Piano World Home Page Forums Our Most Popular Forums Piano Forum Fascinating review of the history of Equal Temperament

I found this and put it on my site. I hope you like it. Let me know what you think.

http://howtotunepianos.com/an-interesting-discussion-of-equal-temperament/

I'm surprised no one has any comments about this podcast, good or bad.

I gave up after a few minutes when the guy says ET sounds good in all keys. No. It sounds okay in all keys, maybe. I've read quite a bit about temperaments since 30 years - I've always been more interested in the temperaments themselves than the (often incorrect) "historical anecdotes" about them.

I had the chance already in 1990 to experiment with temperaments, using my Kurzweil digital piano. Not only using the well-known WTs, but also modifying them and ending up creating my own. Or, for example, staying in just intonation in real time as you play/modulate keys, either by programming the lowest note on the keyboard to set the root (here the temperament's current key) or using MIDI, etc. Just like singers in a choir adjust their intonation as the score modulates, etc.

I'm so used to my custom UT now after all those years - I tune my acoustic the same. To me, ET sounds off in the keys I'm used to hear differently now. I guess many people can say the very opposite, instead preferring ET. And it's totally OK with me and understandable. It's often just about getting used to hear something. Just like people in foreign countries who use different exotic intonations probably find our "Western" temperaments to sound weird. As long as we are happy to hear what we play/sing, I guess that's what matters.

Listen to the whole thing. It is not what you think. There are many intelligent comments on both sides. I guarantee you will find it fascinating. Listen to how Kepler describes the difference between the M3 and the m3. That alone is worth the listen.

Interesting post - Thanks Mark.

33 minutes for part one.... Maybe someone can quote the intelligent comments?

I think there's only one part.

From memory:
Relationship of equal temperament to the church's view of perfection.
Mathematical explanation.
Cool recording of a Bach prelude in Ab (C tuning), C (C tuning), and ET.
Discussion of the violent opposition to the book.
Something about Kepler's outrageous views on music.

Thanks!

>Something about Kepler's outrageous views on music.
I need to read up on that

I can't believe I listened to the whole thing. It wasn't until I studied acoustics in college that I became aware of the issue with temperament. Up until then a piano was either well tuned or out of tune. Come to find out a piano is never "in tune."

I hate to open the temperament can of worms, but as a composer I've sought tuning systems that would represent my music better. I had my piano tuned to EBVT III once, it sounded fine but didn't sound significantly different to ET and I didn't get the impression that different keys had different characters. I would be the first to tell you that Gb and F# are not the same note, but from a practical standpoint ET works better than anything else I've heard. So if someone has heard a temperament that works better for them I'd like to know about it.

I read about a piano dealer who had an employee to tune all their new pianos with a basic guitar tuner... no mention of temperament. Apparently the pianos were tuned well enough to sell and keep them in business.

I think what it all boils down to is how does it sound to the player?

We can make things overly sophisticated, but sometimes simple works best.

By-the-way, I prefer ET.

Rick

The truly astounding thing is that the notes as derived by the ancients and semi-ancients, by getting the most notes that sound good together, should come up with a 12 note scale that is so close to the equal temperament system of 12 notes, that people like myself, with an untrained musical ear, can not hear the difference. There is no physical law that this early system of notes and tuning should have anything to do with a scale that is created by making each succeeding note higher in frequency by the ration of the 12th root of 2 (equal temperament).

But they did not start with 12 notes. That is why the keyboard is 7 white notes to 5 black notes.

(Ratio, not ration)

If you had listened to the podcast you would have heard a comparison of Pythagorean tuning vs. Equal Temperament that is clearly at odds with your statement. Playing in the key of Ab on a piano tuned to Pythagorean Tuning has many notes that sound sour and out of tune. The podcast makes clear why this is the case and it is the basis for the argument that has raged for centuries.

Greetings,
It depends on what your definition of "works" is. ET is a very simplified intonation, in that all keys are alike and everything is averaged to the lowest common denominator,(13.7). WT is far more complex, (like the music that was being composed under its influence.) This complexity alters the relative musical values of the intervals, (via dissonance/consonance contrasts). This means that to play the passages most expressively requires the musician understand the changed values, (F# is so strong that virtually ALL composers used it sparingly, like salt). Musicians that are too lazy to learn HOW to use the resources of WT will continue to favor what they are used to. I have seen this for years. I have also seen the epiphanies, which make all the effort worthwhile.

Temperament, like food, can offer variety, and there are many that are more comfortable with blandness and sameness than complex, spicy, and varied. Bless their hearts, and if they ever want to change the intonational rut they are in by seeking more challenge, there are many techs that can now supply it.
Regards,

It's not a law of physics, it's just a strange piece of luck.

Vibrating strings and air columns produce overtones by dividing into equal parts, so you get the whole thing making the fundamental, dividing into two to make the octave, into three to the octave and a fifth, and so forth. Once you have the fifth and the octave, you can invert to get the fourth, and go around the circle of fifths.

The ratio for the pure fifth is 3:2, which is 1.500000:1. Now here's the piece of luck: 2^(7/12) = 1.498307. The root approach just by luck comes very close to matching the ratio approach for the fifth and its inverse, the fourth. So, you can go around the circle, and have it close correctly.

Now the bad news:
1. The root approach doesn't come nearly as close for many of the other ratios.
2. The circle doesn't close if you use the pure ratio 3:2 for your fifth.

So, you can tune by roots, by pure ratios, or you can tweak, tinker, and fudge it in a number of different ways. Mostly, we use the roots (equal temperament), unless we specifically want to try one of the other ideas.

it's still raging LOL

If you have access to a digital piano which offers different temperaments, you could certainly experiment and especially hear the differences right away (instead of tuning a real piano). Werckmeister III would be one to test - certainly a more "pronounced" UT compared to EBVT III. And then you could also figure out that the most wider than ET major thirds in Werckmeister III go a bit too far and choose another temperament, somewhere between Werckmeister III and EBVT III.

I use my own custom UT on my pianos since 1991, so I guess it works well for me.

Care to post a recording in a few different keys?

I did say to the untrained musical ear, like myself. I could not hear the sour notes in that short excerpt. I might have been able to home in on it in a longer passage. OK, so some people are gifted with a good musical ear from birth, many of us are not.

"it's still raging LOL"
Ditto

No problem but it won't be on the acoustic since it will be tuned in six weeks. So if you don't mind digital piano examples, I'll try to find some time this weekend to create short comparisons between ET, Werckmeister, my custom UT, etc.