by Robert Asmussen, PhD
This chorale, "Meine Seele erhebet den Herr", was chosen both for its brevity and for its absence of tonal contradiction. Although this chorale fits nicely within the constraints of 5-limit just intonation, it nevertheless contains some dissonance which would be noticed in other tuning systems, notably equal temperament.
The fraction representing the frequency for each note, given as p5/p6 in each line of the Csound score, is multiplied by 82.407, which is an octave equivalent of E2. For instance, in the first event of the Csound score is the following line:
i1 0 2 0 6 1 ; (B4, Rule: 2.c)
For this event, parameter fields are defined as follows:
p1 (instrument number) is 1
p2 (start time) is 0
p3
(duration) is 2
p4 (unused) is 0
p5 (frequency numerator) is 6
p6
(frequency denominator) is 1
The frequency for this event is therefore 6/1 * 82.407, which is 494.442 Hz.
Both traditionally notated and Csound versions are given.
sr = 44100
kr = 441
ksmps = 100
nchnls = 1
instr 1
a1 pluck 9000, (p5/p6)*82.407, (p5/p6)*82.407, 0, 1, 0, 0
out a1
endin
instr 2
a1 pluck 9000, (p5/p6)*82.407, (p5/p6)*82.407, 0, 1, 0, 0
out a1
endin
instr 3
a1 pluck 9000, (p5/p6)*82.407, (p5/p6)*82.407, 0, 1, 0, 0
out a1
endin
instr 4
a1 pluck 9000, (p5/p6)*82.407, (p5/p6)*82.407, 0, 1, 0, 0
out a1
endin
; Chorale File Number: 032400b_.sco
; Riemenschneider #130
; "Meine Seele erhebet den Herr"
; Key: E Minor
; 1/1 = E2 (E2 = 82.407 cps)
t 0 60 ; tempo 60 beats per minute
; Measure 1 Beat 1 Chord Type: i
i1 0 2 0 6 1 ; (B4, Rule: 2.c)
i2 0 2 0 4 1 ; (E4, Rule: 2.a)
i3 0 2 0 12 5 ; (G3, Rule: 2.b)
i4 0 2 0 2 1 ; (E3, Rule: 2.a)
; Measure 1 Beat 3 Chord Type: V6/III
i1 2 2 0 36 5 ; (D5, Rule: 15.a)
i2 2 2 0 18 5 ; (D4, Rule: 15.a)
i3 2 2 0 27 10 ; (A3, Rule: 15.c)
i4 2 2 0 9 4 ; (F#3, Rule: 15.b)
; Measure 2 Beat 1 Chord Type: III
i1 4 1 0 6 1 ; (B4, Rule: 8.b)
i2 4 1 0 18 5 ; (D4, Rule: 8.c)
i3 4 1 0 3 1 ; (B3, Rule: 8.b)
i4 4 1 0 12 5 ; (G3, Rule: 8.a)
; Measure 2 Beat 2 Chord Type: V4/3
i1 5 1 0 6 1 ; (B4, Rule: 16.a)
i2 5 1 0 15 4 ; (D#4, Rule: 16.b)
i3 5 1 0 8 3 ; (A3, Rule: 16.d)
i4 5 1 0 9 4 ; (F#3, Rule: 16.c)
; Measure 2 Beat 3 Chord Type: i
i1 6 1 0 6 1 ; (B4, Rule: 2.c)
i2 6 1 0 4 1 ; (E4, Rule: 2.a)
i3 6 1 0 12 5 ; (G3, Rule: 2.b)
i4 6 1 0 2 1 ; (E3, Rule: 2.a)
; Measure 2 Beat 4 Chord Type: V6
i1 7 1 0 6 1 ; (B4, Rule: 15.a)
i2 7 1 0 9 2 ; (F#4, Rule: 15.c)
i3 7 1 0 9 4 ; (F#3, Rule: 15.c)
i4 7 1 0 15 8 ; (D#3, Rule: 15.b)
; Measure 3 Beat 1 Chord Type: VI6
i1 8 1 0 32 5 ; (C5, Rule: 17.a)
i2 8 1 0 4 1 ; (E4, Rule: 17.b)
i3 8 1 0 12 5 ; (G3, Rule: 17.c)
i4 8 1 0 2 1 ; (E3, Rule: 17.b)
; Measure 3 Beat 2 Chord Type: V6/5/III
i1 9 1 0 32 5 ; (C5, Rule: 16.d)
i2 9 1 0 18 5 ; (D4, Rule: 16.a)
i3 9 1 0 27 10 ; (A3, Rule: 16.c)
i4 9 1 0 9 4 ; (F#3, Rule: 16.b)
