Septimal Passamezzo Cadence in Just Intonation & Multiple Edo's

The classical passamezzo cadence, transformed into a septimal cadence, and tuned into just intonation and into the following equal division of the octave: 12, 15, 17, 19, 21, 22, 24, 26, 29, 31, 34, 36, 38, 41, 43, 46, 53, 55, 56.

Air for Recorder, Fortepiano, Cello, by Claudi Meneghin [Fokker Periodicity Block 20c&21c]

A short Air for recorder, fortepiano, cello, in Fokker 20c&21c periodicity block.

Scala File of the Tuning:

58.72

117.44

176.16

234.88

293.60

352.32

411.04

469.76

528.48

587.20

645.92

704.64

763.36

822.08

880.80

939.52

998.24

1056.96

1115.68

1174.40

1200.00

Claudi Meneghin - Chaconne et Fugue à 5 "Les Regrets" en 46edo

This is Claudi Meneghin's Chaconne et Fugue à 5 "Les Regrets" en 46edo, for Recorder, Cornett, Viola da Braccio, Bassoon, Gamba, Continuo, in C minor. 

Notation: 46edo with standard accidentals (sharp = +5/46, flat = -5/46), plus some symbols from Turkish Maqam, used in an inconsistent way:

• One-vertical-line sharp: +1/46;
• One-vertical-line-and-three-oblique-line sharp: +2/46;
• Two-stroke flat: -4/46;
• Two-vertical-line-and-three-oblique-line sharp: +6/46;
• Mirrored flat: -1/46.

Bach - Ricercar a 6, Tuned into Vicentino 1/4-Comma Adaptive Just Intonation [31edo]

We present Bach's Ricercar a 6, from the Musical Offering, tuned into Vicentino 1/4-Comma adaptive just intonation. This tuning is implemented here as 31-equal division of the octave, but fifths and minor thirds are raised by 5.18 cents, which equals 31-edo approximation of a quarter-comma (i.e. 1200*(log_2 (3/2) - 18/31)). In this setting, fifths are just, and major thirds are tuned at 387.1 cents (+0.79 cents from just). Minor thirds are tuned at 314.86 cents (-0.79 cents from just).

Bach - Ricercar a 6, Tuned into Vicentino 3rd-Comma Adaptive Just Intonation [19edo]

We present Bach's Ricercar a 6, from the Musical Offering, tuned into Vicentino 3rd-Comma adaptive just intonation. This tuning is implemented here as 19-equal division of the octave, but fifths and major thirds are raised by 7.22 cents, which equals 19-edo approximation of a third comma (i.e. 1200*(log_2 (3/2) - 11/19)). In this setting, fifths are just, and major thirds are tuned at 386.17 cents (-0.15 cents from just). Minor thirds are tuned at 315.79 cents (+0.15 cents from just).

Sound Production: (c) Claudi Meneghin, copyright claim SRu 1-345-269 August 01, 2018 at the Library of Congress.

Fugue on Elgar's Enigma Theme [Microtonal, 50 Adaptive Just Intonation]

A Fugue on Elgar's Enigma Theme, for Organ, in 200-equal division of the octave. In two sections, 200-edo is reduced to 50-edo, close to Zarlino's meantone (2/7-comma). In the other two sections, 200-edo is used as adaptive just intonation (à la Vicentino) in that 50-edo fifths, minor thirds, and harmonic sevenths are raised by 6 cents, whereas 16/9-sevenths are lowered by 12 cents.

 

Enharmonic Cadence: Gm Gbb7 Gm Ebb7 in 31edo

 

Enharmonic Cadence: Gm Gbb7 Gm Ebb7 in 31edo, close to quarter-comma meantone.