2023-03-19

Claudi Meneghin: Four Pieces in 15-equal Division of the Octave

We present four pieces by Claudi Meneghin, in 15-equal division of the octave, notated as usual in the following way:

  • B~C = 0 ¢
  • D = 240 ¢
  • E~F = 480 ¢
  • G = 720 ¢
  • A = 960 ¢
  • #/b = +/- 80 ¢

1) Cuckoo-Rag fugue


Cuckoo-Rag fugue is a one-minute fugue recorder, cor anglais, clarinet, bassoon, using a rag-like subject and the cuckoo tune as a countersubject. Tuning is 15edo (15 equal division of the octave), used in the following two ways: in the first part of the fugue, the entries of the fugue are each one at a fifth from the preceding one, whereas in the second part at a fourth.


2) Micro-Fugue on "Scotland the Brave"


A five-part microfugue  (in 15-equal division of the octave) on a theme derived from "Scotland the Brave", for Soprano & Alto Sax, Bassoon, Bass Clarinet, Suckbut, in the tonality of C. Each entry is a fourth higher (+480 ¢ in 15edo) than the preceding one, thus the fugue gets back to the initial tonality C after five entries (5*480 ¢ = 2400 ¢).


3) Tocada, for 2 Organs


A piece for 2 organs, in three movements (Preludi i Fugat, Chaconne “La Gamme”, Fugueta). 

    1. Preludi & Fugat
      The Preludi (Catalan for "Prelude") is made up by 5 sections, each at +720 cents from the preceding one. Each one, internally, sticks to the following modulation structure : 0, +400, +800, 0, +720;
      The Fugat (Catalan for "Fugato") is made up by 5 sections, each at +240 cents from the preceding one and ends on C (pedal).
    2. Chaconne “La Gamme” (French for "The Scale")
      This chromatic piece is made up by 15 sections, each at +80 cents from the preceding one (starts from F and ends to F), plus a Coda, made up by the following chord progression: (D,C,F,A) - (E,B,E,G#) ~ (240,0,480,880) - (400,1120,400,800)
    3. Fugueta (Catalan for "Little fugue") This fast movement is made up by five main sections obeying the following modulation rules:
      1st: C +720 +720 +720 +720 +720
      2nd: C +480 +480 +480 +480 +480
      3rd: C +240 +240 +240 +240 +240  (modified mirrored theme)
      4th: C +480 +240 +480 +240 +480 C
      5th: = 1st, with added bass in the beginning exposition
      Coda
4) 3-in-1 Canon for 3 Violins


A 3-in-1 Canon for 3 Violins (without bass), made up by sections each one modulating towards a tone (+240 ¢).

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2023-03-12

 

The Hexadecimal Representation of Pi by Sounds, Implemented  in 16-edo & DTMF


a) 128 hexadecimal digits of Pi, played in 16-equal division of the octave.

16edo is notated as Mavila, with G = 675 ¢, implying # = -75 ¢ and b = + 75 ¢, with opposite effects with respect to the customary accidentals.



b) 128 hexadecimal digits of Pi, played in DTMF.

This is implemented as in the following 4x4 kepypad:


where * represents F and # represents E.

Each hex digit gives rise to two simultaneous sounds, according to the above table.

DTMF is well approximated by the 14-equal division of a sharp octave, as large as 1213.44 ¢, hence it's notated here as 14-equal division of the octave. This implies that G = 693.39 ¢, and there are two chains of 7 fifths, separated by a # = 86.67 ¢.



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