Was equal temperament caused by the invention of the piano, or was it inevitable?

Question

Historically, which key a piece of music was written in made a big difference. Toccata and Fugue in D minor for instance had to be played in that key or it wouldn't sound right.

But over the last couple of centuries, tonality has become less and less important in music. Pieces are freely transcribed into different keys, whether to match a singer's range or for some other reason.

A large part of why this is possible is because the piano is tuned with equal temperament, so that it can be used to play in any key without being much out of tune.

The piano was more of a tool than an instrument, allowing practice accompaniment in any key.

It is also an excellent tool for composition, as one can almost play with one hand and write with the other. Switching back and forth with almost any other instrument would be very awkward and tiring.

Unfortunately when one writes music on a piano, any concept of tonality is lost.

Most modern music is written without tonality, and most newer instruments are tuned with all notes based on equal 12^th root of 2 frequency intervals. This is very convenient in many ways, and very unfortunate in others.

The question is, was it inevitable that music would eventually have lost tonality, even if the piano (or some equivalent instrument) hadn't been invented?

Answer 1

The earliest use of equal temperament was on fretted instruments with fixed frets. The ratio of 17:18 for the string length for successive frets is a good approximation to equal temperament. The errors were well within the tolerance of other intonation issues such as non-uniform gut strings, and the different amounts of string bending on different frets because of the height of the action.

Not all early fretted instruments had fixed frets - for example the frets on lutes were loops of gut tied around the neck and were adjustable.

It is probably safe to say that no keyboard instruments were routinely tuned in equal temperament for the first 1400 years of their history - there are mosaics depicting organs played by keyboards, and texts describing the sounds they produced, that date from 400 AD.

Equal-tempered tuning on a harpsichord certainly doesn't sound "better" for the historical style of playing. Harpsichord tone has more high harmonics than piano, which increases the difference in effect between just intonation major thirds and equal tempered. Most "serious" modern harpsichordists would use appropriate historical temperaments, and different temperaments for music of different periods. Harpsichords need much more frequent tuning than pianos, and harpsichordists learn to do it themselves, just like guitarists, string players, etc. Technically, it is much easier than piano tuning because the string tension is much lower, and a "non-expert" tuner is less likely to physically damage a harpsichord than a piano.

To answer Tim's comment, unequal temperaments did not only "sound better" in "just one key". For example, in the commonest meantone temperament used in the 16th century, where the tempered note names are C C# D Eb E F F# G G# A Bb B C, any major scale from two flats through to three sharps is "in tune", and in fact all those scales have exactly the same frequency ratios between the notes, so there is no problem with modulations within that part of the circle of fifths. But if you attempt to go outside that range and play an "Ab chord", the notes G#-C-Eb sound horrible, and so does a B chord with B-Eb-F#.

The various "well-tempered" tuning systems devised in the 18th century were useable in every key, though every key had its own slightly different sound - and it is clear that from the music that composers like Bach made deliberate use of that fact. The typical patterns of harmony and counterpoint are different in different keys. Some of those "well-temperaments" were still used by piano tuners even into the early 20th century. Much "romantic" 19th-century piano music was written in keys using many "black" notes for technical reasons, and it is probably not a coincidence that in some well-temperaments, the groups of keys on "opposite sides" of the circle of fifths (e.g. Bb-F-C-G-D compared with E-B-F#/Gb-Db-Ab) had distinctly different sound qualities.

Some modern harpsichord music is (probably) intended to be played in equal temperament - for example this:

Answer 2

Even without the piano (or even keyboard instruments), there were other forces pushing toward something close to equal temperament.

The common narrative is that chromatic music was instrumental in the use of temperaments that were more equal. While that is a factor, it's important to look at how chromatic music could be even in the 1600s. Frescobaldi's Fiori musicali, for one example, was an incredibly popular set of keyboard works published in 1635. However, when the more chromatic ricerars are performed on organs in the meantone temperaments popular in that day, they sound positively awful to modern ears that are not used to such wild deviations from equal temperament.

