As a guitarist we often swap guitars or retune to make certain songs easier to play, or to be able to get a certain tamber put of the note. But I never considered it as a way to address temperament.
It's interesting to think how much of music theory emerges out of reconciliation with available instruments, as opposed to reconciliation with the ear.
Since you're a guitarist, there's also this Swedish guitar, which purports to solve the tuning problem (which I tend to think is not a problem but an essential part of the instrument's sound) https://youtu.be/-penQWPHJzI
But the normal, "imperfect" guitar does not sound bad. I would also say, this "imperfection" gives a guitar its typical sound in the first place, so it's not a "problem".
Both guitars in that video are great, but indeed quite different.
Prediction: society demotes all of the auto-tuning and AI art to training status, and actual art produced by himans with pulses is preferred.
My favorite style of music (Psytrance) almost requires digital "perfection".
It's even not really possible to create a "properly sounding" Psytrance bass-line¹, not even a most basic variant, without doing some math (or using tools that will do that math for you). Frequencies, pitch, tempo, and phase need to match constantly and absolutely perfect, or it won't sound properly. Any "humanization" on any preset would kill the sound instantly!
For that reason creating Psytrance is a very "mechanical" task that only machines can perform with the required precision. (And not every machine is good enough for that actually. You need for example oscillators with very high precision or you will experience unwanted artifacts, especially on higher frequencies, that could destroy the sound).
Something that could create "perfectly matching" chords that don't include any dissonance would be really useful to get the (most of the time) desired "ultra-clean" Psytrance sounds. The usual alternative is to filter out all dissonance. But that's a lot of work, or in "bigger" chords or soundscapes outright impossible (even when you slice the sound in the frequency spectrum with all kind of tricks; filters also produce artifacts… And trying to get rid of those artifacts, like phase imperfections, changes the sound again in often undesired ways. A "perfect" tuning form the get go would maybe help with such things).
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¹ Here two of the better tutorials for Psytrance bass-lines:
https://www.youtube.com/watch?v=m40xkEkrEKo
https://www.youtube.com/watch?v=-4B1NcdNJjE
And if you're lazy see here for a VST plugin send form the gods:
B) this is a subjective point, and one accepts your POV as valid
C) your POV may prove a minority one over time. Or not.
B), C)
I don't think all that electronic "magic" will go away anytime. It's more or less a prerequisite to create some kinds of sounds, which you just can't "manufacture".
It's not only about pure electronic music.
Almost all modern productions in all kinds of genres are depended on the usage of computers (and other machines). All that tech makes modern sounding peaces possible in the first place.
Even seemingly "maximal analog" music (like for example classic orchestra) sounds on a record the way it sounds because there was a lot of digital processing to remove all kinds of imperfections form the recorded raw audio, and of course a lot of of other post-processing.
Also I think it's clear what the majority prefers: People are asking actually for better produced pieces, otherwise the market wouldn't have moved that way.
Back in the day you would need to record and produce in one of that big, very expensive, well know studios somewhere around the world if you wanted to land a hit. The tech in those studios is worth millions to this day. Nobody would have invested in such a thing if people wouldn't have liked the results coming out there. (Today it's thankfully much cheaper to have a good recording; actually some small HW setup and a powerful PC with SW for only a few thousand bucks is more or less enough to sound absolutely professional, if you only know what you're doing of course).
On the other hand your actually right in some sense:
In a lot of genres "absolute perfection" isn't a goal. We use computers to remove "random (human / physical) imperfection" but add in on the other side some "humanization" into the sounds by digital means.
I think there is at the moment even a kind of trend to add more realistic, powerful, and interesting "humanization" possibilities to digital instruments. ("Humanization" or "randomization" knobs aren't anything new, but those functions get extended lately I think; for example you can use now AI instead of simply adding some randomness to some parameters).
So yes, we want to keep "natural" sounds to some degree. But by now we're using computers to artificially make the things that we're producing digitally sound more "natural". :-)
I think the core point here is control. To have something sound really great you need to be able to control every aspect of the sound, even the most tiny details. "Imperfections" are OK, or even actually desired, but only as long as they're added deliberately and remain controllable.
How to tune synthesizers this way? What and where to buy?
Edit: this table says that Access have hardware synths with Hermode tuning: http://www.microtonal-synthesis.com/micro_af.html . Elsewhere I see Waldorf listed as having offered Hermode in some models.
We've had self-tuning instruments for thousands of years. Vocal harmony has almost always been perfectly tuned for its key. Likewise orchestral strings are fretless and can produce perfect intervals. Equitemperment was an innovation in the 17th century because it approximated the perfect intervals very well ("sounded good") but also permitted the ability to simultaneously represent scales based on every note in the circle of fifths ("sounded interesting"). But the "real" chords were always (well, since the late middle ages) understood to be integer ratios.
To be clear, I'm trying to explore the idea that individual songs have optimal tunings because they only use certain intervals. So, something more fine grained even then singing for a particular key.
So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways.
Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.
(This is also the same mechanism at work when an entire choir singing an unaccompanied piece goes flat without realizing it. Someone will not quite make an ascending interval, and everyone else will adjust to cover it.)
(1) Example: "get up an get out" by Iggy Pop. https://www.youtube.com/watch?v=R1ld5jG3f-M
So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird.
This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.
usually that’s not the case though. typically it’s individual notes. much harder to precisely and accurately modulate tape velocity (especially by hand).
This sort of hybrid tuning is common in barbershop quartet singing as well.
Also the tonal glides sound like an old broken record player. (This creates a sensation of "wobbling speed", which sounds just wrong).
Hmm, my ears are still ringing, even while writing this; that was not a pleasant experience to be honest…
I guess I need some ear-bleach. Psytrance to the rescue! Let's see, maybe, hmm, Talpa¹, or maybe better that old Atma set²?
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I think a clearer demonstration might be to have a side by side comparison of a fairly simple tune in 12TET vs in this dynamical tuning.
Still, it's kinda like alien music and it's certainly creative.
https://en.xen.wiki/w/Adaptive_just_intonation
But there seem to be differences. Some demos have those tonal glides (that I don't like) but some don't (and sound just great).
Could someone explain in a "TL;DR" what's going on here?
But I see, that wiki I just found seems to be full of info. But it will take time to read all that… Would prefer to have some VSTs to just play around with. Any tips?
Another thing that happens is that both English and French change their pronunciation over time. After English imports a word, the French pronunciation may change making the English word look odd or not even look connected. Not sure that this happened to “timbre” but it did happen to words like “chief” and “chef”. Both were imported from French but at different times. “Chief” when French used the hard ‘ch’ sound and “chef” when French had switched to the soft ‘sh’ sound.
https://www.merriam-webster.com/dictionary/timbre https://en.wiktionary.org/wiki/Timbre
EDIT:to be clear, I'm not disagreeing with most of what you're saying. 12-TET can't represent the desirable perfect fractions, and in a system which can (such as a just intonation system), the starting point does matter. And maybe a vocalist or a violinist would play D# and E♭ subtly differently, I don't know. My main point is just that in a whole lot of contexts, such as when playing a piano, there is no difference between the notes. Your comment made it look like there's always a difference between theory and practice which makes D# and E♭ different in practice, when that's often not the case. We do use 12-TET in practice.
I assume it all breaks down if they need to play alongside a keyboard (or fretted) instrument.
However, being perfectly in tune is also a big red herring kind of thing. People, especially people who like seeing math in music, get obsessed with chasing ideas of perfection in music and music is art... it isn't supposed to be perfect. To have sounds at perfect intervals or sounds perfectly in tune is after a certain point just an annoying detail compared to literally every other aspect of a piece of music.
A lot of advanced digital synthesizers will carefully detune oscillators from each other so they aren't "perfectly in tune" in order to get thicker sounds.
