an Unequal Temperament

The clavichord needs to be tuned every two or three weeks, and it doesn’t take long to do it. I have taken this as opportunity to experiment with unequal temperaments.

Back in piano tuning school, we were taught to always tune in equal temperament, which has many advantages. It makes all of the keys equally usable, and is almost universal nowadays for everything except early music (up through J. S. Bach, maybe a little further – some extend the use of unequal temperaments on into the Classical era of Haydn and Mozart.)

Hermann Helmholz in his nineteenth-century book “On the sensations of tone” speaks ill of equal temperament, especially for the training of singers (see chapter 16 for an extended discussion of tempered intonation). For example: “The singer who practices to a tempered instrument has no principle at all for exactly and certainly determining the pitch of his voice.” (p. 326)

So when I tuned the choir room piano about six weeks ago, I decided to apply one of my clavichord tunings and see how it sounds. So far, so good: none of the choristers have yet complained, and I think that I prefer it to equal temperament. The “good” keys (C major, F and G major, etc.) are cleaner than they are in equal temperament, and the keys with two sharps or flats are almost as good. The keys with three and four flats and sharps are about like they are in equal temperament. The others? Not so much. The crunchiest is G flat major, as described below; it is barely usable, with D flat major about as bad. Is that too great a price for the improvements in the other keys? That is an open question.

For those who might be interested, here is my tuning plan, such as it is. On the clavichord, I don’t follow a plan, beyond making the fifths and thirds increasingly “noisy” as they move around toward the back side of the circle of fifths (that is, the G flat to D flat fifth, or maybe the D flat to A flat). The details differ every time I tune it, depending on whether I am in a mood that day to favor the sharp keys or the flat keys.

Tuning a piano is a bigger undertaking, so I was more careful:

The Foundation

Tune the A-440 from the tuning fork, then down an octave to the next A, the one on which you will base the tuning.

Tune the following intervals:
F-A pure (no beats. This is a considerably smaller major third than equal temperament)
A-E pure
C-E pure (that is, tune the C based on the E that you have just tuned)
Check F-C; should be about one beat
Check F-A-C triad; should be almost pure
Check A-C-E minor triad: should be pure or almost pure

Tune C-G pure
Check C-E-G triad; should be pure

Tune G-D, about 1 beat narrow
Check D-A (down a fourth from the D), should be about 1 beat wide; adjust D to balance the D-A fourth and the G-D fifth

Tune G-B pure
Check B-E, should be about 2 beats
Check G-B-D triad, should be almost pure
Check G-B-E minor triad (first inversion), should be clean but not pure.

Tune the F to F octave.

This completes the white notes for the temperament octave.

The Balancing

Now for the fun part: the black notes, which are a matter of tradeoffs.

Tune the following intervals:
F up to B flat, about 2 beats wide
B down to F sharp, about 2 beats wide
A up to C sharp, about 1 or two beats wide

Check the intervals from F sharp to A sharp, which will be fairly clean, and F sharp to C sharp, which will be noisy, 3 or 4 beats. Check the F# - A# - C# triad. This will be the worst in the temperament because of the fifth.

Adjust these three pitches (F#, A#, C#) to your satisfaction, checking the major and minor triads (most of them in one or another inversion) that they complete: B flat major, B flat minor, B minor, F# minor, A major, F# major. They will have varying degrees of cleanliness; which of them are better is up to you.

Take a deep breath.

Tune the B flat up to E flat (interval of a fourth), about 1 beat wide.
Check B-D#, should be fairly clean. Check B major, likewise fairly clean.

Tune the E flat down to A flat (interval of a fifth), about 1 beat narrow.
Check the A flat-C-E flat triad. It should be fairly clean. Adjust E flat and A flat to your preference.

Check A flat-D flat, compare with the F# - C# fifth, adjust the C#/D flat so that these two intervals beat at about the same speed, about three beats, checking the thirds from A to C# and A flat to C so that they are both acceptably clean (they will not be pure). This is a point where you could choose to favor the sharp keys over the flat keys by making A-C# cleaner than A flat – C, or vice versa if you would prefer to favor the flat keys. That may depend on what music you plan to play on the instrument before its next tuning. Check the other triads that include A flat and D flat.

Check all major and minor triads. The best way to do this is by going around the circle of fifths, starting with the C major triad and moving either direction (C-G-D-A etc. or C-F-B flat-E flat etc.). The triads should get increasingly “noisy” in a smooth progression up to the G flat major triad, then gradually smoother as you go on back down the other side toward C major. The minor triads should do likewise, starting with A minor.

It is up to you as to how extreme you make the temperament, and you can favor the sharp keys over the flats or vice-versa; the above is only a guideline, especially the latter part of it on the black notes. It is all a matter of tradeoffs.

The Rest of the Piano

From here, tune pure octaves as usual, up to the top and then down to the bottom. The one wrinkle for me was that the octave check intervals I normally use in equal temperament – chains of chromatic tenths in the treble, which should gradually increase in beat speed as one ascends – do not work at all. The chromatic thirds even in the temperament octave will have radically different beat speeds. Same for the low bass, where I likewise check with the interval of the tenth, also the minor seventh (or rather, minor fourteenth – the seventh plus an octave) which in the low bass beats slowly enough to be useful). But with the unequal temperament, about the only way to check the octaves is with the fourth and fifth that lie within the octave that you are tuning; are they what one would expect, given the degree of beating in those intervals in the temperament octave? Remember that the beat speeds will be faster as one goes up and slower as one goes down.

For further study

If these matters are of interest, you might look in a library for Owen Jorgensen’s book “Tuning the historic temperaments by ear” (Michigan State Univ. Press, 1991) which appears to be out of print.

Here is a discussion of the book in the excellent forum “Piano World.” Notice in particular the remarks by Bill Bremmer, an experienced piano technician. He gives a very different “recipe” for an unequal tuning, based on the Thomas Young Well Temperament (1799), which leaves the F-A and C-E thirds somewhat impure, but would make the more distant triads (F# major, C# major) significantly cleaner than the plan outlined above.

Also, here is a website that discusses historical temperaments, giving a good overview of the subject. The author (Kyle Gann) gives the pitches in cents, which shows the difference of each pitch from its equally-tempered equivalent (in equal temperament, each half step is 100 cents, with 1200 cents to the octave). This would be more useful than tuning-by-ear accounts such as mine if one is tuning with the use of an electronic tuner.

But I leave you with the lesson I have learned from all this: the precise details of an unequal temperament are of little importance, especially on instruments such as the clavichord and harpsichord which are easily re-tuned. I have tried to suggest some basic principles, and encourage those interested to experiment freely on their own instrument.

The details matter somewhat more on a piano, and quite a lot on a pipe organ, for which a change of temperament is a multi-day operation and definitely not to be undertaken lightly or as an experiment.

