Quelle:
MEISTER, Seite 117 (Angabe ganzer Cent-Zahlen) T 65
Sechs- und Zwölfteilung des
pythagoreischen Kommas
Verteilung
des pK º 23.46 cent Verteilung
des pK im Quintenzirkel
f
- 3.910 c - 1/6pK . -
1/6pK
b - 1.955
f
. .
es
- 1.955 b - 1/12pK c - 1/6pK
gis + 9.775(!) es f
│ g
cis - 1.955 gis .
│ .
fis - 1.955 cis b
│
d
h - 1.955
fis - 1/12pK │ - 1/6pK
e - 3.910
h . es───────┼────────a
.
a - 3.910
e
│
d - 3.910
a + 5/12pK gis
│
e - 1/6pK
g - 3.910
d . │ .
c - 3.910
g
cis │ h
================== - 1/12pK
fis - 1/6pK
-
23.460
. .
.
-
1/12pK - 1/12pK
|
|
Quinten |
|
Quarten |
|
Großterzen |
|
Kleinterzen |
|
|||||
|
f |
698.045 |
c |
501.955 |
f |
392.180 |
a |
305.865 |
c |
|||||
|
b |
700.000 |
f |
500.000 |
b |
394.135 |
d |
305.865 |
f |
|||||
|
es |
700.000 |
b |
500.000 |
es |
396.090 |
g |
303.910 |
b |
|||||
|
gis |
711.730 |
es |
488.270 |
gis |
409.775 |
c |
301.955 |
es |
|||||
|
cis |
700.000 |
gis |
500.000 |
cis |
411.730 |
f |
288.270 |
gis |
|||||
|
fis |
700.000 |
cis |
500.000 |
fis |
411.730 |
b |
288.270 |
cis |
|||||
|
h |
700.000 |
fis |
500.000 |
h |
411.730 |
es |
288.270 |
fis |
|||||
|
e |
698.045 |
h |
501.955 |
e |
398.045 |
gis |
300.000 |
h |
|||||
|
a |
698.045 |
e |
501.955 |
a |
396.090 |
cis |
301.955 |
e |
|||||
|
d |
698.045 |
a |
501.955 |
d |
394.135 |
fis |
303.910 |
a |
|||||
|
g |
698.045 |
d |
501.955 |
g |
392.180 |
h |
305.865 |
d |
|||||
|
c |
698.045 |
g |
501.955 |
c |
392.180 |
e |
305.865 |
g |
|||||
|
Intervall-bezeichnung |
Quotient |
Dezimal-zahl |
Centwert des Intervalls |
Frequenzbeispiele (Zahlen in Hz) |
|||||||||
|
|
|
|
|
|
|
|
|
||||||
|
Oktave |
2/1 |
2.0 |
1200.000 |
c |
262.5 |
>440.0< |
a |
||||||
|
gr.Septime |
256x6Ö32/243 |
1.8771201 |
1090.225 |
h |
492.8 |
413.0 |
gis |
||||||
|
kl.Septime |
3/4Ö8 |
1.7838101 |
1001.955 |
b |
468.3 |
392.4 |
g |
||||||
|
gr.Sexte |
32xÖ2/27 |
1.6761050 |
894.135 |
a |
>440.0< |
368.7 |
fis |
||||||
|
kl.Sexte |
256x12Ö27/243 |
1.5784634 |
790.225 |
gis |
414.4 |
347.3 |
f |
||||||
|
Quinte |
4x6Ö2/3 |
1.4966161 |
698.045 |
g |
392.9 |
329.2 |
e |
||||||
|
Tritonus |
256x12Ö32/243 |
1.4062511 |
590.225 |
fis |
369.2 |
309.4 |
es |
||||||
|
Quarte |
3/2x6Ö2 |
1.3363480 |
501.955 |
f |
350.8 |
294.0 |
d |
||||||
|
gr.Terz |
64x3Ö4/81 |
1.2542428 |
392.180 |
e |
329.2 |
275.9 |
cis |
||||||
|
kl.Terz |
3/3Ö16 |
1.1905508 |
301.955 |
es |
312.5 |
261.9 |
c |
||||||
|
Ganzton |
8x3Ö2/9 |
1.1199299 |
196.090 |
d |
294.0 |
246.4 |
h |
||||||
|
Halbton |
256/243 |
1.0534979 |
90.225 |
cis |
276.6 |
231.8 |
b |
||||||
|
Grundton |
1/1 |
1.0 |
0.000 |
C |
262.5 |
220.0 |
a |
||||||
Abweichungen der
Tonstufen bei Modulationen (Zahlen in Cent)
in der Tabelle zur Graphik „Profil“:
