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Page 23: Musical Tuning and Notation

TUNING:
The history of the Kayenian music starts around the year 500 of the Kayenian Era, which is equivalent to approximately 250 of the Christian Era. Around that time, Uigar Uitance (a priest working in a temple in the south of Grilania) developed a system of 16 tones per octave, based on the relation of the natural overtones. Her system was promptly introduced in the Conclusist Church where it survived, in the orthodox mono-conclusistic branch of that church, until the Unification in 1684. Outside the Church, as well an in its liberal poly-conclusistic branch, the system of Uitance was used until 1191 when it was replaced by the system of the Gindolonian mathematician Wayt Shoureek. His system comprises 19 tones per octave and three different intervals.

The tones are numbered according to the 6-D system as is customary in the Kayenian Empire. The 'standard octave' comprises the tones between 512 and 1024 cycles per Kayenian second (equal to 1.190 sec.). This system is now used throughout the Empire. The tuning of Uitance may still be heard in very conservative temples or historic festivals whereas the tuning of Intooseel, an aliquot tuning, is too experimental to be used by many musicians.
 
 Name  Ratio  Frequency
 fractions decimal  cent log 1900  / Kay sec / sec 
 1
1 / 1
  1.000000
 0.00
 0.00
 512.00
 276.48
 2
128 / 125
  1.024000
 41.06
 65.01
 524.29
 283.12
 3
16 / 15
  1.066667
 111.74
 176.92
 546.13
 294.91
 4
9 / 8
  1.125000
 203.91
 322.86
 576.00
 311.04
 5
75 / 64
  1.171875
 274.58
 434.75
 600.00
 324.00
 10
6 / 5
  1.200000
 315.65
 499.78
 614.40
 331.78
 11
5 / 4
  1.250000
 386.31
 611.66
 640.00
 345.60
 12
32 / 25
  1.280000
 427.37
 676.67
 655.36
 353.89
 13
4 / 3
  1.333333
 498.05
 788.58
 682.67
 368.64
 14
512 / 375
  1.365333
 539.11
 853.59
 699.05
 377.49
 15
64 / 45
  1.422222
 609.78
 965.49
 728.18
 393.22
 20
3 / 2
  1.500000
 701.96
 1111.44
 768.00
 413.72
 21
25 / 16
  1.562500
 772.63
 1223.33
 800.00
 432.00
 22
8 / 5
  1.600000
 813,69
 1288.34
 819.20
 442.37
 23
5 / 3
  1.666667
 884.36
 1400.24
 853.33
 460.80
 24
128 / 75
  1.706667
 925.42
 1465.25
 873.81
 471.86
 25
16 / 9
  1.777778
 996.09
 1577.14
 910.22
 491.52
 30
15 / 8
  1.875000
 1088.27
 1723.09
 960.00
 518.40
 31
125 / 64
  1.953125
 1158.94
 1834.99
 1000.00
 540.00
 1'
 2 / 1
  2.000000
 1200.00
 1900.00
 1024.00
 552.96

Table 1: The tuning according to Shoureek.

 
NOTATION (of pitch):
The base for both the notation and the keyboard is a difference in status of the tones within the octave. Under normal circumstances tones 1, 5, 13, 20, 24 and 1' are considered 'main tones' whereas 3, 11, 22 and 30 are 'side tones'. These ten tones form 'scale F', by far the most usual scale of the Kayenian music. All other tones are considered to be either flats of sharps of these ten notes.

Note that there is a gap of three tones between most main tones, with the exception of 13 and 20 which are separated by two tones only. This asymmetry provides surveyability for both the notation and the keyboard. Moving the shorter distance between other main-tones generates four other scales.
 
 Z 1 4 10  12 14 20 22 24 30 1'
 S  1 3 5 12 14 20 22 24 30 1'
 F 1 3 5 11 13 20 22 24  30 1'
 T  1  3 5 11 13 15 21  24 30 1'
 P 1 3 5 11 13 15  21 23 25 1'
Table 2: The five classical scales of the Kayenian music.

Kayenian music is noted down on ten vertical lines, divided into two groups offive. Each tone is symbolized by two notes, one above the other, and a connecting line. The upper note, which can be either on one line or in between two lines, signifies the absolute pitch. The lower note, which can only be on the line, signifies the status of the tone as mentioned above (from left to right: main-tone, flat side-tone, side-tone, sharp side-tone, main-tone, CAESURA, main-tone, flat side-tone, side-tone, raised side-tone, main-tone) always according to scale F. The two notes above each other on the same line, sometimes needed to note down tone 2, 13, 20 or 30 are written as one.

NOTATION (of duration):
A cross line through the line which connects two notes doubles its duration, and a second cross line quadruples it. An open note has half the duration of a filled one and a cross line will dissect it again. Notes can also be connected to form complicated rhythms. Another method to note down the duration of tones, introduced by the composer Snifoot, is to connect a number of notes will an arc and note the total duration under this arc. This way a duration of 1/3 or 1/5 can be written. Periods of silence are written as the non existing side-tone between tone 13 and 20 would be written. These 'rests' are usually written as squares.

After the introduction of the notation described in short above, and the keyboard of Hanook Zeep, Shoureek's system made a rapid advance within the boundaries of the Kayenian Empire.
 

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