When the U. S. Constitution was written, figured bass in music was already falling out of vogue.
Even so, I think that figured bass gives us a few insights into how the Founding Fathers reasoned about what needed to be written down and what could be reasonably inferred by the reader.
This is important in light of people today who claim to be both “conservative” (not in any manner that would have made sense to the Founding Fathers) and “originalist” in their reading of the Constitution.
Originalists claim that they interpret the Constitution as it was written, not as any modern person wishes it had been written.
There is a more honest kind of originalism in music in the trend towards historically informed period instrument performances of music of the 17th and 18th centuries.
Recordings of such performances supposedly let us hear the music in a way that’s closer to what the original composers would have heard in their lifetimes.
Johannes Pachelbel probably did not intend his famous Canon and Gigue in D major to be performed by fifty violins (with enough violas and cellos to balance) at a slow tempo. And maybe he would be shocked to see four double basses playing that famous bass line, or any double basses at all.
A brief overview of figured bass
For the purpose of this article, I assume that you know how to read music, and at least the basics of tonal harmony. But maybe you can still get something out of it if you know neither notation nor harmony.
For much Baroque music for ensembles, from quite small (the quartets that would play so-called “trio” sonatas) to choir and orchestra, it was expected that a musician would play a keyboard instrument, like the harpsichord or the organ, from a partially written part.
This is “basso continuo,” or “figured bass” in English.
The left hand part (the bass, with bass clef) would be the same as the part for the bass instruments, like cellos or bassoons. For the right hand part (with treble clef), the composer would give some indications as to chords, but giving the performer a lot of flexibility as to which exact notes to choose.
For example, consider these four measures:
The piece seems to be in D minor. The first measure is probably supposed to be a tonic chord (Roman numeral i in “Roman numeral analysis”).
The bare minimum required for harmony for the first measure would be a minor third, F in this case. Since it’s the first chord of the piece, the composer probably also wants the fifth in there for a fuller sonority. And an octave would round it out nicely.
The performer may choose whatever combination of notes is comfortable, provided the notes are all above the bass. This may be indicated with the numbers 8, 5, 3 below the staff, like this:
The octave in this illustration is actually a double octave, the fifth is actually a twelfth, and the minor third is actually a minor tenth. But that sort of thing is okay as long as we can obtain the specified intervals by subtracting octaves.
Since pretty much all chords should have a third above the bass (except triads in second inversion, seventh chords in third inversion, and certain harmonic anticipations), to write the 3 is often not strictly necessary, and so it may be omitted.
The fifth of the chord is not actually required to define the harmony, unless it be diminished or augmented, and so it may be left out, and the 5 may be omitted just like the 3. And the octave is, in a way, redundant, so it may also be left out, and the 8 may be omitted just like the 5 and the 3.
So then we don’t need any “figures” for the first chord. Suppose the second chord is supposed to be a minor subdominant chord (iv). It then needs its own third, B-flat in this case, and maybe also the fifth (D) and octave (a higher G).
But now our choice of notes for the second chord is constrained by what we played in the first measure. This would be wrong:
That’s because the four “voices” are all moving in parallel motion by the exact same interval, which is unacceptable in this style of music, and probably most other styles of music.
This rule does not apply to an instrument with a part that is completely in parallel with another instrument (e.g., double basses in parallel octaves with the cellos).
But when voices are to be independent of each other, parallel fifths and parallel octaves should be avoided (parallel thirds are acceptable provided there aren’t too many of them consecutively).
This would be much better:
I don’t like the parallel movement from a third to an octave, but in the context of a concert rather than an examination, probably no one would criticize you for it.
The tie here merely indicates a common tone held over; in actual performance it would probably be a good idea to strike the note again, especially in the case of a harpsichord.
It is more likely that the composer meant the second chord to be a triad in first inversion, in which case he may indicate that with the numbers 6 and 3 (I use the pronoun “he” because we’re talking about the Baroque era here and the composer would almost certainly have been a man).
The 6-3 chord allows us to move to perfect intervals by contrary motion:
The move from a perfect fourth to an augmented fourth (a tritone) by parallel motion is acceptable, I think.
