The equally tempered scale is dirty

[jancivil]

[...]The thing I replied to was you going for this to make 5/4 pointless. I'm confused (that doesn't mean 'please explain it some more again').

Just saying that if you're using all "pythagorean" intervals, such as 81/64 major thirds, that's quite probably not different enough from equal temperament to justify the extra effort in building instruments.

ET is 13.69¢ sharper than 5:4; 81:64 is ~8¢ sharper than ET. What is your actual point? This was word salad.

[jancivil]

I'm not qualified either, but I know better than this. That guy is wrong, that is a corruption and only a stupid person acts to vacate centuries of thought with that shite. Talk about futile. The whole idea of these intervals is expression and it's founded in the voice, the accent, the ethnicity. The theory is part of philosophy also. I don't know, maybe there is some coincidence in something that winds up being more or less 50¢ to the next note, but cart doesn't pull the horse.

I'm taking this guy as an indication because he's still at least a professional musician, and he's also an Arab musician. He could've made the extra piston 40 or 30 cents, he could've added a second piston, or he could have gone for a slide trumpet, but he didn't. He went to great lengths to be able to play Rast and Bayati on trumpet, so if this guy thinks an exact 50 cents piston is a good solution to that problem, I think that's a good clue, even though the fact that it's a trumpet and it's also used to play western music (like Jazz) forces it to be equal temperament.

You had 'this guy' say that you only use the 24-note scale. That was the actual thing I was addressing.
Now another guy; the same 'guy' or a different guy that really wants to get the maqams on the instruments? Name him if he is your appeal to authority. I'm doing my best to be fair, but at this point it's clear you're engaged in an exercise to minimize the importance of things that aren't ET and you seem ready to see what you can get past me: "even though the fact" (trumpet is a different animal than a fretted string instrument) and yet another reason it's different in practice than a baglama or saz; you have an argument you've half-refuted yourself.
It isn't worth the trouble to build a fretted string instrument other than the way you've stated because _, yet there isn't any be-cause, there is your opinion that 14¢ isn't anything, and some waffling. And there are ouds built for a long long time where people totally thought it worth the trouble. I studied this, I believed it was worth the trouble, I'm sure I can hear why. You predicted futility in the thread and it seems a self-revelating prophecy.

I'll bring in an actual case:

Ibrahim Maalouf:
"This trumpet that he [his father] invented is really pure genius. He invented the only Arabic instrument in which you blow, that allows you to play all modes, all scales, in all the tonalities," Maalouf says. "This does not exist in Arabic music. It's not only a trumpet that makes you play quarter-tones. He invented a way to blow in the instrument. He invented a new way to play the trumpet."

Maalouf says there are many links between Arabic and Western music. He says when he's playing jazz, he can incorporate Arabic scales thanks to one specific similarity.

"There's this note that we actually call 'the blue note' and I believe it's a heritage from African music," Maalouf says. "Those notes that are right in the middle, between a note and another note, those are 'blue notes' that you bend with the lips. From these kinds of scales, I can switch to music that is very close to Arabic feelings."

http://www.npr.org/2013/03/31/175598222 ... instrument

[jancivil]

I don't have a problem with imaginary numbers, but there are probably more natural alternatives to a scale, that just divides an interval from one frequency to its double value into equal parts. I'd say it is lazy work.

The equal-temperament 5th is 700 cents wide, instead of 702. That's pretty damn natural I'd say, especially for a tuning system based on consecutive 5ths (almost all western tuning systems are based on consecutive 5ths - they have to, because of harmony).

It's clear enough that the fifth was considered crucial behind this reasoning. As it happens, yes, in antiquity 'Pythagoras' and even better 'Fang' found these things to be true, so a 12 equidistant semitones out of 12th root of two can be noticed to only f**k with the 3:2 by -2¢. So you're actually using the word 'natural' which applies, kinda sorta, to one of the results of 12th root of two and irrational numbers as if it tells us the system is natural enough. This is bullshit, I'm sorry.

I wouldn't say it's 'lazy work', it didn't happen overnight but temperament of what was once natural went on for a long time, behind key changes becoming more and more important to composers.

[jancivil]

So, here's Maalouf who is bending notes from 24 to get the actual Arabic intervals. Making a trumpet into an Arabic-friendly thing is not the same thing as building an instrument to suit an intonation.

When you state 'I think it's only worth it when...' I have to ask, how interested are you in the practice? I don't have a worldview that got me to the thing, I think there are things besides 12tET that are musically compelling. I think '12tET' as we have it is good for a whole lot of things. BUT. I can't stand a strobe-tuned guitar; I looked into piano tuning as a profession at one time, so I know you do not simply strobe-tune a piano. The best-sounding pianos are artfully tuned and maintained. Vibraphones; what actually happens? I don't believe 12 totally equal divisions of an octave happens materially. You can force it in virtuality or maybe electronically, but the results of material on a planet obey other laws too.

