Tuesday, August 16, 2011

Harmony Revisited, Part 1

More and more, when I'm thinking about what is right or wrong with a piece of music, it is harmony that seems to be in question. The unrelenting dreariness of a lot of the music written between 1920 and 1960 is really a problem of harmony. The "emancipation of the dissonance" meant that the 'harmony' was always the same. Instead of the age-old principle of dissonance--resolution we just had dissonance--dissonance. How could that possibly work?
I choose this Bach chorale, not for its emotional content, but simply as an example of real harmony. The many chorales of Bach were collected soon after his death and published for the use of musicians, mostly composers. There have been several editions, but in one form or another, the collection has been in print since 1765. I would suspect that nearly every composer has a copy. Bach was a crucial figure in the move towards the system of tuning we use today: equal temperament. In order to make full use of the possibility of modulation, every key had to be usable. In the older tuning systems the key of C major was perfectly in tune, but a key like A flat major would be horribly out of tune. Equal temperament solves the problem. The period from Haydn to Beethoven made full use of this freedom of modulation. Here is another example of harmonic mastery:
The basic principle of harmony was the tension between dominant and tonic. Here Beethoven manages to be clearly in the key of A major while avoiding landing on it as much as possible. This gives the harmony a floating feeling as opposed to the solidity of Bach's harmony. The tonic/dominant tension was extended with secondary or applied dominants and the extremely useful devices of mixture (using harmonies borrowed from the minor in major keys and vice versa), the diminished seventh chord (which, due to its symmetry can go in any direction), the augmented sixth chords (which sound like a dominant, but actually prepare a different dominant) and the Neapolitan, which is a clever way of modulating to an unexpected key. The opening of "The Tempest" sonata by Beethoven shows his kind of harmonic thinking:
The harmonic 'system'--if we can call it that--of the Classical Period offered an incredible array of harmonic possibilities both flexible and powerful. The music of Haydn, Mozart and Beethoven is inconceivable in the absence of the harmonic system they used to such miraculous effect. Alas, after the death of Beethoven in 1827, it began to collapse as composers began to dilute the basic relationships to the point where the tensions gradually disappeared in a morass of chromaticism. Composers like Chopin, also a remarkable harmonist, began using remote harmonies just for their color without the preparation that Beethoven would have found necessary:
Throughout the 19th century, harmony becomes more and more of a problem and some started to think that it needed to be completely replaced by a different system. The main candidate was Schoenberg's 12-tone method that uses all the possible notes in a specific order, subjected to contrapuntal treatment. So the whole axis of consonance/dissonance disappears. Here is an example:
Though there is much to be said for this music--especially in terms of its suitability to the times--it has not been accepted by audiences except in small doses. One critic said that Schoenberg could empty any concert hall. I think the problem comes back to harmony. This music is all dissonance.

In another post I will take up what followed the atonal phase and the attempts by the minimalist and process composers to reinvent harmony.


Nathaniel Garbutt said...

Actually, There are references to equal temperament going all the way back to the start of the 17th Cent but it was usually dismissed as inferior due to the sacrifice of all pure thirds. It seems to have come to the fore in the late 19th early 20th Century, especially with the mass production of instruments.

Bach was very involved in tuning and creating his own cyclic temperaments (can play in all 12 keys without re-tuning) which usually are derived from a mean tone tuning system (1/4 comma mean tone contains a wolf interval which was considered unusable) and are not equal. His student Kirnberger also developed a number of temperaments that are cyclic.

Bach most likely didn't have equal temperament in mind when he wrote the well tempered clavier but one of these other temperaments which were called wohl temperiert or well temperaments

There are a number of other cyclic temperaments that are not equal, Werckmeister, Young, Vallotti, etc that were used throughout the late 18th early 19th centuries and these temperaments maintain a bias towards certain keys as you mention but eliminate the wolf interval. These temperaments are what was in peoples mind when they talk about a particular key having a certain colour or mood. Equal temp. removes this flavour completely - Beethoven used particular keys for particular moods (tempestuous c minor etc) for a reason.

Bryan Townsend said...

Thanks for sharing your thoughts on equal or sort-of equal temperaments in tuning. But I fail to see what it has to do with my post which doesn't even mention tuning systems nor does it mention bias towards particular keys.

Equal temperament may render all keys largely equivalent on the piano (though the soundboard and case are still going to favour certain resonances), but when you start talking about an orchestra, all the instruments, strings and winds, have different resonances in different keys--and this has nothing to do with temperament but rather with open strings and range.

Nathaniel Garbutt said...

I re-read my post and it comes across a little terse. My apologies.

I was responding to your second paragraph just under the Bach chorale vid.

I read and understood that as saying something very similar to a lot other things I've read recently relating to Bach, equal temperament, giving the overall impression that equal temperament is a good tuning system for western, common practice tonal music, it alone solves all the issues that existed with modulation and that it's roots are with Bach.

While I appreciate the need for brevity and simplicity in blog posts, as they have a large intended audience, but I feel that paragraph is slightly misleading in that equal temperament was well known before Bach's lifetime but was largely considered undesirable.

I also think that the tendency of lumping cyclic and equal temperaments together devalues the large concerted efforts of many composers/theorists of the day to avoid actual 12 tone equal temperament to preserve either as many pure thirds as possible or compromise that for cyclic convenience but try to maintain the differing colours and the 'emotive qualities' the non equal temperaments brought to the expression in tonal music.

Regarding your comment, I understand what you say when you talk about different instruments having different resonance frequencies and how they respond the acoustic environment etc but Temperament, though subtle actually can have pretty huge impact in how music sounds. The distance between two semitones are no longer uniform as in equal temperament but you now have semi tones that are wider or narrower which creates different beating for different chords in different keys.


I think this clip gives a pretty good demonstration on how the subtle changes in tuning have quite a large impact on the harmony and the piece as a whole.

Anyway...I've enjoyed reading your blog over the last few days and there is a lot of interesting material. I only commented here because this association of equal temperament with Bach has become a little bit of a pet peeve as it keeps cropping up.

Bryan Townsend said...

Please accept my apologies, Nathaniel! Looking back over my post I see that I DID mention equal temperament after all. Sorry! I am actually quite familiar with Werckmeister III and other historic tuning as I used to live with a harpsichordist who used historic tunings and I heard her set her temperament about once a week.

You are quite right, the various historic tuning systems that preceded equal temperament did not originate with Bach, nor is there any reason to believe that in the Well-Tempered Clavier he was advocating equal temperament. I recall an article in Early Music decades ago in which they did extensive research to determine what temperament the Well-Tempered Clavier was actually intended to use--and it wasn't modern equal temperament!

Thanks for the clip! It gives a nice demonstration of those tuning systems. For the whole picture, though, it is a good idea to have an example of mean-tone as well so we can hear how truly awful an untempered A flat chord can be!