«Blue Golden Fugue» is a blues-flavoured fugue for Baroque Trumpet, Oboe, Clarinet, Bassoon. Tuning is a Golden 13-tone scale constructed in the following way: the Golden Ratio ~ 833.09 cents is iterated 13 times, landing to 10830.174 cents; this means 9 octaves plus 30.174 cents. This amount is uniformly distributed along the 9 octaves, so that we have a tempered 1203.353 ¢ octave.
This system coincides with 92.5656 cET.

The 2-5-1 cadence, transformed into the Orwell tuning, defined by the just perfect twelfth (3/1) being divided into 7 equal steps. One of these steps (as large as 271,71 ¢) represents 7/6; three represent 8/5. Alternately, one third of the «fifth harmonic» 5/1 also makes a good orwell generator, at ~ 12/7 or 928.77 ¢ = 1200 - 271,23 ¢.
Orwell is so named because 19 steps of 84edo, i.e. 19\84, is a possible generator; however, here Orwell has been implemented as 22edo generated by 5\22 = 272.727 cents.
The 2-5-1 cadence has been transformed into the Orwell tuning by mapping each fifth (meant as a generator) into 5\22 = 272.727 cents, then rearranging the resulting notes in 22edo; 22-edo has been notated by using the customary linear notation.

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).

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).

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)

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¢.