As noted in other comments, this also applies to singing and arbitrary pitch instruments, possibly at a subconscious level, and it has the opposite "mathematical" implication than you seem to think: any fixed tuning is a serious constraint that makes some chords sound wrong, and only being able to tune individual notes perfectly allows the introduction of aesthetically pleasing imperfections.
one of those methods is called a “chorus” effect. this is extremely common across effect platforms and is not limited to synthesizers / keyboard-type instruments.
Keep in mind also that a lot of musicians with "perfect" pitch have to deal with performing situations where the main pitch is not the standard A=440 Hz. For instance in the Baroque repertoire which I perform often, the most common pitch is around A=415, which is around a half step lower, but there are other tunings that pros have to deal with which are both above and below A=440 (European orchestras often tune higher, music before the Baroque is often at A=390, music from the classical period is often around A=430, etc.).
That's not true at all. A lot of string players learn to play in orchestras or chamber style, which means they're only playing with other stringed instruments, and they absolutely are taught dynamic tuning by ear, which uses just intervals.
This is a weird way of looking at it. String players aren't sitting there consciously thinking of their tuning as they play - they're doing it by ear in real-time. The tuning they use will be the one that best harmonizes with the other notes being played at that moment.
> And it sounds off for music that doesn't largely sit in a single key signature anyway,
That's actually where the ability to adapt tuning dynamically is the most powerful - it allows you to be in tune relative to other pitches being played in that moment, not just in tune relative to some absolute benchmark that nobody is going to be able to hear anyway (because almost nobody has perfect absolute pitch).
Well, that's your problem. You're using a keyboard, which doesn't permit you to harmonize dynamically the way an unfretted string instrument does.
Even within a particular key, the pitch that sounds the best for a particular note will depend on which other notes within that key you're attempting to harmonize with. A keyboard can't do that.
"Unfretted string ensembles, which can adjust the tuning of all notes except for open strings, and vocal groups, who have no mechanical tuning limitations, sometimes use a tuning much closer to just intonation for acoustic reasons. Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings.[4]"
It was routine even in my high school brass section to pitch down the major 3rds.
the most important element here is how it sounds to our ears. not how closely it tracks to an equation.
And you're right, we don't play "based entirely on just intervals." What we do is constantly adjust our intonation depending on whether we need it to be "just" with respect to something else (like other notes in a chord), or whether we are free to use a more "melodic" intonation. See https://www.youtube.com/watch?v=QaYOwIIvgHg for a good demonstration -- note that he talks in formal terms like "play x in the Pythagorean system," but I think you can largely see this as a rationalization of what players do naturally).
Finally, the presence of vibrato doesn't really obviate intonation concerns, sadly. There's a lot of theoretical debate about how the pitch of a vibrated note is perceived (is it the highest pitch in the range that determines whether the note sounds in tune? etc.), but in practice you can easily verify that adding vibrato to an out-of-tune scale will not make it sound any more in tune, nor will adding it to a shift mask a slightly-missed shift (if only!).
There exist equal temperament guitars, but they're usually custom built:
https://guitargearfinder.com/faq/true-temperament-frets/
In any case most people don't mind such small differences, especially that guitars aren't terribly precise to begin with - a player can easily get 10 cents of a semitone on each individual string when playing a power chord with distortion, bringing the whole thing to just intonation.
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Hi! I am not a musician. Did you mean that true temperament guitars are the ones with squiggly frets, instead?
My understanding was that true temperament [0] is not the same as equal temperament [1]. I also believe that both pianos and guitars are typically tuned to equal temperament [2], but you may well be right about guitars.
Maybe somebody can shed some more light on this. Thanks!
[0] https://www.truetemperament.com
Even if you take out the dynamics of vibrating strings, the idea of 'frets' is to 'pre-divide' the string into its intervals for you. For example, the 12th fret is the halfway point on the string.
But look at the bridge of any guitar. Clearly, the saddles are not all an equal distance from the nut, so the 12th fret can't be actually halfway down all of them.
