In 2005, Izmirite qanun maker Ejder Güleç & Sons manufactured a qanun according to my instructions containing 79 tones to the octave.

The tuning developed by me (79 MOS 159-tET) that is implemented on this qanun for the first time constitutes the backbone of my doctorate dissertation.

A picture of the 79-tone qanun is given below:

In order to achieve minute tuning adjustments on the qanun, I have installed fine-tuners on every string beyond the bridge thanks to the suggestion of M. Sc. Uğur Keçecioğlu:

Let us now zoom in on the mandals:

Mandals corresponding to natural pitches can be discerned right away from their royal fuchsia colouring. From the naturals (which denote non-accidented pitches according to the International diapason) one can go 7 mandals down at most to the flats, 8 mandals up at most to the sharps and 12 mandals at most to the double-sharps.

79 MOS 2º159-tET (79-tone Moment of Symmetry out of 2 degrees of 159-tone equal temperament) is a tuning derived from dividing the yegah-neva octave logarithmically into 159 equal parts and picking 79 tones from within.

To download a detailed MS EXCEL file regarding the application of this tuning to the qanun, click here.

Should you desire to prepare a 79-tone qanun using a tuner that accepts cent offsets as input, you ought to affix the mandals as shown below:

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Step     Cents     Tone/Octave/Offset       Pitch

72:       -106 cents   B-1,-6 cents           IRAQ – Si

73:       -91 cents     B-1,+9

74:       -75 cents     B-1,+25

75:       -60 cents     B-1,+40

76:       -45 cents     C0,-45

77:       -30 cents     C0,-30

78:       -15 cents     C0,-15

  0:          0 Cents      C0,0                      RAST   -  Do  (262 Cps)

  1:         15 cents      C0,+15

  2:         30 cents      C0,+30

  3:         45 cents      C0,+45

  4:         60 cents      C#0,-40

  5:         75 cents      C#0,-25

  6:         91 cents      C#0,-9                    Do#

  7:        106 cents     C#0,+6                   Reb

  8:        121 cents     C#0,+21

  9:        136 cents     C#0,+36

10:       151 cents     D0,-49

11:       166 cents     D0,-34

12:       181 cents     D0,-19

**************************************************

  6:          91 cents     C#0,-9                    Do#

7:         106 cents    C#0,+6                   Reb

  8:         121 cents    C#0,+21

  9:         136 cents    C#0,+36

10:        151 cents    D0,-49

11:        166 cents    D0,-34

12:        181 cents    D0,-19

13:        196 cents    D0,-4                   DÜGAH   -  Re

14:        211 cents    D0,+11

15:        226 cents    D0,+26

16:        242 cents    D0,+42

17:        257 cents    D#0,-43

18:        272 cents    D#0,-28

19:        287 cents    D#0,-13                   Re#

20:        302 cents    D#0,+2                    Mib

21:        317 cents    D#0,+17

22:        332 cents    D#0,+32

23:        347 cents    D#0,+47

24:        362 cents    E0,-38

25:        377 cents    E0,-23

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19:        287 cents   D#0,-13                   Re#

20:        302 cents   D#0,+2                    Mib

21:        317 cents   D#0,+17

22:        332 cents   D#0,+32

23:        347 cents   D#0,+47

24:        362 cents   E0,-38

25:        377 cents   E0,-23

26:        392 cents   E0,-8                   SEGAH   -  Mi

27:        408 cents   E0,+8

28:        423 cents   E0,+23

29:        438 cents   E0,+38

30:        453 cents   F0,-47

31:        468 cents   F0,-32

32:        483 cents   F0,-17

33:        498 cents   F0,-2                   TSCHARGAH   -  Fa

34:        513 cents   F0,+13

35:        528 cents   F0,+28

36:        543 cents   F0,+43

37:        558 cents   F#0,-42

38:        574 cents   F#0,-26

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26:        392 cents   E0,-8                   SEGAH   -  Mi

27:        408 cents   E0,+8

28:        423 cents   E0,+23

29:        438 cents   E0,+38

30:        453 cents   F0,-47

31:        468 cents   F0,-32

32:        483 cents   F0,-17

33:        498 cents   F0,-2                   TSCHARGAH   -  Fa

34:        513 cents   F0,+13

35:        528 cents   F0,+28

36:        543 cents   F0,+43

37:        558 cents   F#0,-42

38:        574 cents   F#0,-26

39:        589 cents   F#0,-11                 Fa#

40:        604 cents   F#0,+4                  Solb

41:        619 cents   F#0,+19

42:        634 cents   F#0,+34

43:        649 cents   F#0,+49

44:        664 cents   G0,-36

45:        679 cents   G0,-21 

***************************************************

39:        589 cents   F#0,-11                 Fa#

40:        604 cents   F#0,+4                  Solb

41:        619 cents   F#0,+19

42:        634 cents   F#0,+34

43:        649 cents   F#0,+49

44:        664 cents   G0,-36

45:        679 cents   G0,-21            (Only the interval between these two is a 23 cent comma.)

