Just Intonation: And the Combination of Harmonic Diatonic by A.D. Fokker

By A.D. Fokker

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Additional info for Just Intonation: And the Combination of Harmonic Diatonic Melodic Groups

Example text

This illustrates the modulation so often achieved by means of an enharmonic change in the diminished seventh chord. ,.... r" 15. Inversion, liaison by b and d L (te : mey = 6: 7). The centres here are e and a L (me: tey = 16: 21). Y: Iq: .... :aq: i' r- I d L : e :1# : g # : b or mey : me : way : süh : te d L : 1L: g L : aL: b mey: sey: ley: tey: te Pairs of leading notes are e and 1L. g # and aL (me : sey = süh : tey = 20: 21). Again 1Land 1#, gL and g# (sey : way = ley : süh = 14: 15). 16. Inversion, liaison by d L and 1# (mey : way = 7 : 9).

Y . t . ~:": I ;t; I pr COMBINATIONS OF THREE OR MORE MELODIC CENTRES 47 In the first case the centre j (jak) has the function of atonie. The other centres can in their function be compared to dominant and subdominant. Companion scales starting on the fifth and on the seventh have been added in the examples. Ninth harmonics and subharmonics have not been used, though there is no reason to avoid them. Finally the centres can be taken at distances a supersecond apart. It will be impossible to avoid the scales sometimes proceeding parallel to the bass (or the treble) with equal steps.

Qrdcts .. -=.. 1~rl I i - i-son. i-son. ·te e-le---i-5On. i__ . i-50n. r clfttt\(lr rI Ky-ri •• e e-•• le-.. i-an. in the functions of : lak ley nze--te mey I I way dok--sok It is important, in this mode, to realize that by the c1early different intonation of I and I L the domination of either the centre a or the centre d mates itself distinctly feU. 2. Examples in lour parts. Mr JAN VAN DIJK, teacher at the Toonkunst Conservatorium at Rotterdam, kindly composed a number of exercises in four parts exemplifying the various combinations of two melodie eentres and their subscales reviewed in Chapter 11.

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