[Edited 12/18/18 to add: Here is an article from the excellent (and free!) online journal "Vox humana," describing one of the oldest extant pipe organs in the world. It is in the village of Rysum in North Germany, built some time around 1450 and little modified since then. Of interest for the topic of my essay is a playing of the triads of the circle of fifths in the organ's temperament, quarter-comma meantone. It is a brief sound file, 32 seconds, and a good demonstration of unequal temperament on an organ; the "distant" keys at the backside of the circle of fifths are quite dissonant. There are weeks when my off-the-cuff clavichord temperament is almost this extreme, but I would not do this to the choir room pianoforte. The whole idea of temperament is to make these "distant" triads and keys either equal to all the others (equal temperament) or cleaner in varying degrees than they are in meantone (unequal "well" temperaments).]

Scales (with an afterword on Modes)

My piano student figured out on her own how to play a C major scale. We had introduced the concept of thumb-turns in the context of something she was playing, and she took it from there. It showed up in one of her improvisations (complete with the correct right hand fingering, which I did not teach her). I pointed it out to her and told her it was important. We then worked out the left hand fingering; I emphasized that for now scales must be SLOW and steady, thinking about good tone and hand position; we added them to her practice routine, which now (I hope) begins as follows:

Prayer
Scales
Other Stuff

She returned for the next lesson with C major, one octave, hands separately, played slowly and accurately.

So far, so good.
For as long as she is a musician, she will be playing scales. As will I.

But I got away from them for a number of years in midlife. I was bored with them, and focused instead on the pieces I was trying to learn. Insofar as I was doing technical work at all, it was more from the Brahms “Fifty-One Exercises” than anything else.

Then I began to improvise.

Dupré’s course on improvisation begins with the harmonization of the major scale, then minor. I spent a long time with this, in all keys. Scale in the soprano. Scale “en taille” (in the tenor). Scale in the pedals, or the left hand bass. It was a grind, but over the years since then it has proven increasingly worthwhile that I spent the time on this.

After Gerre Hancock published his book on improvisation, I found that he too began with scales, in a considerably freer approach. Unlike Dupré, Hancock encouraged creative harmonization in any style that takes your fancy in the moment.

That finally made it fun to play scales. When I am practicing free (non-hymn-based) improvisation, I often begin with a few scales – harmonized or contrapuntally oriented (or best of all, both), and let them lead me in whatever direction the ensuing music wants to go. Even when the work at hand is preparation to improvise on a specific tune, I might begin with the scale for the keys I hope to use in the improvisation before beginning to “learn the tune” (playing it in unison, and taking it from there).

-----------------------
Afterword:
Much more could be said about scales. I content myself with a final observation:

Play in and with the Modes.

Work with them in the same manner as major/minor: the scale in the soprano, chords harmonizing each note of the scale, up and down, slowly. Later, the scale in an inner voice or the bass. Do it in as many keys as you can. This remains for me a work in progress. If you ask me to knock out a quick harmonized scale in F sharp Mixolydian with subsequent improvisation, the results would likely be less than professional. But I am working on it.

The secret is to think “Where is Do?” In the above case, Mixolydian has the keynote on Sol, so Do is on B. Five sharps. It also helps – a lot – to notice that Mixolydian is Major with a flat seventh degree. So I can think “F sharp major” and play E naturals. All four of the Modes have near neighbors that are helpful in this manner:

Dorian – like natural Minor, with raised sixth degree
Phrygian – like natural Minor, with lowered second degree
Lydian – like Major, with raised fourth degree
Mixolydian – like Major, with lowered seventh degree

A benefit of this sort of work is that one soon gets a feel for the mode. What chords make a good cadence? What chord combinations work well, which ones not so much? What chords work well with specific scale degrees?

And: What is the characteristic ethos of the mode? Mixolydian has a sober dignity to it that I love: Lydian is the most joyful of modes, even more than Major: Dorian is like Minor but with greater strength and a yearning that comes from the raised sixth degree: Phrygian is strange, something all its own. To explain it I commend to you the magnificent Third Tune of Thomas Tallis (the Third Mode being another name for Phrygian), and the Fantasia on this tune by Vaughan Williams.

That brings me to another benefit of work with the modes: you might start sounding like Vaughan Williams. Or Herbert Howells.

I suspect that these composers got their “sound” in part from long exposure to the Modes – for RVW, it was his work with folksongs; for Howells, his work with the Tudor Church Music project. I can imagine them playing around at a piano with these things, finding the characteristic harmonizations and melodic patterns.

An improvisation, and a way forward

Last night, I had the pleasure of attending a concert by Olivier Latry, organist of Notre Dame de Paris, professor of organ at the Paris Conservatoire. My respect for him is very great; he is my “go-to” person for his recordings of the complete organ works of Messiaen. Here is one of his Messiaen tracks from YouTube, the final movement of the Livre du Saint-Sacrement. He played no Messiaen in last night’s concert, but there was plenty of other fine music, notably (in my opinion) his playing of Duruflé’s Prelude and Fugue on the name of Alain.

And an improvisation.

I did not time it, but my estimate is that it ran about twenty minutes. It was based on the chant “Dies irae” plus a cheerful triadic tune often played by the local university marching band, as well as polka bands everywhere:

In heaven there is no beer:
That’s why we drink it here.

The envelope containing the tunes was solemnly presented to Mr. Latry; after some difficulty opening it, he set the tunes on the music rack and played them for the audience. After a few moments, off he went, starting with the “In heaven” tune – dark, in minor, low in the tenor/bass register. That proved to be the main theme of the improvisation, complete with a fine large four-voice fugue before a concluding toccata passage. “Dies irae” was in a decidedly secondary role, though it was present as a dark undertone.

In conversation afterwards, my friend Jean and I wondered how he could do such a thing as this. Both of us have heard many improvisations after the French manner, and they often come across as somewhat formulaic. Latry’s piece on this night did not seem that way at all. It seemed more a creation of the moment rather than random tunes pasted into a form.

Some thoughts, and a way forward:

I admit to a twinge of discouragement as I drove home. I will never, ever play like that!

As I have written elsewhere, “Someone is always better. Don’t let that bother you.” That helped, as did the corollary: “Be the best that you can be.” That thought leads to the organ bench, and perhaps renewed intensity to my work on improvisation. At present I am overwhelmed with repertoire and anthem accompaniments to prepare for the next fortnight of services, but at least there are three piano improvisations in the music list to keep me working at the skill.

“Be the best that you can be” also leads me to think more seriously: How did he do that?

Upon a night’s sleep and consideration, I suggest some possibilities. The improvisation was in essence Theme and Variations; he may have had that form in mind before the evening began, at least as one of several possibilities. The key (though not the mode: lots of movement between major and minor, and probably other modes) was that of the two tunes, and I do not recall any significant modulations from the home key, not in the sense of a sonata-allegro form or even an ABA ternary form (staying in the home key is fully appropriate for Theme and Variations). That covers two of the major decisions the player must make.

There was plenty of variety in color and dynamics, plenty of rise and fall of energy level. At one point I noticed how my heart was racing, my palms sweating as he built to an intermediate climax on full organ, and I was grateful for being swept away by the music (as I was, beginning to end). [I will add that Keith Jarrett does this too, at the piano; it is one of the strengths of his long-form improvisations.]

