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  • andybrom



Have you ever heard of it…equal temperament? And if so, do you know what it is and what it does??

If the answer is ‘No’, don’t worry, you’re not the only one!

Equal temperament is the thing that makes our western music different from all other world music – it is the difference between Japanese Shakuhuchi flute playing and a Chopin nocturne. It is something that most people do not know about or find too hard to understand.

So what is this difference?

A Shakuhachi is totally bound in nature; the instrument’s construction, its music and its symbolism. The Chopin nocturne on the other hand, is a piece for piano – a manmade instrument bound by artificial constraints and tuned to equal temperament.

But let’s go back to the beginning- to Pythagoras – 2 ½ thousand years ago.

It was Pythagoras who discovered the relationship or ratios between notes. Legend has it that Pythagoras heard a blacksmith strike 2 pieces of metal and was stunned by the relationship between them both. On inspection he discovered that one piece of metal was exactly half the size of the other. What was even more fascinating was that the smaller of the two sounded the same note as the larger, only higher; a ratio of 2:1( if you are visual think of it as red and light red – the same colour just a different density). He then decided to experiment further with these different sized bits of metal and came to the conclusion that if you strike a piece of metal two thirds the length of the original a new note will sound (green) but one that is 5 notes higher than the first (2:3). He then proceeded to see how many different notes he could discover by making each bit of metal 2/3’s smaller. All was very good for the first 12 but after that the notes were excruciatingly close to already discovered notes, but not quite (think of a clock where the nighttime hours are not quite in alignment with the day time hours.).

This is called the Pythagorean Comma and didn’t cause much trouble for musicians until we became greedy and decided we wanted music which was more lush, textural and complex than just a single line of music (think Gregorian Chants). When this happened and voices started to sing together (polyphony), the church insisted that only a few perfect intervals could be used, the 4th, 5th and octave. This was because these intervals are close to the beginning of the Pythagorean Comma and work nicely together.

But once again this was not good enough for us; we wanted to add new sounds. In the early 15th century an English man called John Dunstable started adding intervals of a 3rdand 6th to his music. The problem with was that to make these sound nice, people had to move their perfect intervals a little up or down to accommodate for the 3rds and 6ths. The second you change the purity of these notes you take the music from being totally organic and natural to being man-made. Musicians thought it was worth it though because the musical results were beautiful chocolaty harmonies which enticed the listeners of the day.

Once composers heard these harmonies, a plague of them spread across Europe where everyone was adding 3rds and 6ths and by the Renaissance they were common place.

What was the effect of all of this?

Well let’s use our clock analogy again. Just say we have the 12 hours on the clock face but the distance between each of those numbers is not exact. The first few are quite well spaced but as we go further around the dial the distance becomes less exact. Some hours may consist of 60 minutes but some maybe 57 and some 64. And let’s make it even more tricky and say that everyone has a different clock face. Although they are similar to each other, they are in no way universal.

This is what musicians had to put up with in the Renaissance and Baroque periods. Every composer had a slightly different tuning system to fit all the 12 notes into an octave. This was called ‘mean temperament’ and musicians had to tune their instruments (especially difficult for keyboard and fretted instruments) to the specific tuning of whoever they were working for at the time.

Composers, instrumentalists, instrument makers and scientists knew what they needed to make this situation better. It was to somehow have a system where the 12 notes of the octave were arranged so they fitted into the octave perfectly (equal temperament) not just ‘well’. This would take their music as far away from the organic music of the Shakuhachi as possible but would allow composers to write precisely what they wanted to and have it sound the same everywhere it was performed. And everyone had a try, including Galileo, Boyles and Stevin. In fact Stevin discovered the precise mathematical formula to have this perfect spacing between every note. It was 1.059463094 times the frequency of the note below!!

This is great in theory but hopeless in practice as the only way to tune instruments was totally aurally- there were no electronic tuners to give you the exact distances only a very well-tuned ear!

So thank goodness for J.S. Bach!! In 1722 he wrote the 48 Preludes and Fugues while working for Count Leopold in Cothen castle, East Germany. What was so amazing about these pieces was that somehow Bach (or one of his students) had managed to tune his clavier so that at one sitting Bach could play in all the major and minor keys. Now this wasn’t an ‘equal tempered’ keyboard but as the title says a “Well Tempered” one. And once discovered people across Europe were not suddenly being able to tune their instruments to well or equal temperament but what it did do was open the door for people to know that it could be done. Once the unobtainable 4 minute mile was achieved it gave people the inspiration to push it even further- so with tempering.

But the final turning point in making our tuning in the West totally different from all other ethnic or world forms of tuning came about in the 1800’s with the Industrial Revolution and Victorian Engineering. With the explosion of technology, machinery and factories, new instruments like accordion’s, clarinets, valved horns and pianos etc could be made, or partially made, on the production line of factories to the specific measurement set down by Stevin all those year before.

And what is even more amazing about the complicated and difficult story is that by the mid 1800’s equal temperament was the ONLY form of tuning. All the strange tempering of the previous 100’s of years had disappeared.

I suppose the obviously question is why? Why did we in the West go out of our way to change our form of music form being natural to being totally man made? And the reason is simple; all the beautiful harmonies, exotic sounds, strange man made instruments that we have today could have only come about with equal temperament. In fact almost every piece of music written after the 19th century could not have been conceived without it. I for one have been grateful that equal temperament has come about to give me music by composers such as Richard Strauss, Shostakovich, Mahler and the like.


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