And yet, composers wrote this music and performed it on instruments at that time. Composers (and apparently listeners) appreciated the greater contrast provided by intervals that were more or less "in tune." I still remember the first time I noticed the compositional use of tuning for effect, where I was looking at an aria written around 1700 that briefly modulated through A-flat minor while the text was declaring something was "horrible, horrible!" Yes, the harpsichord accompanying that aria would likely have sounded quite "horrible" at that point in the piece with its harsh intervals that would seem very "out of tune" to modern ears.

So, strictly speaking, it wasn't necessarily chromaticism alone that drove the move toward equal temperament. Composers had been using chromaticism and tuning for effect for centuries before keyboard instruments came to be tuned in something approaching modern equal temperament.

The main thing I'd add to other answers here so far is the role of other instruments. Fretted instruments have already been mentioned as a very early use of equal temperament (long before keyboards approached it). But I mean also the use of various instruments in the increasingly large ensembles of the 18th and 19th centuries. We tend to obsess over temperaments in keyboard instruments mainly because there is the most discussion in historical treatises about how to temper keyboard instruments. But that's simply a practical concern that grew first out of organ tuning, as organs have long sustained tones and timbres with rich sets of harmonics that makes tuning choices particularly important. Later, temperaments became important to harpsichord and other keyboard players, as these instruments were some of the only ones that required the detailed knowledge of tuning to maintain them. A harpsichord needs to be frequently tuned, and unlike other instruments like strings (bowed or plucked) that typically only needed a few intervals tuned, a keyboardist needed to know how to create adequate relationships between all of the 12 chromatic pitches in the octave.

My point is that our perspective is biased toward keyboard instruments in tuning discussions because practically that's one case where knowledge of tuning was important historically.

However, if one considers the practical considerations of playing in large ensembles with baroque instruments, it's easy to see how tuning compromises would generally lead to something approximating equal temperament.

Baroque wind instruments, in particular, didn't have most of the valves and keys of modern orchestral instruments. A natural brass instrument without valves would be in-tune for some notes in its natural harmonic series, but other notes were often approximated through changes in embouchure and sometimes holes in the instrument that could be strategically used to better approximate chromatic notes or those not in the harmonic series of the fundamental of the instrument.

Meanwhile, woodwinds with few (or no) keys depended on all sorts of cross fingerings, half hole techniques, etc. to approximate chromatic notes. These tunings could be all over the map. Skilled wind players would learn to use different fingerings in different circumstances -- some fingerings might be higher in pitch (and appropriate for a leading tone), others might be in the middle of the chromatic range. Some might be better for softer or louder notes, but might be more or less out of tune.

Now imagine ensembles like those seen in Bach's Brandenburg Concertos and think about the challenges inherent in having all of those instruments trying to intermingle and be in tune with each other. You have brass pitched in one key (and in tune for most notes in that key), but woodwinds might be primarily pitched in another key and using chromatic fingerings attempting to be in tune with everyone else. And these all needed to play well with the strings (who had more flexibility in tuning their individual notes, but mostly tended to anchor to the perfect fifths in their tuning) as well as whatever keyboard in whatever temperament that was accompanying them.

If one reflects for a moment on the disaster inherent in trying to mesh all of these tuning considerations together, it's easy to see that the larger ensembles of the 18th and 19th centuries required gradual compromises to a standard tuning across the scale. All of the tuning debates about organ tunings and meantone and well-temperament fly out the window when you're just trying to have the flute, the oboe d'amore, the horns, and the strings sound okay when playing along with harpsichord in several keys.

So, as instrument builders started to invent and add keys and valves in the late 18th and early 19th centuries to wind instruments, the obvious choice was to approximate something like a compromise temperament where all the chromatic intervals of the scale were roughly equal. Players of these instruments were already doing this in large ensembles, out of necessity. The expense of creating these more complex instruments increased, so gone were the days when a wind player might expect to have several instruments pitched in many different keys. Instead, the new holes and keys and valves were meant to make instruments useful in just about any key. Wind players today might choose to still have two instruments (usually one pitched in a flat key and one in a sharp key, like the B-flat vs. A clarinet) for convenience in fingering, but the new systems for chromatic scales on instruments were necessarily close to equal temperament simply to allow ensembles to play together reasonably in tune.

None of this takes away from the role that keyboard temperament theories and increasing chromaticism may have played in leading to equal temperament, but the simple fact of larger ensembles trying to play in tune in several keys was also likely to lead toward a compromise tuning for the chromatic scale anyway -- regardless of the piano or even the use of keyboard instruments generally.