There were elements that I recognized – the fugue, several passages of toccata figuration with the tune in double pedals, a couple of hymnlike variations in homophonic chords (like the one at the very beginning), some unison lines, one of them taking it down to the slow-speaking bottom note of the keyboard on a reed stop that he seemed to particularly like.

Aside from the unteachable genius of the thing, most of the rest was virtuosity of passagework in hands and feet.

That is why the second volume of Dupré’s improvisation course begins with a “Table of daily exercises at the piano” - pages of scales in thirds, sixths, octaves in all major and minor keys, as well as chromatically (adding fourths and tritones to the other intervals). Then arpeggiated chords – triads, seventh chords of all sorts. Discussion of pedal scales and exercises to attain an equal level of virtuosity with the feet. Dupré titles this first chapter: “The Piano, basis of technique at the Organ.”

My eyes glaze over and despair sets in. But at least I can “see in a glass darkly” how this could be done. Mr. Latry has most certainly done these things, and I would suspect that he continues to work at them regularly. I suspect, also, that he knows the two-volume Dupré course intimately as student, performer and teacher, for it has been the foundation of the French manner of improvisation for decades.

Dupré then turns to Harmony in chapter two. He begins with the observation that the player must have a spontaneous, immediate facility with harmonization, a knowledge of every possible chord that could harmonize each note of a melody [the jazzmen say this too, in their own way]. Pages of exercises follow: triads, chords of the seventh and ninth, modulations, “resolution of polytonal aggregations” (p. 23) – or as Mr. Hancock used to say, “Salvation is just a half-step away.” Again, in all major and minor keys, with the goal of the absolute and effortless harmonic control that someone like Mr. Latry demonstrates.

This is a long path.
But it is the path that, I suspect, has brought Mr. Latry to his present level of skill as an improviser.

Dupré eventually gets around to the treatment of Themes and their analysis as to how they can best be presented rhythmically, harmonically, etc. – and contrapuntally, with canon, imitation, ornamented chorale with contrapuntal accompaniment (e.g., after the manner of Bach), fugue. And then, forms: binary, ternary, symphonic forms, many others.

Some of the finest improvisers, after years of work, reach this level. These are the players that Jean and I have heard who play amazingly, and with great effect, but their work has a hint of the formulaic. They have mastered all of Dupré’s formulas.

Mr. Latry (and a handful of others: among the Frenchmen, I put Daniel Roth in this category, and certainly Messiaen when he was still with us) has gone beyond this. He has made all of this work so natural and automatic that he probably does not need to think about it at all. Like Keith Jarrett at the piano, he simply starts to play, with at most some general ideas as to form – which may, in the execution, turn in quite a different direction than it began.

Again: I will never, ever play like that!

[Edited to add: There is another side to this - see the next essay.]
[See also this, from Glenn Osborne's fine improvisation blog, as to his theory of "how do they do this?" -- deeper study of solfege, harmony and counterpoint in the French system than is typical in the American training of organists and other musicians.]

What brought me back down to earth this morning was my humble little clavichord. After Matins I opened it up and improvised for a while, simple four-bar phrases in G major. The clavichord by its nature works against any thoughts of virtuosic display. It rewards quiet, careful playing – at least for me at my elementary stage as a player of this instrument.

Mr. Latry’s improvisation and its ripples this morning have nonetheless brought me to a revelation. Dupré’s course has been on my shelf for decades, ever since Gerre Hancock named it in a workshop as essential – this was in my first years as an organist, when I was self-taught and working toward my Associate certificate (AAGO), before graduate school. Hancock’s own book on improvisation is probably a better starting place now, but he had not then written it.

Back then, I spent much time on the first, “preparatory” volume of Dupré. This work was what got me through the improvisation requirement for the AAGO (barely, with the minimal passing grade). The second volume frightened me so thoroughly that I have hardly touched it. Not least, it is in French; I do not think that it is available in translation. But as Hancock said all those years ago, “Don’t let that put you off. It is easy French.” And it is, most of it musical terminology.

Paging through the book this morning, all of a sudden, without realizing how I have gotten here, I see that I am ready for it.

I will likely never get far up the path – there are too many weeks when there are other more pressing demands on my practice time. I may never get past the first chapter with all its forbidding pages of exercises in thirds and sixths and arpeggios of every sort. But I think that I must take care not to get stuck there. I think that after some work on these things, I could profit much from the rest of the book.

Jesu, juva.

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A YouTube search for “Olivier Latry improvisation” brings many results. Here is one that has not so many views as most of them. I chose this because it shows him at work with something a lot more important than a polka song and a showpiece improvisation in the middle of the U.S. – an improvisation, a defiant statement if you will, for the memorial Mass at Notre Dame for the victims of the three coordinated suicide bombings of November 13, 2015, which killed 128 persons in Paris.

This is why one studies improvisation, or for that matter any kind of music: to have the tools for when it becomes your duty to make a musical statement where no words suffice.

Work over your head

“Work over your head,” writes Steven Pressfield in his book “Turning Pro.”

It would be easier to do otherwise. Then, I might not be terrified on Sunday mornings. I cannot recall a Sunday, not in thirty years of playing, without something that was on the edge of going wrong, something that has kept me awake on Saturday night.

Weekly improvisation has made it worse. When we have practiced a written composition sufficiently, there is much that could go wrong, but it is unlikely to entirely fall apart, at least when playing from the score. An improvisation? If it goes badly, it can be memorably awful. There is no limit as to how bad it can be.

Even if it goes well, there are always aspects which could be better. Where are the beautiful lines, the harmonies, the elegance and precision of form that were effortless in practice? Instead, the voice leading is awkward, the transitions are clunky, the phrases and periods are out of proportion, even the tune slips out of control.

Postludes at the organ are the worst. I played one of them on Sunday. [Here is the link, including the closing hymn to put the improvisation into its context.] It was a tune that I do not like, but it was the closing hymn and it needed a big, loud postlude to finish it off.

I was terrified.

Somehow, I got through it more or less in accord with my plan, scribbled on a piece of staff paper: introduction based on the first phrase, going forward with the tune mostly in the pedal, a middle section on the manuals, based mostly on the third phrase with movement through some of the flat keys, a return to the tonic for a mostly straight up play-through of the tune (in the pedals) with imitative work in the manuals.

But how to finish it off? With my piano preludes, I tend toward extended codas, most often at a soft dynamic. That is partly by preference, but I have found the coda to be useful because it is flexible. It can be long, short, or absent without harming the overall form. That allows me to finish the piece precisely at 9:00 a.m. For this postlude, a gentle ending would not do. I consider the final phrase of the hymn tune to be its weakest point, which was all the more reason that the improvisation needed a big ending.

