What was used before Equal Temperament (ET) was "invented" in modern times? The short answer is Just Intonation (JI), Meantone (MT) and Well-temperaments (WT) and immediately preceding ET, Quasi-equal Temperament (QET). In the diagram below JI is left out as it mainly pre-dates the formulation of what we now know as Western music.
Put simply:—
JI has mostly pure chords in the Tonic key only;
Meantone has pure major thirds but narrow fifths (slightly flat) in up to 8 keys; and
WT has a pure major third in the Tonic key only, and varying major thirds and narrow fifths in nearly all keys - except the notorious Wolf tone in one last 5th, the dumping ground resulting from all those adjusted 3rds and 5ths.
Apart from the ancient Greek Pythagorean Temperament (which is quite horrible imho) the standard "refined" tuning of medieval times was Just Intonation (JI, which incidentally is the traditional Indian tuning - the equivalent of Ptolemy's Intense Diatonic Scale) which had pure beatless thirds, fourths, fifths, etc - in fact all the intervals were pure - which restricted the ability to modulate to other keys. Chords with JI with pure thirds and Perfect Fifths are I, iii, IV, V & iv (and... i, ♭II, ♭III, iv, ♭V & v! )
[#This explains why early music had few key changes - not because they were primitive or inarticulate, but simply because the more you strayed from the tonal centre of the tonic, the worse it got. Chords and melody were naturally sweet and there was little need to change key anyway (most composers and musicians later earnt their livelihoods courtesy of Roman Catholic Church, why everyone composed religious spiritual works in order to put food on the table).]
Next, the earliest great-sounding temperament that allowed a fair bit of modulation was 1/4 comma Meantone, first documented and formulated in the early 1500's by Pietro Aaron (he didn't invent it, he just worked out how to write out the formulae). It has 8 keys with pure beatless major thirds and 4 which are more or less unplayable. This is what I use 80% of the time. When C is the root it has pure major 3rds and slightly narrow 5ths in Eb, Bb, F, C, G, D, A, & E. There has to be some "rob Peter to pay Paul" going on to get the pure thirds, and this was acheived by narrowing the fifths by about 5 or 6 cents. (By contrast, ET has near-perfect fifths of 2 cents sharp, 702 instead of 700, but woefully sharp thirds of around 14-17 cents.) Picture a sitar and how the movable frets are staggered, to get an idea of how everything has to add up correctly at the twelfth fret to get the octave right.
The next major development was the invention of the Well-temperaments, beginning with Werckmeister (this is most probably what Bach and many of the early Masters used) and later Kirnberger (my next favourite after 1/4-comma meantone). These temperaments both have pure beatless thirds and slightly narrowed beating fifths in the root key making the Tonic key extremely nice on the ear - but with less and less refinement of keys as one progresses through the cycle of fifths. For example, in C major, the E is tuned to ≈386 cents instead of the 400 cents in ET and the fifth narrowed from 700 to around 695. In other keys eg F and G the third won't be pure (it is maybe 7 or cents flatter than the Equal Tempered third) but still sounds fairly sweet. This allows freer modulation into the dark-sounding keys of MT without the harshness, at the expense of losing the pure 3rds of 7 other keys as previous.
People who are only used to ET have become so accustomed to the beating of major thirds that when they first hear a beatless pure third they may complain that it is "lifeless" because it isn't beating!
Anyway, more Well-temperaments followed - Vallotti, Young, Neidhardt, etc - all heading closer and closer to quasi-equal and further away from pure tuning. The theory is that the humans somehow or other tolerate major thirds that are 14 cents sharp in ET, and after prolonged exposure it becomes "normal". Likewise in Meantone and Well-temperaments, the 5 or 6 cents narrowed fifths are also tolerated by the ear (humans can't distinguish b/n intervals played separately that are 2 or 3 cents apart. Played simultaneously though, the human ear detects the beating).
The question of importance arises therefore, which is really just a matter of personal preference, as to whether the pure thirds and narrow fifths of MT and WT are "better" than the near-perfect fifths and extremely sharp major thirds of ET. It depends largely on the type of music being played and the kind of sound sought.
Anyway, back to Period temperaments... With the revolution of the Romantic era came new types of temperaments, new forms of expression, and the breakaway from organised religion to Nature worship in litersture, art and music. It is my judgement that religious music sounds most whole and spiritual in pure tuning systems, and the shift toward sensuality and hedonism is why the old tunings were replaced. Everyone wanted to get funky and the pious catherdral vibe just didn't cut it. Imho that is why and what brought about the change to ET (equal temperament) in order to facilitate the modern trend. Out with Creationism and God, in with Science, Darwin's theory of Evolution, and Industrialisation. Modulation is an ET thing, a hallmark of music since the start of the 20th century.