For this reason, a guitar is fretted in a way that is actually more of an approximation of equal temperament than actual equal temperament. It's rarely far enough out to be bothered about.
'True temperament' is a bit of a misnomer. There's no such thing as 'true' temperament. 'Temperament' by definition means a 'tempering' of the 'true' interval (the pure/just intonation).
SOME sort of temperament is required on a fretted instrument precisely because of the question that this article addresses: on a guitar, you can only pick one 'pitch' for a fret, even though the 'correct' frequency for a D# may well be different than the 'correct' frequency for an Eb depending on the key in which they appear.
So calling it 'true temperament' is a bit naughty. All it means is that it's trying to iron out some of the approximations which are inherent in the instrument design to get it closer to 12-TET.
A "spherical cow" model of a guitar would be equal temperament, but that ignores the messy reality of how strings behave - chiefly they need to be some distance above the fretboard and pressing them naturally bends the string ever so slightly.
this is why a guitar using equal temperment can play consistently in-tune with itself as well as with other instruments tuned in the same system. it’s not about perfection according to some abstract mathematical model.
Guitars are almost never perfectly in tune according to that standard, but like I said - people generally don't mind.
this has not prevented it from being a versatile instrument that is quite capable of being played “enough” in tune with ensembles of other instruments, such that the vast majority of people hear zero problems.
how is what we hear in music less relevant than whether or not a given instrument is not perfectly in tune, mathematically speaking, if that variation in tuning is imperceptible to human hearing?
Which is okay. I like to bend notes too, but just call it what it is.
As it happens I've been trying to work out what exact intervals are used for the two-chord leitmotif heard in "The Sandman" series, I'm not sure if they're regular microtones or just some sort of eerie detuning (surprisingly I can't find any discussion of it online either).
* what an incredible show!
The one exception is harmonics which are based upon integer ratios rather than 12-TET.
If you're playing a C in C major and I'm playing a G, it may sound best if my G is close to a perfect fifth from your C in just intonation. This is why string sections often sound so sickly sweet, like A Capella.
On the other hand, if you are playing a C and a G on the piano, and I'm also playing a G, then it will sound best if I play the same G as you in 12-TET. If I were to play the "correct" G against your "wrong" G, it would sound out of tune.
Context is everything.
As you may notice, G doesn't have a sharp or a flat in C major! If string players relied upon accidentals to tell them how to tune a particular note, they would be out of luck seven twelfths of the time.
That process of adjustment: called intonation, happens after resolving which pitch class I want to play. It's not something that an arranger can control through the use of enharmonic spelling, but it doesn't stop them from trying!
One more extreme example is two pianos tuned to 12-TET, but one is half off. They are made to be played together by two closely in sync pianists for a few more complex songs that need 24 steps between octaves.
Overall I do find the system confusing enough to wonder if a better one won't one day catch on. And it might already have, I know some musicians who can't read sheet music but play by chords. It seems more limited in the level of detail you can specify, but works plenty well for the songs they want to play.
That would something that only happens very rarely, like for just 1/10000th the pianos people will encounter in their lives...
I wonder if AI will do the same thing in music, it will use the "perfect" tuning suitable for a particular piece of music and dismiss this idea of a universal tuning scale.
AI just literally, fundamentally can't "dismiss the idea of a universal tuning scale", because whatever per-piece optimisations it can come up with still need to be realised by physical instruments at some point. The idea of a good-enough compromise solution that allows you to play a wide variety of pieces on a single instrument is just too damn important.
In popular commercial music you do literally have a different instrument (synth setup) for each song.
But even if we talk about guitars and saxophones, I was speaking about AIs which directly output a sound file, not a music sheet. So they can synthesize a fake saxophone which is tuned in a weird non-physically possible way, as if each note was played by a different physical saxophone that the musician switches to.
