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The sound/tuning of a piano. Please have a listen.

That E is out of tune on the recorded piano. You can hear the wavering in the pitch. That's a sign that one of the strings for that E is not in tune.
 
Listening on my phone (so the usual caveats apply)….

The first one is closer to just intonation. The second one is (almost surely) equal temperament.

Major thirds are a fair amount sharp of “pure” in equal temperament. Almost all VI’s and real pianos are tuned in equal temperament. So, most people get used to that sound.

Just intonation and other non-equal temperaments can sound beautiful in some circumstances, like your isolated chord. But they have major drawbacks when you move to other chords/keys, though. For instance, using the first example’s tuning of the note E, play an A major chord. Or E major. Doesn’t sound so nice now, does it?

You can do some reading on temperaments if you’re interested in learning more.
 
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erica-grace said:
Then howcome it sounds perfectly fine if the bass notes are E?
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The joys of piano tuning and harmonics. My father-in-law used to be a piano tuner and listening to him talk about everything involved in tuning a piano well, it's becoming a lost art.
 
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Interesting. I prefer the sound of the first, pitched down example as well.

Pianoteq has that slider where you can "age" the piano tuning by increments, though I have no idea what it's based on, and I tend to like it pitched to about 15% out of tune. I wonder how exactly "in tune" a high-end concert piano actually is on average? Or how close one should expect in a more humble nightclub where the house piano is tuned regularly, but less often?
 
Because you might be hearing a "B" harmonic on the G ( I believe the 5th harmonic of a G would be a B) and if the B you're playing isn't in tune it will clash with the B harmonic of the G.
 
Again, do a lot of reading about equal temperament to understand this phenomenon. In equal temperament, all 3rds and 6ths will "beat."

In the case of the first of your newest examples (which is in equal temperament), the fifth partial of the G almost--but-not-quite coincides with the second partial of the B. Since they don't quite coincide, you'll hear that rhythmic wobble in the resulting sonority. In piano tuning, we listen for and use that beat speed to decide how to tune intervals correctly. In this case, we would describe the beating as a 5:2 coincidence.

In your second recent example, you have lowered the B. Now, the fifth partial of the G almost perfectly coincides with the second partial of the B. Since the 5:2 coincidence partials match, you don't hear beating. This is the essence of just intonation.

In your third example, you are comparing the equal tempered upper B with the note that is an octave below it, a lower equal tempered B. In traditional practice, the first B was most likely tuned first, then the lower B was tuned to sound like a pleasing octave with it. So, of course they sound good together. (To be honest, as a piano tuner, the octave doesn't sound all that great to me, though it's acceptable).

Since you like the second example, you are discovering just intonation, and your preference for it. Again, to understand the drawbacks of it, tune the B as in the second example, then play a B major chord, and an E major chord. You'll discover that they sound terrible! So, in just intonation, some chords sound great, some sound kinda acceptable, and some sound terrible. You can mostly get away with using just intonation in simple music that doesn't use a wide palette of chords and doesn't modulate to other keys.

Equal temperament can be described as a system in which all like intervals (say, all major 3rds) sound either "equally good," or "equally bad," depending on one's perspective. They'll all have beating, and that beat speed will about double as you go up one octave (since an octave is a 2:1 frequency ratio). It's the most consistent tuning that we can do, since music in equal temperament sounds pretty much the same in all keys. That's it's advantage, and why it has been so widely adopted.
 
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I am a pianotuner for 30 years now and tune by ear. Had a three year education at a piano school for tuning and revision. Equal temperament in layman’s terms is as follow. In every key the intervals must have the same discrepancies. Those are ….octave pure in the largest parts of the piano. Octaves in the discant and bass are ‘stretched‘ , slightly larger. The ear perceives this as better/fuller. A fifth is a tiny bit smaller than a pure fifth. A fourth a tiny bit larger than a pure fourth. A major third is MUCH larger than pure and is beating faster and faster the higher you play thirds in succession on the piano. this way you can play in every key without encountering unplayable intervals. All other tunings have preference that makes a certain key sound better but others much worse. Pure tuning is nice for three chord songs the rest sound like crying wolves !:emoji_fingers_crossed::emoji_blush:
 
OK, to demonstrate the good and bad parts of tuning a piano in just intonation, I made a little voice-leading piece in just intonation.

The first and last part uses the "in tune" chords (I bet erica-grace will like that part), and the middle part uses the "bad" chords. I improvised a few takes, then had to clean it up a fair amount; it was hard to remember to mainly use the good or bad chords in each part.

To repeat, the tuning is the same in the whole piece: just intonation. I think you'll be able to hear a dramatic difference between the good and bad parts. I'm calling it "Just Intonation - the Promise and the Penalty." :grin:

View attachment Just Intonation - the Promise and the Penalty(Joe_D).mp3
 
pianistje said:
I am a pianotuner for 30 years now and tune by ear. Had a three year education at a piano school for tuning and revision. Equal temperament in layman’s terms is as follow. In every key the intervals must have the same discrepancies. Those are ….octave pure in the largest parts of the piano. Octaves in the discant and bass are ‘stretched‘ , slightly larger. The ear perceives this as better/fuller. A fifth is a tiny bit smaller than a pure fifth. A fourth a tiny bit larger than a pure fourth. A major third is MUCH larger than pure and is beating faster and faster the higher you play thirds in succession on the piano. this way you can play in every key without encountering unplayable intervals. All other tunings have preference that makes a certain key sound better but others much worse. Pure tuning is nice for three chord songs the rest sound like crying wolves !:emoji_fingers_crossed::emoji_blush:
Click to expand...

Oh wow - you are right!
 
Talking about just intonation versus equal temperament, there are a whole bunch of tunings that tried to get the best of both worlds (pure intervals versus equally (but very little) dissonant intervals which has the flexibility that you can play in any key). For example the tunings/temperament of Werckmeister.

Some piano libraries have a list of tunings that you can choose from.

As I am used to hearing equal temperament, in comparison, just intonation (Pythagorean tuning and I believe there are a few other tunings that you may call just intonation?) always sound a bit sour to me.

A long time ago I visited a concert of Terry Riley (a composer of minimal music) who had a piano and a piano tuner on tour to keep the piano to such old tuning. This is one of the played piano pieces from the album "The Harp of Albion". I find this piece strangely appealing:



And he is not afraid to play "wolf notes" (the intervals that sound dissonant).

I once played on a church organ in Holland, in an old non-equal temperament. As I improvised, I could circumvent the dissonant intervals.
There were other players that tried to play a classical piece of which they had taken the paper score with them, but sadly not in the correct key, so it sounded rather dissonant.
 
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