How are your Köchels?

In the world of musicology, I doubt anyone is quite so famous as Ludwig Ritter von Köchel, pictured left. That's because he catalogued Mozart's music in the 1860s and thus bestowed on every Mozart composition then known the 'K' numbers that have adorned them ever since. Mozart, of course, being the veritable God of classical music, Herr Köchel therefore has acquired some of his glory by reflection!

So, whilst non-musicologists might talk about Mozart's Symphony No. 41 -or, conceivably, his Jupiter symphony- those in tune with their inner Köchels know it as K 551. Similarly, Mozart's Requiem is now given the Köchel number K 626.

Before I go any further in this piece, I first want to step back a bit and think about how you might, in principle, go about cataloguing the works of great composers: what different methodologies might you employ, for example?

Well, putting it very simply, there are two fundamental approaches that might be used: put together a list of compositions in chronological order, or put the list together thematically. In the chronological case, you would end up saying (hypothetically!) that K1 was written when Mozart was an embryo and K626 when he was in his dotage, aged 35. If someone asked you 'when was K300 written', you could approximate and say 'probably around 1772ish', and you wouldn't be a hundred miles off! In the second, thematic, case, you would instead say (for example) that K1-K55 are all the symphonies; K56-210 are all the concerti and so on. In this thematic case, the 'size' of the K number wouldn't tell you when it was written, but it would tell you something about the type of work it was.

A lot of people like chronologies: they have a natural sense to them -of people growing older, of works becoming more mature as the composer likewise developed and matured. For those composers whose works we list by opus number (i.e., the 'published number'), the opus number itself is a form of chronological 'tagging': Op.1 would be the first thing a composer had published; Op. 95 might be the last thing published (as would be true of Benjamin Britten, for example). You therefore know ahead of time that Op. 1 would be a youthful work, and Op. 95 was probably scribbled on a death-bed somewhere. Chronology is "natural" where thematic organisation feels like the work of a committee or someone with obsessive compulsive disorder!

However natural they feel, however, chronological lists are problematic for one big reason: cooking one up requires you to know where a composer was on any given day and what he (or, more rarely, she) was writing at the time. For 20th Century composers such as Britten or Vaughan Williams, this isn't an insuperable challenge, as they were both inveterate letter writers and/or diary keepers. Their lives were quite well documented by the popular press of the day, too... and time hasn't yet wrought havoc on assorted document collections and archives. There is thus plenty of evidence for modern-day composers for a chronological catalogue of their works to be plausible -and plausibly complete.

But when dealing with composers from much earlier periods, the evidence starts to get patchy, or go missing for various reasons and thus be, intrinsically, less complete than you'd really like it to be. Chronological lists become much harder to stitch together in consequence ...and thus you will find most of the musicological catalogues of composers like Vivaldi, Bach or Haydn to be thematic in nature, largely because no other approach is practical for someone who's been dead more than 200 years and whose papers have been dispersed, destroyed by war and fire ...or never existed in the requisite detail in the first place.

If you take Bach's catalogue, for example: he has "BWV" numbers, and if the number is in the range of 1 to 224, you know the work involved is going to be a cantata. If it's got a number somewhere between 525 and 721, though, it will be an organ work of some kind. A similar approach is true for Vivaldi's catalogue: he has "RV" numbers, and if the RV number is in the 460s, it's probably going to be a bassoon concerto; if it's in the early 700s, it's an opera. Thematic catalogues can be a bit annoying, in that the number tells you nothing about whether it's an early work or a properly mature one... but given the lack of evidence from the early 1700s, that sort of information can be tricky to get hold of at all, so the catalogue-makers aren't really depriving you of information.

One of the main problems with doing a chronological listing, even ignoring the issue of whether the documentary record is actually complete enough to make it worthwhile, is that the resulting index tends to be gapless. That is, you list all the stuff a composer wrote in the 1800s as numbers 1 to 86; the first composition of 1810 is thus number 87; the last composition of 1819 is number 223; the first composition of 1820 is 224... and so on. But what happens if you later discover a new composition that was written in 1807? Strictly chronologically, maybe it should be assigned number 68... but what of the existing 68? Does that now become 69, and every other piece shuffles along one place as well? That's a lot of re-numbering if so! What you tend to find instead is that the new composition will be given the number 68b, leaving the original 68 as 68a. Which is fine... except that now your index isn't strictly numerical. That causes problems later on when you want to sort compositions by their catalogue 'number', when it isn't really a number field at all! Another approach is simply to tack the new composition onto the end of the list -so, maybe, it gets given index number 1022 -which saves on the renumbering, but at the (fairly major) expense of rendering your chronological list now decidedly non-chronological!