So you put forth '53 equal temperament', which does what? Clearly there is enough context to see that you're skewing to 'equal temperament'. But 53 instead of 12 makes a great argument against 12tET, what it does is bring all of these JI results in a chart (which tracks way back to antiquity, 31/53rds of 2:1 etc).

Arabic music is talked about in terms, 'quarter tones', but how do you reconcile this thing you understand, 25 equal out of approximation of specific ratios, with 24?? "24" is a convenience. I think it is not the system in actual use. Look at the oud!
Maalouf says 'this is quarter tones' after talking about blues bends, though. More interest in the issue tends to reveal more interest in practice.
I think reducing to 'ET, only with some 40¢ something' is lazy. First thing I did, being skeptical, was look up 'baglama intonation', sure enough I found ratios.

[Nystul]

I only learned percussion instruments, but I think the physical nature of a brass instrument dictates a lot of just intervals. When someone plays an open C followed by open E they are using the fourth and fifth harmonic partials for that tube. Sometimes different valve combinations (or slide position) could give the same notes but with different intonation. Thus the concept of temperament wouldn't really apply. Player can also affect the intonation with technique which could be a good thing or a bad thing.

Mallet instruments are generally tuned to equal temperament AFAIK. They could be tuned to anything, in so far as the notes are independent of each other. But the point is you can't change the intonation on demand, so it needs to just work for everything. Which basically is the point of 12 TET. It more or less just works.

In real world, the physical nature of the instrument determines what you are stuck with. A singer or violinist has to work at intonation whether he wants to or not. A pianist always gets the predetermined pitch whether he wants to or not. Other instruments are somewhere in between, but you are stuck with the reality of that instrument. The idea that an electronic musician could choose whether to worry about this stuff or not is somewhat novel. But if you do choose to try for better intonation, it's not going to be a situation where you can load a .tun and it will always work. It will be a craft to work on like using EQ or anything else.

[jancivil]

Well, brass instruments are very complicated beasts. The so-called equal temperament for a valve instrument does pretty much seek that in the valved results - trueness of the player's technique being equal - but there is a lot of stuff to understand because of the 'conflict' with open tones. So the embouchure is used to navigate these waters. It's not real useful to put it beside a fretted string instrument for discussion of an intonation system. It is tempered and adjusting intonation is, technically, tempering.

I think vibraphones are a real good example of 12tET working really well, inasmuch as it is that thing. I would like to see precisely what a tuning is, anyway.
A piano has a feature of the overtones going more and more out the higher you go so stretch tuning is used. This I think is going to be less of an issue with vibes and maybe even less so with xylophone.

if you do choose to try for better intonation, it's not going to be a situation where you can load a .tun and it will always work. It will be a craft to work on like using EQ or anything else.

Yeah, and it's going to depend on the instrument and its idiosyncrasies. I'm working with VSL alto flute and VSL vibes. They do seriously different things with a given tuning (in this and other projects a different 'A =' basis) and many 'answers' end up being through pitch wheel/pitch bend lane.

There is almost no such thing as truly equal temperament, I think. Typically a vibes is the tuning standard in a band if you have it but I doubt it's going to totally agree with the guitarist's strobe tuner thing.

I'm using an angklung library also, and I think if I get extensive with it I'm going to worry about it having been forced to 12tET.

[D.Josef]

I have a more practical question.

In your experience / opinion, is it worth using a well (as opposed to an equal) temperament in modern music, and have pianos and other keyboard-like instruments tuned to such a system?

From what I understand, well temperaments like Werckmeister or Kirnberger 3 sound similar to meantone (pure thirds) in near, and to Pythagorean (pure fifths) in far keys. They seem to have a huge cult following, some stating that playing Bach on anything but is a sacrilege.

From a listening point of view, Baroque music does sound really nice and colorful (chromatic, lol) on these temperaments. Do you see it as "historical tuning" for playing "old music", or is it a viable alternative of 12tET for writing new pieces, and maybe for use in pop music?

[jancivil]

I reckon the tuning JS Bach used is a valid tuning for that music. If it sounds good, it is good. I don't know from experience what to say about particular tunings for particular, actual applications there.
I'm looking at some things just now and they don't seem very different in principle than trying to get more just intervals, in a compromise.

