Tendency (music)

tendency one calls the kind in the music, how with a music instrument the tones of the clay/tone system are one on the other fine-co-ordinated. Another name for it (in particular with key instruments) is temperature.

Each clay/tone has another function, z in each scale. B. can the E the basic clay/tone of the e Dur scale, the second clay/tone of the D major or - Moll scale or the Quinte of the A major scale its. For everyone of the possible functions result different ideal frequency - conditions of the tones to each other, which must be brought however among themselves in agreement, over upto be able to play the instrument in several desired kinds of clay/tone. This means to be received compromises: The more purely one a certain kind of clay/tone is correct, the impure is other kinds of clay/tone.

This problem becomes particularly significant with the Mehrstimmigkeit, if different tones are to together-sound, in addition on the same instrument.

Table of contents

overview

it gives oneMultiplicity of systems to join in the tones of the clay/tone system. The most important tendency systems are:

the tendencies to make only statements about frequency conditions of the individual tones to each other. It does not become a statement about the absolute pitchand/or. the frequency made. The absolute frequencies are specified by the indication of the pitch of the initial clay/tone or by the clay/tone A'. 1939 were specified the frequency of the standard tuning tone A' with 440 cycles per second. All other tones of a tendency become than interval with help of the unit Cent or by indication of the frequency relationship determines.

The choice of the tendency depends on which music is to be played. Those today predominantly used equalequivalent tendency is suitable for music after 1800. Earlier music or non-European music (world music) lives very strongly of the Intonationsreinheit or different Tonartcharaktern. These demands cannot be served by the equallevel tendency. In the context of historical performance practice age music therefore older tendency systems are investigated again strengthened, in order adequate showed to make possible.

history

antique one

the first theoretical descriptiona tendency system comes from Pythagoras from Samos. Pythagoras was a philosopher, a mathematician and a religion founder of the antique ones emigrated after Unteritalien. It was the view, the entire cosmos (in particular the constellation of the heavenly bodies) obeys simple numerical ratios and the music is image of the cosmos.

Itexamined the intervals between string parts with integral Längenverhältnissen on the Monochord (z. B. a string, if it is divided in half, sounds higher a Oktave than in its full length; the associated numerical ratio is thus 1:2). It described the natural intervals so for the first time,from the overtone row admits are.

Pythagoras introduced a siebentönige scale on the basis of the pure Quinte (with the numerical ratio 2:3 simplest after the Oktave). The tones are determined thereby outgoing from an initial clay/tone by Quintschritte and transponiert into a common Oktave. The resultis the Pythagorei tendency.

Didymos „the nature third ( 4 led about 100 years after Pythagoras: and the pure tendency originated in to 5) into the scale.

the Middle Ages

the clay/tone system of the Pythagoras were transferred by the Romans and in medieval Europe. Monochorde, bell playsand organs were pythagoreisch tuned and in Gregorian making music practice related. The early Mehrstimmigkeit preferred the intervals actually pure in the pythagoreischen tendency (the complementary intervals of Quinte and Quarte as well as Prime and Oktave).

Renaissance

in the Renaissance gave it above all to twofor the clay/tone system important developments:

  • The increasing Chromatik in the Vokalpolyphonie extended the clay/tone supply finally to 12 tones.
  • The dissonance feeling changed. The third, which was felt in the Middle Ages still as dissonance, will to „the secret main interval “, comes thus into mode and becomes so ever more important.

New orientation at the third and the need of a chromatic scale led to problems with the quintbasierten pythagoreischen or also the pure tendency:

  • Twelve Quinten laminated one on the other do not result in closed Quintenzirkel. The 13. Clay/tone is higher around the pythagoreische comma than the output clay/tone.
  • FourQuinten laminated one on the other (z. B. C - G - D - A E) do not result in a pure large third. The fifth clay/tone is higher around the syntonische comma than a pure large third on the output clay/tone. Tondokument ? / License

one selected, the new sound ideal accordingly,the pure large third (with the numerical ratio 4:5 next-simpler after Quinte and Quarte) as new master interval and developed the so-called mitteltönige tendency. One introduced in order to be involved to the syntonischen comma from the way, easily, from those four one on the other laminated made smaller Quinten onepure large third form.

