who asked the first question? - International Research Center For ...

Gerhard Kubik, if you want to count the vertical distance between anytwo simultaneously sounding notes in sub-Saharan polyphonic music,you should “skip one step” on a scale. So, say, if we are in “C major”scale (white keys starting from “C” to the next “C”), and if we havesomeone singing the pitch “C”, the other (top) voice would be singingnote “E” on top of “C” (as we need to skip “D” which is next to “C” –you remember, we need to skip the next note), or, if we want to sing alower harmony, we need to sing “A” below the same “C” (again, weneed to miss the next note “B” below the “C”). In this kind of scale wewill always have the same vertical distance. In music this particulardistance (between “C” and “E”, or between “C” and “A”) is called“third”. To be more precise, the third can be “major” or “minor”, but Ithink we can skip this technical detail from our current discussion (moresaw in traditional music the third if often between the major and minorthirds and is sometimes referred as “neutral” third). As a matter of fact,the existing system of labeling the intervals as “second”, “third”, etc. ismathematically controversial. The distance between “A” and “C” inactually “2”, not “3”, so it would be more correct to call “A-C” distanceas “second” not the “third”. The same way the distance between thesame notes is “0”, not “1”. I sometimes jokingly tell my students that“musicians are the worst mathematicians, because in music 3+3 equals5” (try to put two “thirds” together on a piano and you will get the“fifth”). The same way according to the “musical logic” 2+2=3 (becausetwo seconds together make up a third). All mathematical equation areincorrect using the existing incorrect numeral names of the musicalintervals. Russian composer Sergey Taneev, who actually was the firstto record and transcribe the traditional polyphonic songs of NorthCaucasians in the 19 th century, and who is best known as the teacher ofRussian composer Tchaikovsky, suggested to use another,mathematically correct name-numbers. For Taneev the same notedistance (unison) is “0”, the distance between “A” and “B” is“prime”(1), the distance between “A” and “C” is “second”(2) etc. Ofcourse, this brings us to the mathematically more coherent system andsuddenly all the equations become correct (like 2+2=4), but,unfortunately, the force of tradition prevailed (once again!) against thesound argument, and we still call “A-C” interval as a “third”. Of course,Taneev was by no means the first to pay attention to this odd arithmeticof musical intervals. This has been a topic for discussions from Guidod’Arezzo and Boetius (11 th and 13 th centuries).‣ One of the difficulties of this system is that the scale that we just usedfor the counting of the vertical distance – C-major scale (the set of sevenwhite keys from “C” to the next “C”) – is only one (and not the mostpopular) possible scales, used in sub-Saharan Africa. Scales in Africa(as in some other regions of the world) often have less that seven notes.Imagine, for example, to have the same C-major scale, but instead of thewhole set of the seven white keys (C, D, E, F, G, A, B) omit the “B” and34