Posted by digitallogic 4 days ago
This is incorrect. If you watch a video like [0], the squiggles aren't real, they're an artifact of a rolling shutter camera. A real slowmo camera will correctly show the entire string vibrating[1].
The rest of the article is correct, but you can't see harmonics happening to the string.
[0] https://youtu.be/XOCGb5ZGEV8 [1] https://youtu.be/6sgI7S_G-XI
You poke a spot where a given harmonic doesn’t vibrate, and that takes energy away from the other harmonics that do need to vibrate at that spot.
If we’re just talking about visually being able to see them, I suppose that’s a different question. Maybe on an incredibly low pitched string, or with a strobe light playing at a synced frequency? But in terms of what the string is doing, it is vibrating as the sum of its harmonics.
But you absolutely can if you rest a finger on a node and pick it, producing primarily the harmonic. You can even see the lesser vibration at the nodes with your eyes.
Actually depending on microphone or instrument interface, you can see stuff that's beyond the range of hearing too.
Also, on a low-frequency long-string like an upright bass, if it is bowed at the halfway node, you still hear mainly the fundamental but the second harmonic is naturally emphasized more than usual, and you can also see half the string making its contribution as pictured, with the naked eye.
...is this correct? You can say this about any oscillating phenomenon - that doesn't mean it's not 'real'. The "squiggles" are an artifact of the frequency of the string and the scan rate of the rolling shutter. You'll also see artifacting from a global shutter camera, where the "squiggles" will be an artifact of the string frequency and the frame (rather than scan) rate.
Or do I misunderstand?
I've been playing guitar for 25 years, and it seems to me that I can look at the "squiggles" from a rolling shutter capture of a string and tell you which string it is (and possibly, if I'm having a particularly sharp day, whether it's E or drop-D). I've never tested myself this way - am I certain to fail? :-)
The most obvious example of this would be the wagon-wheel effect, where a spoked wheel can appear to rotate at a different speed and direction than its true rotation when captured by a camera under certain conditions.
I've never tried it.
How do you distinguish vibration from squiggles? To me these seem like the same concept, at the very least over time. The moment simply doesn't matter except to neurotic people without a solid understanding of harmonics and especially of sound.
Different guitarists use different diameter strings because the diameter determines the tension when you tune to pitch. Different people prefer different tension. Most shredders prefer light tension. Most jazz players prefer high tension.
The diameter is compensated at the bridge and in some guitars the nut. When you press a thin string to a fret, the center of the string is closer to the fret than when a thick string is pushed to the fret. Thicker strings compensate for this by using slightly longer length which you can adjust at the bridge.
One type of non parallel frets are called true temperament frets. They are sort of parallel but squiggly. This results in better intonation closer to that of a piano.
Another type of non parallel frets is multi scale or fanned frets. This allows the bass strings to have a longer scale length, which allows you to use relatively thinner strings for bass notes. This is important because when strings get thicker relative to their length, they start to behave more like cylinders with thickness rather than ideal springs, and sound rather nasty because harmonic overtones are out of tune with the fundamental.
When the string's action is higher above the frets, the tension increases more when fretted than open, to a greater degree than low action.
So the saddle for that string needs to be positioned such that the plucked portion of the string is slightly longer than it would need to be if the tension were the same as the open string.
James Taylor compensates by tuning everything down a few cents, between -12 at the low E and -3 at the high E, with a little break in the pattern with -4 cents at the G to deal with its weirdness. Good electronic tuners have "sweetened" presets which do something similar.
He keeps writing "for western people" but some parts of these are inherent in the human ear evolution and rather universal. All around the world we can find pentatonic music for example, even from ancient peoples, and this includes e.g. West African cultures, China, etc. And traditions that have microtonal inflections will still place the same emphasis on the octave, the fifth, major/minor third, etc the microtones add different flavors but it's not some widely different thing, which is why e.g. middle eastern or Indian songs e.g. can still be played on pianos, simplified (to the nearest approximation) but still retaining a lot, just losing their full flavor.
Though yaman raga is very popular and has a regular third, while other ragas still have a third-ish note, but microtonically adjusted up/down from the major and minor variants.