By the consequence of eleven centraltonus towards Quinten

it - B - G - D - A E - H - Fis - Cis - Gis one received the twelve

tones of our abendländischen clay/tone system to F - C -.

Tondokument ? / License

Thus one received eight large thirds as desired purely. (z. B. C - E by four mitteltönige Quinten C - G - D - A E); four thirds had to remain impure (z. B. H-this, is there this as it therefore not joined in and thisto four mitteltönige Quinten over H is, but to eight mitteltönige Quinten under H; see. above Quintfolge).

In addition, the solution of all problems was not the mitteltönige tendency .

  • From this system many intervals, which cannot be expressed by integral breaks, resulted what a contradiction to the pythagoreischenView of the music represented. The cause for it are in favor of the third purity the introduced centraltonus towards Quinten, for the one string length relationship of <math> 1: \ sqrt [4] {5}< /math> applies, which not when rational number is representable.
  • Twelve mitteltönige Quinten laminated one on the other result in a clay/tone, around the small Diësis in such a way specified more deeplyis as the output clay/tone (see. Problem of the pythagoreischen tendency).
  • The Quinte As - it and/or. Gis - this is too large around the small Diesis, since as „alias Gis “not when mitteltönige Quinte is tuned under it, but eleven mitteltönige Quinten over itlies (see. above Quintfolge). This Wolfsquinte in such a way specified sounds very impure. In centraltonus towards tendency kinds of clay/tone which contain this Quinte therefore, sound (z. B. E flat major or Cis Dur), extremely dissonance and is everywhere useful for the representation of certain Affekte.

Tondokument ? / License

sat down nevertheless the mitteltönigeTendency through. Modulatori development, how it became later usual, was a little common in the Renaissance. One got along therefore first with the well sounding range of kind of clay/tone. In order to make also further kinds of clay/tone playable in centraltonus towards tendency, key instruments with z became. B. 31 tones in thatOktave built, which could not intersperse itself however.


baroque

in the course 17. Century this restriction was felt increasingly on central kinds of clay/tone as disturbing. In order to become freer in the choice of the kinds of clay/tone, one began, to develop tendency systems in those all kinds of clay/toneare playable, if also not all in same quality. But reductions in the purity of the thirds had to be accepted. These tendencies were called property temperatures or tendencies well-being-kept at a moderate temperature, contrary to now as „badly “felt centraltonus towards tendency. Examples for this are the tendencies of Andreas Werckmeister, in particular the Werckmeister in such a way specified iii-temperature (Tondokument ? / License) or the tendencies of the Orgelbauers Gottfried silver man.


However there was no temperature, which interspersed itself universally like before times the mitteltönige tendency (with the new temperature beginnings by the way simply did not disappear). By the exampleOne can see Werckmeisters that first also not absolutely one aimed at establishing a uniform tendency. It describes Musicali temperature “different temperatures, which can more or less be suitable depending upon need in its most important work „.

In principle one (with Werckmeister and others) knows two beginningsdifferentiate:

  • Some systems strove to let the kinds of clay/tone with few signs sound as clear as possible in addition, those with many signs, although with more clouded sound of making playable. (Example: The Werckmeister ii-temperature.)
  • other systems tried to make all kinds of clay/tone as well as possible playable. (Example: ThoseWerckmeister iii-temperature). This beginning led at the end of the development to the today common level temperature. With this beginning one must accept however relatively matte sound of all kinds of clay/tone to one - contrary to the central kinds of clay/tone in the beginning described above -.

One already

looked for equalequivalent temperature in the Renaissance for methods to tune the sounds level. Since it is not possible to join in on federation instruments each clay/tone individually it comes to problems. (Because z. B. in equal, large, centraltonus towards tendency the not all thirds are, would have upthe A-string the fourth federation the string for the large third Cis on 4/5 of the length shorten, on the H-string is not this „alias “it however not as large third to be joined in. The string would have here in centraltonus towards tendency on 25/32the length to be shortened.)

the possibilities of the Wurzelrechnung to this time there, could one was still limited the level half-tone with the relationship <math> 1: \ sqrt [12] {2}< /math> do not compute yet. Nevertheless one could build a equivalent Griffbrett, there one geometrical methods for the sew-wise construction of simple root conditions to the handhad. The venezianische musician and music theoretician Gioseffo Zarlino 1558 already describe such a method.