Remember what I said earlier about thirds in almost every chord: the 3 figure is unnecessary, so we can omit it, leaving only the 6:
Now suppose the second chord is supposed to be a Neapolitan chord, with E-flat instead of E-natural above the bass. The composer would indicate that as flat 6.
The perfect parallel fourths are perhaps objectionable, but that’s a problem that would not arise if we omitted the double octave in the previous measure.
In a D major context, the composer would also have to specify flat 3, but a flat by itself would be understood to mean a lowered third.
Or maybe just flat 6 would be sufficient. Though a Neapolitan chord seems a bit too modern here.
In either context it would be unnecessary to specify that the flat 6 is to be doubled as a flat 13, and there wouldn’t be the opportunity for the flat 13 in the first place with a less full chord in the first measure, like I said earlier.
Let’s go back to the first inversion triad for the second chord, and move on to the next measure, a dominant seventh chord. Since the fifth and third are understood, the 7 figure would be sufficient.
However, since this is in a minor key, we also need to specify a raised third, in this case with a sharp.
The tie once again indicates a common tone. For the last chord, the composer might want a major third, in which case the figure would be just a sharp.
The fifth is omitted from the final chord because it is preferable to resolve the G to F-sharp than to A. I suppose this is why Baroque composers generally eschewed dominant sevenths for the penultimate bar.
With a dominant triad instead of a dominant seventh, there can be an octave in the penultimate measure, which as a common tone becomes the fifth of the final tonic chord.
You might be wondering: what kind of composition consists of just four measures? Maybe a short section out of a longer composition, in a very slow tempo.
In which case playing one block chord for each note of the figured bass might be unsatisfactory. It might be better for the performer to play some arpeggios, or in some other way noodle around:
It might seem like a lot is being left up to the performer here, but a lot of this would have been the result of an application of common sense and good taste.
Even so, this is in many ways quite a modern demonstration of figured bass. For one thing, the continuo player would not be given a sheet with a blank treble clef staff in which to write his realization.
Instead he would have been given a bass instrument part (like the cello part) with figures, and he’d have to realize those figures on the spot at the concert. Or maybe rehearsal.
Thus it made sense that they wrote the figures above the part instead of below it as we do now.
Modern editions of Baroque music tend to have figures that are more explicit than a Baroque musician would have expected or wanted. Some editions go so far as to include figured bass realizations.
I write figured bass realizations, but I want to be clear that they are suggestions, and that the performer is free to invent his or her own realization.
Thus, like other editors, I write my realizations with smaller noteheads (unless I forget that step in my final review; you might be able to find an example of that in something I uploaded to IMSLP years ago).
The harmonic palette of Baroque composers was limited compared to their counterparts of the Romantic era, but, on the plus side, this allowed Baroque composers to be more concise with the figured bass.
For example, let’s say you’re writing a piece in D minor with figured bass that modulates so that you need an F-sharp major chord. If F-sharp is in the bass, your figures would need to indicate that A needs to be raised to A-sharp and C to C-sharp.
However… a chord consisting of F-sharp, A-sharp and C-natural would have been odd in a Baroque context. Therefore, sharp 5 would be understood as implied from sharp 3. Assuming of course the player even decides to include a fifth in the chord.
Figured bass in Vivaldi
This might all seem very abstract and not applicable to actual music, so let’s go to an actual musical composition that has been played and recorded by many different ensembles: Antonio Vivaldi’s powerful and mildly Brucknerian Concerto No. 8 in D minor from his “La Stravaganza” collection.
Given that we’re talking about a dead white guy with hundreds of recordings of his music in various record companies’ catalogs, you might think I’m not too concerned about some of his music being obscure.
And it helps the D minor Concerto that it comes from a named collection, but it’s still relatively obscure compared to the hits of “Le Quatro Stagioni.” In the Naxos Music Library, there are 385 recordings of the G minor “Summer” Concerto, compared to only sixteen recordings of Stravaganza No. 8.
