Tuning

The tuning systems seek to build a series of vibratory frequency relationships that give rise to the notes of a scale. These relationships are studied independently of the absolute pitch of any of the notes, and are described exclusively as intervals between them. The sections that follow refer to the absolute pitch standards, not to the tuning systems of the scale.

Tuning in music is the process of adjusting the pitch of a sound until it matches a reference musical note. Doing this with your voice is called "being in tune" and is one of the ear training skills.

Tuning standards in history

Various systems of musical tuning were used to determine the relative frequency of the notes of a musical scale, also throughout history various tuning standards have been used in an attempt to fix the absolute pitch of the scale. In 1955, the International Organization for Standardization set the frequency of the A at 440 Hz. But different tuning systems were used in the past.

16th century

In the mid-1500s Michael Praetorius had rejected several high tuning standards (above 480 Hz) because they caused the thinnest violin strings, which at the time were made from animal intestines or guts, to break. Until the 19th century there was no concerted effort to standardize musical tuning, and throughout Europe it varied greatly. Even within the same church, over time the tuning could vary due to the way in which the organs were tuned. Generally, the end of organ pipes was hammered in or out (taking a slightly conical shape) to slightly raise or lower the pitch. When the ends of the tubes ended up cracking and breaking, they were all trimmed, thus increasing (sharpening) the overall tuning of the entire organ.

17th century

The levels of tuning not only varied in different places or at different times, they could also vary in the same city. A 17th-century London cathedral organ could be tuned five semitones lower than a virginal (keyboard instrument) from the same city.

18th century

You can get some idea of tuning variations by examining old hairpin tuning forks, organ pipes, and other sources. For example, a small English reed tuning fork (or “chorale tuning fork”) from 1720 played the la (found five white keys to the right of middle c on the piano) at 380 Hz, while the organs played by Johann Sebastian Bach in Hamburg, Leipzig and Weimar were tuned to the la at 480 Hz, a difference of four semitones (four contiguous piano keys). In other words, the la produced by the English fingerboard sounded like a c# on the organs that Bach played at the same time.

The need to standardize the tuning levels (at least within the same city or the same country) arose when the combined performance of organ music with instrumental ensembles began to become popular. One way in which tuning began to be controlled was through the use of fork tuning forks, although they did not agree here either: a tuning fork associated with Georg Friedrich Händel, circa 1740, was tuned to an la 422.5 Hz, while one from 1780 was at 409 Hz (almost a semitone lower). Remember that the current la corresponds to the frequency of 440 Hz. Towards the end of the 1700s, the la was tuned within the range of 400 to 450 Hz.

19th century

Throughout the first half of the 19th century, there was a tendency to raise the pitch of the orchestra. This was probably due to orchestras competing with each other, trying to fill ever-larger concert halls with a brighter sound than their competitors. They were aided in their efforts by the improved durability of the violins' e string (the highest of the four strings). Animal gut strings couldn't take as much tension, but the newer steel strings could take more tension without breaking.

The increase in tuning pitch in this period has been reflected in the surviving fork tuning forks. A tuning fork from 1815 from the Semperoper - the Dresden opera house - gives a la 423.2 Hz, while one from eleven years later produced 435 Hz. A tuning fork is preserved in the La Scala theater from Milan that produces an la of 451 Hz.

Legalization of the 435 (1859)

The most intense opponents of the upward trend in tuning were the singers, who complained about the effort involved in following the tuning of the orchestras of the time. Probably due to these protests, the French government enacted a law on February 16, 1859 establishing the la above center c at 435 Hz. originated from a commission appointed by the Secretary of Public Works at the time to establish a uniform fingerboard, which presented its conclusions on February 1, 1859. The law dictated by the French state agreed to the adoption of a mandatory fingerboard pattern in musical establishments authorized by the State. The standard tuning fork emitted an la that vibrated at 870 Hz (so the "middle la" was at 435 Hz. This was the first attempt to standardize tuning to such scale, and became known as the “normal tuning fork.” It became quite a popular tuning standard even outside of France.

