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

The 79-tone tuning developed by me (79 MOS 159-tET) which has been 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. Starting 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 to the sharps on the other direction 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    B3,-6 cents        IRAQ  –  Si

73:       -91 cents     B3,+9 cents

74:       -75 cents     B3,+25 cents

75:       -60 cents     B3,+40 cents

76:       -45 cents     C4,-45 cents

77:       -30 cents     C4,-30 cents

78:       -15 cents     C4,-15 cents

0:          0 cents     C4,0 cents         RAST  -  Do (262 Cps)

1:          15 cents    C4,+15 cents

2:          30 cents    C4,+30 cents

3:          45 cents    C4,+45 cents

4:          60 cents    C#4,-40 cents

5:          75 cents    C#4,-25 cents

6:          91 cents    C#4,-9 cents       Do #

7:         106 cents    C#4,+6 cents       Re b

8:         121 cents    C#4,+21 cents

9:         136 cents    C#4,+36 cents

10:        151 cents    D4,-49 cents

11:        166 cents    D4,-34 cents

12:        181 cents    D4,-19 cents

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6:          91 cents    C#4,-9 cents       Do #

7:         106 cents    C#4,+6 cents       Re b

8:         121 cents    C#4,+21 cents

9:         136 cents    C#4,+36 cents

10:        151 cents    D4,-49 cents

11:        166 cents    D4,-34 cents

12:        181 cents    D4,-19 cents

13:        196 cents    D4,-4 cents        DÜGAH  -  Re

14:        211 cents    D4,+11 cents

15:        226 cents    D4,+26 cents

16:        242 cents    D4,+42 cents

17:        257 cents    D#4,-43 cents

18:        272 cents    D#4,-28 cents

19:        287 cents    D#4,-13 cents      Re #

20:        302 cents    D#4,+2 cents       Mi b

21:        317 cents    D#4,+17 cents

22:        332 cents    D#4,+32 cents

23:        347 cents    D#4,+47 cents

24:        362 cents    E4,-38 cents

25:        377 cents    E4,-23 cents

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19:        287 cents    D#4,-13 cents      Re #

20:        302 cents    D#4,+2 cents       Mi b

21:        317 cents    D#4,+17 cents

22:        332 cents    D#4,+32 cents

23:        347 cents    D#4,+47 cents

24:        362 cents    E4,-38 cents

25:        377 cents    E4,-23 cents

26:        392 cents    E4,-8 cents        SEGAH  -  Mi

27:        408 cents    E4,+8 cents

28:        423 cents    E4,+23 cents

29:        438 cents    E4,+38 cents

30:        453 cents    F4,-47 cents

31:        468 cents    F4,-32 cents

32:        483 cents    F4,-17 cents

33:        498 cents    F4,-2 cents        CHARGAH  -  Fa

34:        513 cents    F4,+13 cents

35:        528 cents    F4,+28 cents

36:        543 cents    F4,+43 cents

37:        558 cents    F#4,-42 cents

38:        574 cents    F#4,-26 cents

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26:        392 cents    E4,-8 cents        SEGAH  -  Mi

27:        408 cents    E4,+8 cents

28:        423 cents    E4,+23 cents

29:        438 cents    E4,+38 cents

30:        453 cents    F4,-47 cents

31:        468 cents    F4,-32 cents

32:        483 cents    F4,-17 cents

33:        498 cents    F4,-2 cents        CHARGAH  -  Fa

34:        513 cents    F4,+13 cents

35:        528 cents    F4,+28 cents

36:        543 cents    F4,+43 cents

37:        558 cents    F#4,-42 cents

38:        574 cents    F#4,-26 cents

39:        589 cents    F#4,-11 cents      Fa #

40:        604 cents    F#4,+4 cents       Sol b

41:        619 cents    F#4,+19 cents

42:        634 cents    F#4,+34 cents

43:        649 cents    F#4,+49 cents

44:        664 cents    G4,-36 cents

45:        679 cents    G4,-21 cents

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39:        589 cents    F#4,-11 cents      Fa #