Thematic catalogues can also suffer from this 'lack of space for subsequent inserts' problem, of course: if numbers 1-224 are all cantatas and 225-228 are oratorios, you have a problem when you stumble across a new cantata in a dusty, long-forgotten archive. Do you give it number 224b, or number 229? 224b would still place it in your catalogue in the correct 'section'; 229 saves messing up your existing numbering scheme... but now it's not a strictly thematic catalogue any more, as cantatas might appear anywhere, not just in one nicely-numbered and discrete chunk.

This is something that afflicts the Vivaldi catalogue, for example: most of the violin concerti are to be found around the RV 200s... except for the pile of them that were discovered in the past couple of decades, which all got new RV numbers in the 800+ range! Bach has been similarly afflicted: the BWVs in the 1081+ range are all 'late arrivals' occasioned by archival research and the turning up of previously lost manuscripts.

Some thematic catalogues saw this problem coming and tried to head it off by not allowing one thematic section to flow on numerically into the next. For example, put all concerti in Section 1, numbered 1 to 124; then all masses into Section 2, themselves numbered 1 to 18. In other words, the numerical assignment resets between thematic sections. If you then discover a new violin concerto, it can be tacked on to the end of Section 1 as number 125 without that new number assignment affecting anything in Sections 2 and onward. The classic example of this sort of 'sectioned thematic' catalogue is that produced by Anthony van Hoboken as he catalogued the works of Joseph Haydn: in his catalogue, you will find 35 separate sections, within each of which compositions are arranged roughly chronologically. Thus a Haydn symphony might be numbered 1/23 whilst a mass might be 22/7 (because section 1 of Hoboken's catalogue is for symphonies, and section 22 is for all masses). It's a nice approach that gives you plenty of slots into which to fit 'new discoveries' without having to re-number everything.

There's just one problem with Hoboken's catalogue: it's possibly the worst implementation of a good idea I know of! If only Anthony van had, indeed, decided to number his thematic sections 1 to 35. But no: he decided to get all Roman on us, so we have I, II, III, IV, V, VI and the rest. Interesting thing about Roman 'numerals': every database on the planet regards them as text fields and sorts them accordingly! Then he had second thoughts about some of his sections, so we end up with "Ia" as 'overtures': mixing Roman numerals and ordinary alphabet is a recipe for disaster, sorting-wise! And the result of mixing Roman numerals, alphabetic suffixes and Arabic numerals within sections is, frankly, ghastly to look at! Hob. XXIVb:11 and Hob. XXVIa:28 are pretty damned scary things, if you ask me!

Cut a long story short: Hoboken's catalogue is high on my list of 'catalogues I'd like to re-work, properly'!

Anyway, fascinating as all this may be, what's it got to do with your Köchels?!

Well, I think the big take-away from all the above is that for any composer who is dated before the 20th century, you're likely to want to catalogue thematically ...and with gaps between the sections allowing late discoveries to be inserted into the catalogue without disturbing everything else.

Sadly, this is precisely what Ludwig Ritter von Köchel did not do! His catalogue is chronological, for a very-much-18th-century composer, and the numbering is entirely sequential, so new arrivals either get relegated to an appendix or enter the main catalogue with an assortment of 'a,b,c,d,e' suffixes.I will mention in passing that Köchel had good reason to adopt a chronological approach: Mozart himself kept a work catalogue from the early 1780s until his death, and entered each new work in there, with a date and location. If the composer himself is keeping chronological tabs on things, it's not an unreasonable approach to take just a few decades later on, either. Unfortunately, Köchel reckoned without Mozart's human fallibilities: yes, he recording things in his own catalogue... but did he record them accurately? Did he record them completely? And what of the works he wrote before his own catalogue was started, from the 1760s to about 1782? Given he died so young, the un-self-catalogued years account for about 2/3rds of Mozart's entire lifetime! In retrospect, and with 20:20 hindisght, Köchel's ground-breaking work can be seen to have been based on a misjudgment as to the reliability of the Mozart chronology he would depend on.

