So we could we say Roshan and Jorgensen are in agreement, even though they've never met
(obviously).
I have an 1864 Steinway concert
grand at hand and may try these tomorrow, but only on the center strings off 3 octaves to be tuned without stretch.
I have to put it back to ET for when the owners return Sunday....or I could leave it and see if they notice.
I could then put it back to ET next weekend.
See what happens. (They are friends, so it won't be a big deal.)
I could then compare Anthony's Kirnberger III to Roshan's just
by changing out the various offsets (I hope)....
Thanks for this discussion. It's been stimulating.
Richard
------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------
Original Message:
Sent: 09-13-2019 18:09
From: Jason Kanter
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)
------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)
Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)
Cents
C |
0.00 |
C# |
91.45 |
D |
193.16 |
D# |
294.87 |
E |
386.31 |
F |
498.29 |
F# |
589.74 |
G |
696.58 |
G# |
793.16 |
A |
889.74 |
A# |
996.58 |
B |
1088.02 |
C |
1200.00 |
Offsets in Cents from Pure Octave Equal Temperament
C |
0.00 |
C# |
−8.55 |
D |
−6.84 |
D# |
−5.13 |
E |
−13.69 |
F |
−1.71 |
F# |
−10.26 |
G |
−3.42 |
G# |
−6.84 |
A |
−10.26 |
A# |
−3.42 |
B |
−11.98 |
C |
0.00 |
Frequencies in Hz
A0 |
27.50 |
A#0 |
29.25 |
B0 |
30.84 |
C1 |
32.90 |
C#1 |
34.68 |
D1 |
36.78 |
D#1 |
39.01 |
E1 |
41.12 |
F1 |
43.87 |
F#1 |
46.25 |
G1 |
49.19 |
G#1 |
52.02 |
A1 |
55.00 |
A#1 |
58.50 |
B1 |
61.67 |
C2 |
65.80 |
C#2 |
69.36 |
D2 |
73.56 |
D#2 |
78.01 |
E2 |
82.24 |
F2 |
87.74 |
F#2 |
92.50 |
G2 |
98.39 |
G#2 |
104.03 |
A2 |
110.00 |
A#2 |
117.00 |
B2 |
123.35 |
C3 |
131.59 |
C#3 |
138.73 |
D3 |
147.12 |
D#3 |
156.03 |
E3 |
164.49 |
F3 |
175.48 |
F#3 |
185.00 |
G3 |
196.77 |
G#3 |
208.06 |
A3 |
220.00 |
A#3 |
234.01 |
B3 |
246.70 |
C4 |
263.18 |
C#4 |
277.46 |
D4 |
294.25 |
D#4 |
312.05 |
E4 |
328.98 |
F4 |
350.96 |
F#4 |
369.99 |
G4 |
393.55 |
G#4 |
416.13 |
A4 |
440.00 |
A#4 |
468.01 |
B4 |
493.40 |
C5 |
526.36 |
C#5 |
554.91 |
D5 |
588.49 |
D#5 |
624.10 |
E5 |
657.95 |
F5 |
701.92 |
F#5 |
739.99 |
G5 |
787.10 |
G#5 |
832.25 |
A5 |
880.00 |
A#5 |
936.02 |
B5 |
986.79 |
C6 |
1052.73 |
C#6 |
1109.83 |
D6 |
1176.98 |
D#6 |
1248.20 |
E6 |
1315.91 |
F6 |
1403.83 |
F#6 |
1479.98 |
G6 |
1574.19 |
G#6 |
1664.51 |
A6 |
1760.00 |
A#6 |
1872.04 |
B6 |
1973.58 |
C7 |
2105.45 |
C#7 |
2219.65 |
D7 |
2353.97 |
D#7 |
2496.41 |
E7 |
2631.81 |
F7 |
2807.66 |
F#7 |
2959.96 |
G7 |
3148.38 |
G#7 |
3329.01 |
A7 |
3520.00 |
A#7 |
3744.08 |
B7 |
3947.16 |
C8 |
4210.90 |
Features and Modifications
Pure Major Third: C-E.
Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.
Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.
The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.
The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.
------------------------------
Roshan Kakiya
------------------------------