79-tone qanun recipe
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 my own 79 pitches. Click here to download a special MIXED-SAGITTAL font featuring all the accidentals in the 79-tone tuning. Additionally, a Mus2 template file to get started composing with this font right away is available at this link.
APPENDIX dated May-July 2012:
“MANDALATURA” qanun notation
As can be inferred from its name, I came up with a qanun notation that utilizes numerals instead of accidentals in a similar way as Tablatura does for Guitars. Mandalatura, which was hatched on the spot during a spontaneous dialogue with Qanun-player and dear friend Esra Berkman (a devotee also of the 79-tone qanun) inside a classroom of YTU SANTAS Department, is, in summary, this:
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1.While Tablatura directly uses numbers instead of noteheads, Mandalatura features customary staff with ordinary noteheads as well as numerals alongside them.
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2.Whereas numbers on the Tablatura staff represent finger positions over alluded instrument strings, on the Mandalatura staff they (either written to the left or right of noteheads) express minutely the mandal (metallic lever) raising-lowering operations on the qanun. As a general rule, it is proper for these numerals, which function as accidentals analogous to the sharp/flat symbols, to be written on the left of the noteheads in like manner.
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3.Mandalatura numerals indicate, in the form of negative integers, how many mandals from the unaccidented note (natural mandal) down to a maximum of -12 should be lowered, and conversely, how many mandals, in the form of positive integers, from the unaccidented note (natural mandal) up to a maximum of 12 (with or without the + sign prefix) ought to be raised.
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4.Number zero ( 0 ) returns, as is obvious, to the unaccidented note (natural mandal). In theory, license has been given to traverse 12 mandals down and 12 mandals up from the naturals. On the 79-tone qanun, the bottom limit for flat-wise mandals is -7, and the upper limit for sharp-wise mandals is +12. Needless to say, circumstances are sure to change in the case of other qanuns.
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5.Henceforward, a key signature can be defined right after the clefs at the beginning of the stave in the form of a column of numerals. One may prefer a double-stave (two-handed) transcription scheme for the qanun, and the count of staff lines could be determined varyingly as required by the composer.
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6.As long as the pitch subtlety and structure characteristic of distinct resolution tunings are maintained on the qanun, one can switch from one to the next quite consistently using the same Mandalatura engraving – without recourse to redefining each time a new palette of accidentals. In the case of tunings that cannot be easily swapped thus, one only needs to modify the mandal numerals of the noteheads accordingly.
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7.Should a particular octave division be specifically desired, it can be indicated at the start of a work by its alias (e.g. 53-tET, 72-tET, 79MOS159-tET...). It goes without saying that, if the volume and sequence of mandals change, glaringly divergent intervals will sound from two dissimilar qanuns reading the same Mandalatura score. Additionally, it will become necessary to implement a highly peculiar mandal configuration to be able to descend all the way down to minus 12, and even fill in the gaps between currently affixed series to ascend up to plus 12 mandal positions allowed by this notation. On the other hand, the encumberance of sharps-flats in Turkish Maqam music is henceforth dealt with in the body of qanuns thanks to Mandalatura. Furthermore, composers who write for this instrument can now better visualize the technical features and limitations of the instrument.
Provided below is an example in Saba notated using the Mixed Sagittal Microtonal Notation System for 79 MOS 159-tET followed by its matching Mandalatura counterpart.
To immediately start composing in 79-tone detail using Mandalatura, you can acquire a Mus2 template file of the above score and its integer accidentals palette from this link.
Similarly, the Mus2 template file of the equivalent 79-tone score can be downloaded here.
Happy composing!