Even the greatest of composers sometimes have difficulty with the big ending -- Bruckner, for one, whose endings can be among the most majestic of all but sometimes (I think) fail to carry off the grandeur of his intent -- but even (once or twice) Beethoven, and perhaps Bach -- I have never been happy with the ending of the Piece d’Orgue, for example. How does one make it sufficiently weighty to finish the piece, without bombast? In my practice this week, the ending was never satisfactory. I focused on it with my Saturday practice, striving to keep it short, and I think that it was still a bit overdone in the actuality on Sunday.

But it could have been worse. There was a chance that it could have been as bad as it was in some of my practicing.

I wish I could do it like Mozart. Earlier this month I had occasion to play his piano sonata, KV 545 in C major, as the prelude for a funeral. It is not a piece that is “big” in any dimension; it is gentle, playful in the closing rondo, but never loud. The endings of the three movements are simple, and absolutely right. When he is working on a larger scale, his endings are no less perfect. It may be that the ensemble that finishes off Act Two of Figaro is the most perfect ending in all of music, not only in itself but in relation to the rest of the opera. [The linked performance here is faulty in some technical respects, but the singers are among the finest, starting with Hermann Prey and Dietrich Fischer-Diskau, with Karl Böhm and the Vienna Philharmonic]

I studied the finale as a project while in graduate school, my admiration increasing all the while. The pacing, the tonal structure, the manner in which one by one all of the characters appear, all the tangled comic threads of plot are brought together, and the buildup of intensity… Oh, to make music like that!

In my opinion, each number in Figaro is a miracle; it is totally beyond me how anyone could create anything so perfect; nothing like it was ever done again, not even by Beethoven (Johannes Brahms, quoted in Wikipedia, s.v. “The Marriage of Figaro”)

Another example, one that we sang last season, is the “Worthy is the Lamb” which concludes Handel’s Messiah (see Here, and Here). It is enormous (especially the Amen) and it could not be any less without falling short in relation to the oratorio as a whole, to say nothing of its great Subject. When the trumpets come in with the stretto on the final page, the sopranos and trebles singing the final fugal entrance that begins on high A, swooping down an octave and a half to the low D, any listener who is paying attention is carried right up to the heavenly places. Or there is the ending of Bach’s “St. Anne” Fugue, which I played twice for funerals in the last fortnight. The manner in which the voice in the tenor soars up through the alto in the final cadence to finish on the B flat is extraordinary. Every time, it is as if my spirit is soaring up with it into the eternal dance of the Trinity.

My work will never be at that level. But I would like to make music with integrity on the scale that is appropriate to my place and time, whether it is in performance of music by others, or my improvisations and hymn playing. That will not happen if I play it safe.

Footnote:
I was not kind to the hymntune, which appears in only one hymnal, the Hymnal 1982 of the Episcopal Church – the one we use. I must say more, because the composer, Erik Routley, was one of my teachers, and it was named for another, James Litton.

I wrote of Dr. Routley here, and cannot speak too highly of him. Few people have been more important to me. But I do not think that this tune is among his best. For that, one might look at Augustine, for the George Herbert text “Let all the world in every corner sing” (H-82, number 402) or Woodbury for the Charles Wesley text “Come, O thou Traveler unknown” (H-82, number 639).

Reading Music

This year, the Youth Choir has only one new chorister, plus two older choristers who have returned after some years away. Last year, we had a much larger number, but whether one or a dozen, I must teach them to read music. I wish I could say that all of our choristers can sight-sing with ease; they don't. But I have learned to set the standard lower: I would like for them to be able to find the place where we are rehearsing, follow their part in a choral score, sing or speak the rhythms accurately (at least to the level of eighth notes, dotted quarter/eighth patterns, triplets, and occasional sixteenth note passages), and have the basic concept of solfege.

I often draw a chart on the board that outlines the basics:
- follow the notes
- rhythm
- pitch
- other stuff

Follow the Notes:
A chorister is not going to get far if he is not in the same place on the page as the rest of the choir. Or even on the same anthem! It continues to surprise me how often a young chorister can appear to be singing merrily along through ten minutes of work on an anthem, and upon closer examination, she is looking at a completely different anthem. We had one example of that yesterday form a second-year chorister: We were rehearsing the preces and responses by William Byrd; he had the responses by William Smith, bound in the same book. Granted, the text is the same, but I should have caught his mistake more quickly. And (ideally) so should he. So, the first part of following the notes is Finding the Place -- the right anthem, the right page, the right part of the page. It helps when the director is consistent in his announcements: "page six, the second system, third measure." Or as those influenced by Gerre Hancock would say, "Six, two, three," expecting the choir to find it from that - they can, and many choristers seem to enjoy the challenge of moving so quickly.

To this end, I pair a new chorister with a more experienced singer, perhaps one or two years older, or even much older (e.g., middle school or high school). They share one music folder. At first, the new singer watches the older one follow the notes with his finger, then (perhaps on the second or third time through a passage) they trade; the new singer has the folder and follows the notes, with the older singer watching and helping when she gets off-track.

The new choristers invariably want their own choir folder; it is one of the marks of Belonging to the Choir. And I have too often given it to them too early; I did this last year with some of the new singers, and it was in the long run a setback for them. Perhaps a month or so of rehearsals is right for folder-sharing; enough time so that the new singer can confidently follow notes and find the place.

What is "Follow the Notes?" I learned this from watching James Litton work with his probationers at Trinity Church, Princeton many years ago. I tell the choir to follow the notes; they put their finger on the first one, I play a passage (a short passage, perhaps one or two measures at first), they go from one note to the next. I stop suddenly, go around the room, and see if they have it. If not, I help them find it. Over time, the passages get longer, up to several pages sometimes -- but the limit then becomes the practical rehearsal value, for part of what we are doing is having the choir hear a new passage so that they can sing it.

And that is what we do. We follow the notes for a large enough chunk to work on, then we immediately sing it. But (usually) not with words, not yet. For we have more to do.

Rhythm
Rhythm notation is easier to learn than pitch notation, so we start there. I use the Kodaly rhythmic syllables: "Tah" for a quarter note, "Ti" for an eighth note. Longer durations are multiple "Tahs" -- a dotted half note would be "Ta - ah - ah" with an emphasis on each of the three beats.

The very first stage is aural. Especially if there are a lot of new singers (like last year), I will clap a short rhythm, speaking the "Tah's and Ti's", they repeat it back to me. That way, they learn what the durations mean. Then we would work from an example on the whiteboard, speaking/clapping it as I point to the notes. Then we would do the same from an anthem score -- often, I have taken my example from an anthem that we are learning -- speaking it (and following notes as we do so), then singing it on the Tah's and Ti's.

My goal is for the choir (and especially the new singers) to get to where we can sight-read the rhythms directly from the printed music, using the tah's and ti's and speaking the rhythms. They usually catch on to this quickly, within a few weeks or a couple of months.

Even much later, and with an adult choir (if they have learned the Tah's and Ti's), we will use the rhythmic syllables for sight-singing and rehearsal. I use them myself when I work on the congregational hymns, and sing them to myself in the liturgy as I play, especially when it is a situation where the congregation's sound lags behind the organ.

Another advantage of this work is that it breaks the common pattern where a new singer is following the words and not the notes. She must somehow learn to do both at once, but it helps to ignore the words at first.

