21–30 of 164 posts
Bach explored another consideration, key changes within compositions, quite thoroughly: for example: https://en.wikipedia.org/wiki/The_Well-Tempered_Clavier . You can also consider the group theoretic explanation as well (sorry paywall): https://www.jstor.org/stable/3679467
There was 12 notes before there was even division. It was Bach that pushed equal temprament (equal spacing). Before that, the ratios were actual ratios (perfect 4ths and 5ths), though you couldn't just transpose music and expect to sound good.
Not really. Equal temperament was being advocated both in China and Europe long before Bach was born. In Europe, it was the lute players that pushed for it, because it matters more for fretted instruments, where any temperament other than equal causes conflicts and inconsistencies on the neck.
Earlier quoted context omitted.
There are guitars with frets that aren't straight lines that try to address some of the problems: https://guitargearfinder.com/faq/true-temperament-frets/
I'm a bit confused by that article. It says things like "the problem is that equal temperament isn’t perfect" and "because guitars are imperfect instruments, they can never be completely in-tune" and "if you tune your open strings perfectly to pitch, you may still notice that some chords sound slightly out-of-tune." That doesn't sound like a description of a problem with equal temperament. In fact, the whole point of…
I'm not crazy about the sound, myself. It's kind of like a guitar sample played through a MIDI keyboard.
Since Fifths sound so great, why not just keep doing that? When we get to the next octave, then come back down. If we get to a place that's "pretty darn close" to another note, then stop. The Python explanation looks like:
f = 440
for i in range(13):
print(i,f)
f = f * 3/2
if f > 880: f=f/2.0
0 440
1 660.0
2 495.0
3 742.5
4 556.875
5 835.3125
6 626.484375
7 469.86328125
8 704.794921875
9 528.59619140625
10 792.894287109375
11 594.6707153320312
12 446.00303649902344
Earlier quoted context omitted.
I'm a bit confused by that article. It says things like "the problem is that equal temperament isn’t perfect" and "because guitars are imperfect instruments, they can never be completely in-tune" and "if you tune your open strings perfectly to pitch, you may still notice that some chords sound slightly out-of-tune." That doesn't sound like a description of a problem with equal temperament. In fact, the whole point of…
I mentioned this fretboard yesterday in another thread ( https://news.ycombinator.com/item?id=32626218 ). One of the main proponents of the design talks about its advantages here: https://youtu.be/D8EjCTb88oA I'm not crazy about the sound, myself. It's kind of like a guitar sample played through a MIDI keyboard.
From the small clips I've heard, it sounds great to me, especially when the guitar is playing alone. Back when I played a lot of guitar I was often pretty bothered by intonation issues, even with decent gear that was setup well and didn't seem to bother other (much better) guitarists. But of course guitars often play together with 12-TET instruments that are likely to be much more accurately tuned (like a piano or organ), and it makes sense that the every-so-slightly out-of-tune nature of guitars has become part of what sounds distinctively guitar-like, especially the specific tuning you're likely to hear a lot with common guitar chord voicing in many styles of music.
We've seen this before: and it's likely wrong. He ended his experiment too soon at 24 divisions, but even a little googling should have told him to go to 31, which is more accurate than 12. The 12-note scale long predates the notion of just or equal temperament.
Simplicity is incredibly powerful.
Another possible explanation, which I'm surprised the author didn't go through is the "Circle of Fifths" which basically says: Since Fifths sound so great, why not just keep doing that? When we get to the next octave, then come back down. If we get to a place that's "pretty darn close" to another note, then stop. The Python explanation looks like: f = 440 for i in range(13): print(i,f) f = f * 3/2 if f > 880: f=f/2.0…