My cs department had a cool project class where you built what was basically a raspberry pi with a microcontroller by hand, and you had to use the dumb speaker and controller to make your own music firmware to produce notes. the challenge involved, was basically, the processor’s clock wasnt fine grained enough to produce perfect notes. I wanted to make a simon says toy but the notes were off. I approached my professor with my problem and he said I could cheat the processor clock in a clever way to get what i wanted and it was such a “oh wow computers are magic” to me, i got the notes i wanted. disappointingly the TA grader wasnt that impressed but that proff ended up offering me a job before I graduated.
Define off tune? 12 TET? Just intonation? Bohlen-Pierce (56 TET) ?
The "in tune" notes are as much a function of culture as physics.
Huh? Pitch ratios are not a social construct, it's just arithmetic.
But in the case if sound, I would have expected the skew to be less of a problem. Also surprised how the orof instantly know. It took me a while to figure out. How did you fix it? Cool story!
Proof is left as an exercise to the student. ;-)
That is not really true. You usually have a couple of clock sources on a MCU, but the clock gets propagated down the clock tree and the source, and most of the times, the PWM has the same source clock as the CPU. Indeed, I think if you're before the PLL the clock is more accurate as in you get less jitter but the overall drift is the same. You might have distinct clock sources but you need a specific hw and a specific configuration.
This worked well in 1980's microcomputers which used an accurate, crystal oscillator clock. IC's like the MOS6502 or Intel 8086 don't have built-in clocking. The boards were large and costly enough to afford a clock; and often it was dual purposed. E.g. in Apple II machines, the master oscillator clock from which the NTSC colorburst clock was derived also supplied the CPU clock.
These processors had no caches, so instructions executed with predictable timing. Every data access or instruction fetch was a real cycle on the bus, taking the same time every time.
Code that arranged not to be interrupted could generate precise signals.
Some microcomputers used software loops to drive serial lines, lacking a UART chip for that. You could do that well enough to communicate up to around 1200 baud.
This sounds like they were most likely bit banging square waves into a speaker directly via a GPIO on a microcontroller (or maybe using a PWM output if they were fancy about it). In that case, the audio frequency will be derived directly from the microcontroller's clock speed, and the tolerance of an internal oscillator on a microcontroller can be as bad as 10%.
That’s an issue with tuning instruments in general, and why pianos are generally slightly out of tune as a compromise.
As you get used to a particular guitar and strings, as you train your ear, you can also learn to work around the imperfections by adjusting how you hold down the strings (even with a fretted guitar, you can slightly repitch a string by holding it differently).
Been thinking of going a bit lighter recently, and also getting a classical.
Doesn't help that most tuners are still dog slow, none of the beginners courses properly tell you how the guitar actually works, or what a "chord" really is. They're all just "play this and don't worry about it". To be fair it does get you going.
Disclosure: String player.
And the fingering for a given melody may just lay across the strings better one way than another.
On a church gig in the 90s, I encountered an organ which was not tuned in equal temperament so that playing guitar with the organ always sounded out of tune (something I only discovered once Mass began since we had rehearsed with a piano) and I had to switch to bass to be able to play an accompaniment that sounded decent.
Most brass instruments have three valves. The first lowers the pitch by a tone. The second lowers the pitch by a semitone. The third lowers the pitch by a tone and a half. If you need to lower the pitch by two tones, then you press the second and third valves at the same time, and that works fine. However, if you need to lower the pitch by three tones, then you need to press all three valves at the same time. However, that adds the length of all the valve loops together to the total length of the instrument, whereas to lower the pitch by a fixed interval you need to multiply the length of the instrument by a certain amount, and so to truly lower the pitch by three tones you need to add a little bit more length beyond that supplied by pressing all three valves together. That's what the finger loop on the tubing for the third valve is for, so you can slide it out a bit for certain low notes.
A 12 TET chromatic is 2^(1/12), and a 12 TET fifth would be 2^(7/12). A perfect fifth is a 3:2 ratio. Those numbers are slightly different, and that’s enough to understand it. Another way of thinking about it is that if you were to complete the cycle of fifths purely by stacking fifths, you should end up on the note you started with but many octaves higher. But you should be able to see that starting on C1 and going by octaves will produce a number that is purely powers of 2, whereas stacking fifths will necessarily involve powers of both 2 and 3, so they can never be equal, I can stack fifths and never land on my original note’s octaves.