Pitch
This is harder. Much harder.

Again, I use the Kodaly/Curwen solfege syllables, with movable Do: Do-Re-Mi-Fa-Sol-La-Ti-Do.
These go much further into the past, back to Guido of Arezzo in the early middle ages. And they remain essential, in my opinion. Others differ -- there are other systems, such as singing by interval. But this is what I teach.

The foundation is in our warmups. We always do scales - a descending scale down from Do to the bottom, then a turnaround and back up to the top. This is because descending patterns are better vocally for developing ease with register shifts. And with the children, we use the hand-signs (depicted in this article on the Kodaly Method). It gives them a tactile experience to go with the singing, and gives me a way to "line out" melodies. After they become thoroughly comfortable with scales and the hand signs, I will change directions in the middle of the scale, go back and forth stepwise, and try to "trick" them. They enjoy this.

After that is comfortable, I introduce skips in the melody. I begin with something like this:
Do-Re-Mi -- Do-Mi
where they have just sung the target of the skip and it is fresh in their memory.

All of this is by sound, rote, and hand-signing. It must be transferred to the page.

The first step is to write a scale on the board, with the solfa names. We sing from the board as I point to the notes; we go back and forth up and down the scale, and maybe do skips. Later, I will write an example from the music we are learning on the board and we will do the same; I point, they sing. Immediately after, we look at the printed score and do the same passage. Often, this is a hymn tune, for they are excellent material for this sort of work.

If the choir gets far enough along with this, we will eventually try to sight-read hymn tunes or anthem material on the solfa syllables, or do a second reading on the solfas after we have read it with the rhythm syllables. Most years, we don't develop much skill with this, though we often reach the point where we can slowly puzzle out a new tune with solfas as a group, the most experienced singers obviously taking a lead and the younger ones following.

I wish we could get further.

Other Stuff

That is, everything else that a music score tells us:
- words (vital for a singer! And this includes the vast domain of diction, phrase shaping, etc.)
- dynamic and tempo markings
- articulations (e.g., accents, breath marks)
- background material (composer, author, etc.)

And much more.

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Reading Music is a lifelong journey, a path I continue to walk. I can do no more than help the young people start down the path. But I am obliged to do at least that much.

Many children's choirs (and adult choirs too) don't do this. It is slow, it takes rehearsal time (though not so much when you are using the songs and anthems they are working on as your teaching material). And most choirs are working toward a more immediate result -- that anthem next month, or the Christmas concert. I believe that this shortchanges the choristers.

Again, I wish we could do more. I feel badly when singers that I have trained audition for other groups -- for example, the voice trials at every summer's RSCM Course. I wish that they would be far superior to the singers from other choirs -- but that is Pride talking, and I must ignore it. And when the occasional person comes through the choir and goes on to be a professional musician, I wish that I could have given them a more thorough training. But at least they have the concepts, which may make their collegiate training a little easier.

One of my young people from years ago, now the principal flutist with a mid-level symphony in the southeast, came back from her first semester at college amazed that her flute teacher expected her and the other students to learn their parts in solfege. She thanked me for getting her started.

More broadly, and probably of more importance, I hope that I can help equip these young people to sing in church and community choirs throughout their life, and intelligently sing the Songs of Zion, the hymns of the church.

The Nativity of St. John Baptist: a Movie and a Hymn

In 2006, there appeared a worthwhile cinematic telling of "The Nativity Story." I loved it: I watched it at the cinema about a half-dozen times that December, and donated a copy of the DVD to the public library.

One of my favorite scenes is the portrayal of the Visitation of the Blessed Virgin Mary to her cousin Elizabeth:
Part 3 of 10
The clip begins with the Annunciation. The part about the Visitation begins at 6:30 in the clip. If I remember rightly, the actress who plays Elizabeth, Shohreh Aghdashloo, is herself a Palestinian Christian. She well portrays this great and holy woman.

The story continues in the next clip, part 4 of 10, which recounts the Birth of St. John Baptist and his Circumcision.

Here is the whole movie.


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The office hymn for this Feast is number 271 in the Hymnal 1982, Ut queant laxis (The great forerunner of the morn).

It from this hymn that the master teacher and Benedictine monk Guido of Arezzo (born 991 or 992, died after 1033) derived what we now know as solfege, and as a corollary invented the modern system of musical notation. Both innovations were aimed at making it easier for choristers to learn the plainsong chants of the Church.

Guido noticed that the six scale steps are clearly outlined as the first note of the first six phrases of this tune, and he assigned the text syllables from these points to the scale degrees: Ut - Re - Mi - Fa - Sol - La. Here is a little YouTube clip that perfectly illustrates what is happening: it shows the plainchant with the appropriate syllables outlined in boxes.

To appreciate Guido's leap of imagination, one must recall that the song was not written down for him to look at, not in a form like this. What he had was a text with squiggly lines above it, which very roughly indicated the shape of the tune, and the tune which he had learned by ear. All of the tunes, the enormous mass of Chant for the liturgical year, had to be transmitted by ear from generation to generation.

Guido realized that if one extracted these six pitches and named them, the pitches would have the same name in any chant, any musical composition, and they could then be written down in a clearly indicative manner, including the relationships of half steps and whole steps (the half step is always between Mi and Fa). Further, the entire corpus of chant could be notated with these syllables (and the use of Hexachords, which are multiple overlapping sets of these six pitches).

This changed the world.
(Well, at least the world of music.)

"Ut" was changed to "Doh" some five centuries later because the vowel was thought to sound better in the voice, and "Si" was added about that same time for reasons that are too complex to here recount; in part, it allows one to dispense with the system of overlapping hexachords. In English-speaking countries, "Si" was changed to "Ti" in the nineteenth century so that each syllable would begin with a different letter.

Figured Bass, Handel, and Good Habits: An Update

As described here (January 11 entry), I have tried to work on figured bass and score reading this spring.

Many times before I have begun the new year with a new Project, and it has fizzled within a few weeks, as Lent and Easter approach. I sought this year to at least keep a "placeholder" in my day for this work. I might only work at it for five or ten minutes on a busy day. That is not enough to make any progress, but it is enough to keep it habitual.

In January, I began working partly a page at a time with C.P.E. Bach's "Essay on the True Art of Playing the Clavier," and mostly with the final part of Handel's Messiah (see here), which we sang on April 14 as I mentioned the other day. In terms of the figured bass aspects, it went well. Over these three months I developed a moderate facility with the piece and my skills improved.

But until mid-March, I had overlooked one step, which I now realize is crucial:

After the day's work on a passage of music, take the score away from the keyboard and conduct it.

The results amaze me: I have a greater understanding of the musical score -- even the parts of the "Amen" fugue that are complex -- and a good comfort level of reading the score, and hearing the sounds in my ears. I might actually learn to do this!

