Costa: "Diesis Progression" in 22-edo: 1/4-tone Horn Quartet скачать в хорошем качестве

Costa: "Diesis Progression" in 22-edo: 1/4-tone Horn Quartet

Listen to this music in high-quality audio in BandCamp at https://microtonalharmonyproject.band... as part of the album "Cortege" of 22edo music: https://microtonalharmonyproject.band... The step size of 22-edo (equal division of the octave) is 54,5 cents, very slightly larger than a "usual" quarter-tone; however, 22 has much better and consistent approximations of the overtone series than 24-edo. The edo-step can be called a "Diesis", which originally refers to the difference between an octave and 3 stacked just major thirds (from C: C and B#) which has a size of 41 cents, close to the 54 cents of 22-edo and still closer to the 39 cents of 31 edo. An even smaller sized interval would be the "comma", of which there are several kinds: the syntonic comma is the difference between 4 stacked fifths and a pure major third - the ratio 80:81 with an interval of 21.5 cents. What 22 does is that is fuses both the diesis and the comma in the same interval: it´s edo-step. So (from C) 80:81 (the comma) is Ev - E and 225:256 (diesis) is B - C. This piece offers the 4-part harmonization of an ascending and then descending line in the range of an octave +1 note; the relation between each pair is unique, encompassing all combinations of the harmonics, 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 taken in pairs; this is what the circle graph to the right shows (which I used for the no so simple task). The numbers above each half-bar show the partial of the upper-voice (diesis line), the number in between indicate what ratio is being approximated by the diesis, and the number at the voices indicate common notes between adjacent harmonies and what partials they correspond to. The third staff shows the fundamental pitch of the harmony. Another point the might be interesting to note: I've worked a bit with filtering the notes in each voice according to the corresponding "height" of the partial. I noticed as a horn player that for instance overtone 11 in a mid-register (baritone) will sound dissonant, no matter how in tune; but using a mute, that is, filtering the lower partials, particularly the fundamental, suddenly makes the interval "harmonic", consonant or accoustically meaningful to the ear/brain. My explanation is that for us to understand the harmonic function of a pitch, its fundamental should be in the hearing range (above 25 hz) OR much/most of the sound energy should be in a register corresponding to that range in the harmonic series; that's why a chord low in the piano register is still understandable, the pitches have in their timbre very little of a sinusoidal component and a lot of higher overtones. The effect of those adjustments in spectrum/colour are huge. For a similar harmonic study - but in 31-edo, go to    • Fabio Costa: "Enharmonic Study"  (31-edo) ...   MIDI recording made using commercial samples, Reaper (DAW), DaVinciResolve (Video), GIMP (Graph).