I think the No. 8 needs to reach a wider audience. One of the obstacles is that the expected continuo instrument for No. 8 (and indeed the whole collection) is not a harpsichord but an organ, as in pipe organ.
There are several passages in Concerto No. 4 in A minor that make the requirement of an instrument with sustaining power abundantly clear. However, as this recording shows, it can still be quite impressive even without organ.
I’ve begun arranging the twelve concerti for a fuller orchestra in the hopes of enabling more modern orchestras to play these, and also to bring to the foreground the Brucknerian aspects of this music.
I consider it more important to highlight the intense drama that I hear in this music than to present it like Vivaldi would have heard it in his lifetime.
Clearly I’m not an originalist in music. Unless I can prove that Vivaldi, like Hindemith, intended his musical scores to be useful (Gebrauchmusik), and not regarded as Holy Scripture that must not be modified in any way (dogmatic Urtext).
At the same time, however, I could boast that I am more of an originalist because I’m striving to follow an aspect of these compositions that is typically ignored for Vivaldi’s more famous compositions: the figured bass.
Not only does figured bass help me check for wrong notes, it even gives me ideas for what to write for the instruments Vivaldi did not include in his original conception.
For example, what should I give the horns or trombones to play? In some cases it might be appropriate to write for them chords sustained for longer than the harpsichord or even the piano could hold.
Most musicians nowadays are quite used to reading engraved music (whether from physical engraving plates or from computer files), so the handwriting of old publications is a little bit of a shock.
The symbol for a sharp was an X, which looks like what I very occasionally used in handwritten sketches or school exercises for a double sharp. So that threw me for a little bit of a loop at first.
The symbol for a flat is essentially a downward arrow, and it’s easy to see how it is the precursor for our modern flat symbol.
The rule about accidentals and barlines hadn’t been developed yet. An accidental could be understood to apply to two consecutive notes that are meant to be the same in pitch, even if separated by barlines.
But if there were intervening notes of different pitches in the same bar, the accidental would have to be written again. One example of that is a repeated F-sharp in the excerpt at the top of this page.
The most relevant difference here is that instead of indicating raised or lowered non-third intervals with a prefix symbol in the figured bass, the composers would “slash” the number, and this slash could occur as a sort of suffix.
Adding to the confusion for modern musicians is that a single-stroke slash means sharp, but the two-stroke slash means flat. The old notation for flat 7 was particularly confusing: it looks more like a natural symbol (which was also used at the time).
Another 18th Century practice that is likely to confuse musicians today, even if they’re aware of it, is that for some minor keys, composers used key signatures with one fewer flat, e.g., C minor with two flats instead of three.
In Concerto No. 10 in C minor, for example, Vivaldi writes a lot of A-flats in the first few measures. But A-flat is not in the key signature, so, as you can imagine, a modern musician might easily get confused and play A-flat when A-natural is meant.
The F-sharp major chord example does come from “La Stravaganza,” but at the moment I don’t remember where from.
More telling is the attitude towards repeated chords. In measure 10 of the Concerto No. 8, the continuo musician is to play the A just below middle C followed by the A an octave lower.
The first A is explicitly to be played with a seventh chord, and the third sharp, that is C-sharp and G (the fifth, E, may be omitted). But is the next A supposed to be played with C-natural but no G?
If that doesn’t look wrong to you, play it for yourself on the piano. Clearly Vivaldi meant for the next A to have the same kind of chord.
In the modern practice of figured bass, we don’t repeat figures, but instead use what I like to call “continuation dashes.” Thus the performer gets a neat and concise visual cue that he or she may simply repeat the previous chord.
Though in this case I prefer to take this opportunity to move the right hand in motion contrary to the left hand.
For the triad following the 6-4 chord, I don’t consider it necessary for the figures to specify the fifth, so the 6-4 to 5-sharp [3] in the source becomes 6-4 to sharp [3] in my edition. The performer may very well drop the fifth even if explicitly indicated.
The Adagio is fifteen measures long, longer than the 4-measure example earlier but still of such a nature as to make realizing the figured bass as plain block chords inadvisable.