40:        604 cents    F#4,+4 cents       Sol b

41:        619 cents    F#4,+19 cents

42:        634 cents    F#4,+34 cents

43:        649 cents    F#4,+49 cents

44:        664 cents    G4,-36 cents

45:        679 cents    G4,-21   (Only between these is a 23 cents comma)

46:        702 cents    G4,+2 cents        NEVA  -  Sol

47:        717 cents    G4,+17 cents

48:        732 cents    G4,+32 cents

49:        747 cents    G4,+47 cents

50:        762 cents    G#4,-38 cents

51:        777 cents    G#4,-23 cents

52:        792 cents    G#4,-8 cents       Sol #

53:        808 cents    G#4,+8 cents       La b

54:        823 cents    G#4,+23 cents

55:        838 cents    G#4,+38 cents

56:        853 cents    A4,-47 cents

57:        868 cents    A4,-32 cents

58:        883 cents    A4,-17 cents

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52:        792 cents    G#4,-8 cents       Sol #

53:        808 cents    G#4,+8 cents       La b

54:        823 cents    G#4,+23 cents

55:        838 cents    G#4,+38 cents

56:        853 cents    A4,-47 cents

57:        868 cents    A4,-32 cents

58:        883 cents    A4,-17 cents

59:        898 cents    A4,-2 cents        HÜSEYNI  -  La  (440 Cps)

60:        913 cents    A4,+13 cents

61:        928 cents    A4,+28 cents

62:        943 cents    A4,+43 cents

63:        958 cents    A#4,-42 cents

64:        974 cents    A#4,-26 cents

65:        989 cents    A#4,-11 cents      La #

66:       1004 cents    A#4,+4 cents       Si b

67:       1019 cents    A#4,+19 cents

68:       1034 cents    A#4,+34 cents

69:       1049 cents    A#4,+49 cents

70:       1064 cents    B4,-36 cents

71:       1079 cents    B4,-21 cents

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65:        989 cents    A#4,-11 cents      La #

66:       1004 cents    A#4,+4 cents       Si b

67:       1019 cents    A#4,+19 cents

68:       1034 cents    A#4,+34 cents

69:       1049 cents    A#4,+49 cents

70:       1064 cents    B4,-36 cents

71:       1079 cents    B4,-21 cents

72:       1094 cents    B4,-6 cents        EVDJ  -  Si

73:       1109 cents    B4,+9 cents

74:       1125 cents    B4,+25 cents

75:       1140 cents    B4,+40 cents

76:       1155 cents    C5,-45 cents

77:       1170 cents    C5,-30 cents

78:       1185 cents    C5,-15 cents

79:       1200 cents    C5,0 cents         GERDANIYE  -  Do

1:        1215 cents    C5,+15 cents

2:        1230 cents    C5,+30 cents

3:        1245 cents    C5,+45 cents

4:        1260 cents    C#5,-40 cents

5:        1275 cents    C#5,-25 cents

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72:       1094 cents    B4,-6 cents        EVDJ  -  Si

73:       1109 cents    B4,+9 cents

74:       1125 cents    B4,+25 cents

75:       1140 cents    B4,+40 cents

76:       1155 cents    C5,-45 cents

77:       1170 cents    C5,-30 cents

78:       1185 cents    C5,-15 cents

79:       1200 cents    C5,0 cents         GERDANIYE  -  Do

1:        1215 cents    C5,+15 cents

2:        1230 cents    C5,+30 cents

3:        1245 cents    C5,+45 cents

4:        1260 cents    C#5,-40 cents

5:        1275 cents    C#5,-25 cents

6:        1291 cents    C#5,-9 cents       Do #

7:        1306 cents    C#5,+6 cents       Re b

8:        1321 cents    C#5,+21 cents

9:        1336 cents    C#5,+36 cents

10:       1351 cents    D5,-49 cents

11:       1366 cents    D5,-34 cents

12:       1381 cents    D5,-19 cents

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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.