Just why the intervals of the fifth and fourth should have been chosen for this parallel music, which is excruciating to our modern ears, is not positively known. The simple obvious answer to the riddle is that Hucbald and his contemporaries based their theories on the theories of the Greeks, who regarded the fifth and fourth as consonances nearest the perfect consonance of the octave and unison. But in that case we have to ask ourselves why Hucbald and his followers regarded the diaphony of the fourth as pleasanter than that of the fifth which they none the less acknowledged was more nearly perfect. Dr. Hugo Riemann has suggested a solution to this difficulty which is in substance that organum was an attempt to assimilate elements of an ancient art of singing practised by the Welsh and other Celtic singers. The Welsh scale is a _pentatonic_ scale, that is, a scale of five steps in which half steps are skipped. In terms of the keyboard, it can be represented by a scale starting upon E-flat and proceeding to the E-flat above or below only by way of the black keys between or by a similar progression between any other two black keys an octave apart. In such a scale parallel fourths are impossible, as indeed they are in the Greek scales of eight notes upon which the church music was based; but whereas the progression of the fourths in the Greek scales is broken by the imperfect and very unpleasant interval of the tritone, in the pentatonic scale it is interrupted by the pleasing major third. Such a progression of fourths and thirds seems to spring almost naturally from the pentatonic scales and was very likely much practised by the ancient Welsh singers.[65] A comparison of two examples will make the difference obvious. [Illustration: Music] The presence in the octatonic scale of the disagreeable tritone, marked with a star in the example, forced even Hucbald and Odo to make some provision for avoiding it. This consisted in limiting the movement of the 'organizing’ voice. It was not allowed to descend below a certain point in the scale. In those cases, therefore, in which the _cantus firmus_ began in such a way that the organizing voice could not accompany it at the start without sinking below its prescribed limit the organizing voice must start with the same note as the _cantus firmus_ and hold that note until the _cantus firmus_ had risen so that it was possible for the organizing voice to follow it at the interval of the fourth. In the same way the parts were forced to close at the unison if the movement of the _cantus firmus_ did not permit the organizing voice to follow it at the interval of a fourth without going below its limit. The following example will make this clear: [Illustration: Music]