Well vs. Equal Temperament (2000)

- pure major/minor

- pythagorean

- mean tone

- werckmeister/kirnberger, which i've heard mentioned as a good option for acoustic pianos a few times (i suppose i should try it)

For any besides ET, you have to specify the root/base note.

I think my synths have these options as well, so if you know anybody that has one, you can try it yourself. I think for string instruments, a few cents difference is pretty audible, but not so much for, say clarinet which doesn't have the sharp transients, unless you're playing above the treble clef staff. and then when you hit a track with overdrive/distortion, reverb and delay, it becomes very hard to discern differences.

His point is not helped by making false claims such as "Equal temperament actually did not come into use until the 20th century."

More importantly, the idea that Bach's WTC was intended to "demostrate the varying key colors in well tempered tuning as one progresses around the circle of fifths" sounds pretty uncanny when you know some context. As an organist, Bach was used to being heavily restrained in which keys and intervals could be used while dodging the many obstacles that were dissonances in the instrument's tuning.

The purpose of Well temperament, used on the harpsichord, was to get rid of those limitations and gain the ability to transpose everything freely while remaining consonant and in-tune. In this way, the Well temperament can be seen as an approximation of equal temperament in a time when the mathematical tools to achieve it were not really known.

To me, it's pretty clear that the WTC is Bach gleefully exploring the freedom of transposition-invariance and free modulation. In other words: Bach would have loved the equal temperament, and this article would likely give him a hearty chuckle.

I like natural intervals, but dividing the octave in 12 tones is a rather inappropriate way of using them. European classical music adopted this system early on, and therefore was doomed to end up on the equal temperament at some point. It's not the ultimate system nor the end of temperaments, but it's been really, really useful.

I probably could have phrased my comment a little bit more delicately, but my point was in reaction to the article, not the overall concept of tunings and temperaments. What drives me nuts are these "you're doing it all wrong" types articles about something that really makes very little difference to most people. Especially this one, in which the author really didn't bother to provide any auditory demonstration of a purely auditory phenomenon.

Is there any evidence for this narrative? Like anyone from the time writing about this who said "the keys are not all identical, but this well-tempered tuning is the best we are capable of doing."

> The purpose of Well temperament, used on the harpsichord, was to get rid of those limitations and gain the ability to transpose everything freely while remaining consonant and in-tune.

It was certainly designed to make all keys usable, but it doesn't necessarily follow that all keys were intended to be identical.