None of that applies to music. Nobody who studies this stuff seriously is under any sort of illusion that 12-TET is the "right" way to play music. I know a fair few professional musicians, and I've "talked shop" with as many of them as I could, and the deficiencies of 12-TET recurringly come up. There is nothing here to "dismiss".
Don't get me wrong: The idea of computationally-optimised tuning sounds really interesting, and the discussion of what we should be optimising for would itself be fascinating to follow. It's just that people are already doing that sort of thing manually today, so there's no big "oh no we're doing it wrong" dismissal of the status quo waiting at the end.
But how would we know that? People thought music was figured out and then atonal music was invented/discovered/re-discovered (whatever you prefer).
We are somewhat speaking about different things. You talk about people playing instruments, and you are sort of right, all possibilities were explored.
I'm talking about audio files with songs, many of which are currently being produced with software using a specific tuning (typically 12-TET). But in this world the tuning is just an artifact of the production process, it's not fundamental like in your world.
The current picture producing AIs don't start with a blank digital canvas and drag digital brushes over it, they synthesize the image in a holistic way and in this world the "brush" can be unique at each position.
More precisely, I'm thinking that music producing AIs could make music where the first 5 seconds of the lead instrument uses 12-TET and then switches to another, the backing bass track uses a different tuning, the vocal sings to yet another one yet it all comes together beautifully. And the tunings used could morph during the song duration. In a way this means that there is no tuning at all.
What I'm saying is that the situation with Go was completely different. The Go community was utterly convinced that the state of the art was within a couple stones of the hand of god, and Alpha Go thoroughly disabused them of that notion. The status quo was completely shattered, and the community's understanding of the game as a whole was completely upended. It's entirely fair to describe the situation as "and then AlphaGo appeared and dismissed all this"
The situation in music is very different. Ethnomusicology has been a thing since the mid-20th century, and musicology in general has swung away from prescriptivism and more towards descriptivism. There can be no earth-shattering revelations here, not because our current understanding of music is unassailable, but simply because there is no earth to shatter to begin with. AI-drive computational music might produce some innovative work around how we understand pitch and tunings, but that work won't dismiss our current understanding of those things, it'll sit alongside it.
Ok, this is fairly long winded, but the point is that I take issue with the "dismiss" part of it all, I guess.
(I also agree with others in this thread that the popular commitment to equal temperament is exaggerated -- it's not all that uncommon to hear good musicians of various styles playing/singing/synthesizing "out of tune" music for various effects).
Looks quizzically at 44.1kHz-u16 audio sink.
Pretty sure I can, actually; my computer's speakers certainly do, barring a rare handful of groups of songs that were recorded at the same time and place.
In a similar way, people have been using particular tunings for their songs for a long long long time. The idea of a universal tuning scale is relatively new. No need for AI to point us away from it, we already did that ourselves.
As someone who hasn't taken any musical theory or similar, it was quite interesting to hear.
That's just changing a convention, not a tuning in the sense talked elsewhere in this thread (how we divide notes), but "what our starting frequency is".
A=432 and A=440 is just as arbitrary. They just had to pick something so they would all match.
The main difference is that 432 is associated with a set of new age, healing, "universe", etc. BS claims in certain "spiritual" circles...
In baroque music, ~430 and 415 are also very common since they are thought to be the historical pitches of "A"
That's so low, it's more like playing the piece a three semitones lower than an alternate choice for A4.
If the piece was in A, it would be more like playing it in F# (while still using A=440).
(Of course if you did that, the "sweet-spots of 12TET and its off-notes would be different, than if you played with A=360)
Tuning your orchestra high was sort of the 19th century equivalent of the modern loudness war. The problem is that orchestras tuning to ever higher pitches meant that singers had to sing higher to match, and it was putting serious strain on their voices, which can easily lead to injuries.
Having some sort of agreement setting a standard was just something of an "enough is enough" sort of moment. It just amuses me to no end that this was achieved by writing it into the Treaty of Versailles, of all things. We're settling a freaking world war, so let's make sure we settle the issue of orchestra pitch as part of the treaty.