; Measure 3 Beat 3 Chord Type: III (+2)
i1 10 1 0 6 1 ; (B4, Rule: 8.b)
i2 10 1 0 18 5 ; (D4, Rule: 8.c)
i3 10 1 0 27 10 ; (A3, Rule: 23{D->A})
i4 10 1 0 12 5 ; (G3, Rule: 8.a)
; Measure 3 Beat 4 Chord Type: i7
i1 11 1 0 6 1 ; (B4, Rule: 4.c)
i2 11 1 0 18 5 ; (D4, Rule: 4.d)
i3 11 1 0 12 5 ; (G3, Rule: 4.b)
i4 11 1 0 2 1 ; (E3, Rule: 4.a)
; Measure 4 Beat 1 Chord Type: iv6/5
i1 12 1 0 16 3 ; (A4, Rule: 14.a)
i2 12 1 0 4 1 ; (E4, Rule: 14.c)
i3 12 1 0 12 5 ; (G3, Rule: 14.d)
i4 12 1 0 8 5 ; (C3, Rule: 14.b)
; Measure 4 Beat 2 Chord Type: iv7 (-3)
i1 13 1 0 16 3 ; (A4, Rule: 14.a)
i2 13 1 0 4 1 ; (E4, Rule: 14.c)
i3 13 1 0 12 5 ; (G3, Rule: 14.d)
i4 13 1 0 4 3 ; (A2, Rule: 14.a)
; Measure 4 Beat 3 Chord Type: V/III (microtonal change in soprano)
i1 14 2 0 27 5 ; (A4, Rule: 15.c)
i2 14 2 0 18 5 ; (D4, Rule: 15.a)
i3 14 2 0 9 4 ; (F#3, Rule: 15.b)
i4 14 2 0 9 5 ; (D3, Rule: 15.a)
; Measure 5 Beat 1 Chord Type: III
i1 16 4 0 24 5 ; (G4, Rule: 8.a)
i2 16 4 0 18 5 ; (D4, Rule: 8.c)
i3 16 4 0 3 1 ; (B3, Rule: 8.b)
i4 16 4 0 6 5 ; (G2, Rule: 8.a)
; Measure 6 Beat 1 Chord Type: III
i1 20 2 0 6 1 ; (B4, Rule: 8.b)
i2 20 2 0 18 5 ; (D4, Rule: 8.c)
i3 20 2 0 12 5 ; (G3, Rule: 8.a)
i4 20 2 0 12 5 ; (G3, Rule: 8.a)
; Measure 6 Beat 3 Chord Type: III6
i1 22 2 0 36 5 ; (D5, Rule: 8.c)
i2 22 2 0 18 5 ; (D4, Rule: 8.c)
i3 22 2 0 12 5 ; (G3, Rule: 8.a)
i4 22 2 0 3 2 ; (B2, Rule: 8.b)
; Measure 7 Beat 1 Chord Type: V/III
i1 24 8 0 27 5 ; (A4, Rule: 15.c)
i2 24 8 0 18 5 ; (D4, Rule: 15.a)
i3 24 8 0 9 4 ; (F#3, Rule: 15.b)
i4 24 8 0 9 5 ; (D3, Rule: 15.a)
; Measure 9 Beat 1 Chord Type: V/III
i1 32 8 0 27 5 ; (A4, Rule: 15.c)
i2 32 8 0 18 5 ; (D4, Rule: 15.a)
i3 32 8 0 9 4 ; (F#3, Rule: 15.b)
i4 32 8 0 9 5 ; (D3, Rule: 15.a)
; Measure 11 Beat 1 Chord Type: iv6
i1 40 2 0 4 1 ; (E4, Rule: 13.c)
; (doubled E4 stands out)
i2 40 2 0 4 1 ; (E4, Rule: 13.c)
i3 40 2 0 8 3 ; (A3, Rule: 13.a)
i4 40 2 0 8 5 ; (C3, Rule: 13.b)
; Measure 12 Beat 1 Chord Type: i6/4
i1 42 1 0 24 5 ; (G4, Rule: 2.b)
i2 42 1 0 4 1 ; (E4, Rule: 2.a)
i3 42 1 0 3 1 ; (B3, Rule: 2.c)
i4 42 1 0 3 2 ; (B2, Rule: 2.c)
; Measure 12 Beat 2 Chord Type: i6/4 (+4, 4 in bass)
i1 43 1 0 24 5 ; (G4, Rule: 2.b)
i2 43 1 0 4 1 ; (E4, Rule: 2.a)
i3 43 1 0 3 1 ; (B3, Rule: 2.c)
i4 43 1 0 4 3 ; (A2, Rule: 22{E->A})
; Measure 12 Beat 3 Chord Type: V
i1 44 1 0 9 2 ; (F#4, Rule: 15.c)
i2 44 1 0 15 4 ; (D#4, Rule: 15.b)
i3 44 1 0 3 1 ; (B3, Rule: 15.a)
i4 44 1 0 3 2 ; (B2, Rule: 15.a)
; Measure 12 Beat 4 Chord Type: V7
i1 45 1 0 9 2 ; (F#4, Rule: 16.c)
i2 45 1 0 15 4 ; (D#4, Rule: 16.b)
i3 45 1 0 8 3 ; (A3, Rule: 16.d)
i4 45 1 0 3 2 ; (B2, Rule: 16.a)
; Measure 13 Beat 1 Chord Type: i
i1 46 4 0 4 1 ; (E4, Rule: 2.a)
i2 46 4 0 3 1 ; (B3, Rule: 2.c)
i3 46 4 0 12 5 ; (G3, Rule: 2.b)
i4 46 4 0 1 1 ; (E2, Rule: 2.a)
e
Robert Asmussen
2008