The soundist Vincenzo Galilei, father of the Galileo Galilei, did not give up to simple integral conditions nevertheless. It shortened the string per federation on 17/18 of the length. Inthe theory arrives it thereby with the twelfth half-tone with the Oktave, in practice is however quite useful not completely the result, since the clay/tone is increased by the thickness of the federation and by the finger pressure still another little. The string length can also after the construction of the Griffbretts by the repositioning of the bar to be still minimum corrected, so that the result becomes still better.

Mathematicians and music theoreticians tried in the following scarcely 200 years to determine with different methods more exact numerical values for the level temperature.In 19. Century finally generally became generally accepted the level temperature.

Today it gives to be correct again discussions over it, as for example organs should. Many historical compositions proceed from different sound characteristics of different kinds of clay/tone and chords, which are not reproducible on equivalent been correct instruments. This is in particular for historical performance practice of importance.

numerical values

the following table the Dur indicates - to scale of different tendencies in cent (rounded):

Name Prime large second large third Quarte Quinte large sixth large seventh Oktave
pure tendency 0 ,204 ,386 ,498 ,702 884 1088 1200
Pythagorei tendency 0 ,204 ,408 ,498 ,702 ,906 1110 1200
1/4-Komma-mitteltönige tendency 0 ,193 ,386 ,503 ,697 ,890 1083 1200
equalequivalent tendency 0 ,200 ,400 ,500 ,700 ,900 1100 1200

voices of instruments

as voices (English tuning) of Instruments designates one the attitude of the pitch. Depending upon instrument this becomes as whole (z. B. Wind instruments), in individual strings and layers (caper instruments, guitar), in each individual clay/tone (harp) or also within a clay/tone (piano, organ) been correct. In the last group several strings or whistles are to be tuned for being correct a clay/tone. If music instruments are wrong or badly been correct („are detuned “), sound it „diagonally “and inharmoniously.

Most instruments can be been correct within more certainly structurally given borders, but givesalso instruments, which are not only very aufwändig be correctable due to their building method or. For this above all instruments from the range Percussion and the Idiophone , in addition, bell plays count.

When being correct instruments one can differentiate three kinds:

  • the tendency of an instrument „in itself “(importantly with the palpation and stringed instruments)
  • the tuning of several instruments
  • the tendency of an instrument on absolute pitches

the manual process of being correct is different from instrument to instrument with one another. With wind instruments this takes place usually via change of the pipe length, with Streichern via the change of the string tension.With key instruments each individual clay/tone must be usually tuned. The tendency of an ensemble takes place usually after the most inflexible instrument. Those are usually the key instruments, in the orchestra the woodwind instruments (usually the oboe). If no reference instrument is available, knows a tuning fork, a Stimmpfeife, orelectronic being correct equipment as an assistance to be used.

By the frequency of the being correct procedure many experienced instrument valleyists developed a kind absolute hearing for their Stimmtöne (basic tones with Bläsern, empty strings with Streichern).

Electronic music instruments do not have to be tuned partly. With qualitatively inferior electrical organs is an accurateTendency even of disadvantage. Since with them tones from a only one high basic frequency are produced by frequency slicing, phase responses from simple completerational divisions of the frequency, which can lead to interference distortions, result. In order to prevent, easy tendency error is inserted. In all other respects the frequency relationship leaves itselfthe level tendency by a completerational frequency divider do not realize.

see also

partial clay/tone row, cent, interval, of piano tendency

tendencies

pure tendency | Pythagorei tendency | Aulos modes | Mitteltönige tendency | Silver man concern temperature | Well-being-kept at a moderate temperature tendency | Werckmeister tendency | Kirnberger tendency | Equalequivalent tendency

Web on the left of

tendencies in music history and - practice

mathematical views

lexical

software

  • Scala - Freeware - program for providing, analyzing and manipulating scales andTendencies (Linux, MacOS, Windows)
  • Mutabor - live-making music with micro tones (Windows)
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