However, this is the first example that I’ve seen where it is clearly indicated that the continuo player is to play arpeggios: notice the words “Arpeggio con il Cembalo”:
Still, there is room for interpretation. One way to realize this is that each note in the figured bass gets a rolled chord followed by a more pronounced arpeggio, which may change direction. Something like this:
I haven't yet made the right hand notes small because I’m still working on this file.
These few bars are replete with examples of figures that are less explicit than I would like but also a few that are more explicit. After a 5-4 triad anticipation, I generally don’t consider it necessary to specify 5-3, or 5-sharp [3].
Because this passage goes far afield harmonically, it is necessary for the figures to be quite clear. But there is that annoying tendency to assume that a certain accidental just continues to apply, like the measure in which the first violins have a C-sharp whole note, which the continuo player may or may not be fully aware of.
In the ensuing Allegro in 3 / 4 time, I worry about having too many figures. In Vivaldi’s time, he could safely have assumed the continuo player would understand a harmony to persist through different inversions of the bass note.
Think of, for example, the notes E, G-sharp, B-natural and D in close succession in the bass, followed by C-sharp, A and E. The figures 7-natural 5-sharp [3], 6-5-natural 3, sharp 6-4-3, natural 6-sharp 4-2, 6, sharp [3], sharp 6-4 might seem overly fussy.
I’m still using Finale 2010. Which may be unfortunate because Finale 2012 added support for figured bass. But they put that under the Lyrics tool?
It’s probably still a lot less laborious than creating a Figured Bass category under the Expressions tool, especially since the stacking of accidentals with numbers in the same Expression has been rather problematic, in my experience.
As you can see in the following screenshot, the way that I’ve been doing it, figures that require both numbers and accidentals have to be composited.
Ten years ago, I would have made this arrangement freely available on IMSLP. But these take time, time that some say I should spend mindlessly applying to hundreds of jobs online. I might eventually publish these in some other way.
Changing technology, changing uses
Charles H. Sherman reminds us, in the preface of each score of a Symphony by Michael Haydn that he has edited, about how Leopold Mozart wrote that Haydn expected continuo even “in the most fully instrumented works.”
By contrast, Joseph Haydn, by the time he went to London, evidently regarded figured bass as something of the past. Listen to his Symphony No. 98 in B-flat major for one salient example.
Technology changes, and the way we use technology also changes. Vivaldi could certainly have used horns, trumpets and trombones in his Stravaganza collection if he had wanted to.
But with the horns and trumpets he would have been severely limited in what notes he could ask them to play, especially in the lower registers.
I doubt Vivaldi would have been too surprised by Michael Haydn’s Trumpet Concerto in D major, which is not to say he would have liked or disliked it. Joseph Haydn’s Trumpet Concerto in E-flat major, on the other hand, would have been a revelation.
Today’s horns have four valves (pistons) and today’s trumpets have three valves. The player is still expected to have proper embouchure or else he or she will not be able to get certain notes with the proper intonation.
The technology for playing recordings of music has also evolved significantly since Vivaldi’s time. Perhaps you’ve heard of player pianos with their piano rolls, a distant precursor of audio cassette and audio disc players.
To celebrate the victory of the British over the French at Victoria, Ludwig van Beethoven wrote Wellingtons Sieg, Opus 91, a piece for Johann Mälzel’s panharmonicon.
The panharmonicon is a sort of barrel organ, which also includes actual percussion, like a triangle and cymbals. But the Mälzel invention musicians are grateful for is the metronome.
Beethoven’s Sieg was popularly acclaimed and critically panned. He made several arrangements, including one for full orchestra with cannons and muskets.
In most recordings of the piece, we hear the dry, rattling sound of muskets, and the perhaps more satisfying sound of cannons. Modern artillery would make for a duller, more continuous and monotonous sound.
