Roshan Kakiya's Stretched Young I (Cent = 31/1900)This image is available at: http://rollingball.com/images/Kakiya-StretchedYoung.pngSystem of CentsCent = 3
1/1900.
This system of cents is appropriate for Pure 12th Equal Temperament.
Roshan Kakiya's Stretched Young I is an Unequal Temperament that is based on Young I and Pure 12th Equal Temperament.
Cents
C |
0.00 |
C# |
96.30 |
D |
197.53 |
D# |
298.77 |
E |
395.07 |
F |
500.00 |
F# |
595.07 |
G |
698.77 |
G# |
797.53 |
A |
896.30 |
A# |
1000.00 |
B |
1095.07 |
C |
1200.00 |
Offsets in Cents from Pure 12th Equal Temperament
C |
0.00 |
C# |
−3.70 |
D |
−2.47 |
D# |
−1.23 |
E |
−4.93 |
F |
0.00 |
F# |
−4.93 |
G |
−1.23 |
G# |
−2.47 |
A |
−3.70 |
A# |
0.00 |
B |
−4.93 |
C |
0.00 |
Frequencies in Hz
A0 |
27.42 |
A#0 |
29.12 |
B0 |
30.76 |
C1 |
32.69 |
C#1 |
34.56 |
D1 |
36.64 |
D#1 |
38.85 |
E1 |
41.07 |
F1 |
43.64 |
F#1 |
46.11 |
G1 |
48.96 |
G#1 |
51.84 |
A1 |
54.88 |
A#1 |
58.27 |
B1 |
61.57 |
C2 |
65.42 |
C#2 |
69.16 |
D2 |
73.33 |
D#2 |
77.75 |
E2 |
82.21 |
F2 |
87.35 |
F#2 |
92.28 |
G2 |
97.99 |
G#2 |
103.75 |
A2 |
109.84 |
A#2 |
116.63 |
B2 |
123.22 |
C3 |
130.93 |
C#3 |
138.43 |
D3 |
146.77 |
D#3 |
155.62 |
E3 |
164.53 |
F3 |
174.82 |
F#3 |
184.70 |
G3 |
196.11 |
G#3 |
207.64 |
A3 |
219.84 |
A#3 |
233.43 |
B3 |
246.62 |
C4 |
262.05 |
C#4 |
277.05 |
D4 |
293.75 |
D#4 |
311.46 |
E4 |
329.29 |
F4 |
349.89 |
F#4 |
369.66 |
G4 |
392.51 |
G#4 |
415.58 |
A4 |
440.00 |
A#4 |
467.19 |
B4 |
493.59 |
C5 |
524.47 |
C#5 |
554.50 |
D5 |
587.92 |
D#5 |
623.36 |
E5 |
659.06 |
F5 |
700.29 |
F#5 |
739.86 |
G5 |
785.58 |
G#5 |
831.75 |
A5 |
880.63 |
A#5 |
935.05 |
B5 |
987.88 |
C6 |
1049.68 |
C#6 |
1109.79 |
D6 |
1176.69 |
D#6 |
1247.62 |
E6 |
1319.06 |
F6 |
1401.57 |
F#6 |
1480.77 |
G6 |
1572.27 |
G#6 |
1664.68 |
A6 |
1762.51 |
A#6 |
1871.43 |
B6 |
1977.18 |
C7 |
2100.86 |
C#7 |
2221.15 |
D7 |
2355.05 |
D#7 |
2497.02 |
E7 |
2640.00 |
F7 |
2805.14 |
F#7 |
2963.65 |
G7 |
3146.79 |
G#7 |
3331.73 |
A7 |
3527.54 |
A#7 |
3745.53 |
B7 |
3957.18 |
C8 |
4204.71 |
Mathematical StructurePythagorean comma = −1.
12/19 Pythagorean comma = 12/19 ×
−1 = − 12/19.a = The amount of the Pythagorean comma by which C-G, G-D, D-A and A-E are each narrower than Just.b = The amount of the Pythagorean comma by which E-B, B-F#, A#-F and F-C are each narrower than Just.c = The amount of the Pythagorean comma by which F#-C#, C#-G#, G#-D# and D#-A# are each narrower than Just.a = 2b.
c = 0.
4a + 4b + 4c =
− 12/19.
4a + 4b + 4 × 0 =
− 12/19.
4a + 4b =
− 12/19.
4 × 2b + 4b =
− 12/19.
8b + 4b =
− 12/19.
12b =
− 12/19.
b =
− 12/19 × 1/12.
b = − 1/19.
a = 2
× (− 1/19).
a = − 2/19.FeaturesArrangement of the Fifths:Pure Fifth narrowed by 2/19 Pythagorean comma: C-G, G-D, D-A and A-E.
Pure Fifth narrowed by 1/19 Pythagorean comma: E-B, B-F#, A#-F and F-C.
Pure Fifth: F#-C#, C#-G#, G#-D# and D#-A#.
Retained elements of Young I:The Major Thirds are symmetrical on either side of F# around the Circle of Fifths.
The Major Third C-E is closest to Just and the Major Third F#-A# is furthest from Just.
The Fifths F#-C#, C#-G#, G#-D# and D#-A# are the same.
Retained elements of Pure 12th Equal Temperament:The Fifth and the Octave will beat at the same rate within the Twelfths E-B, B-F#, A#-F and F-C.
The Fifths and the Twelfths E-B, B-F#, A#-F and F-C are the same.
Every Octave is the same.
The Major Thirds A-C# and D#-G are the same.
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Roshan Kakiya
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