Two Wednesdays ago, I used the full score in the youth choir rehearsal and discovered some weaknesses. Most notably, I got lost in the Amen in the long passages where there is not much text underlay in the vocal parts -- they are simply singing "Amen." I repeatedly drifted from the soprano/treble line to the staff above it, which is the viola part. This was decidedly unhelpful to the choir as I sought to play their parts in places to help them. After rehearsal, I took a pencil and drew lines across the score pages to set the choral parts off from the string parts more clearly. This helped. Last Wednesday, I had to lead the adult rehearsal from the score, playing the bass line and chords and cueing the trumpets at appropriate places, as well as the vocal parts. I am proud to say that it worked! A careful listener would have disapproved of some of my chord realizations, but they were sufficient for the purpose.

And on Sunday, I felt thoroughly comfortable as a conductor. This would not have happened without these three months of work with the figured bass and full score, and the similar preparation of the Mozart piece that we did in January, a much simpler score to follow than the Handel.


I also decided in January that I would not turn on any computers until midday. Instead, I would undertake the important work of the day: Matins, then Practice. I begin after Matins with vocal warmup and practice (again, this is very often a "placeholder," and at most is fifteen or twenty minutes), then Figured Bass/Score Reading, then a bit of Fingering on an organ or piano piece that lies ahead, then my main session of Practice at the piano and organ. I then try to get my office work done in the afternoon (and on Sunday, the evening).

It worked well until mid-March, when it became clear that something had to give in order to get through Holy Week, Easter Day, and the Second Sunday of Easter. I laid the vocal practice and sight-singing aside, and the C.P.E. Bach book. It was tempting to lay Matins aside -- this is, I think, one of the greatest temptations that stands in the way of regular observance of the Daily Office: a busy time comes in one's work or home life, and the Tempter whispers "You could get a lot done in this half-hour. What harm will it do to skip a day?" Then the next day is even busier, and it is easier to skip the Office. Before long, it is a thing of the past. The funny thing is that if one succumbs, one ends up wasting far more than that precious half-hour at other points in the day.

I have been there. Many times. Sometimes -- including this March -- all that saves me is the obligation that for three days of the week, Matins is a public service of worship for which I am responsible. On two of those days, almost no one ever comes, but it remains a fixed Duty. For which I am grateful. Also, I am under a Vow as a Brother of St. Andrew, which includes the Daily Office at least once a day. There have been times that this, too, has been enough to carry me through.

So now, it has been almost a month since I have done my daily sight-singing, any proper and systematic vocal practice, or work with C.P.E. Bach and figured bass (beyond work with the Handel score). Holy Week is past. Easter Day is past. Two Sundays have passed. Now is The Test. Can I pick up where I left off? Today was not an especially good start; I spun my wheels and wasted a lot of time this day. Too much.

Jesu, juva.

Worthy is the Lamb

The Mozart “Inter natos” went well on Sunday. It was a delight for me to be in the midst of the musicians, for in our setup, the choir and organ were on my left, the string players on my right. I think that it gave choristers and instrumentalists more of a sense of mutuality to face one another than is the case in the more usual concert setup, with choir in back, instrumentalists in front.

As I mentioned last time, I have used the Mozart as material for practice in figured bass and score-reading. Today I moved to the next project: the Third Sunday of Easter, April 14, when we are scheduled to sing the final parts of Handel's Messiah – Worthy is the Lamb, Blessing and Honor, and the Amen, with our youth choir and adult choir combined and a yet-to-be-determined complement of instrumentalists (trumpets and organ at least, and I hope for continuo players and perhaps oboes doubling the sopranos and altos, as Handel wrote in the score). That passage from the Revelation of St. John is the Epistle for Easter III, so the choice of music is natural, though I worry that it is too large in scale to fit comfortably in the Sunday Eucharist. Then again, that which St. John described is equally too large to fit – well, anywhere. Not in this universe, but only in that time when all is made new. As is clear in the context from Revelation, and as the Lectionary gets right by placing this Lesson shortly after the Feast of the Resurrection, this is all about the Lamb in the center of the throne, who has done what no one else could do (Rev. 5:1-7), and in so doing has answered every prayer, the prayers of all the saints of every generation (v. 8).

Several years ago, J.M. (who might still be reading these pages) presented the church with the gift of the score and orchestral parts to the Messiah in the fine Watkins Shaw edition published by Novello. This morning was almost the first time I have looked inside the conductor's score – a large-format volume of 283 pages, very handsome. I was almost afraid to do so. If anything in this world is Real Music, partaking of that eternal Song before the throne, this is it. “Worthy is the Lamb that was slain...” How can I even sit down at the piano and play the first chord?

But I must, for more reasons than I can here describe.

Handel is less careful about noting the Figures (the numbers delineating the chords) than was Mozart in the little piece we did last Sunday. He was in a hurry (as can be seen in any account of the composition of this oratorio), and he was going to be playing the continuo, so he put down only the most essential figures. I must pencil in many more, obvious to the greatest continuo player of his age (except perhaps his contemporary over in Leipzig), but not so to a beginner such as I. But already I can see that, as it was with the Mozart, this manner of work is going to give me a much better sense of the score than the way I have previously approached it – for we did this part of Messiah once before, nine years ago when this set of lessons came around in the Lectionary.

We began work on this with the Youth Choir last Wednesday, just five minutes of speaking the text in rhythm for the first pages, up to where the “Blessing and honor and glory and power” fugue begins. There is much to be done. But this is why we are doing the piece, and doing it in this manner: I want to introduce our young choristers to this music. I can hardly imagine what it must be like to be eight or nine years old and sing this music – indeed, encounter it in any form, for I doubt that many of them, coming from homes where classical music is unknown, have ever heard a recording of Messiah.

My hesitation in approaching the Holy as I opened this score is appropriate, and I should feel such a strong sense of it as I did this morning every time I sit down at the keyboard. We cannot do any of this without God's help. Most musicians know that Bach wrote “Soli Deo Gloria” at the end of all of his scores; fewer take note of the “J.J.” at the beginning – “Jesu, juva,” “Jesus, help!” So must we begin such a work as lies before me, before us.

Figured Bass

Following a tip from one of my Old Books, I have been using the figured bass as my primary method of learning the score for the Mozart piece we are singing this Sunday, “Inter natos mulierum” (K. 72 – see here for more about it).

[a Figured Bass was used in the Baroque era to sketch the harmony much in the manner of a jazz "lead sheet," where the melody is given with chord symbols. Figured Bass works from the bottom up instead of down from the melody; the bass line is given, with numbers to indicate what chords are built on it. Here is the Wikipedia article on the subject.]

Score reading and figured bass are skills I am supposed to possess as a Musician. I am not terribly good at either. It is dawning on me that the latter is one of the keys to the former, at least for music from the Baroque up through early Beethoven (he includes figured bass in the Mass in C [1807], but not in the Missa Solemnis [1823]), and score study must start here in any event – something like a Bruckner symphonic score is not going to make much sense if one cannot deal with a Bach aria – or something like “Inter natos mulierum.”

