Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

What I Learned Writing an Album in Just Intonation

osar.fr

Post reply on HN
Print view View original

51–60 of 99 posts

Re: What I Learned Writing an Album in Just Intonation

#51

Post by sporkl »

Overall a good intro on the subject. I feel like at the start it might benefit from being a bit more explicit about pitches being frequencies and ratios being intervals; probably just worth a reminder for people who aren’t as familiar

Might be interesting to talk about how the usual ratios come from the harmonic series. For sounds that don’t produce a harmonic series, other potentially non-integer ratios can actually sound more consonant. The youtube channel New Tonality[0] has a bunch of great videos about this

Also wanted to mention that I’ve been working on a piece of commercial software[1] for working with freestyle/adaptive just intonation, if anyone’s interested

[0]: https://www.youtube.com/@new_tonality [1]: https://www.dmitrivolkov.com/projects/pivotuner/

Re: What I Learned Writing an Album in Just Intonation

#52

Post by olau »

sonorous_sub wrote: post #16
pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

I think you could make the piece more interesting to the casual reader by grounding the subject in its history. It's been suggested by the book below that the dominance of equal temperament in western music is a relatively recent innovation, something like 120 years old, and is perhaps a consequence of the industrial revolution and the demand for mass manufacture of musical instruments having uniform qualities it pro…

If you have not read it, you might find the last part of the blog post most interesting. It covers shortcomings of just intonation.

Re: What I Learned Writing an Album in Just Intonation

#53

Post by the_other »

pyinstallwoes wrote: post #38
the_other wrote: post #22

Earlier quoted context omitted.

Why is it a sensitive subject?

Wait until you hear about A=432Hz

I've heard a little about this one. It's not that interesting, IMO. Some people think tuning even temperament down such that middle A becomes 432Hz (rather than 440Hz) is better for your health as well as the tone. I can get a little "woo" from time to time, but this one left me cold.

Re: What I Learned Writing an Album in Just Intonation

#54

Post by jfengel »

wonger_ wrote: post #7
pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

I am very unfamiliar with the topic. Here's my takeaways from the article: - almost all music I've heard uses 12TET - JI is microtonal / an alternative tuning to 12TET - you're the author of the lovely ambient.garden, which uses JI - the audio widgets and visualizations were very helpful - JI has perfect harmonies, and 12TET approximates those enough to still sound good - JI opens up cool chord options - but there's…

The key to the article, and to all of Western music, is about a set of weird mathematical coincidences involving the twelfth root of two. In particular, that twelfth-root-of-two to the fourth power is almost exactly 4/3, and twelfth-root-of-two to the fifth power is is almost exactly 3/2. And, of course, twelfth-root-of-two to the 12th power is exactly 1.

For some reason, not entirely well understood, when you play frequencies that are nice multiples together, they make pleasant patterns ("consonance"). They interfere and reinforce at regular intervals, and it sounds nice. When you don't get nice ratios, they make irregular interference patterns, and that sounds unpleasant ("dissonance").

So... take a scale (one frequency to twice-that-frequency), divide it into 12 equal parts (geometrically), and you get of those nice patterns. Each successive note is the frequency of the previous note times the-twelfth-root-of-two. That's the "twelve tone equal temperament". It makes it easy to write pretty music just by following some mathematical rules.

There's a Wikipedia article on the-twelfth-root-of-two:

https://en.wikipedia.org/wiki/Twelfth_root_of_two

EXCEPT... that those coincidences aren't perfect. They're very close, but tiny differences matter. Some intervals that should work, don't. Different scales take on different feelings, even though in theory they're just the same thing nudged up a few hertz.

Anyway... that set of coincidences is the basis of all of the music you're familiar with. Other musical cultures also take advantage of it. But there's no fundamental reason why those particular coincidences should be the only interesting music, and so people look around (often, to yet more world musical cultures) for alternatives.

Re: What I Learned Writing an Album in Just Intonation

#55

Post by jerf »

pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

I really appreciate at the end how you explained some of why 12TET is so popular. There was a time when it was the new kid on the block, and there's a reason it took over. Most articles of this type are so busy taking a dump on it that you can't get a clear answer to that question.

I am a firm believer in the idea that if you want to know how to improve on something, you must clearly understand where you are coming from with current practice... and if your understanding of "current practice" is that it is entirely bad with no redeeming qualities, you don't understand current practice. We see that a lot in the programming space; there's a recurring set of ideas like "everything should be visually programmed everywhere!" that always come from people who spend a lot of time complaining about text without demonstrating any understand that it is there for a reason, indeed, many reasons, and if you casually throw all those good reasons away in your attempt to be new and fresh, you are starting so far to the negative that you stand no hope of producing anything new and useful.

