Did the rules of harmony involve considerations of temperament?

[Colin Pykett]

Why are consecutive (parallel) fifths deprecated so strongly in 'classical' harmony (i.e. that from the common practice era)?  One often-quoted reason is that they undermine voice independence, though I've never really understood that since it would also seem to apply to consecutive fourths (wouldn't it?) yet they are allowed. A better reason to my simple mind is that there might have been a desire for music not to sound at all like the continuous parallel modal organum of former times - music was making a big break at that time and when that happens, haven't composers usually striven to remove the more obvious vestiges of former custom and usage?  As part of this transition, other intervals had become playable on the new and expanded keyboards with their 12 notes to the chromatic octave instead of the 7 to the diatonic octave used for the former modal music.  Thirds were of particular interest because harmony depends on triads which are built from 3rds as well as 5ths.

But the introduction of a 12 note scale brought with it the bugbear of temperament, which basically boils down to trying to fit too many pure intervals into the octave.  Hence the arrival of quarter-comma meantone with its many pure thirds but no pure fifths at all - a very different kettle of fish to the previous era of modal music which was stuffed full of pure fifths.  In quarter-comma all the 5ths (besides the unusable Wolf) are not well in tune (getting on for three times worse than in equal temperament).  So is it possible that these out-of-tune fifths were put in there deliberately so that they became more noticeable and possibly objectionable when played consecutively, unlike in the modal era when they were all pure?  At the same time the many now-pure 3rds in quarter-comma were exactly what was wanted by composers who were developing the harmony we know and love.  Is this also why consecutive 3rds are fine even in conservatoires today?

The fact that all keys could not be used in meantone might not have been seen as a major problem at first, since the concept of 'key' as opposed to 'mode' was perhaps still a novelty which was a rich source of exploration.  Perhaps only when that limited novelty wore off and yet greater opportunities for modulation became of more interest did other, less extreme, temperaments become desirable so that all 24 keys could be explored.

So to summarise:

1. The introduction of keyboards with 12 notes to the octave necessarily arose at around the same time as composers wanted to use more intervals than the old modes allowed.  So to explore 'key' rather than 'mode' they had to invent temperament to enable all the new intervals to fit into the octave.

2. One of the earliest temperaments was quarter-comma meantone, in which all fifths were noticeably out of tune (quite apart from the unusable Wolf fifth which we can ignore here).

3. These impure fifths might have been deemed subjectively unattractive, particularly when used consecutively in harmony, unlike in fifth-dominated modal music where all fifths were pure.  Maybe the impurity was deliberate intent.

So was the unavoidable introduction of keyboard temperaments a factor in the way that the rules of harmony necessarily had to evolve?

 

 

[Dafydd y Garreg Wen]

Just a thought to throw into the mix … namely that thirds were considered dissonances by medieval theorists (and presumably practitioners). Whether that is relevant to your hypothesis, I don’t know ….

[Colin Pykett]

3 hours ago, Dafydd y Garreg Wen said:

Just a thought to throw into the mix … namely that thirds were considered dissonances by medieval theorists (and presumably practitioners). Whether that is relevant to your hypothesis, I don’t know ….

I would say that it's highly relevant.  In medieval times, the fifths were pure and most thirds horribly sharp because they used only a diatonic scale for modal music with 7 notes to the octave (basically the white notes on today's keyboards).  This was probably tuned to the so-called Pythagorean scale or something close to it (not that it had much connection with Pythagoras in reality but that's another story).  So it's not surprising that they regarded the pure fifths as consonant and the impure thirds as dissonant in those days.

This lasted until around 1500-1600, when European composers decided they wanted to use more intervals than the old modal system permitted.  So they threw out Pythagorean tuning, added 5 black notes to the octave to enable modulation to be both composed and rendered, and tuned the whole lot to quarter-comma meantone.  It seems to me not mere coincidence that meantone had impure fifths and pure thirds, exactly the opposite of what the old modes imposed, because they could have used any old temperament that took their fancy.  The theorists of the day were certainly up to it in terms of understanding the maths.  However they chose meantone, and thus thirds became regarded as consonant and they have remained so ever since. 

So the story does seem to suggest that the rules of harmony which evolved at that time might have been influenced by the early temperaments used, in particular quarter-comma meantone.  It's just nice to my mind to have more robust explanations for things like the deprecation of consecutive fifths in harmony.

Incidentally, I'm not suggesting any of this is necessarily novel.  Others might have told the story similarly.  However I haven't personally come across it told in quite this way, though that doesn't mean it hasn't been done.

[innate]

I think this is an interesting line of inquiry but is, perhaps, a slightly “keyboard-centric” view. The development of counterpoint in church music from the Ars Antiqua, through the Ars Nova and Machaut, to Landini and a world of parallel sixths and thirds with contrary motion at cadences would seem to be very much based on the sound world of singing, where temperament had different parameters.

[pwhodges]

My feeling is that temperament is not relevant here.  

My experience is, of course, learned; yet I do feel the weakness of harmonies with unplanned parallels quite strongly in even casual listening, and even in some instances where I tolerate them for other aspects of the music, I am saddened by their presence.

Paul