“Keyboard Harmony [which included figured bass] and Sight-Singing” was a one-credit-hour required course for Freshmen in Music at my undergraduate college. It was taught by an adjunct instructor, the young wife of a faculty member in another field. She was a good musician, but had never taught such a thing and had little idea how to do it. I (and most other Freshmen in Music) lacked the background in music theory to make much of the subject, although if properly approached, the figured bass could have itself taught the music theory that I needed. Both teacher and students gave it their best effort, but it was an unfortunate combination, and one hour a week for one semester (with some outside practice squeezed in around many other duties) was far from adequate.

Looking back, I would have profited from laying all else aside for a year and learning the rudiments of Music. No piano lessons (aside perhaps from a regimen of scales and technical drill to avoid losing all facility), no music history, no general studies coursework. I would then have done better at all the other work, and been a much better Musician. But I could not have tolerated such harsh medicine, and it would obviously not fit with the four-year undergraduate curriculum.

Later on, figured bass was one of the skills required for the Associate's Certificate in the organist's guild, the A.A.G.O., where the test was the accompaniment of a recitative at sight [such as the one from Dido and Aeneas given as an example in the Wikipedia article linked above], reading from figured bass with vocal line. I passed, but still did not have a lot of facility with the art. One of the benefits of the Guild's programme of examinations is their old-fashioned emphasis on what should be rudimentary musical skills – rudimentary, but often unknown to working professional organists, pianists, and choral conductors. Figured bass is one: reading the C clefs is another. Harmony, Counterpoint, Fugue, Transposition, Improvisation... the list is long. I am a Fellow of the Guild, and passed tests in these areas, but am hardly more than a beginner in many of them. I hope to do better, in the residue of days granted to me.

Redeem thy misspent time that's past
And live this day as if thy last;
Improve thy talent with due care,
For the great day thyself prepare. (Thomas Ken)

I (and others) would have done better as Freshmen in Music had we been presented as soon as possible with Real Music (for example, the score of “Inter natos mulierum”) and been cajoled into using the figured bass to gain a sense of the piece, harmonically and otherwise. I am finding that no other approach I have used on choral/instrumental scores has led to as thorough an understanding of the piece – and my figured bass skill itself has improved a lot, just from a month or so of work on this one piece. That is important too – rather than reading a lot of different things, stay with one or two representative pieces until they are thoroughly mastered, right up to performance-level.

The best book on the subject is one that I have mentioned repeatedly: “Essay on the true art of playing keyboard instruments” by C. P. E. Bach (1753). A more modern text, which (despite the virtues of Bach's Essay) is needed, is R. O. Morris, “Figured Harmony at the Keyboard” (Oxford Univ. Press, 1933).

Figured bass is also one of the keys to Improvisation, but that is for another essay.

Fundamentals of Musical Composition

Fundamentals of Musical Composition: Arnold Schoenberg (Faber and Faber, 1967).

For the last two months, I have worked my way through this book, and I have hardly scratched the surface: to do it properly, I would need a second transit, with much work at the keyboard. I hope to do this; I hope that my intention may remain until late this fall when I might have time to begin the task, applying these lessons to the work of improvisation at the organ and piano.

Some of my “teachers” are gentle and pleasant: some are prickly. Schoenberg (1874-1951) comes across in this book as a a hard-bitten old drillmaster of a teacher, immensely intelligent, with a vast knowledge of music and little patience for slovenly work or ignorance. Like many other Austrians and Germans of his generation, he fled the horrors of National Socialism, having to start over in his old age as a professor of music at the University of California, Los Angeles, and the nearby University of Southern California. The low level of the American students he there encountered, much lower than what he had known in Vienna, caused him to revise his pedagogy, as his editors describe in the Preface (p. xiii), creating this textbook for undergraduate students of composition and analysis. Schoenberg writes in the Appendix (p. 214): “The principal aim of this textbook is... to provide for the average [music] student of the universities, who has no special talent for composing or for music at all." [my emphasis]

Nonetheless, he took up the task and devoted some ten years and four revisions to this volume. The editors (Gerald Strang and Leonard Stein), who knew Schoenberg well, attest that “all his life Schoenberg laboured to share with his students his knowledge of music” (p. xiv).

One might expect a book from this hand to focus on the areas in which Schoenberg himself worked: the atonal or “twelve-tone” music which he developed with others, notably Alban Berg and Anton Webern, in the early twentieth century. But one finds none of this in the book: he focuses instead on the work of Ludwig van Beethoven, with examples from other classical masters such as Bach, Haydn, Mozart, Schubert, and Brahms. Schoenberg insisted that if one is to compose in a more modern style, one must first master the traditional skills represented by these composers. Copies of Beethoven's piano sonatas and string quartets are essential to a proper study of this book, for Schoenberg refers to them constantly as examples for the student.

He begins with the construction of the Phrase, then the Motive, the connection of Motives into simple Themes such as Sentences and Periods, their accompaniment, and the building from these smaller elements of complete smaller musical forms, such as the ternary Song Form, the Minuet, the Scherzo, the Theme and Variations. From there, he explores the larger forms such as Rondo and Sonata-Allegro. For my purposes, the earlier parts of the book are more applicable – I must crawl before I can walk, and running is out of the question [an example of the latter would be the organ improvisations of Anton Bruckner, which were reportedly large symphonic-scale works similar to what one hears in his orchestral symphonies. I will never reach that level; I will be content if I can improvise a decent prelude and postlude for church].

As I mentioned, I have worked my way to the end of this book. If the Lord allows, I hope to start over in October or November, working with the book while at the keyboard and seeking to imitate the forms as they are used in the works of Beethoven. The inestimable value of this book for the organist and improviser is that Schoenberg shows how this can be done.

To make sketches [or, for the improviser, to try many approaches with a given theme or concept in rehearsal] is a humble and unpretentious approach toward perfection. A beginner who is not too self-assured, who does not believe too firmly in his 'infallibility', and who knows that he has not yet reached technical maturity, will consider everything he writes as tentative (p. 117).

Laudate Dominum

Laudate Dominum, omnis gentes:
Laudate eum omnes populi:
Quoniam confirmata est super nos misericordia ejus:
Et veritas Domini manet in aeternum.

Tuesday is a busy day, and most Tuesdays I do not make it to the bench for practice. Today was an exception; staff meeting was short, allowing me to work out the fingering of the Mozart “Laudate Dominum” (from K. 339, the Vesperae solenne de confessore), for soprano solo and choir.

Link

Interacting with Mozart is one of the chief joys of being a classical musician. As soon as one plays so much as a measure of this little choral piece, one is lifted up into heaven. It is almost too beautiful for mortal ears. How could anyone write something like this?

When one works out fingerings and makes other preparations for rehearsal on a piece, it is what some musicians call “putting it under the microscope.” The musician is privileged to look very closely at the piece. With something as good as this, the closer one looks, the more beautiful it is. Subtle details come to the fore, details that would never be consciously heard in performance. But there they are, each of them contributing to the beauty of the whole.

