Mean tone tuning versus equal temperament

Meantone tuning is one of many tuning systems that was used in the past. Such tuning systems were designed to make certain keys sound the best according to the taste of the times, but at a huge cost. These tuning systems sound horrendous when using mostly black notes and make playing in such keys impossible on a keyboard instrument.

[bazeSC]

I think Baroque musicians were well aware of the equal temperament because it's an extreme case of meantone temperament where the comma is spread across all fifths. It's just that it wasn't the preferred choice for the type of music they wrote. Every instrument has its own timbre and I think organs and harpsichords sound better and more resonant if 1/4 or 1/6 comma meantone temperament is used (assuming that the composer is aware of its limitations). Of course modern music assumes equal temperament and that's what should be used. But I wouldn't say that it's necessarily "better" just more convenient. The interval which is naturally less "stable" (the major 3rd) is sacrificed to make it work but we gain the ability to modulate freely.

[kratanuva]

Technically "equal temperament" is (a) meantone temperament. It's approximately 1/11th comma meantone.

Also, there's nothing stopping all 12 (or more!) keys from sounding good in different kinds of meantone tunings, you just need more notes on your piano per octave.

[Gargantupimp]

Meantone chords sounded so much better than equal (when there was less than one black key) because each chord had its own identity and each had smooth "pearly" intervals which sounded gorgeous. Equal temperament was too samey and stale in comparison. But I understand the necessity for equal temperament in pieces which use a lot of chromatic notes.

[Lucius_Chiaraviglio]

People knew about 12 tone equal temperament in both Europe and China at least as far back as the 1500s -- they just didn't care for it much (although it is possible to find pipe organs dating back to the late 1600s tuned in it -- some organ in the Netherlands comes to mind that I can't remember the name of, but it is also notable for having a pedal mutation stop that goes lower than its lowest unison/octave stop). Well temperaments that were intermediate between meantone and equal temperament persisted all the way into the 1800s, long enough for Sergei Rachmaninoff to claim he was first trained on a well-tempered piano rather than one tuned in equal temperament, and definitely long enough for Beethoven and Chopin to be writing for well-tempered pianos, even with Chopin's extensive use of the flat/sharp keys.

For earlier music, although most keyboard instruments had only 12 notes per octave, some harpsichords and even a rare subset of pipe organs had split flat/sharp keys to enable key signature modulation and even enharmonic playing while using meantone, and some theorists of the time (and later) proposed systems using more than 12 equal divisions of the octave. The most extreme examples known are the arcicembalo and arciorgano of Nicola Valentino of the 1500s -- these had 36 keys per octave, split onto 2 manuals of 19 and 17 notes, but unfortunately the ergonomics turned out to be terrible (as you can see in videos of these instruments being played). More practical harpsichords have been built with 19, 24, or 31 notes per octave (of which videos are also floating around on YouTube). If only we had stuck with harpsichords, and continued with experiments to give them dynamics . . . the piano stole the show from the harpsichord on the basis of having better dynamic control (but at the expense of possibility for variations of timbre), but has a much more complicated and bulky mechanism that is not well suited to building for more than 12 notes per octave.

_Maybe_ you could get 17 notes per octave in without having to sacrifice strings per note (normally 3 except in the bass, although 4 is a possibility exercised in a few instruments), but from photos and videos of pianos having 24 notes per octave, it is evident that either you have to sacrifice strings per note or go to 2 levels (resulting in a humongous instrument), and the designs of the 1930s for this (as sometimes used by Ivan Wyschnegradsky) had not very good ergonomics (better than the arcicembalo and arciorgano, but worse than the above-mentioned other microtonal harpsichords). The Fokker organ of 1951 has 31 notes per octave (in 31 equal temperament, which is approximately 20/83-comma meantone) and at least in principle more ergonomic keyboards and pedalboard, but unfortunately has bad timbre and not much in the way of anything you can do to fix it except by blending it with a choir (or in principle other instruments, but I haven't heard that yet).

Of course, the other problem is that adding more notes per octave on an acoustic instrument -- especially a pipe organ -- is extremely expensive, which is probably the main reason it never gained much traction even in the harpsichord era. The real explosion in use of more than 12 notes per octave has come in the last couple of decades, when synthesized sound that sounds good has become available at an affordable price, along with isomorphic/generalized keyboards that actually have decent ergonomics (for those who want to play the music themselves as opposed to using software to sequence it -- although software sequencing is certainly a valid way of getting around the ergonomics problem, especially if you want the sound of something like woodwind or brass instruments that would need an awful lot of keys or valves to get more notes per octave).