Before Equal Temperament was scientifically and mathematically perfected in the early 1900's, Quasi-equal Temperament, from roughly 1850 onwards, was an approximation that came close, but some of the flat and sharp keys were a bit out. Even to this day not a lot of music is written in, say, Ab minor or Db major, and this is where they plonked the more dissonant intervals, out of the way so they could be avoided in the course of normal play (perhaps you have heard of the Wolf tone of earlier temperaments, which was a particularly out of tune fifth between Db-Ab-Eb). However, the early Baroque and later Classical period of the Masters - Bach, Strauss, Beethoven, Mozart preceded this by up to a century or more.
[Diagram modified from rollingball.com website, which has a lot of detailed info on various temperaments. A strange omission is Strauss 1825-99 (which I have drawn in). Generally the modern era composers all use ET.]
Popular Well-temperaments (as they were called, to differentiate them from the earlier Meantone systems - more on that later) of those eras were Werckmeister and later Kirnberger, of which both had at least three differently tuned versions.
The earlier Meantone temperaments were based on the comma or fractions thereof (without going too far into it, if you tuned a zillion stringed guitar using harmonics at the 5th and 7th frets by the time you got from C to G, D, A, E, B, F#, C#, G#, D#, A#, E#, and finally back to the "C" at B#, that C would be about a quarter of a semitone too high. That is one kind of comma in music).
They came up with 1/4-comma Meantone first, to stretch and shrink various notes to fit within the octave and play reasonably well in tune. Various intellectuals invented 1/5-comma, 1/6-comma, 1/7-comma etc tunings in an attempt to free up the scope of modulations to unrelated keys. The comma was distributed between the notes, making the important ones greatly playable and dumping the remaining trash in unrelated Z-demolished rarely-visited keys.
To this day piano tuners have to be able to count up to seven beats per second for certain notes when tuning. In the old days they tuned more to REDUCE the amount of beating until W. B. White finally figured out the correct beating count for all 88 notes of the piano in 1917. Remember, there were no stroboscopes or tuners in those days! The only way to tune a piano was to count the beating between intervals, eg from middle C, the E above might beat 3 per second but the E below at 2 beats only (just guessing, I'm not up with the correct rates as I'm not a piano tuner!). They had to be able to count up to seven beats per second to tune intervals higher up in the register (lower notes beat a lot slower).
Put simply:—
JI has mostly pure chords in the Tonic key only;
Meantone has pure major thirds but narrow fifths (slightly flat) in up to 8 keys; and
WT has a pure major third in the Tonic key only, and varying major thirds and narrow fifths in nearly all keys - except the notorious Wolf tone in one last 5th, the dumping ground resulting from all those adjusted 3rds and 5ths.
Apart from the ancient Greek Pythagorean Temperament (which is quite horrible imho) the standard "refined" tuning of medieval times was Just Intonation (JI, which incidentally is the traditional Indian tuning - the equivalent of Ptolemy's Intense Diatonic Scale) which had pure beatless thirds, fourths, fifths, etc - in fact all the intervals were pure - which restricted the ability to modulate to other keys. Chords with JI with pure thirds and Perfect Fifths are I, iii, IV, V & iv (and... i, ♭II, ♭III, iv, ♭V & v! )
[#This explains why early music had few key changes - not because they were primitive or inarticulate, but simply because the more you strayed from the tonal centre of the tonic, the worse it got. Chords and melody were naturally sweet and there was little need to change key anyway (most composers and musicians later earnt their livelihoods courtesy of Roman Catholic Church, why everyone composed religious spiritual works in order to put food on the table).]
Next, the earliest great-sounding temperament that allowed a fair bit of modulation was 1/4 comma Meantone, first documented and formulated in the early 1500's by Pietro Aaron (he didn't invent it, he just worked out how to write out the formulae). It has 8 keys with pure beatless major thirds and 4 which are more or less unplayable. This is what I use 80% of the time. When C is the root it has pure major 3rds and slightly narrow 5ths in Eb, Bb, F, C, G, D, A, & E. There has to be some "rob Peter to pay Paul" going on to get the pure thirds, and this was acheived by narrowing the fifths by about 5 or 6 cents. (By contrast, ET has near-perfect fifths of 2 cents sharp, 702 instead of 700, but woefully sharp thirds of around 14-17 cents.) Picture a sitar and how the movable frets are staggered, to get an idea of how everything has to add up correctly at the twelfth fret to get the octave right.
