http://www.skytopia.com/project/scale/third
I would be grateful if you could listen to the tests shown in the link above to explore different aspects of why you found/find equal temperament to be out of tune.yuri wrote: I actually heard equal temperament as hopelessly out of tune. It's built in.
If you find that the Saw wave tests sound out of tune in ET, then do you find the tests with octave partials also sound out of tune?
Glad to hear! Yes, you're right - with vibrato, and/or with simpler timbres such as sine waves and octave partials, and at least for me, it's easy to confuse them.Lorenzo wrote: I must say, your "The 12 Golden Notes" is one of the best analysis I've seen on the subject. At the bottom of the page you have a survey with examples of Just vs. Equal Temperament. I love that "blind" test re the Triad Options!!!!!!! That's exactly what I've been thinking--that the difference is so small, unless you know which you're hearing in advance you may not be able to tell which is which.
Haha, no I composed the music, but even though I play the piano, it's the computer that's playing the music.Lorenzo wrote:I also like your samples of the fugue played on the harpsichord in JI and ET. You say you "knocked up this tune in about an hour." So, that's that you playing!?
Yep I'm a student currently in my last at university, and just about to study tuning and temperament even further for my dissertation. Although I took a keen interest in tuning and temperament years before I went.Lorenzo wrote: Great web site you've got there Dan! Tell us a little about yourself! Are you student or faculty? If student, is your major music, math, or other?
Again, I count the perception of beats to be a different type of consonance to the 12 basic interval types. The first is relating to how harmonic two pitches will sound to form a single timbre. The second type I call 'chromatic consonance', and is related to how 'sweet' intervals will sound. How "chromatically consonant" an interval will sound varies from person to person, from what I've gathered.StevieJ wrote:It's easy to hear when the strings come into tune with each other - the "beats" disappear and there is no clash. This is a perfect fifth, a natural and very sweet interval. Any minute movement of either string away from this interval will produce a "clash" - beats. In equal temperament, perfect fifths have to be sacrificed in order to preserve perfect octaves.
I'd be grateful if you could also try the Sample A/Sample B test that Lorenzon gave above and then maybe visit my third comparison page. If you find that the Saw wave tests sound out of tune in ET, then do you find the tests with octave partials also sound out of tune?
Being a pianist myself, you could well be right! However, the subject is interesting anyway, because it forms an important root of music, at least its harmony (no pun intended!).MTGuru wrote: My subjective impression is that it's mostly keyboard players who fret (!) about academic questions of intonation.
I agree, and I also love the droning sound that just intonation provides. However, I am not looking for that kind of consonance (what I call 'harmonic consonance'), but instead for what I call 'chromatic consonance' which is related to how sweet an interval sounds (and this type varies from person to person). I had to make the JI interval sound timbrally/'harmonically' the same as the equal tempered version, so as to make it fair comparison. It's just unlucky that we have separate the phenomena like this.BoneQuint wrote: But that "plain" sound is what is nice about just intonation, at least with real instruments, as opposed to synthesized ones used in your test.
With real instruments, intonational errors and other complicated phenomena start to creep in, so 'synthesized' sounds are necessary to keep the tests as objective as possible. However, I do agree that the just intonational, droning, timbral effects can be even nicer with real instruments, but I'm pretty sure this is mostly thanks to their almost-but-not-quite-spot-on JI intervals, creating phase-like effects. See my new M.third comparison page, and listen to the "Almost Just Intonation" examples.BoneQuint wrote:The synthesized ones are simple and "artificial" enough to sound plain when the harmonies are too pure.
The other important thing to say is that even with vibrato, the JI sound is still very much in the JI pitch interval range, and far away from ET.
That could well be due to the tiny vibrato. Listen to the appropriate tests on this page, and you'll hear the characteristic droning sound of JI:Jerry wrote: That's interesting.
I listened to those and thought, "Neither sample sounds like just intonation." I could hear the beats, and I didn't hear the characteristic richness.
http://www.skytopia.com/project/scale/third/
Lol! Funny you should say that as I have been playing a few more as of late Anyway, yeah it's down to mathematics in the end. Obviously, JI intervals can be represented by close, but different ratios. At a basic level, with JI, you need two slightly different whole tones (10:9 and 9:8 ) so that you can obtain the different intervals of the octave properly.Lorenzo wrote: I don't know how to explain why, but I think maybe Dan can if we can get him away from his computer games!
I think one of the simplest examples is this: Take the JI major third which is 1.25. Now modulate to E major, and take the major third again. In equal temperament, this is G# or 800 cents. In JI, it falls significantly short of this at 772 cents, and 42 less than the usual JI minor sixth. Then if we ever want to play a minor sixth with C as the bass note, we have a problem houston, as we need two different notes. See this pic, and you can see some of the differently sized gaps between each interval:
http://www.skytopia.com/project/scale/eq-ji.png
Even then, you'll find interval contradictions popping up, as the music will often find it itself slightly transposed up or down a little compared to when it started (at least when changing keys). Also, according to this site, mixing harmony with melody, you can't make all intervals Just with dynamic JI:Jerry wrote: There are now electronic keyboard instruments that can provide "automatic just intonation," which adjusts pitches in real time to create accoustically perfect chords according to whatever base note is used. That's rather similar to what a highly trained chorus does.
http://www.music-cog.ohio-state.edu/Mus ... uning.html