[robertalefkowitz]

I am learning so much from viewing your videos. By listening today I learned about mean tone tuning versus equal temperament.

[aldeayeah]

Playing the Well-Tempered Clavier seems a cool way to check if one's keyboard is well-tuned!

[windowstudiosalt]

Wow… I remember watching an Adam Neely video on tuning. This just gives me even MORE insight on tuning. I can't believe that music has changed so much that Mean tones today sound absolutely horrendous today.

[chrisgoldwire]

The mean tone sound good without the four chords with black notes and its good to hear that the tuners are tryna make the bumps in the worst keys get smother it will be more fun to play with all keys perfect.

[iavv]

Equal temperament did not sound much better. It still sounded out of tune, but just more sharp

[katzuzip]

Amazing information! Nice teaching method too! Regards

[bearfoxwolf]

It's the best compromise for an instrument where you cannot tune the notes individually because everything comes pre-tuned.

[wakkowarner]

That piano you made that recording on sounds familiar.. ;o). Seriously now, after listening to this, one realizes 1) how monumental getting to Equal Temperament was, and how monumental Bach's Well-Tempered Clavier is.

[therealzilch]

Bravo. You've demonstrated that mean tone tuning doesn't work in keys distant from its tuning center. But not a word about how equal temperament gives us thirds in all keys that are harsh and dissonant.

I have no quarrel with equal temperament, it's a great system for highly modulated music. But it's not the _summum bonum._

[freddodudodo]

2, 295E-6 it is the maximum standard deviation that we obtain among all the intervals ratio of a scale with equal temperament. 1, 904E-3 for Pythagorean scale, any other way of constructing the scale gives a result between these two extremes. equal temperament is therefore the most stable and the most compatible for transposition as well as for large ensemble orchestration.

[bragtime]

This video is poorly informed. 12edo (equal temperament) is a meantone tuning, and so are many other edos. 19edo, 26edo, and most notably 31edo are a few edos/temperaments that also support meantone and don't run into the problem you discussed in your video because they're not limited to a 12-note subset. Of course if you use a 12-note subset of meantone then you're gonna get a few wolf intervals, but with edos/temperaments like 19, 31, among others, you can have purer triadic and tetradic harmony than in 12edo, and not have to worry about needing to use wolf intervals since it's an equal temperament, but it'd still be meantone and sound great- better than 12edo.

I'm not an expert microtonalist but I've compared meantones and found that 1/4 comma meantone, which is very well approximated by 31edo, is about ideal for both triadic and especially tetradic harmony (like being able to use the 4:5:6:7 chord, the meat and potatoes of barbershop harmony, which is absent in 12edo). 19edo also has smoother major and minor triads than 12edo but doesn't have a good seventh harmonic.

[thepunontherun]

Was not expecting the equal temperament to make those 4 chords sound that much better.

[buskman]

Yes, all keys in Equal Temperament (ET) sound exactly the same. Interestingly, if you play an unfretted stringed instrument like a violin (or sing), you will automatically play/sing notes in relation to each other that are NOT ET but are, in fact, pure intervals - IOW, closer to what meantone produced in the "good" keys as opposed to ET. When playing/singing along with an ET fixed-tuned instrument you will automatically adjust to match that tuning.

With any temperament used during Bach's (or Mozart's, or Beethoven's and beyond) lifetime you can hear the difference in the sound relationships between the notes in various keys. With ET there is no difference to hear so the "feeling" that existed with various keys then are meaningless today.  

FWIW, no one really knows what specific temperament Bach used for his "Well-Tempered Klavier." Any discussion on the temperament he used is speculation though it's quite safe to say it wasn't meantone or ET. ;)

[TentacleTerrorMusic]

Why do i actually kinda love the out of tune sound of quarter comma meantone

[Reino_X]

Personally I would make sure every key sounds good first and foremost. I wouldnt tolerate a wolf interval. That said I love the mathematically correct sound of mean tone so I would pick my favorite range of keys which is G major to F# or "sharp" keys and have them mathematically correct and then evening the wolf chord among the flat keys C to Db

it would depend how evened out it sounds so I could experiment and try to make more chords mean tone (C-Bb or Db-Eb), it would depend on the sound results

[GlennFiddles]

Although you picked 4 chords that really do sound bad in 1/4 comma meantone, i didn't really love the sounds of those chords - or any major chord - in equal temperament either. As one Turkish classical musician Cinuçen Tanrıkorur once pointed out, thirds in Western equal temperament are quite a mess if you actually listen to them critically.