Answer 3

the piano is tuned with equal temperament

Not necessarily. Pianos were in wide use by the late 18th century, but equal temperament was not until perhaps 100 years later.

The rise of equal temperament seems rather to have been driven by the expansion of modulatory possibilities as the "common practice" system of harmony was expanded, eventually to the breaking point. The piano may have played a role in this (for example, the overtones of a piano are different from those of a harpsichord, so wide major thirds may sound more acceptable on the piano than on the harpsichord).

But did the piano's tonal profile enable equal temperament, or was it caused by equal temperament? Pianos of the 18th century and even early to middle 19th century also have a different tone from today's pianos. Most likely, the piano and preferences for tuning systems evolved together to keep pace with changing musical tastes. Perhaps the tonal profile of the harpsichord would have changed over the course of the 19th century if the piano had never been invented, so equally tempered harpsichords would have sounded better.

In any event, it seems likely that the expansion of the harmonic language would have happened even without the piano, and that it would have led to increased preference for equal temperament.

Answer 4

As it has been explained in many questions and answers - look on the right edge of this site the related questions - the development of the well-tempered piano was a product of the development of the polyphony and the purpose of composers to modulate through all keys and accompany chorals and songs in all keys with claves instruments (cembalos, harpsichords, organs, later the forte-piano and the Hammerklavier. This revolution started already in the 17th century when Werckmeister developed his ideas of the well-tempered tuning.

Werckmeister is best known today as a theorist, in particular through his writings Musicae mathematicae hodegus curiosus... (1687) and Musikalische Temperatur (1691), in which he described a system of what we would now refer to as well temperament (named after Bach's opus, "The Well-Tempered Clavier") now known as Werckmeister temperament.

These quotations show that the WTC by Bach has been composed before the first equal tempered pianowas built but his music has been played by clave instruments, harpsichords and organs.

Answer 5

Up until recently keyboards and fretted instruments were traditionally avoided by orchestras because their equal or quasi-equal temperaments made them out of tune with the other instruments. There is a lot of misinformation - especially in 20th century textbooks - falsely attributing the use of Equal Temperament on keyboard instruments, whereas an exact method of ET tuning was not formulated for the piano (by counting the beat rates for all intervals) until 1917 by W. B. White. The Masters always used meantone or well-temperament. It's only in the last couple of decades that the internet has facilitated the spread of accurate knowledge.

As for fretted instruments the Rule of 18 has been known in ancient Asia since prehistory. Say the scale length is 24 inches, divide by 18, gives the first fret at one and a half inches from the nut, and so on. Such fretted instruments approximate equal temperament very well and thus sound terrible with wind such as brass and fretless strings like violins etc.

Thankfully in the modern age with the simple push of a button one can dial up a faithful historical temperament on a digital piano. It is absolutely amazing to play period pieces by Beethoven, Chopin, etc using quarter-comma meantone with a root of say B flat and witness the beauty and sonority they would have heard back then. With pure major thirds in eight keys and fifths only a few cents narrow the instrument comes alive with beatless resonance.

So yes, the pianoforte is largely responsible for destroying modern music, rendering it toneless and lacking the intrinsic key colour that the great Masters employed so well. You could include the electric guitar as well although they weren't around in the day. If so, I'm sure Beethoven would have instantly smashed up any Fender or Gibson he had the misfortune of hearing.

Answer 6

The piano was more of a tool than an instrument, allowing practice accompaniment in any key.

That's sort of an absurd statement except for the flimsiest of keyboards in the spinet and clavichord class. And those were generally not in equal temperament. The whole point of the non-equal well-tempered temperament was to allow playing in any key, and both well and equal temperament came about at a rather late stage of the evolution of keyboard instruments and affected them somewhat across the board.

Fixed arbitrary notes (as opposed to fixed determined notes like that of a natural trumpet) are nothing that came about just with "modern" keyboard instruments: frets (often adjustable) were certainly in use in many instruments of Medieval times (and getting a fretboard smooth enough to enable fretless play is actually non-trivial), and something like a hurdy-gurdy also relies on fixed notes.