Another way to think of it is that they have to hit every pitch without assistance from the instrument anyway, so they learn to make every note sound “good” rather than hitting a mathematically defined frequency.
Can't we have a system that is optimized for the notes that are actually played in a song rather than the hypothetical set? And what if the optimization is done per small group of notes rather than over an entire song?
If your song is really simple, e.g. only consists of the 3 notes that make up a major triad (root, third, fifth), then this is definitely possible and you can just use natural thirds and natural fifths.
But as you start adding more notes, more chords and perhaps change of keys etc, it starts to break down.
That's the reason why J. S. Bach wrote The Well-Tempered Clavier. It's a collection of 24 preludes and fugues, in each possible major and minor key.
The basic idea was that if every prelude and fugue sounded good on an instrument (organ, harpsichord etc.), than it meant that the instrument was "well-tempered".
Using natural tuning instead of 12-TET would have resulted in some pieces sounding very good and other sounding very bad.
(Though something that happens in just intonation is that you often find out you need more notes than you might have originally thought, because JI makes distinctions between notes that are treated as the same in 12-TET. For instance, you might have 10/9 or 9/8 as your major second, or your minor seventh might be 9/5, 16/9, 7/4, or 12/7 depending on context.)
I don't think any just intonation guitar has been mass produced, but you can definitely build one or modify an existing guitar if you have the right tools and are willing to do a bunch of math and learn how to install frets.
This page is about a JI keyboard I built a while back, but there's also a few pictures of a couple old Harmony guitars I adapted to JI: https://jsnow.bootlegether.net/jik/keyboard.html
Here's a so-so performance of myself playing a Bach piece on a newer and vastly improved version of that just intonation keyboard: https://www.youtube.com/watch?v=rqbWnDhip0A
In 12-EDO the song has 11 distinct pitch classes. (Bach used the tritone, but not the minor second.) In my straightforward JI interpretation, I use 15 pitch classes. (I would have used 16, but my keyboard simply doesn't have a key for that note.)
You can. It’s called adaptive tuning, or dynamic just intonation, and it happens naturally for singers with no accompanying instruments.
It’s impractical on a real instrument, but there’s a commercial synthesiser implementation called hermode tuning.
You’re trading one problem for another, though. No matter how you do this, you will either have occasional mis-tuning or else your notes will drift.
I used to play fretless bass in a garage hip hop troupe that played with heavily manipulated samples that were all over the place in terms of tuning instead of locked to A440, forcing adaptations like "this section is a minor chord a little above C#".
Adaptive tuning is hard to do on a guitar because the frets are fixed. String bending doesn't help much because the biggest issue is that major thirds are too wide in equal temperament and string bending the third makes pitch go up and exacerbates the problem.
You can do a teeny little bit using lateral pressure (along the string) to move something flat. It's very difficult to make adaptations in chords though. A studio musician trick is to retune the guitar slightly for certain sections, though this can screw with everybody else in the ensemble.
Attempts to experiment with temperament using squiggly frets make it clear how challenging this problem is: https://stringjoy.com/true-temperament-frets-explained/
But with the way I played, I'm not even sure how much it mattered. The best tool for enhancing my playing would've been a mute. (And it would have been most effective lodged in my windpipe.)
You can listen to variations here: https://youtu.be/kRui9apjWAY?t=622
0: https://www.guyguitars.com/truetemperament/eng/tt_techdetail...
Additionally, some songs even change keys, which makes “per-song” not enough of a constraint.
With relative pitch music sounds the same even if you deviate from the original equal temperament pitch of the key you started singing even changing the key.
For the same reason if there is a fixed instrument playing at the same time, like a piano accompaniment, it's sound would be used as a reference and the singers would not drift
But for instruments with fixed pitches, like guitar or pianos,12 equal temperament is the best compromise to be able to play in all keys.
You might play a G# note in the context of an E chord (where it's the third), and then you might play it in the context of a C# (where it's the fifth).
These are discernably different pitches, but the same "note", in the same key, in the same song!