Personally I really appreciate 12TET's ability to wrap the harmonies around as you show, and I've never thought about it that exact way, so I also appreciate the visualization. That doesn't mean it needs to be the only tuning used by anyone, though.

On to the music itself. One thing that I have found when I listen to a lot of "microtonal" music is that for music that is nominally more "consonant", it ends up with things I would not call "dissonant" per se (at least, in the traditional ways that 12TET has dissonant intervals), but a whole bunch of intervals I'd just call sour. Now, I won't deny that despite my general openness to alternate tuning pretty much everything I listen to is 12TET and I'm adjusted to that just like everyone else, but when I listen to Baroque-period music in pre-12TET tunings (as they were likely performed then), I hear the differences versus 12TET, but I don't hear that sourness in those pieces. It seems to me that if the goal is to seek greater consonance in tunings (and I acknowledge those who do not have that goal, this post is specifically about those who are seeking that) I would be hearing music that actually is generally more consonant. I would be more interested in alternate tunings if the resulting music was not so sour.

I really appreciate that your "ambient garden" is both different from what I'm used to hearing, but also I find it quite approachable. Sure, a bit of adjustment is necessary, or at least helpful, but it seems like one could actually argue that there is indeed greater consonances, and interesting contrast to conventional intervals, in that music, rather than just... sour intervals everywhere.

Re: What I Learned Writing an Album in Just Intonation

#56

Post by Sesse__ »

pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

My basic problem is that I'm really struggling to hear the difference between many of your samples :-) And I've already got a bit of experience with microtonality (DSP background, playing and have tuned multiple instruments, reasonable pitch perception). One of the big problems for me is that it's not so easy to hear them side-by-side; you have to stop one of them, then start the other (unless you want them both at the same time, which you probably don't), and both the start and stop buttons are pretty laggy. FWIW, most audio comparison tools I've seen (typically centered around compression or restoration) include some way of switching seamlessly between the two, without restarts.

Re: What I Learned Writing an Album in Just Intonation

#58

Post by Levitz »

bigstrat2003 wrote: post #8
pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

I would say that this is way too technical for me, however, I also only have the slightest hint of music theory knowledge to begin with. It seems to me like that isn't a problem though, because this is a very technical topic by nature. Unrelated to the writing, but I was kind of disappointed that when listening to the examples, I cannot for the life of me hear a difference between just intonation and equal temperamen…

It's worth noting that part of the point is showing that the difference can be very small.

The one at https://www.osar.fr/notes/justintonation/#compare is really tiny, the largest difference being 3hz, you can kind of compare side to side using https://www.szynalski.com/tone-generator/ and see for yourself.

The difference is more perceptible below that, in the chord comparisons.

Re: What I Learned Writing an Album in Just Intonation

#59

Post by Levitz »

Sharlin wrote: post #27

Should be noted that any ensemble that consists only of continuous-pitch instruments (eg. strings, trombone, human voice, fretless guitar) is free from the shackles of 12TET and its harmonies naturally tune to as close to "pure" intervals as the performers’ skills allow.

I never thought about this, does a choir left to its own devices naturally gravitate to JI rather than ET?

Re: What I Learned Writing an Album in Just Intonation

#60

Post by banana-lambda »

klik99 wrote: post #41
pierrec wrote: post #3

I'd love to get some feedback on this, because I'm not sure I've hit the original goal of this article. For a long time, the topics of just intonation, harmonic lattices, and of their relationship with temperaments were difficult for me to understand, despite reading the theory on them. It's not until I applied the concepts that could say I understood them. I tried writing the "missing article" that would have given…

I think you need some info in the start of the article about why 12tet was invented, what problems it was solving and how it fails. Like - In Bachs day you'd have to retune the instrument if you changed key signatures and you could only modulate a few steps away before the ratios sounded really bad. So 12TET opens up the possibilities to modulate far away from your original and requires less retuning, at the cost of…

> each key signature in 12TET has a unique sound (Like CMaj vs EMaj) due to inconsistent ratios in perfect fifths

I thought this wasn't true in 12TET, because in that case a perfect fifth interval is always a ratio of the twelfth root of two to power seven, or almost 3/2, no matter the starting point, C or E.

Post reply on HN