The equally tempered scale is dirty

[KoolFartWind]

Can somebody explain any purpose of building an equally tempered scale (which MIDI is based on afaik) despite creating multi-scale instruments ?

Is it true, that we adjust the perceived "impure" sounds via psychoacoustic mechanisms, so that the impression of harmony is implanted ?

To me this sounds like a big scam. I want pure harmonics

[No_Use]

Wouldm't be that hard if we're talking pure MIDI I guess to only go pure (just) intonation (actually there are VSTi's where this can be done via microscales I think, don't use it personally), it could get a bit problematic as soon as real instruments are added I think.

Say you want to record a real piano to pure intonated songs in different keys, you'd either have to constantly re-tune it or have a bunch of differently tuned pianos at specific keys at hand.

[Sendy]

Essentially it's a geometric problem - you can have pure harmonic ratios, but there will be a 'join' when you complete the circle of fifths because following the harmonic framework doesn't quite check out with the maths. That means the price of purer harmonics means less free modulation between keys.

Hence the tempered scale - all notes equally out of tune and you can modulate anywhere. And people are so used to hearing these out of tune notes that the pure ratios sound "bad" to them. I've had people freak out and tell me I'm talking nonsense when I try to explain this. Denial is a terrible thing

If you want pure harmonics - you'll need a synth that can load tuning files. Try Just Intonation and the many variations of tuning you can find. They all have different compromises, different colours and different weaknesses.

[BertKoor]

I want pure harmonics

You can! But not on a physical piano

[vurt]

so is your mom!

[KoolFartWind]

Wouldm't be that hard if we're talking pure MIDI I guess to only go pure (just) intonation (actually there are VSTi's where this can be done via microscales I think, don't use it personally), it could get a bit problematic as soon as real instruments are added I think.

Say you want to record a real piano to pure intonated songs in different keys, you'd either have to constantly re-tune it or have a bunch of differently tuned pianos at specific keys at hand.

Yeah, but why would I want to play a real piano if that real piano is built upon a flawed base ?

Just because over the course of a couple hundred years the people got used to those "impure" harmonics, does not mean, that I have to adjust to that in 2014, I'd say.

If somebody wants to play their impure instrument, I won't stop them from doing it. But my question is, why this standard is so uncritically adopted into composing habits of electronic producers.

@Sendy

Thanks for the input. So it is a tradeoff between "purity" and "modulationability". But there must be a better solution.

[No_Use]

Wouldm't be that hard if we're talking pure MIDI I guess to only go pure (just) intonation (actually there are VSTi's where this can be done via microscales I think, don't use it personally), it could get a bit problematic as soon as real instruments are added I think.

Say you want to record a real piano to pure intonated songs in different keys, you'd either have to constantly re-tune it or have a bunch of differently tuned pianos at specific keys at hand.

Yeah, but why would I want to play a real piano if that real piano is built upon a flawed base ?

Just because over the course of a couple hundred years the people got used to those "impure" harmonics, does not mean, that I have to adjust to that in 2014, I'd say.

If somebody wants to play their impure instrument, I won't stop them from doing it. But my question is, why this standard is so uncritically adopted into composing habits of electronic producers.

Now that I find an interesting question actually.
I don't know the answer though, maybe because we got used to equal tempered over time as Sendy says ?

Are you actually producing in pure intonation ?

If so, if you'd upload a comparison track pure/equally tempered I'd like to give it a listen for comparison, never did that.

[KoolFartWind]

I'm about to do that. But it takes additional time. Hence my rant.

[No_Use]

I'm about to do that. But it takes additional time. Hence my rant.

Hence the tempered scale - all notes equally out of tune and you can modulate anywhere.

Here you go, in a nutshell: Equal is easier.

[JumpingJackFlash]

Just because over the course of a couple hundred years the people got used to those "impure" harmonics, does not mean, that I have to adjust to that in 2014, I'd say.

If somebody wants to play their impure instrument, I won't stop them from doing it. But my question is, why this standard is so uncritically adopted into composing habits of electronic producers.

Partly because that's what people are used to (so they think anything else sounds bad), but also partly because music and mathematics just don't go together anywhere near as well as some people would want them to (remember music is an art, not a science).

