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The natural-harmonic tuning  or  fifth-third tuning

Already several years ago, upon the release of violinist Renate Eggebrecht’s recording of Max Reger’s Sonatas for Violin solo, op. 91, this artist pointed out – in an interview for the magazine Klassik heute in response to the journalist’s question of how she deals with intonation in this music – that in Reger’s entirely polyphonic sonatas it is not possible to perform the pieces in Pythagorean tuning, i.e., with narrow semitones and raised leading tones, etc., nor, even more improbable, in tempered tuning. (Pablo Casals’ idea of an “expressive intonation” is, however, still more unsuitable for polyphony!)

This led to misunderstandings among many music journalists, certainly because many are of the superficial, dogmatic opinion that violinists must endeavor toward the supposedly ideal “tempered” tuning, since otherwise the intonation inevitably has to be “false”. The argument that one had played violin as a youth and therefore knows what one is talking about, etc., is naturally not sufficient - 

For Bach’s solo sonatas, just as for Reger’s solo works, we need an instrument tuned in pure fifths (and precisely be-cause of this it cannot be “tempered”), as well as pure thirds and sevenths. All other expectations are unrealistic. (The simple rule of thumb, # = high, b = low, also leads to a dead end in polyphony.)

Only with exactly in-tune intervals does a coincidence and self-reinforcement of the overtones result. Only in this way does the whole, multi-voice chord have a pure resonance that lingers for a long time in the room.

The violinist Emil Telmányi, who recorded the Bach Partitas in the 1950s, wrote:

Free resonance of overtones depends on true pitch, a well-tuned instrument and ‘absolutely tuned’ and not ‘tempered’ playing. Out of tune chords not only sound false; they have a bad resonance, because of the interference of disharmonizing sound waves and consequently the absence of overtones”. (Musical Times 1/1955)

Intonation is too often distorted into an “ideological topic”: here the “progressive apostles of tempered tuning”, there the “reactionary apostles of purity”. In this way, one can turn, without much reflection, to the day-to-day politics (of music).
A string player who has problems with certain pieces, and, in particular, who can only with great difficulty cope with highly complex, tonal structures, such as Reger’s music, for example, is not helped by this!
Unfortunately, the ignorance in this area is very great and extends to the “scientific” contention that man cannot even hear pure fifths. (Musik Konzepte)
An article on the true art of piano tuning, which appeared recently in a piano journal, was also not able to clear up the confusion.
Violinist Renate Eggebrecht is very thankful for the comprehensive treatment of this subject by Jutta Stüber in the book Die Intonation des Geigers (“The violinist’s into-nation”). Here, historical, theoretical and practical questions are dealt with intelligibly and in great detail:

Not only beginners have problems with intonation. Every violinist, even the best, has them. Whoever doesn’t believe this should get a hold of the famous recordings of Bach’s solo Sonatas and Partitas and listen to the E-Major Partita, for example. In his account of the Grosse Geiger unserer Zeit (“Great violinists of our time”), Joachim Hartnack says that there is hardly a violinist who plays this work absolutely in tune – not even Szeryng or Menuhin.

Whoever wants a more “scientific” point of view should take a look at Martin Vogel’s book Die Lehre von den Tonbeziehun-gen (“The doctrine of the relationship of tones”):
In questions of intonation, most musicians rely on their ears – quite rightly so: an ear oriented on polyphony “hears everything”, hears even deviations of a hundredth of a whole tone. In difficult passages, however, it would be good if the practicing musician – the string player, wind player, singer – were also well versed in theory. Our polyphony requires pure thirds; pure thirds, however, lead to a differentiation between large and small whole tones, between diatonic and chromatic semitones. Whoever is not well versed in the “relationship of tones” will frequently go astray. The ear “hears everything”.

This leads us into the realm of enharmonicism in which many great minds romp about, such as Max Reger (“Oh, there are many, many North and South Poles in the harmony”) , or the composer and music theorist Johanna Kinkel (1810-1858) – see her article on Chopin’s quarter tones.

Jutta Stüber,
Die Intonation des Geigers, vol. 52, 371 pages.
Martin Vogel,
Die Lehre von den Tonbeziehungen, vol. 16, 480 pages. Orpheus-Verlag GmbH
Eduard-Otto-Str. 41
D-53129 Bonn 

Johanna Kinkel,
“Chopin als Komponist” [“Chopin as composer”],
in Dissonanz 8/1986

An excerpt from this article:

The spirit of a new music has come over Chopin; it has revealed itself to him in melodies that flow around him like dreams of the future. The extant intervals are almost too crude and too broad to reproduce his ethereal intervals; for this reason they sneak reluctantly through the chromatic relationships of the scales and search for the even more refined relationships that are offered by enharmonic change.

A pupil of Chopin’s, a very good player, had flawlessly performed a ‘Ballade’, when a lady whispered into my ear: “The piece may indeed be very pretty, but we all think that the gentleman plays wrong notes rather often. Why don’t you play something for us!” One had quite a bit of confidence in my correctness, yet after I had played but a few measures of Chopin, the lady cried out full of dismay: “But, my God, what is that? – You, too, are playing false today!

One must really have strength of character in order to emancipate oneself so far from old music teachers and connoisseurs that one can devoutly work up one’s pieces in spite of all ridicule and disdain. Whoever does not live like a hermit in his practice room will hardly be able to carry through with this without fighting the musical generation that is just now in the process of drying up. We may not deny that we already touching a period of time that recognizes harmonies in modulations which are so finely split that an unprepared or dulled ear hears it as false...
Johanna Kinkel

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... "Was ist das für ein Grün?" - "Was ist das für ein Rot und Blau, das Sie verwendet haben?" waren an mich die Fragen der Maler. "Es sind die gleichen Farben, die jeder Maler auf seiner Palette hat", war meine Antwort.

Eine Farbe bestimmt durch ihre Nähe das Ausstrahlen der Nachbarfarbe, genau so wie in der Musik der Ton im Akkord von seinem Nachbarton seine Klangwirkung erhält. ...

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