SwirlyMaple
Shredder
- Messages
- 1,329
Fixed it for you
In all seriousness though, I agree. There are people who can hear this difference, especially if they have a lot of experience hearing just intonation instead of equal-temperament. On fretless stringed instruments, it's possible to play in just intonation, unlike fretted instruments. And as mentioned, choirs and other singing groups tend to sing in just intonation because they're not constrained to the limitations of fixed-pitch instruments.For anyone who isn't aware, Gb and F# are only the same pitch (enharmonic equivalents) in tempered tuning, which is imperfect tuning. This is also true of all other enharmonic flat/sharp pairs like C#/Db, etc. But it's even worse than that. C in C major is not the same frequency as C in F major, or G major...
Why? It's because "perfect" harmonic tuning (aka "just intonation") is produced from ratios of the root note's frequency in a scale. In just intonation, these are the intervals and sub-intervals that occur in nature due to the harmonic overtone series. In other words, these frequencies "line up" perfectly with the harmonics of a freely vibrating string, and to our ears, they sound verrrrr noice when played together.
Let's see this magical tuning system in action. To get a major second with just intonation, you multiply the root frequency by 9/8. To get a major third, multiply the root by 5/4; a perfect fourth, by 4/3; and so on.
So why don't we use "just intonation"? Let's take an A major scale, and we'll let A4 = 440Hz per common convention. The frequency of the next note, B, is 440*9/8 = 495Hz. The next note, our major third C#, is 440*5/4 = 550Hz. Our perfect fourth, D, is 440*4/3 = 586.7Hz. And so on.
Ok, that wasn't too bad. Let's do the same with a B major scale. We'll start it with the value of B we just calculated above, so that all the pitches will be the same. So, B = 495Hz. Our major second, C#, is 495*9/8 = 556.9Hz. Uh oh. Wait a minute. We just calculated that C# was 550Hz in A major! And now it's 556.9Hz in B major? What the effsharp?!
This is why equal-temperament tuning exists. In short, we only get beautifully-perfectly-harmonious intervals if our instrument is tuned for ONE SPECIFIC KEY. If you apply those nice harmonious intervals to a different key, the frequencies for the pitches are not the same! Thus, the frequency of C in C major is not the same as C in F major, etc.
This is where equal-temperament tuning saves the day. Sort of. It is a way of nudging each of these tuning errors for different keys, so that the tuning for every key is a little bit off, in order to use the same frequencies for A/B/C/D/E/F/G in every key. It makes every key sound a bit crappy, but minimally crappy, so that we can use our instruments to play in any damn key we please.
And if you think you can't hear these tuning errors -- you probably could. Some of them are certainly large enough to be audible to a trained ear. We're just used to hearing these errors because it's the standard tuning in almost everything we listen to, so we don't tend to notice them. We did not merely adopt the dissonance; we were born into it, molded by it.
(A final note: guitars are equal-temperament instruments, so they have the tuning errors explained above. However, they have additional intonation errors from their fretted construction, which means guitar pitches are even further off from the ideal than equal-temperament makes them. So if you sing and play guitar like I do, and find you can't quite always sing those pitches perfectly, don't worry--neither can your guitar.)
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