Or I might be wrong, I know nothing about music[2].
And for earlier stages you can have human raters or similarity with past successful songs.
On top of this, harmony may or may not work the same in 19-TET and 12-TET. With the same example of diminished chords, the diminished chord does not divide the octave in four equal parts in 19-TET. Adim and Cdim are enharmonic in 12-TET, but Adim in 19-TET is A-C-E♭-G♭♭; that is, only C and E♭ are the same.
BTW I was wrong in that Adim is A-C-E♭-G♭. Still not enharmonic to Cdim, and probably diminished chords sound weird in general because G♭-A is four 19-TET steps, which is a 19-TET step smaller than a minor third. It probably sounds halfway between a semidiminished chord and a regular diminished chord.
A computer generated piano performance could pretty easily pick versions of each note that are in harmony with the other notes played at that moment.
I wonder if that would be worth doing? Has it maybe already been done?
Also want to plug my own project, Pivotuner: https://www.dmitrivolkov.com/projects/pivotuner/ . I believe it gives more flexibility and control to the performer than the others on that list. It's not publicly released yet (hopefully soon), but (anyone) feel free to email me if you're curious to try it out!
In other words, it's something someone might use to implement what they asked for - but also lots of other things besides, and it's not meant specifically for that purpose.
(I do apologize if I came across poorly—I couldn’t think of another way to ask the question.)
Both of these are very difficult to do precisely, and come at a significant cost in the agility of the player. They are more equivalent to pitch bending on a guitar than adjusting tuning systems on a violin, which has almost no impact. Instruments with valves and hole covers, like bassoons, make techniques like this extremely difficult if not impossible.
However, the holes in the instrument are drilled at specific places along the length of the instrument corresponding to specific notes. This is what gives the instrument its tuning. Hole positions are calculated and drilled very precisely to make sure that the instrument is in tune. It is not accurate to say that these instruments do not have fixed tuning. The tuning is literally drilled into the body of the instrument.
I don't know much about this, but isn't (b) impossible even if you satisfy (a)? There is no sequence of numbers that contains any arbitrary integer ratio because there are infinitely many possible ratios but only finitely many ratios you can make out of a sequence of numbers.
(Obviously some ratios like 2:1 and 3:1 are more important than, say, 52697:16427. 12-TET chooses to permit 2^n:1 at the cost of all other ratios, which seems like a good tradeoff to me.)
(a) makes it much more restrictive though: you can't even have {f, 2f, 3f} simultaneously. (If 2f = a^m f and 3f = a^n f, then 2^n = a^{mn} = 3^m, which has no nonzero solutions. Equal temperament contains *no* integer ratios at all, other than whole-number multiples).
I'd say it's more likely because intermodulation distortion between frequencies with low-complexity fractions tends to be low-frequency.
You want (a) because it you gives you nice algebraic properties (the music structure is invariant under frequency shifts). You want (b) because small-integer ratios are pleasant sounding -- partly culturally-acquired taste, partly because physics gives musical instruments acoustic spectra in integral multiples of a fundamental frequency: f, 2f, 3f ... nf. Small-integer ratios are naturally occurring and very recognizable.
Modern tuning (C-f "12-TET" in the article) almost, approximately satisfies (a) and (b) simultaneously. "12" means there's twelve tones between f and 2f; the ratio between adjacent tones is defined to be 2^{1/12}. This tuning can't contain both f and 3f (so it fails (b)), but it *can* contain f and 2^{19/12}f ~ 2.9966f, which is actually close enough to 3f to be indistinguishable. (Almost works!) But as you build ratios out of larger integers, it audibly falls apart. The closest you can get to (5/3)f is 2^{9/12}f = ~1.6818f, which is already 10% of the way to the next note. And it rapidly gets worse.
This is why two on-paper-identical notes can end up audibly different, depending on what key you're starting with (and hence how they are approached). There's tension internal to music theory itself.