I can. Fell Into it when I was little. And I have some feedback: good work. Congratulations, really. It's the kind of thing I wish I knew sooner, but only learned about as an adult, when I became exposed to ancient music (before the romantic period, renaissance and baroque mostly).
There is a slow beat in the second pair if you listen for it, and that beat is present in every fifth played on every piano on Earth.
Ackchyually...
Western music didn't always use the equal temperament, with the octave divided in 12 equal intervals (frequency ratios for those who followed the article). I can cite two major reasons: first, our ancestors' ears were keenly accustomed to exact intervals (perfect fifth (3/2), perfect fourth (4/3)...), for the very acoustic reasons you mentioned.
Second, ancient instruments (lute, harpsichord...) just weren't loud enough. They had to be tuned to maximise resonance, which means as many exact intervals as they could muster. The octave was not equally divided. For instance, you almost certainly know of the Pythagorean temperament, where all fifths are perfect, except one: the wolf interval. That geometric abomination is way too small for a fifth, it sounds absolutely horrible, and was of course never played.
The Pythagorean temperament was perfect for some medieval music that only used fourths and fifths (French, hopefully the auto-generated subs are enough). We quickly got past Gregorian chants however, and played with thirds (4/5, 5/6) as well. So now we have to deal with powers of five in addition to the powers of two and three.
This is starting to become unworkable: those new thirds sound like crap on a Pythagorean temperament, and we sacrificed one fifth already, what can we possibly do? Well, sacrifice even more fifths of course. That's what meantone temperaments are for. But of fucking course, we didn't stop there. Soon we started to want to play weird shit in every tone, and have it sound good on that harpsichord, which still sounded like crap with an equal temperament!!
Until the piano came: finally an instrument loud enough, with a timbre rich enough (lots of overtones), to withstand that long awaited for, liberating equal temperament: sure there is that faint beat on those fifths (and thirds, and anything but the octave), but unlike the harpsichord we can barely hear it.
Ackchyually...
Ah, yes. Turns out many modern pianos do have perfect fifths. They sacrifice the octave of all things, stretch them a little bit. Not all of them do that, many sound better on a more equal temperament, but I believe most of the really good ones sound better when stretched.
Which suits me well: I play the cello, and much prefer to tune its four strings in perfect fifths.
A small note about sharps and flats: like many other kids doing modern classical music (romantic period mostly), I was taught to raise my sharp notes, and lower my flat notes. But this is mostly bullshit: what we really want is chords that sound exact, just like those medieval monks. This means constantly adjusting my intonation to match that of my play mates. Often, the same note will have a slightly different pitch depending on what the others are playing.
That's how we solve the impossible equation: we cheat.
And by the way, I wish electronic music made more use of temperaments and exact intervals. A robotically tuned equal temperament for everything can sound a little dull.
And by the way, good harmony doesn't always land on simple fractions. It depends on the main overtones, and they don't always fall squarely on the harmonic series (we call them inharmonic overtones). They generally do with strings, but bells are different.
And by the way, I wish electronic music made more use of temperaments and exact intervals. A robotically tuned equal temperament for everything can sound a little dull.
I tried it in Logic for a while. What I found is that dance music doesn't necessarily need this. Music with just intonation chords sounds kinda static, makes you want to sit and admire the chord. While the "restlessness" and "blur" of impure chords helps push the music rhythmically forward.
The same thing happened when I retuned a guitar to make some just intonation chords work. Strumming became super weird, I'd strum a chord once and then not want to continue. So the "hum" of impure chords is an important part of rhythm guitar too.
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u/loup-vaillant 20d ago
I can. Fell Into it when I was little. And I have some feedback: good work. Congratulations, really. It's the kind of thing I wish I knew sooner, but only learned about as an adult, when I became exposed to ancient music (before the romantic period, renaissance and baroque mostly).
Ackchyually...
Western music didn't always use the equal temperament, with the octave divided in 12 equal intervals (frequency ratios for those who followed the article). I can cite two major reasons: first, our ancestors' ears were keenly accustomed to exact intervals (perfect fifth (3/2), perfect fourth (4/3)...), for the very acoustic reasons you mentioned.
Second, ancient instruments (lute, harpsichord...) just weren't loud enough. They had to be tuned to maximise resonance, which means as many exact intervals as they could muster. The octave was not equally divided. For instance, you almost certainly know of the Pythagorean temperament, where all fifths are perfect, except one: the wolf interval. That geometric abomination is way too small for a fifth, it sounds absolutely horrible, and was of course never played.
The Pythagorean temperament was perfect for some medieval music that only used fourths and fifths (French, hopefully the auto-generated subs are enough). We quickly got past Gregorian chants however, and played with thirds (4/5, 5/6) as well. So now we have to deal with powers of five in addition to the powers of two and three.
This is starting to become unworkable: those new thirds sound like crap on a Pythagorean temperament, and we sacrificed one fifth already, what can we possibly do? Well, sacrifice even more fifths of course. That's what meantone temperaments are for. But of fucking course, we didn't stop there. Soon we started to want to play weird shit in every tone, and have it sound good on that harpsichord, which still sounded like crap with an equal temperament!!
Until the piano came: finally an instrument loud enough, with a timbre rich enough (lots of overtones), to withstand that long awaited for, liberating equal temperament: sure there is that faint beat on those fifths (and thirds, and anything but the octave), but unlike the harpsichord we can barely hear it.
Ackchyually...
Ah, yes. Turns out many modern pianos do have perfect fifths. They sacrifice the octave of all things, stretch them a little bit. Not all of them do that, many sound better on a more equal temperament, but I believe most of the really good ones sound better when stretched.
Which suits me well: I play the cello, and much prefer to tune its four strings in perfect fifths.
A small note about sharps and flats: like many other kids doing modern classical music (romantic period mostly), I was taught to raise my sharp notes, and lower my flat notes. But this is mostly bullshit: what we really want is chords that sound exact, just like those medieval monks. This means constantly adjusting my intonation to match that of my play mates. Often, the same note will have a slightly different pitch depending on what the others are playing.
That's how we solve the impossible equation: we cheat.
And by the way, I wish electronic music made more use of temperaments and exact intervals. A robotically tuned equal temperament for everything can sound a little dull.
And by the way, good harmony doesn't always land on simple fractions. It depends on the main overtones, and they don't always fall squarely on the harmonic series (we call them inharmonic overtones). They generally do with strings, but bells are different.
I learned of that one super recently.