“Philosophical” tuning (430.54)

However, variations continued. The normal tuning fork of the la at 435 Hz resulted in a middle C tuned to 258.65 Hz. An alternative tuning, known as “philosophical tuning” or “scientific” made set the do to exactly 256 Hz, a number very close to the previous one that resulted from raising the integer 2 to the 8^to power (2⁸ Hz). This normalized do, resulting in la 430.54 Hz, gained some popularity due to its mathematical convenience, since the frequencies of all do /i> would be a power of 2. But this standard never received the same official recognition as la 435 Hz and was not widely used.

20th century (440)

In 1936 an international conference recommended that the la above middle c be tuned to 440 Hz. The standard was accepted by the International Organization for Standardization in 1955 (and it was reaffirmed by them in 1975) as ISO 16. The difference between this tuning and the "normal tuning fork" was due to confusion about what temperature the French standard should be measured at. The initial standard was la 439 Hz, but it was replaced by la 440 Hz after complaints about the difficulty of reproducing 439 Hz in the laboratory because 439 is a prime number.

Despite this confusion, 440 Hz is now used pretty much all over the world, at least in theory. In practice, orchestras tune to the la generated by the lead oboist, rather than to some electronic device (which would be more reliable), and the oboist himself does not use such a device to tune his instrument in the first place, so there may still be a slight difference in the exact tuning used. Solo instruments such as the piano (who the orchestra tunes to when they have to play together) are sometimes also not tuned to the la 440 Hz. very slight tendency to raise the standard tuning, although it has been almost imperceptible.

XXI century (442 and 444)

At least in the chamber and symphony orchestras formed by students of current European music conservatories, a 442 Hz la produced by an electronic device is taken as a reference. In theory studies, they continue to speak of 440 Hz for the la, but instrumental practice is considered alien to this subjection. Although the oboe continues to be the instrument in charge of giving the reference to the rest of the orchestra, the oboist tunes his instrument in situ with a digital tuner. This is true even among early music groups, who tend to tune to 415 Hz (one tempered semitone below 440 Hz) for Baroque music and to other tunings such as 465 Hz for certain music such as early Venetian Baroque, 392 Hz for Baroque. French (and in some cases English from Purcell's time), or 432-435 Hz for Classical and early Romantic repertoire.

The la (in hertz) throughout history

• 505,8 Hz: Renaissance (The Halberstadt organ), Germany
• 446 Hz: Renaissance (instruments of wood wind).
• 424.2 Hz: Michael Praetorius, Germany (1619)
• 415 Hz: wood wind instruments, tuned with the Parisian organs (sixteenth centuryXVII and XVIII).
• 465 Hz very used tuning in Germany in the centuryXVII
• 480 Hz: German organs playing Bach (principles of the 18th century).
• 422,5 Hz: Diapason associated with Georg Friedrich Händel (1740).
• 409 Hz: English fingerboard (1780).
• 400 Hz: fingerboard (ends of the 18th century).
• 450 Hz: fingerboard (ends of the 18th century).
• 423,2 Hz: an art galleries of Dresden (1815).
• 435 Hz: fingerboard (1826).
• 451 Hz: La Scala de Milan.
• 430.54 Hz: “philosophical” or “scientific” tuning.
• 452 Hz: “synphonic tone” (middle centuryXIX).
• 435 Hz: “French tone” state commission of French musicians and scientists (16 February 1859).
• 432 Hz: Giuseppe Verdi wrote his Réquiem using the official French standard tone fingerboard at 435 Hz. Later, he indicated that 432 Hz would be slightly better for orchestras (1874)
• 435 Hz: “international tone” or “normal dialogue”: Vienna Congress (International Tone Conference, 1887). The current bandoneon.
• 444 Hz: camera tuning (ends of the 19th century).
• 440 Hz: United Kingdom and United States: (principles of the centuryXX.).
• 440 Hz: International Conference (1939). See: 440.
• 440 Hz: International Standardization Organization (1955).
• 440 Hz: International Standardization Organization ISO 16 (1975).
• 442 Hz to 445 Hz (called brilliant tuning): the current bandoneon. (This is an instrument of tongue, not affinable by the interpreter.)
• 442 Hz: Instruments of the violin family.

