which contradict with an accoustic precision the entire foundation of orchestral intonation. To begin with, there is no tonality, in which all five pitches of the open strings could be used impunibly: at a first superficial glance it would seem that there are three such tonalities, – F major, C major, G major,
Plus the three relative descending melodic minor keys. Nevertheless, with a few rather simple experiments it is easy to prove the contrary, which is exactly as follows:

• I. In C major it is not possible to use the open strings E2—A2 of the double-bass, the A3 of the cello, the A4 of the viola and the A4—E5 of the violin.
• II. In G major – the E2 of the double-bass and the E5 of the violin.
• III. The tonic of F major is not available on open strings, which is why on the given tonality it is not possible to establish one unified rule. Everything is determined by those tonalities from which we have come to this F major. If the modulation tok place from C major, then only the pitches C and G of the open strings would be appropriate, while all the others would be excessively high, whereas if it would be a sudden modulation from A major (assuming the tonic a, lying on the open string), then the opposite would be the case – all the other pitches of the open strings would be appropriate except for C and G, which would turn out to be excessively low.
• IV. Similar double aplications are feasible on the relative minor tonalities of D minor, A minor and E-minor: if they happen to be the source tonalities, then undoubtedly it is particularly their tonics are given on open strings, and the limitations of their usage consist merely of the following: in D minor, the undoubtedly low pitch would be the descending C, in A minor it would be C and the descending G, whereas in E minor it would be C, G and the descending D; if we approach these keys from their relative major keys, then the forementioned pitches would be in tune, while all the other open string pitches would be excessively high. Any move upwards of downwards from the pitches of the open strings in all the mentioned cases would be at an interval of a comma (80:81); this practically always demands the replacement of the open string with the corresponding pitches, taken by ear on the adjacent lower string.

The following experiments undoubtedly prove the validity of my position. They were written for the particular purpose of being tried out on a violin, in this case the durations of the notes are of little consequence: the important thing is to adhere to the unbreakable chain of dyads. The pitches, placed below into the bass-clef, present themselves as the actually heard combinational tone, complementing the major sixth, for the purpose of obtaining a full triad: they are indicated for the purpose of exact tuning with the ear of this interval – al the others are in essence octaves and unisons.

The whole article read in Musician I 2010.

• Arseny Avraamov
  
  
  
  “Muzyka” weekly newsletter, September 5, 1915, Moscow, Vol. 5, N.222, pp.315-318