350-1.