To make things even more fun, there have been four distinct editions of the Köchel catalogue:

• The original in 1862
• A minor revision in 1902
• A major revision in 1937 (with two reprints)
• Another major revision in 1964

This makes the 1937 edition K³ and the 1964 one K⁶ ...and yes, that means some compositions have different K numbers, depending on whether you are referring to their K¹, K³ or K⁶ numberings. Köchel's own K 76, for example, was a symphony that is now (in the K⁶ edition) called K 42a.

In short, the Köchel catalogue is, in my humble opinion, no longer really fit for purpose and is much the worse for wear as a result of (a) choosing the wrong organising strategy (chronological instead of thematic) to begin with; and (b) having been subject to significant revision since its inception. I rather hubristically have decided to re-catalogue Mozart's work with a new catalogue of my own devising!

Any new catalogue of Mozart's music, then, needs to be thematically organised. Additionally, the thematic 'sections' need to be non-contiguous, so that if we discover a new symphony, it doesn't mess up the numbering for all his other works. Within each thematic section, because it's nice to know that Piano Concerto 23 was written before Violin Concerto 16 (this is just an example!), we shall adopt the chronological ordering of the current K⁶ catalogue. However, we are not trying to be strictly and truly chronological, so we do this chronological-within-thematic-sections ordering strictly on the basis that it's a one-time ordering. That is, new additions will be merely tacked on to the end of their respective thematic section, without any attempt to shoehorn them into their 'proper' place chronologically. In this new catalogue, in other words, there will be no use of 'a,b,c,d,e' suffixes. There must also be no Hoboken-esque use of Roman numerals or other non-numeric characters (such as the colon or forward slash that separates Hoboken's thematic sections from his numerical numbering within a section). The resulting catalogue numbers need to sort correctly in databases, computers and digital music players, in other words!

I'm going to call this new catalogue the Dizwell Catalogue of Mozart Compositions, because my old domain was called 'dizwell.com' and my email address still belongs to that domain: the name 'dizwell' itself is a portmanteau of Disraeli and Wellington, my two favourite 19th century statesmen... which has no bearing on anything at all, I realise, but it is what it is! Mozart's compositions will thus acquire new 'dizwell numbers', indicated by a "DZ" prefix and then a five-digit number, whose construction principles I'll now go on to explain.

To work out what composition gets which DZ number, I first decided to chop Mozart's output into the following thematic groups (which I here sort alphabetically) :

• Chamber works
• Choral works
• Concerti
• Keyboard works (piano, harpsichord, organ etc)
• Operas
• Orchestral works
• Symphonic works
• Vocal works

Note that I separated out his symphonies from all the other things he wrote for large orchestra: there are enough of them to make that a worthwhile distinction to make. I wouldn't do it for most other composers who might number just 4 or 5 symphonies in their output, for example. You could argue that a single category for 'concerti' is too broad; indeed, it would be possible, probably, to say that about any of these categories. Why not split them up a bit, into... I don't know... say, 'Violin concerti', 'piano concerti', 'other concerti' and so on? Well, it's a fair criticism and I can only say that I pulled the above list together based on a considered weighing up of utility versus precision. That is, I think it important to find a concerto -any sort of concerto- distinct from (say) an opera. But I simply don't think it useful to split the operas up into (for example) different sections depending on whether they are opera seria, opera buffa, serenata drammatica, feste teatrale or what have you. The precision of the finer-grained split isn't useful to me when I want to listen to his music, so I decided not to go there.

