Temperament scale: concept, history of occurrence and foundations of music theory

2024 Author: Leah Sherlock | [email protected]. Last modified: 2023-12-17 05:25

One of Johann Sebastian Bach's most famous creations is called the Well-Tempered Clavier, or "HTK" for short. How should this heading be understood? He points out that all the works in the cycle were written for the clavier, which has a temperamental scale, that is, the one that is typical for most modern musical instruments. What are its features, and how did it appear? You will learn about this and much more from the article.

General information

The tempered scale assumes that each octave (the distance between the same notes of different pitches) is divided into a certain number of equal intervals. In most cases of using such a tuning, the sounds are arranged in semitones. If we imagine a piano keyboard, then exactly this interval is equal to the distance between eachadjacent key. The same can be said about any other keyboard, wind or other instrument.

For example, on a guitar, between adjacent notes on the same string, an interval of a small second is placed, which is equal to half a tone.

Temperament value

The name of this system comes from the Latin root meaning measurement. Therefore, this achievement can be attributed not only to music theory, but also to mathematics. Indeed, attempts to develop such a system since ancient times were made by people who were professionals in these two areas of knowledge, and also knew other sciences, for example, physics. And this is not surprising, since in this case a person is dealing with air vibrations, which produce sounds.

Mathematical calculations helped researchers to systematize the sounds that make up the octave in this way, in order to make some performing tasks easier for musicians. For example, the introduction of the temperamental system of music made it possible to significantly simplify the transportation of works. Now playing the same composition in different keys does not require repeated learning. If a person knows the basics of music theory and harmony, then he will be able to play a piece in any key. Many years of experience allows you to do it quickly enough.

Features

Temperamental tuning proved to be useful primarily in the performance of vocal music. With its introduction, singers got the opportunity to perform works in the most convenienttone for them. This means that vocalists have got rid of the need to overexert their vocal cords, taking too low or high notes that are uncharacteristic of their range. Of course, such free handling of musical material is not welcome in all genres. First of all, it concerns classical music. For example, the performance of opera arias in other than original keys is considered unacceptable.

It is also unacceptable to transport symphonies, classical instrumental concertos, sonatas, suites and works of many other genres. Unlike pop music, tonality is much more important here. History knows examples of some composers having a "colored" musical ear. That is, for these artists, each key was associated with a certain shade. Scriabin and Rimsky-Korsakov differed in this perception of music.

Other classical composers, although they did not have such a "colored" perception of sound, still distinguished tonalities by other characteristics (warmth, saturation, and so on). Transportation of their works into arbitrary keys is unacceptable, as it distorts the author's intention.

Indispensable helper

However, even such composers did not deny the importance of equal temperament for the development of musical art. The free transition from one key to another has not only an obvious "practical" benefit, since it allows performers to be comfortable whenplaying and singing. With the right choice of tonality, the vocalist's voice sounds much brighter and more natural than when he does his best to perform uncharacteristic for his range (low or high) notes.

Temperature scale (and hence free change of keys) provides the ability to write works with a large number of tonal deviations and modulations. And this, in turn, is a vivid visual technique that was widely used in classical music. With the advent of the era of pop art, the use of modulations has become even more important. So, in jazz improvisations, harmonic sequences are often used, moving from one key to another. Therefore, the temperamental scale can be called one of the engines of progress in music.

History

Theoretical research in the field of music began in ancient times. One of the first scientists who began to pay attention to the system was the ancient Greek mathematician Pythagoras. However, even before the birth of this outstanding person, there were many musical instruments with an already formed system. The people who played them often had no idea either about the physical properties of sound or about the basics of music theory. They learned their art, comprehending many of its wisdom intuitively.

That is, at that distant time, people by trial and error learned the acoustic laws that underlie musical theory and harmony. And these sciences, as you know, are not inferior in their complexity to higher mathematics. One thinker later said,that musicians and composers are unconsciously engaged in solving the most complex physical and mathematical problems. The first serious researcher of these issues was the already mentioned Pythagoras.

Pythagorean system

An ancient Greek scientist conducted experiments with the sound of the simplest musical instrument, which consisted of a wooden body and a sound source stretched over it - one single string.