Particular features of the instruments

In addition to the discrepancies in terms of the frequency of the la, even when a tuning fork has been set in a chamber group or in an orchestra, each instrumental family presents peculiarities in terms of the mode of production of sounds, which can cause differences in the frequency of the same corresponding notes.

• Fixed sound instruments that are affinable in a relatively simple way, with a keyboard or without it, such as the piano, are usually tuned by the tempered system.
  

  Circle of fifths corresponding to the Vallotti temperament of 1/6 comma, according to Tartini. It is a circular irregular temperament (without fifth wolf)
• The key, on the other hand, is usually refined by a historic temper like Valotti, Kirnberger III or Werckmeister III.
• Instruments such as the tube organ, which have fixed sounds, but do not conform frequently or easily, if they are old, they may have a mesotronic tuning, Valotti or even a pitagric. Currently, the organs are refined according to the style of the organ. The organs placed in places where it is usually played with other instruments, such as the auditoriums, are refined in the same temperament.
• The guitar and other string instruments in the mast, tune their strings by fourth or fifth just in the case of the ropes in the air, and by semi-tempered the placement of the frets. In popular music, if an electronic tuner is used, this will follow the tempered system for string tuning.
• The string instruments rubbed without frets in the mast, such as violin or violet, also fineen the air ropes by just fifths, but enjoy free will in terms of the height of the sounds of the pissed strings, although in practice the performers apply a fixed technique for the production of the notes. The slogan in this case is to make large tones and small diatonic semitones, as in the Pythagoras system, and instead, make the third small harmonics as in the fair system.
• Wind-metal instruments with keys, valves or pistons refine the tempered system in terms of these mechanisms, and according to the harmonic series in terms of the sounds obtained as harmonics of a base note corresponding to a given position of them. The harmonic series also strictly follows the instruments without any mechanism that alters the actual length of the tube, such as the natural trumpets or trumpets. The harmonic series presents a wide variety of intervals between its notes: fair fifths and fourths, large and small tones, fair thirds, various types of semitones and even “prohibited” notes such as the multiples of 7, 11 and 13.
• Wind-madera instruments have their keys or holes arranged according to the tempered system, but some notes can be made as harmonic of others, which results in just intervals that are somewhat different.
• Vocal music has the freedom of tuning; the above mentioned applies for rugged string instruments: a tendency to pythagorean scales to refine melodic passages. However, in order to improve the sound of the chords, it can be tried to tune in for as far as possible fair intervals, especially the third ones, which means making them considerably smaller. Although this practice is rare because of its difficulty and is reserved for highly experienced choirs, cases of regular vocal ensembles such as The Sixteen, Stile Antico or Ensemble Clément Janequin, among others, are known.

Thus, in these ensembles one can reach an “agreement” in the case where any detuning is going to be perceived clearly (as in the string quartet or in a reduced vocal ensemble) or one trusts in tolerance of the human ear regarding detuning, especially in large ensembles such as the orchestra or choral masses, where statistics play a not insignificant role in the final result.

To appreciate the detuning produced when tuning the open strings by perfect fifths or by the tempered system (with an electronic tuner), we can see that in a cello the difference is less than 6 cents for the c string when the a string is at 220 Hz (65.406 Hz vs. 65.185 Hz). This produces 0.22 Hz beats that are one beat every 4.5 seconds. This is the result of accumulating three times the difference between a fifth tempered and a perfect fifth, when the fourth string is tuned from the first.

In the case of the violin, the la string is the second, tuned to 440 Hz, and the cumulative difference up to the g string (the fourth string) corresponds only to two fifths. In this case, the difference is less than 4 cents, with a beat of 0.44 Hz (195.99 Hz vs. 195.55 Hz), which produces a beat every 2.26 seconds. Although the detuning interval is smaller than in the case of the cello, the beats are faster because the notes are higher.