On a bonus track for Antal Doráti’s recording of Wellingtons Sieg with the Minneapolis Symphony, Deems Taylor explains of the British and French muskets fired for the recording, that
Both types are muzzle-loading weapons, and firing them was a laborious procedure. The musketeer has to bite the cartridge tab, pour some powder in the pan, the rest in the muzzle, cram the paper and the lead ball over it, and ram the entire load with a metal ramrod. ... There were three misfires, but this is not unusual for flintlock muskets. ... Over sixty musket shots were recorded over the rest of the afternoon. … the best sounding shots were selected for the master tape.
The selected sound clips were then mixed in with the Minneapolis Symphony performance.
In this video of a youth orchestra performance, the mock artillery sounds don’t come through as well as I would have liked:
You could probably tell from the beginning I was eventually going to get around to the Second Amendment, the most misread part of the entire U. S. Constitution.
A lot of weapons today don’t even require much skill. The only reason I would ever want to shoot an M16A2 again is to earn a Rifle Expert badge. Apparently I can’t buy an M16A2. Rightly so, that’s a weapon of war.
I suppose I would have to settle for an M16A2-style AR-15. You can buy a scope for the AR-15, but what’s the point? Judging by a Google Image search, a lot of AR-15s don’t even have the triangular sight post.
I guess you’re supposed to shoot those from the hip in the general direction of your targets, press the trigger and just let the damn thing spray a whole bunch of bullets.
Some of them are bound to kill or at least injure people. But injure them so severely they might wish they had died.
I’m sure getting shot by a French musket would hurt like hell, and it might even kill you. But if it doesn’t kill you, recovery might be a simple matter of getting the bullet removed and some stitches.
Surviving a mass shooting injury might mean getting a body part amputated. Doctors have noticed injuries even worse than those inflicted by modern hunting rifles.
Just as Vivaldi would be impressed by today’s trumpets, Thomas Jefferson would be impressed by today’s rifles. They’re so easy to reload, and they can shoot so much without jamming.
And I think he would be shocked by the idea that individuals, some of them not quite right in the head, think they have an individual right to such weapons of mass murder.
If they had had knowledge about the future of weaponry, I think the Founding Fathers would have been very explicit in that the right to keep and bear arms is a state right, not an individual right.
Many of you disagree with me on this, even those of you who are not lawyers and are not constrained by Supreme Court decisions on this matter.
But some of you have acknowledged that the first clause of the Second Amendment is a meaningful part of it, and not just filler to increase the word count.
Conclusion
In the 18th Century, lawmakers were economical with their use of words, just as composers were economical with their use of musical symbols. Just as Vivaldi or Bach would not write a flat or a sharp if he didn’t think it necessary, Jefferson or Madison would not write a “prefatory” clause if he didn’t think it necessary.
For what it’s worth, I am an originalist when it comes to interpreting the U. S. Constitution, in the sense that I think we must consider the original context and determine anew what would have been reasonably inferred back then. But, since I’m neither judge nor lawyer, this might not be worth much.
Another commonly misunderstood part of the Constitution is Article II, Section 1, and here historical context also helps us arrive at the correct interpretation. “The executive power shall be vested in a President of the United States of America.” That’s unitary executive authority, right? Just shy of royal authority, constrained only by specific democratic processes?
Having freed themselves of King George III’s tyranny, the American people were very wary of any central authority. So wary that they held off establishing a central federal government for years after declaring independence from Britain.
A little history lesson should be enough to make it clear that Article II was not intended to give the president the sort of unchecked power the proponents of the unitary executive theory claim that it does.
And yet some very smart people, like lawyers in President Obama’s administration, have fallen for the unitary executive theory. And of course also some very dumb people, like dumbass you know who.
University of Michigan Law Professor Julian David Mortenson reminded us, in an article published in the Atlantic a couple of months ago, that “executive power” is merely the power to execute the law.
Mortenson reviewed thousands of documents from the time the Constitution was drafted, including those collected in the Documentary History of the Ratification of the United States Constitution.
This review confirmed what Mortenson surmised from his elementary school history class: the Founding Fathers never intended the president to be in any important way like a king.
Otherwise, they would have said so. And they probably wouldn’t have bothered to devise a whole system of checks and balances.
They may have failed to foresee a lot of 21st Century problems, but they were aware of the danger of foreign influence. And rightly so.