Mathematically, there are two sizes of semitone and two sizes of whole tone, and this isn't generally practical for Western music (with its strong reliance of harmony).

Assuming you have instrumental music with several different notes sounding at any given time. It is virtually impossible to stick to nothing but "pure" ratios without re-tuning everything every time there is new chord.

You can fix one pure interval, but then another interval will be out as a result. You can't have your cake and eat it! (Or you can, but it's very difficult and you end up making other compromises to compensate such as "simplifying" the music).

You could of course try with just monophonic music; music with just a single line, no harmony, then it might work (better)... But I wonder exactly why you want these pure ratios anyway? - It doesn't make music sound any "better" (often the opposite, but this is of course subjective).

[Nystul]

The math problem here causes all sorts of problems. Any kind of temperament you choose to use will present a different set of compromises. Even in a carefully chosen key there are likely to be a few very screwy intervals which will sound worse than equal temperament. I think this is usually what will drive people crazy more than the pure intervals themselves. That is not to discourage use of different temperaments, but to say that each of them has weak points.

Of course, when you are not limited to a fixed temperament, you can change the pitch of notes here and there to make pure intervals. This is what you hear from a barbershop quartet, for example. But the math issue still leads to a compromise, because some impure intervals may be needed to avoid having the tuning drift higher or lower over time. It's not trivial to have a computer algorithm spit out great tuning adjustments. I remember experimenting years ago with a dynamic tuning script available in Kontakt. The results were interesting and pretty cool. But from what I remember it changed the pitch of held notes to match the new chord. This gets back to the inherent problem, because you typically want the held note to maintain pitch and the new notes to adjust to it. But once you do that, how do you get back to your initial tuning? It has to be fudged at a point where the listener wouldn't notice.

My conclusion is, unless you are making some minimalist thing with like one chord, whatever you do is probably going to be a little bit "dirty". There may be better solutions than equal temperament, but they are going to be on a case by case basis.

[jancivil]

It is virtually impossible to stick to nothing but "pure" ratios without re-tuning everything every time there is new chord.

If you change key very far you will run into variances that you may find too harsh. I am failing to feature situationally what you mean, really, with 'every time there is a new chord'. The chords in this just intonation I'm about to give amount to the same number of chords in 12tET per that particular tonic (ie., so long as the 12 resemble 12tT, which is a temperament of just such a rational intonation, this difference you're on about will only appear per a new tonic.).

Sendy mentioned the geometric issue, which is fundamentally this disagreement between 3:2 and 2:1, so we have 'Pythagorean comma' to force 3:2 (out to twelve places) into 2:1. Thus begins temperament.

Here are 12 totally useful major chords in the one 'tuning':

1:1 5:4 3:2 = "C Maj"
16:15 4:3 8:5 = "Db Maj"
9:8 45:32 9:5 = "D Maj"...
6:5 3:2 16:9
5:4 8:5 15:8
4:3 5:3 1:1 (2:1)
45:32 16:9 16:15 (32:15...)
3:2 15:8 9:8
8:5 1:1 6:5
5:3 16:15 5:4
16:9 9:8 4:3
15:8 6:5 45:32

and anything you can think of in the scope of 12 tones is true. And they're more 'in tune', at least if we like the physical definition.

And then you do this //It doesn't make music sound any "better"//
Well, it is true that singers and instrumentalists that can vary their intonation tend to adjust to purer intervals in ensemble, while forming harmonies together. This is something known; it is one tell-tale sign of someone using samples that are absolutely the one thing actually, so strategies are devised and tried.
VSL's interface provides for scala files in VI Pro (as long as the file gives 12 tones), which can be set to be rooted in any of twelve roots. So you form a matrix of for instance a just intonation on 'C' and should we modulate to 'Eb', switch to the matrix where Eb is 1:1. There is this known, definite reason for this. It is not exotic.

Mathematically, there are two sizes of semitone and two sizes of whole tone.

Well, depends on where you draw the line. For semitone, I can't be sure which two you like; I imagine you refer to major tone and minor tone, ie., 9:8 vs 10:9.