Any good composition of music creates its own little universe, its “subcreation” in Tolkien's terms. A masterwork is fine-grained, as it were – it is, ideally, a perfect little world at every scale, from largest to smallest. It is in this manner, among others, that our creative work is in the image of the One who made a universe such as the one we inhabit, beautiful beyond imagining at every scale from galactic clusters to quarks and neutrinos. For those with eyes to see, the closer one looks, the more beautiful it is.

Mozart is better at this work of subcreation than most of us, one of the best that has ever lived. One sees this in the “microscopic” details. There is a ten-bar introduction. Much of this material recurs as the piece progresses – but never quite in the same form. A note might differ here, or there; now the soprano is singing it, now the choir. It is analogous, perhaps, to nature's dislike for exact repetition; a snowflake is a snowflake, but never exactly the same.

And there is what I call a “Mozart moment” at the end of measure 62, a moment that no one else could have conceived. He has completed the re-statement of the main musical material, the “A” section. The choir has sung the “Amen.” He could stop here, finishing with a cadence to the tonic chord, the choir holding the chord for a couple of measures of figuration in the accompaniment. The piece would be perfectly balanced, and a masterpiece we would still be singing and playing. But he does more: in the sixth and final beat of measure 62, the bass line (in the choral bass part and the accompaniment) goes C# - D instead of the expected C – F. It is a “deceptive cadence,” to use the term from music theory.

Mind you, this is not something abstruse; it is a simple device known to ten-year-old choristers and piano students, and frequently encountered in music of Mozart's time, including his own. But what a cadence! The soloist, who has been silent for twenty bars, comes in at precisely this moment on a sustained high F, the tonic note, as the choir drops out for a measure's rest. It is as if she is floating through the air like an angel. The harmonies circle around one last time through a ten-bar coda as she sings a gentle little cadenza, as if she does not wish to leave this place of beauty, the choir sings a simple V-I cadence as if it were the most normal thing in the world, and it is done.

No one but Mozart could have written these ten measures. It is one of his gifts to use the simplest of materials in obvious ways (well, obvious after he has done it) that are graceful, fitting, and perfect.

I love Bach. I spent much of December living with the Canonic Variations on Vom Himmel hoch, and it is every bit the equal of this Laudate Dominum as a masterpiece of artistic creation. Is Mozart better than Bach? Or what about Beethoven – there are transitions from recapitulation to coda in his works that are as magical as this one.

They are all miracles, all of these composers. We have not just one manner of subcreation, but many – as many, perhaps, as there are people, if everyone were granted opportunity to develop their creative potential. And all of them, and their subcreations, part of the larger Creation, this world full of beauty.

Soli Deo gloria.

Gradus ad Parnassum, or The Old Books are Best

This summer, I seek to improve my skills at improvisation. To that end, I have gone back to one of the basic tasks of the musician: Modal Counterpoint. This is the third time (at least) that I have sought to climb this mountain, at roughly fifteen-year intervals. It was a required course as an undergraduate, and I returned to it in preparation for the F.A.G.O. examinations in the 1990's. Here I stand again, in the Year of our Lord 2010, at the foot of the slope.

I began with the text I used in the 1990's. After three days, I tossed it on the discard pile. Instead, I returned to the source: Johann Joseph Fux (1660-1741), and his Gradus ad Parnassum, in a translation from the Latin by Alfred Mann. It is superior in every way to any modern text that I have encountered on the subject.

Needless to say, my opinion is not shared by the authors of said modern texts. An example of their views:

"The teaching of Counterpoint has for centuries past been confined to the system called Academic Counterpoint, embodied in the Five Species, first organized by Fux in his Gradus ad Parnassum (published 1725). . . . [T]he rigid adherence to a cantus firmus in even notes (already obsolete in the sixteenth century), and the exclusion, both of the ecclesiastical modes and of the rhythmic diversity of voice leading in the vocal polyphony, gives a highly artificial and stylistically misleading picture of the contrapuntal practice of the sixteenth century." [from the Preface to Direct Approach to Counterpoint in 16th Century Style (Gustave Fredric Soderlund), 1947, pg. vii]

Soderlund's book is useful, much better than the 1990's text that I discarded, and I have it alongside Fux for my work. But Soderlund misses the point; Fux wishes to teach his students about the contrapuntal practice of the sixteenth century, but not by directly imitating it, as Soderlund and the other modern theorists would do. Instead, he created an artificial method, the "Species Counterpoint" (or "Academic" Counterpoint as Soderlund called it).

"My object is to help young persons who want to learn. I knew and still know many who have fine talents and are most anxious to study; however, lacking means and a teacher, they cannot realize their ambition . . . Seeking a solution to this problem, I began, therefore, many years ago, to work out a method similar to that by which children learn first letters, then syllables, then combinations of syllables, and finally how to read and write." [from the Author's Foreward, Gradus ad Parnassum, p. 17-18]

I am no longer young, but I want to learn. And, unlike the imitative methods of the modern texts, the Five Species teach the student to manipulate the notes in such a way that the skills can be applied to one's own musical time and place.

Standing at the foot of the mountain, with the intent this time to work through the subject at the organ rather than on paper, and seeking to apply it to my own "compositions," I am daunted. It seems, at times, like a pathless wilderness. But it is not, and others have walked this path ahead of me, mighty men of old.

Joseph Haydn had sung under Fux's direction as a choirboy. After his voice change, when he and brother Michael were living in dire poverty in Vienna, Joseph taught himself to compose from the Gradus. "Haydn took infinite pains to assimilate the theory of Fux; he went through the whole work laboriously, writing out the exercises, then laying them aside for a few weeks, to look them over again later and polish them until he was satisfied he had done everything exactly right." (G. A. Griesinger, Biographical Notes on Joseph Haydn, p. 10; quoted in Alfred Mann's Introduction to his edition of Gradus ad Parnassum, p. xi). Wolfgang Mozart worked through Fux at his father's knee, and again under Padre Martini in 1770. As a teacher in his own right, Mozart continued to use Fux with his students. Some years later, Ludwig van Beethoven sought lessons from Joseph Haydn, and, finding him uncongenial as a teacher, turned to Johann Schenk, and finally Johann Georg Albrechtsberger. All three of these teachers based their instruction of this unruly young man on Fux.

Other students who learned from Fux's treatise include these, as listed in Mann's introduction (p. xiv): Cherubini, Berlioz, Chopin, Paganini, Hummel, Liszt, Schubert, Bruckner, Brahms, Richard Strauss, Hindemith.


There is one other Old Book that I should mention: the Essay on the True Art of Playing Keyboard Instruments, by Carl Philipp Emmanuel Bach, 1753. This spring, I worked through part of it, especially the section on Fingering (about a quarter of the book). I have seen many presentations of that subject, and Bach's Essay surpasses them all. Indeed, most later authors on this subject simply borrow from Bach, and present the material with less clarity.

My college and graduate textbooks and teachers mentioned these Old Books; they could hardly avoid it. But they did not use them, nor did they assign readings or exercises from them. I wish they had. Perhaps we are so fallen from the level of past generations that we are incapable of learning as they did. But the path is still there for those who want to attempt it.