How many different notes are there in an octave? What about note names? The answer to the second is very interesting and this is part one of an exploration of that question.
Bach's Well-Tempered Clavier (henceforce WTC) consists of two books each containing prelude and fugue pairs in 24 different keys. Why 24? Well, if you look at a keyboard, you'll see there are 12 notes in the octave. Allowing for both major and minor keys we therefore have 24 major+minor keys to choose from and Bach wrote a prelude and fugue in each key in each book of the WTC.
But if we look at the key signature, it tells a different story. A key signature may consist of 1-7 sharps or 1-7 flats or nothing at all. Allowing for both major and minor keys that gives us 30 different keys.
Here are the 15 major keys that the key signature gives us (with the ones Bach uses in WTC in bold):
C# F# B E A D G C F Bb Eb Ab Db Gb Cb
The corresponding relative minors (with the ones Bach uses in WTC in bold again) are:
A# D# G# C# F# B E A D G C F Bb Eb Ab
Notice that the extra keys possible but unused by Bach are enharmonic with keys that are used. Db major is enharmonic with C# major, Gb major with F# major and Cb major with B major. Similarly A# minor is enharmonic with Bb minor, D# minor with Eb mintor and Ab minor with G# minor. That is not to say that Db major is the same as C# major—for one they have different key signatures and the names of each degree of the scale is different (more on that later). They may even sound different depending on the tuning system used.
But this explains why Bach wrote in 24 major+minor keys, even though notation provided him with 30—he avoided enharmonic duplicates.
But this isn't the whole story. Notice that:
The reason behind these two facts will be the subject of the next part.
by : Created on Aug. 30, 2005 : Last modified Aug. 30, 2005 : (permalink)
I'm just about to release MorphGNT 5.07 and, shortly after that, a major new release I'll designate 6.07.
I've decided not to reset the minor release number on a new major release to emphasis the fact that 5.07 and 6.07 are identical in the data they have in common, the 6-series just adds some extra data.
I haven't yet decided just how much extra data will make it in the 6-series releases, but one new addition will be a column containing the surface form / inflected form / reflex (take your pick of terminology) of each word taken in isolation.
What do I mean by "taken in isolation"? Well a word like μετά could appear in the text as μετά μεθ' μετ' or μετὰ depending on the text after it. This new column normalises that to μετά. This happens to also be the lemma so it might not be clear what the extra value is in this case. So consider the text in Matthew 1.20 which reads:
παραλαβεῖν Μαρίαν τὴν γυναῖκά σου
Note that τὴν has a grave accent and γυναῖκά has two accents. If you were to ask someone what the accusative singular feminine article is, they'd say τήν not τὴν. Similarly, if you asked someone what the accustive of γυνή is, they'd say γυναῖκα not γυναῖκά. The reason for the differing accentuation in the text is the context: final syllable acute becomes grave unless clause-final and enclitics like σου throw their accent back to the end of the previous word.
Sometimes you want to treat the variations these cause as distinct, sometimes you don't. By including the extra column, users of MorphGNT will have the best of both worlds.
Here is a list of possible differences between the existing text column and the new column:
The new column normalises all these differences.
by : Created on Aug. 30, 2005 : Last modified Aug. 30, 2005 : (permalink)