'Semitone'
25:24, 256:243, 135:128, 18:17, 16:15, 2187:2048, 27:25...
{the smallest is ~70.7¢, the largest ~133.2¢. 18:17 ~99¢.}

https://en.wikipedia.org/wiki/Pythagore ... ean_tuning

As far as trying to convey to you why I would want it, I would have to bring you up to speed on, for me some pretty basic things, I guess. There is more to music than 12tET, quite a lot more.

I set up a new matrix to deal with one note last night. I might use the pitch bend lane extensively. I use samples a lot. There is no guarantee of consistency unless they're all retuned. I have ideas about it and I am very sensitive to intonation deviances. A lot of the time with samples - a bass guitar can really deviate off of a strong pluck, all else being equal - there are things I would like to sound better. Things that eg., string players do... There are expressive things from an intonation 'on this instrument' I want, it sounds right to me. Then there are notes that mess with other things in the arrangement, so here's another intonation, or I'm kind of good with the pitch wheel.

The difference between 12tET major third and a 5:4 is nearly 14¢. I've made corrections WAY below one cent that were very obvious to me.
Why would I not like 5:4 'better'? {IN A HARMONY}
As per melody: Why do the Indians have 22 srutis? Why did al Farabi do all of this work in rational intonations (toward ultimately a 25-note gamut)? Why did the Ancient Greeks come up with all of these intervals quite smaller than a semitone? Think. Those kinds of remarks reveal the corruption out of 12tET. Fortunately we have more available through tech today. The techniques VSL avail us of are certainly not just for the Turkish segment of their market, although that drove it somewhat.

[jancivil]

dynamic tuning script available in Kontakt. But from what I remember it changed the pitch of held notes to match the new chord. This gets back to the inherent problem, because you typically want the held note to maintain pitch and the new notes to adjust to it. But once you do that, how do you get back to your initial tuning? It has to be fudged at a point where the listener wouldn't notice.

Not possible in Kontakt I think but with more tones available this is achievable.

IE: one way to come away with '22 Srutis" is to take the 10 of 12 that are not 1:1 and 3:2 and apply syntonic comma (81:80).

https://en.wikipedia.org/wiki/Just_into ... ian_scales

So now, much more flexibility, and harmony can be had. But that said, if I really needed a solid pedal and a lot of cute intonation, I would use two instruments.

[D.Josef]

Yeah, but why would I want to play a real piano if that real piano is built upon a flawed base ?

Just because over the course of a couple hundred years the people got used to those "impure" harmonics, does not mean, that I have to adjust to that in 2014, I'd say.

If somebody wants to play their impure instrument, I won't stop them from doing it. But my question is, why this standard is so uncritically adopted into composing habits of electronic producers.

@Sendy

Thanks for the input. So it is a tradeoff between "purity" and "modulationability". But there must be a better solution.

Well, . You sound a bit like a kid who just found out there is no Santa Claus.

There is NO good solution, really. The twelve-tone chromatic scale, and even the diatonic scale, will always be "imperfect" in some way or another. (Do google tuning systems, it's a super interesting area.)

The equal temperament is not more or less dirty than any other system - it just spreads the imperfection around in an equal layer, while others "concentrate" it in intervals that are "less used".
Equal temperament is optimized for ease of modulation, and for various people and instruments playing together without difficulties.

So no, you aren't playing a faulty instrument. Western music involves compromise, but compromise does not equal "dirtiness".

[Sendy]

Thanks for the input. So it is a tradeoff between "purity" and "modulationability". But there must be a better solution.

There is a solution - dynamic tuning. Any instrument with a continuously variable pitch, like the human voice, can play exactly the right note in any given context. But on a keyboard instrument that gets a little trickier. If you've ever wondered why a barbershop quartet has a unique sound that "pops", it's because they're choosing their pitches dynamically and not on a rigid scale like us keybores have to .

My solution is just to use subtle microtuning, stretch octaves, and lots of pitch modulation. Instead of trying to be harmonically pure, most of the time I'm just trying to get away from the 12-TET sound, which I believe is beginning to subconsciously chafe a lot of listeners. Instead of trying to get more focus, I'm defocusing, because I believe that music which stays rigidly on the 12-TET grid and doesn't even use pitchbend and vibrato expressively can often sound like homogenous computer crap.

Basically, the more you can use the "inbetween" notes - via any means possible - the more interesting your music is. That's my theory anyway.