The next major development was the invention of the Well-temperaments, beginning with Werckmeister (this is most probably what Bach and many of the early Masters used) and later Kirnberger (my next favourite after 1/4-comma meantone). These temperaments both have pure beatless thirds and slightly narrowed beating fifths in the root key making the Tonic key extremely nice on the ear - but with less and less refinement of keys as one progresses through the cycle of fifths. For example, in C major, the E is tuned to ≈386 cents instead of the 400 cents in ET and the fifth narrowed from 700 to around 695. In other keys eg F and G the third won't be pure (it is maybe 7 or cents flatter than the Equal Tempered third) but still sounds fairly sweet. This allows freer modulation into the dark-sounding keys of MT without the harshness, at the expense of losing the pure 3rds of 7 other keys as previous.
People who are only used to ET have become so accustomed to the beating of major thirds that when they first hear a beatless pure third they may complain that it is "lifeless" because it isn't beating!
Anyway, more Well-temperaments followed - Vallotti, Young, Neidhardt, etc - all heading closer and closer to quasi-equal and further away from pure tuning. The theory is that the humans somehow or other tolerate major thirds that are 14 cents sharp in ET, and after prolonged exposure it becomes "normal". Likewise in Meantone and Well-temperaments, the 5 or 6 cents narrowed fifths are also tolerated by the ear (humans can't distinguish b/n intervals played separately that are 2 or 3 cents apart. Played simultaneously though, the human ear detects the beating).
The question of importance arises therefore, which is really just a matter of personal preference, as to whether the pure thirds and narrow fifths of MT and WT are "better" than the near-perfect fifths and extremely sharp major thirds of ET. It depends largely on the type of music being played and the kind of sound sought.
Anyway, back to Period temperaments... With the revolution of the Romantic era came new types of temperaments, new forms of expression, and the breakaway from organised religion to Nature worship in litersture, art and music. It is my judgement that religious music sounds most whole and spiritual in pure tuning systems, and the shift toward sensuality and hedonism is why the old tunings were replaced. Everyone wanted to get funky and the pious catherdral vibe just didn't cut it. Imho that is why and what brought about the change to ET (equal temperament) in order to facilitate the modern trend. Out with Creationism and God, in with Science, Darwin's theory of Evolution, and Industrialisation. Modulation is an ET thing, a hallmark of music since the start of the 20th century.
Before Equal Temperament was scientifically and mathematically perfected in the early 1900's, Quasi-equal Temperament, from roughly 1850 onwards, was an approximation that came close, but some of the flat and sharp keys were a bit out. Even to this day not a lot of music is written in, say, Ab minor or Db major, and this is where they plonked the more dissonant intervals, out of the way so they could be avoided in the course of normal play (perhaps you have heard of the Wolf tone of earlier temperaments, which was a particularly out of tune fifth between Db-Ab-Eb). However, the early Baroque and later Classical period of the Masters - Bach, Strauss, Beethoven, Mozart preceded this by up to a century or more.
Popular Well-temperaments (as they were called, to differentiate them from the earlier Meantone systems - more on that later) of those eras were Werckmeister and later Kirnberger, of which both had at least three differently tuned versions.
The earlier Meantone temperaments were based on the comma or fractions thereof (without going too far into it, if you tuned a zillion stringed guitar using harmonics at the 5th and 7th frets by the time you got from C to G, D, A, E, B, F#, C#, G#, D#, A#, E#, and finally back to the "C" at B#, that C would be about a quarter of a semitone too high. That is one kind of comma in music).
They came up with 1/4-comma Meantone first, to stretch and shrink various notes to fit within the octave and play reasonably well in tune. Various intellectuals invented 1/5-comma, 1/6-comma, 1/7-comma etc tunings in an attempt to free up the scope of modulations to unrelated keys. The comma was distributed between the notes, making the important ones greatly playable and dumping the remaining trash in unrelated Z-demolished rarely-visited keys.
To this day piano tuners have to be able to count up to seven beats per second for certain notes when tuning. In the old days they tuned more to REDUCE the amount of beating until W. B. White finally figured out the correct beating count for all 88 notes of the piano in 1917. Remember, there were no stroboscopes or tuners in those days! The only way to tune a piano was to count the beating between intervals, eg from middle C, the E above might beat 3 per second but the E below at 2 beats only (just guessing, I'm not up with the correct rates as I'm not a piano tuner!). They had to be able to count up to seven beats per second to tune intervals higher up in the register (lower notes beat a lot slower).
How they did it is a bit of a lost art. An expert piano tuner trying to faithfully reproduce period tunings has to abandon their normal ET regime to tune pure major thirds and narrow fifths. Adding the Railsback curve to that makes it all the more complicated, but a competent piano tuner doesn't have a problem with any of this. It is their art.
