Interval between each pitches on one string, (knowing that we have same intervals for each strings):
| intervals between each fret | intervals from 1rst free string |
| fret01:
1,0 594 751 fret02: 1,0 618 818 fret03: 1,0 851 064 fret04: 1,0 882 353 fret05: 1,0 810 811 fret06: 1,0 833 333 * fret07: 1,0 692 308 fret08: 1,0 935 252 fret09: 1,0 921 053 fret10: 1,0 963 855 fret11: 1,0 769 231 fret12: 1,1 020 408 fret13: 1,0 833 333 * fret14: 1,1 025 641 fret15: 1,124 031 fret16: 1,1 034 483 fret17: 1,1 fret18: 1,1 363 636 fret19: 1,135 fret20: 1,1 277 533 fret21: 1,1 523 438 |
fret01:
1,0 594 751 fret02: 1,1 250 373 fret03: 1,2 207 852 fret04: 1,3 285 015 fret05: 1,4 362 179 <- fret06: 1,5 559 026 fret07: 1,663 619 fret08: 1,8 192 093 fret09: 1,9 867 681 fret10: 2,1 782 638 fret11: 2,3 458 226 fret12: 2,5 851 922 fret13: 2,8 006 248 fret14: 3,0 878 683 fret15: 3,4 708 597 fret16: 3,8 299 143 fret17: 4,2 129 057 fret18: 4,7 873 927 fret19: 5,4 336 907 fret20: 6,1 278 626 fret21: 7,0 614 044 |
We decided according
to strings diameter used: 1,17mm [46] - 0,91mm [36] - 0,66mm [26] - 0,43mm [17]
- 0,28mm [11] - 0,23mm [09]
and 4 fingers freting convention, to tune the strings between them with the
interval 1,4 362 179 (notice that 4+ = 1,4 142 136 = 2 power 1/2 or 2 root 2).
We started with the diapason A0 = 55Hz for the lower string and them build up
all the scale.
Resulting pitches
in Hertz and notes with cents on the 6 strings' neck of the Meteor 9 tones electric
guitar
|
fret
|
I
|
II
|
III
|
IV
|
V
|
VI
|
VII
|
VIII
|
IX
|
X
|
XI
|
XII
|
XIII
|
XIV
|
XV
|
XVI
|
XVII
|
XVIII
|
IXX
|
XX
|
XXI
|
|
| string 1 | 336,1Hz E3+34 cents |
356,1Hz F3+34 cents |
378,12Hz F#3+38 cents |
410,3Hz G#3-21 cents |
446,5Hz A3+25 cents |
482,7Hz B3-40 cents |
522,94Hz C4-1 cent |
559,14Hz C#4+15 cents |
611,44Hz D#4-30 cents |
667,75Hz E4+22 cents |
732,1Hz F#4-19 cents |
788,43Hz G4+10 cents |
868,88Hz A4-22 cents |
941,29Hz A#4+17 cents |
1 037,83Hz C5-14 cents |
1 166,56Hz D5-12 cents |
1 287,23Hz E5-42 cents |
1 415,95Hz F5+23 cents |
1 609,04Hz G5+45 cents |
1826,26Hz A#5-36 cents |
2 059,57Hz C6-28 cents |
2 373,34Hz D6+18 cents |
| string 2 | 234Hz A2#+7 cents |
248Hz B2+7 cents |
263,25Hz C3+11 cents |
285,66Hz D3-48 cents |
310,87Hz D#3-1 cent |
336,075Hz | 364,08Hz F#3-28 cents |
389,28Hz G3-12 cents |
425,69Hz G#3+43 cents |
464,9Hz A#3-5 cents |
509,7Hz C4-45 cents |
549Hz C#4-17 cents |
605Hz D#4-49 cents |
655,34Hz E4-10 cents |
722,56Hz F#4-41 cents |
812,18Hz G#4-39 cents |
896,2Hz A4+32 cents |
985,82Hz B4-3 cents |
1 120,25Hz C#5+18 cents |
1 271,48Hz D#5+37 cents |
1 433,92Hz F5+45 cents |
1 652,37Hz G#5-9 cents |
| string 3 | 163Hz E2-19 cents |