He invented his own system, which was called Pythagorean. The sounds in it were arranged in pure fifths. The use of such a system allowed some instruments to reduce the number of strings. Prior to this, all instruments were arranged like a harp, that is, each of their strings could produce only one note. Finger pinching was not used. However, with the introduction of the Pythagorean system, the musicians still could not change the key of either the entire work or any part of it. This tuning system was used until the Middle Ages. Then the organs for the performance of church music were tuned according to the ancient Greek model. This system, in addition to the listed disadvantages, had two more disadvantages. Firstly, the scale in them was not closed. This means that having started playing the scale from to, it was impossible to come to the same note, but of a higher octave.

And secondly, instruments tuned in this way always had several so-called "wolf" sounds, that is, keys or frets, whose sound knocked the axis out of the key in which the whole instrument was tuned.

Music before the Baroque

Musicians, composers, and instrument makers in the Middle Ages were constantly searching for the perfect tuning. Traveling theater performers were famous for their virtuosic playing of the lutes. To the accompaniment of this instrument, comic verses on topical topics were performed. Artists had to re-tune their instrument in search of the right key to match their voice range, and this involved more than loosening or tightening the strings, as is the case today.

This procedure required a change of frets. They were not firmly attached to the fretboard as they are on modern guitars. Then they were replaced by harnesses made of animal skin, and freely moving along the fingerboard. So, when rebuilding the instrument, these frets had to be moved as well. It is no coincidence that in those days they joked that lute players spend a third of their lives tuning the instrument.

Besides, in the Pythagorean system there was no concept of enharmonic equal sounds. That is, the note "F sharp" did not sound then like "G flat".

Different options

A near-modern tuning system dates back to the time of Johann Sebastian Bach.

It was called "well-tempered tuning". What was its essence? As already mentioned, before that there were no enharmonic equal sounds. That is, if a modern piano existed then, then between the keys "do" and "re" there should have been twoblack: C sharp and D flat, instead of today's one that performs both of these functions.

During the time of Johann Sebastian Bach, music in keys with a large number of sharps and flats gained wide popularity. Composers began to use a tricky move - for the convenience of performance, they often made enharmonic substitutions. For example, instead of "G flat" they began to write "F sharp" in the scores. But these notes were not equal to each other at that time. That is, their sound, albeit not much, but different. Therefore, listening to such music made people feel a little uncomfortable.

Inaccurate but convenient

But a way out of this situation was soon found. Two notes located between adjacent steps of the scale were replaced by one that was between them. This sound was only approximately equal to these two notes, or rather, it was their average value. But, nevertheless, such an innovation opened up opportunities for composers and performers.

Natural and tempered scales

A natural scale is one that contains only the main steps of the scale. The ratios between them are as follows: two tones - a semitone - three tones - a semitone. According to this scheme, the simplest folk instruments are tuned: pipes, pipes, and so on.

Each of them can only be played in two keys - major and minor.

The emergence of a new order

In the 18th century, several music theorists proposed the introduction of a new tuning. ATIn it, the octave was divided into 12 notes, lagging behind each other by exactly half a tone. This system is called equal temperament. She had many supporters, but there were also a sufficient number of harsh critics. The role of the creator of the tempered system is attributed to several people at once. The names of Heinrich Gramateus, Vincenzo Galilei and Maren Marsenna sound most often in this connection.

Contradiction

To the question "What scale is called equal temperament?" The following answer can be considered quite complete: "This is a system where an octave contains twelve notes arranged in semitones." Some critics of this approach to instrument tuning said that it is not perfectly accurate, and natural tuning sounds much cleaner. It is in this system that amateur musicians from the people sing and play. In the memoirs of the writer, composer and music theorist Vladimir Odoevsky, one can find a story about how he once invited one such singer to visit him. When Odoevsky began to accompany the guest, he heard that the temperamental scale of the piano did not match the notes that this person sang.

After that incident, the composer tuned his piano in a different way. His sound is close to natural.

Conclusion

It happened in the nineteenth century. But disputes between supporters and opponents of the even temperament system in music still do not stop. The first of them protect the possibility of a free transition to different keys, and the second stand for the purity of the instrument's tuning. There are also othersmore exotic customization options. An example is the microtone guitar. But the vast majority of instruments in the world still have an equal temperament.