For the purely selfish reason that I enjoy listening to symphonies, choral and orchestral works above everything else and therefore want them listed first in any music player library I might use, I next assigned a two-digit number to each of these categories as follows:

• 01 = Symphonic works
• 02 = Choral works
• 03 = Concerti
• 04 = Orchestral
• 05 = Opera
• 06 = Keyboard works
• 07 = Chamber works
• 08 = Vocal works

Within each of these categories, I then sorted the works in ascending order of their existing Köchel (K⁶, not K¹) number and assigned a new three-digit number to each. To take the example of the first few symphonies, therefore:

K⁶ number	Date of Composition	DZ Genre	DZ Sequence		Name of Composition
K. 16	1764	01	001		Symphony #1
K. 17	1764	01	002		Symphony #2 (Doubtful)
K. 18	1764	01	003		Symphony #3 (copy from K.F. Abel)
K. 19	1765	01	004		Symphony #4
K. 19a	1765	01	005		Symphony (See K. A223)
K. 22	1765	01	006		Symphony #5
K. 42a	1767	01	007		Symphony #43 (See K. 76)
K. 43	1767	01	008		Symphony #6
K. 45	1768	01	009		Symphony #7 reworked as Overture to "La finta semplice" (See K. 51/46a)
K. 45a	1768	01	010		Symphony #7a "Alte Lambacher" (See K. A221)
K. 45b	1768	01	011		Symphony #55 (See K. A214)

So that shows you the K⁶ Köchel numbers, the date of composition and the ordinary 'name' of the symphony. As symphonies, they are all in the Dizwell genre category '01'; they are then assigned numbers 001, 002, 003 and so on in sequence, governed by the ascending K⁶ numbering they already have, which essentially reflects their ascending date of composition. That is, as the Köchel number increases, so does my three digit number. Note that the resulting DZ number bears no relation to the 'name' of a piece: Symphonies '43' and '55' are not in their correct order at all, going by name: despite the late numbers in their names, they are in fact early symphonies and therefore get early Köchels. They thus end up with early DZ numbers too. (NB: be aware that the table above came from a very, very early version of my cataloguing work, so few of those numbers apply to the named works these days. But the principle remains the same)

Having thus assigned thematic and sequential numbers within the thematic sections, you join the two-digit and three digit numbers together to create a single DZ number. Thus symphony no 35 is DZ 01048 - and you pronounce that as 'Dee Zed Oh One Oh Four Eight', not as 'Dee Zed One Thousand and Forty Eight': the leading zeroes in each part of a DZ number are significant and need to be pronounced so you know they are there! Tag your music files with that number at the front of your 'album name' and you will discover that Mozart's music comes in nicely-discrete 'chunks' in your music player, making it easy to scroll for a symphony here, an opera there, a string quartet somewhere else...

As a thematic section ends and a new one begins, the sequential number resets. Thus:

DZ Number	K⁶ number	Name of Composition
01064	073m	Symphony #47
01065	073n	Symphony #45
01066	073q	Symphony #11
02001	020	Motet "God is our Refuge" (Psalm 46:1)
02002	033	Kyrie for SATB & Strings
02003	034	Offertory for Soprano, SATB & Orchestra "In Festo St. Benidicti"
02004	047	Offertory "Veni, Sancte Spiritus" for Soprano, Alto, Tenor, Bass, SATB & Orchestra

Here we see the symphonies end at DZ 01066 and the choral works begin at DZ 02001; the different works in the 02 section then ascend numerically from that point on. Should we discover a new symphony, it can be assigned DZ 01067 without that meaning that the choral works need to be re-numbered.

I'm not going to claim the DZ numbers are pretty: they definitely aren't. I am going to claim they are useful, however, because they preserve the intent behind Köchel's original catalogue within a broadly-thematic approach that itself is very helpful to a listener of Mozart's music who searches for something to play by the broad 'genre' it belongs to. DZ numbers will, in short, serve to order Mozart's music in a audio player's library in a sensible, useful manner: they will sort numerically, without complications introduced by adding letter suffixes to things or by using Roman numerals. And whilst it is true they aren't pretty, they are at least not as butt-ugly as Hoboken numbers are for the works of Haydn!!

No doubt this classification scheme may contain errors (a work assigned to the Concerti may yet turn out to be a Choral work, for example): happily, the scheme can accommodate re-assignments between sections if they ever need to be made, which I shall do over the years to come, no doubt. I don't expect Radio 3 will start announcing "Mozart's Requiem, DZ 02082" any time soon, however, so I have provided an on-line catalogue of Mozart's works, allowing easy conversion between the current Köchel number and the new DZ number (or vice versa). Being a digital catalogue, it can be easily consulted, searched, filtered and sorted as the mood takes you. Enjoy!