172,7Hz F2-19 cents |
183,38Hz F#2-15 cents |
198,98Hz G2+26 cents |
216,54Hz A2-27 cents |
234,11Hz | 253,61Hz B2+46 cents |
271,17Hz C#3-38 cents |
296,53Hz D3+17 cents |
323,84Hz E3-31 cents |
355Hz F3+28 cents |
382,37Hz G3-43 cents |
421,38Hz G#3+25 cents |
456,5Hz A#3-36 cents |
503,32Hz B3+33 cents |
565,75Hz C#4+35 cents |
624,23Hz D#4+5 cents |
686,7Hz F4-29 cents |
780,34Hz G4-8 cents |
885,69Hz A4+11 cents |
998,84Hz B4+19 cents |
1 151Hz D5-35 cents |
| string 4 | 113,45Hz A#1-47 cents |
120,2Hz B1-46 cents |
127,63Hz C2-43 cents |
138,5Hz C#2-1 cent |
150,72Hz D2+45 cents |
163Hz | 176,5Hz F2+19 cents |
188,73Hz F#2+35 cents |
206,39Hz G#2-11 cents |
225,4Hz A2+42 cents |
247,12Hz B2+1 cent |
266,13Hz C3+30 cents |
293,3Hz D3-2 cents |
317,73Hz D#3+36 cents |
350,32Hz F3+4 cents |
393,77Hz G3+8 cents |
434,5Hz A3-32 cents |
477,95Hz A#3+43 cents |
543,13Hz C#4-35 cents |
616,45Hz D#4-16 cents |
695,2Hz F4-8 cents |
801,12Hz G4+37 cents |
| string 5 | 79Hz D#1+27 cents |
83,7Hz E1+27 cents |
88,87Hz F1+31 cents |
96,44Hz G1-28 cents |
104,95Hz G#1+19 cents |
113,46Hz | 123Hz B1-7 cents |
131,42Hz C2+8 cents |
143,7Hz D2-37 cents |
157Hz D#+16 cents |
172Hz F2-26 cents |
185,32Hz F#2+3 cents |
204,23Hz G#2-29 cents |
221,25Hz A2+10 cents |
243,94Hz B2-21 cents |
274,2Hz C#3-19 cents |
302,56Hz D#3-48 cents |
332,82Hz E3+17 cents |
378,2Hz F#3+38 cents |
429,26Hz A3-43 cents |
484,1Hz B3-35 cents |
557,85Hz C#4+11 cents |
| string 6 | 55Hz A0 |
58,27Hz A#0 |
61,88Hz B0+4 cents |
67,14Hz C1+45 cents |
73Hz D1-10 cents |
79Hz | 85,57Hz F1-35 cents |
91,5Hz F#1-19 cents |
100,05Hz G1+35 cents |
109,27Hz A1-12 cents |
119,8Hz A#1+48 cents |
129Hz C2-24 cents |
142,18Hz C#+44 cents |
154Hz D#2-17 cents |
169,83Hz F2-48 cents |
190,89Hz G2-46 cents |
210,64Hz G#2+25 cents |
231,71Hz A#2-10 cents |
263,3Hz C3+11 cents |
298,85Hz D3+30 cents |
337,03Hz E3+38 cents |
388,37Hz G3-16 cents |
|
interval
|
1,0 594 751 | 1,1 250 373 | 1,2 207 852 | 1,3 285 015 | 1,4 362 179 <- | 1,5 559 026 | 1,663 619 | 1,8 192 093 | 1,9 867 681 | 2,1 782 638 | 2,3 458 226 | 2,5 851 922 | 2,8 006 248 | 3,0 878 683 | 3,4 708 597 | 3,8 299 143 | 4,2 129 057 | 4,7 873 927 | 5,4 336 907 | 6,1 278 626 | 7,0 614 044 |
First observation: our mode is no octave basis, it teases it!
To clone this scale
by sinus waves let's use the sampler.
MIDI accepts 128 notes per channel
The Meteor guitar has (21 (frets) + 6 (free stings)) x 6 = 132 notes - 5 similar
on fret V) = 127 different pitches : perfect! It fit.
But, our sampler accepts 87 notes, and our MIDI keyboard accepts only 73 notes:
damned, not enough keys!
We need the (73 notes) keyboard to play to compose the music "Forbidden Games".