46:        702 cents   G0,+2                 NEVA   -   Sol

47:        717 cents   G0,+17

48:        732 cents   G0,+32

49:        747 cents   G0,+47

50:        762 cents   G#0,-38

51:        777 cents   G#0,-23

52:        792 cents   G#0,-8                   Sol#

53:        808 cents   G#0,+8                  Lab

54:        823 cents   G#0,+23

55:        838 cents   G#0,+38

56:        853 cents   A0,-47

57:        868 cents   A0,-32

58:        883 cents   A0,-17

***************************************************

52:        792 cents   G#0,-8                   Sol#

53:        808 cents   G#0,+8                  Lab

54:        823 cents   G#0,+23

55:        838 cents   G#0,+38

56:        853 cents   A0,-47

57:        868 cents   A0,-32

58:        883 cents   A0,-17

59:        898 cents   A0,-2                  HÜSEYNI   -  La

60:        913 cents   A0,+13

61:        928 cents   A0,+28

62:        943 cents   A0,+43

63:        958 cents   A#0,-42

64:        974 cents   A#0,-26

65:        989 cents   A#0,-11                 La#

66:       1004 cents  A#0,+4                  Sib

67:       1019 cents   A#0,+19

68:       1034 cents   A#0,+34

69:       1049 cents   A#0,+49

70:       1064 cents   B0,-36

71:       1079 cents   B0,-21

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65:        989 cents    A#0,-11                La#

66:       1004 cents   A#0,+4                 Sib

67:       1019 cents   A#0,+19

68:       1034 cents   A#0,+34

69:       1049 cents   A#0,+49

70:       1064 cents   B0,-36

71:       1079 cents   B0,-21

72:       1094 cents   B0,-6                 EVDJ  -  Si

73:       1109 cents   B0,+9

74:       1125 cents   B0,+25

75:       1140 cents   B0,+40

76:       1155 cents   C1,-45

77:       1170 cents   C1,-30

78:       1185 cents   C1,-15

79:       1200 cents   C1,0                  GERDANIYE  -  Do

  1:        1215 cents   C1,+15

2:        1230 cents   C1,+30

  3:        1245 cents   C1,+45

  4:        1260 cents   C#1,-40

  5:        1275 cents   C#1,-25

***************************************************

72:       1094 cents    B0,-6                EVDJ  -  Si

73:       1109 cents    B0,+9

74:       1125 cents    B0,+25

75:       1140 cents    B0,+40

76:       1155 cents    C1,-45

77:       1170 cents    C1,-30

78:       1185 cents    C1,-15

79:       1200 cents    C1,0                 GERDANIYE  -  Do

  1:        1215 cents    C1,+15

  2:        1230 cents    C1,+30

  3:        1245 cents    C1,+45

  4:        1260 cents    C#1,-40

  5:        1275 cents    C#1,-25

  6:        1291 cents    C#1,-9                 Do#

  7:        1306 cents    C#1,+6                Reb

  8:        1321 cents    C#1,+21

  9:        1336 cents    C#1,+36

10:       1351 cents    D1,-49

11:       1366 cents    D1,-34

12:       1381 cents    D1,-19

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When the strings are being tuned to diatonic naturals, first A is taken to be 440 Cps; then D-A is adjusted to be a pure fifth; then one goes 7 mandals down from the course of D and the pitch of 6 mandals up from the course of C is made unison with this pitch; C-G is tuned to a pure fifth; after the octave of C is adjusted, F-C is tuned as a pure fifth; E is tuned to a unison with the pitch obtained by going 7 mandals down from the natural of the course of F; finally, E-B is tuned as a pure fifth. Check if the pitch of seven mandals up from the course of B is the same as the natural of the course of C.

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79 MOS 159-tET which I applied to my qanun by considering several criteria such as the ability to actualize all the modulations and transpositions in the nature of maqam music on paper, to conform with the notation and comma conceptions in effect, to obtain the pitches correctly and fully, to close the cycle with an uninterrupted chain of perfect fifths, and to not exceed the capacity of Turkish instruments, can also be explained as follows:

1. The interval of a pure fifth obtained from the inversion in the octave of the third harmonic is divided logarithmically into 33 equal parts:

    1/33 of log(10) [4/3] * 1200 / log(10) 2 =

    498.045 / 33 =

    15.0923 cents

2. The 15.1 cent comma is stacked 79 times:

    15.0923 x 1  =  15.0923 cents

    15.0923 x 2  =  30.1845 cents

    15.0923 x 3  =  45.2768 cents

    etc...

    15.0923 x 79 = 1192.29 cents

3. Once the pitch at the seventy ninth step is rounded to the octave, viz. 1200 cents, a larger comma appears between the 78th and 79th steps:

    (1200-1192.29) + 15.0923 =

    7.71 + 15.0923 =

    22.80273 cents

4. If this larger comma is moved between the 45th and 46th steps, an interval of a pure fifth is attained at the 46th step:

    (15.0923 x 45) + 22.80273 = 

    679.1523 + 22.80273 =

    701.955001 cents =

    log(10) [3/2] * 1200 / log(10) 2

5. Thus, a system that closes in 79 tones through a cycle comprising 33 tempered (meantone) fifths and 46 pure fifths is obtained.

If the pure fifth is coded as A, and the tempered fifth as B, the cycle of fifths follows this pattern:

            ab ab ab aab

            ab ab aab

            ab aab

            ab ab aab

            ab aab

            ab ab aab

            ab aab

            ab ab aab

            ab aab

            ab ab aab

            ab aab

            ab ab aab

            ab ab

For an interview (in Turkish) with reporter Sirel Ekşi dated 27 November 2005 on the subject of the 79-tone qanun, click here.

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I have attempted a few clumsy recordings with the 79-tone qanun. You can choose and listen to them in the Music Player below.

In order to notate 79 MOS 159-tET, I have adapted the Sagittal Microtonal Notation System developed by George Secor and David Keenan to 79 my tones. In order to download the accidentals font in this tuning, click here.