The harmonious tone network:

If you like to tune a accordeon, you find the guidance in addition on the side: tuning

Tone names and relation on the keys (buttons) on the treble side are derived from this table:

** D

* F

* As 128:81

* Ces 256:135

* Eses 512:225

* A

* C 80:81

* Es 32:27

* Ges 64:45

* Heses 128:75

* E 100:81

* G 40:27

* B 16:9 (7:4)

* Des 16:15

Fes 32:25

* H 50:27

* D 10:9

F 4:3

As 8:5

Ces 24:25

Fis 25:18(11:8)

A 5:3

C 1:1

Es 6:5

Ges 36:25

Cis 25:24

E 5:4

G 3:2

B 9:5

Des 27:25

Gis 25:16(13:8)

H 15:8

D 9:8

F * 27:20

As * 81:15

Dis 74:64

Fis * 45:32

A * 27:16

C * 81:80

Es * 243:200

Ais*225:128

Cis * 135:128

E * 81:64

G * 243:160

B *

Eis*675:512

Gis * 405:256

H * 243:128

D *

F **

His *

Dis ** 1215:512

Fis**728:512

A **

C **

In the treble side the following tones are present on pull: Each line corresponds to an act row. The arrangement of the keys on the accordion is in such a way, that the 2nd Row is shifted a half key to the right. And 3rd Row again a half key to the right etc..

-

-

* B 16:9(7:4)

-

-

-

* D 10:9

F 4:3

-

-

Fis 25:18(11:8)

A 5:3

C 1:1

-

-

Cis 25:24

E 5:4

G 3:2

-

-

Gis 25:16(13:8)

H 15:8

D 9:8

-

-

If one selects C* to as starting point like that is on the following table other tones are attainable on the keys.

-

-

-

B 16:9(7:4)

Des 16:15

-

-

D 10:9

F * 4:3

As * 8:5

-

-

A * 5:3

C * 1:1

Es * 6:5

-

-

E * 5:4

G * 3:2

B * 9:5

-

-

H * 15:8

D * 9:8

F ** 27:20

Which fingering technology is used, depends on the music piece.

To the table:

Each step from above downward is one: Quint 3:2  
Each step from down upward is one: Quart of 4:3 Reversal of the Quint
Each step from left to the right is one: small third 6:5  
Each step from right is one to the left: large sixth 5:3 Reversal of the small third
Each step from on the top right to the left down is one: large third 5:4  
Each step from left is one down to the right above: small sixth 8:5 Reversal of the large third
Each step from left to the right above down is one: small seventh 9:5 (the small seventh lasts to 7:4 purely)
Each step from right down to the left above is in: small whole tone 10:9 Reversal of the small seventh (not 8:9!)
Further chords come only two cells or steps far away forwards, since they are formed by addition of the basic intervals
  large seventh 15:8  
  Small Sekund 25:24 (chromatic half-tone)
  large Sekund 8:9 (large complete tone)
  Excessive quarte/decreased quinte 25:18 (tri tonus)

One needs only to look at the table from 1:1 to see these connections to the suroundung intervalls.

Maj. and Min. Intervalls are always in a direct tree angle connection. The tones C, E, G (1:1, 5:4, 3:2) and A, C, E (5:3, 1:1, 5:4) form together a square. If one shifts the triangles or the square over the tone network, all possible Maj. and Min. chords can be read off. Even if tone conditions look complex, relative relationship under the neighbouring fields is always alike. Registered conditions multiply from a column or line to the next. If Conditions are divisibly by 2 them are divided by 2. That corresponds to a shift downward one Oktav (transponiert). With the Diatonic accordion this tone network serves as basis for being used for tuning. In the example, C Maj.- A Min. is used, it can be selected however each tone in the tone network as starting point with the ratio 1:1. This is done by imaging two layers by one above the other, the table in two levels introduces itself. In one level only the tones are located and in the other level tone conditions. Shifting layers functions in in perpendicular dare-right direction and diagonal direction. The tone relationship in parentheses, is the one pure seventh chord relationchip (7:4).For Fis and Gis also pure harmonious exist, those would be: (11:8) and (13:8). In the following some scales and the intervals occurring therein.

Pytagorei tendency:

Cumulative intervals:

1

9:8

81:64

4:3

3:2

27:16

243:128

2

Note:

C

D

E

F

G

A

H

C

Inc.intervals:

9:8

9:8

256:243

9:8

9:8

9:8

256:243

9:8

Inc.. Cents:

204

204

90

204

204

204

90

204

Pure tendency:

Cumulative intervals:

1

9:8

5:4

4:3

3:2

5:3

15:8

2

Note:

C

D

E

F

G

A

H

C

Inc. Intervals:

9:8

10:9

16:15

9:8

10:9

9:8

16:15

9:8

Indication explanation:

Indication:

English Bez.

Ratio:

Effect

(x) *

(plus)

81/80

Increased by 21.5 cents

* (x)

(minus)

80/81

Degraded by 21.5 cents

(x) #

(sharp)

25/24

Increased by 71 cents

(x)b

(flat)

24/25

Degraded by 71 cents

© johann pascher