In my usual application of these things, which is Vienna Instruments Pro 2, for modulating music more generally I would tend more towards "JI" /this root/ moving to the /next root/ by a switch than these things, however. IE: typically I have designed something that gives me an alternate tuning, saved that matrix of articulations and calling that is just a matter of a keyswitch.
OTOH: A single tuning eg., 'Werckmeister' is a best compromise for the material at hand and I imagine these things are well-thought through by their practitioners. I've never done it. I did play some JS Bach seriously in my life but it was on a guitar. The 'early music' practice was new to me at the time and I think to most people.

[jancivil]

I investigated the vibes, marimba I have at hand, which is VSL Percussion lib. And they are stretched, I would not be able to honestly say they are so faithful to ET. I think VSL probably did not retune, but that's what they got on the soundstage.

To return to the other thing, I think those things do not have to relegated to the bin of dusty history. Also, I'm not doing really any tonal->modulation type music, I use more than one intonation sometimes in one part in music that is modal and retains 'tonic'. Or there is an alternate that is similar in principle to maqam modulation. Right now I'm using whatever works which = less pitchbend lane worries; a number of things in different parts, some of which are not behaving according to theory or my available mechanisms very well at all.

Everything I do is 'new music', and it's all about practice to me.

[engineer]

I want pure harmonics

You can! But not on a physical piano

Well, there are indeed pieces for piano (sometimes they were formerly written for cembalo or other string music instruments) which require pure tuning and the piano will be trimmed for this before the "gig".

The thing is that pure tuning causes less interferences of the tones and sounds more "boring" but is suits well for large harmonies with many intruments. Most string music with orchestras really need pure tuning otherwise it is ugly

For electronic music there is vibrato present in many voices (and heavily used), so the difference might be smaller.

Anyway: Switching the instrument to p.t. is worth a try. The question is only how to transmit the detailled scale: pure tuning works for one scale only. For synths this usually would be the C-Major, so the MIDI will have to be transposed. (This at least is the way I do it with my FPGA-synths).

[Sendy]

I have a more practical question.

In your experience / opinion, is it worth using a well (as opposed to an equal) temperament in modern music, and have pianos and other keyboard-like instruments tuned to such a system?

From what I understand, well temperaments like Werckmeister or Kirnberger 3 sound similar to meantone (pure thirds) in near, and to Pythagorean (pure fifths) in far keys. They seem to have a huge cult following, some stating that playing Bach on anything but is a sacrilege.

From a listening point of view, Baroque music does sound really nice and colorful (chromatic, lol) on these temperaments. Do you see it as "historical tuning" for playing "old music", or is it a viable alternative of 12tET for writing new pieces, and maybe for use in pop music?

What do you mean by viable? Will the music work in well temperament? Of course! Will it sell? Probably no more than it would in E.T. Will it sound better? Quite possibly, depending on what the composition does and if it takes the tuning into effect.

A lot of the time I've heard music in the past that was "different" and I couldn't put my finger on it, then later on I learned it was the temperament that made it more exotic, or made the harmonies more colourful. Some pop artists experiment with it, I believe Eminem as quoted as an example, because that's not exactly highbrow music so basically, yes. Go for it

Are non E.T. tunings just a historical artifact? Certainly not for me.

[MadBrain]

I want pure harmonics

You can! But not on a physical piano

Well, there are indeed pieces for piano (sometimes they were formerly written for cembalo or other string music instruments) which require pure tuning and the piano will be trimmed for this before the "gig".

The thing is that pure tuning causes less interferences of the tones and sounds more "boring" but is suits well for large harmonies with many intruments. Most string music with orchestras really need pure tuning otherwise it is ugly

For electronic music there is vibrato present in many voices (and heavily used), so the difference might be smaller.

Anyway: Switching the instrument to p.t. is worth a try. The question is only how to transmit the detailled scale: pure tuning works for one scale only. For synths this usually would be the C-Major, so the MIDI will have to be transposed. (This at least is the way I do it with my FPGA-synths).

See http://www.midi.org/techspecs/midituning.php. Synths generally implement the "SCALE/OCTAVE TUNING 1-BYTE FORM" (tune the 12 notes of the octave by -64..63 cents) because that's the more appropriate tuning system for arabic/turkish/balkanic musicians.

[jancivil]

*the* more appropriate tuning for three, perhaps similar but not identical systems? I can't tell what you're saying. Everybody should tune ~64 cents flat to begin with? Why is that. Why is this there any more appropriate tuning? For all music in all three types?
Arabic music is not Turkish music. Balkans music is neither. Where do you get this stuff?
All I see there is a dump format where various things are described in hexadecimal. The first one listed is -64. I would think that is listed first as it's half of 128, MIDI spec, ya know?

Tell you what, go to youtube and find posts of oud players.
First thing I see, 'Oud tuning by ear' {"Middle Eastern Oud players tune by ear"}, he starts with C = 261.4. Then "Learn Maqam Bayati on Oud" and this one begins with that middle C. It's a little sharper than the other one, I'm assuming more or less A 440, ie., C = 261.626. I do not know why one prefers somewhere between 1 and 2 cents flatter than essentially A 440 like that, but that's his ear. I find other things which seem quite at variance with these notions. I've been looking at these musics off and on for a while, and I think there is no universal thing except for 'International Standard, A = 440hz' going on really.

If we move to Persian music, absolute pitch is antithetical to the aesthetic.

In any case, your assertion looks strange, and I have no idea what it has to do with 'pure harmonics' on a piano, which probably indicates just intonation type of basis. But giving pitches in that kind of system is something different than the harmonics. You're going to get harmonics out of nature the same no matter what.
So per harmonics and what we seem to find preferable in the piano, we have things to temper some more again up in higher range hence 'stretch tunings'.

The vibes patch I checked went quite sharp as you go higher, which is the usual practice.

google images result, stretch tuning

[MadBrain]

*the* more appropriate tuning for three, perhaps similar but not identical systems? I can't tell what you're saying. Everybody should tune ~64 cents flat to begin with? Why is that. Why is this there any more appropriate tuning? For all music in all three types?
Arabic music is not Turkish music. Balkans music is neither. Where do you get this stuff?
All I see there is a dump format where various things are described in hexadecimal. The first one listed is -64. I would think that is listed first as it's half of 128, MIDI spec, ya know?

Tell you what, go to youtube and find posts of oud players.
First thing I see, 'Oud tuning by ear' {"Middle Eastern Oud players tune by ear"}, he starts with C = 261.4. Then "Learn Maqam Bayati on Oud" and this one begins with that middle C. It's a little sharper than the other one, I'm assuming more or less A 440, ie., C = 261.626. I do not know why one prefers somewhere between 1 and 2 cents flatter than essentially A 440 like that, but that's his ear. I find other things which seem quite at variance with these notions. I've been looking at these musics off and on for a while, and I think there is no universal thing except for 'International Standard, A = 440hz' going on really.

If we move to Persian music, absolute pitch is antithetical to the aesthetic.

In any case, your assertion looks strange, and I have no idea what it has to do with 'pure harmonics' on a piano, which probably indicates just intonation type of basis. But giving pitches in that kind of system is something different than the harmonics. You're going to get harmonics out of nature the same no matter what.
So per harmonics and what we seem to find preferable in the piano, we have things to temper some more again up in higher range hence 'stretch tunings'.

The vibes patch I checked went quite sharp as you go higher, which is the usual practice.

google images result, stretch tuning

Woa, calm down.

The guy was asking specifically on how to transmit scale tunings:

Anyway: Switching the instrument to p.t. is worth a try. The question is only how to transmit the detailled scale: pure tuning works for one scale only. For synths this usually would be the C-Major, so the MIDI will have to be transposed. (This at least is the way I do it with my FPGA-synths).

Afaik there are 2 common ways to do this. One is to use scala .scl files, but this might not be a very good plan for adding tuning support to FPGA-based synths (you'd have to setup file transfer, and then parse text data within the FPGA... probably a way overdesigned way of doing things).

The other way is to send MIDI Tuning over sysex, but if you read the document you'll see that there are essentially TWO midi sysex tuning systems:

- The first one that sends a full 21 bit tuning for each one of the 128 MIDI notes (in ~0.0061 cent increments). This lets you do stretch tunings, but is very inconvenient to edit on a synth with a small LCD screen, and is generally overdesigned, and I don't suggest implementing it.

- The second one, which was added to the spec later, only supports the 12 notes from C to B and repeats for each octave. It only lets you detune notes in 1 cent increments, which gives you a range from -64 to 63 cents because MIDI does everything with 128 values. If you have some Roland, Kurzweil or Korg keyboard, this is the system that they implement and you can edit the tuning on the keyboard itself.

The reason why keyboards implement the second, more limited MIDI standard is that 99% of the people who are going to bother with scale tuning in first place are Arabic, Turkish or Balkanic musicians like this guy who need a practical way of playing Rast or Bayati (or the Turkish equivalents).

[jancivil]

So, that -64¢ is only there because it's the first thing the MIDI spec document lists?
You have some right glib things to say about Arabic etc tuning above and now this, literally "the more appropriate tuning system for arabic/turkish/balkanic musicians".
Maybe proof-read yourself somewhat?

Thanks for clarifying. I wonder who this was perfectly clear to before I posted my problem with it.
So rather than "the more appropriate tuning system for arabic/turkish/balkanic musicians", it's in your estimation the more useful way to define pitches out of the MIDI spec, because of small displays on particular synths; additionally, in your assessment the user for all such retuning on hardware synths statistically belongs to these three groups. Glad that's sorted. :>)