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Table 5-7 gives a close approximation of the equal-tempered scale over one
octave when the sample size is 16 bytes. The " Period " column gives the
period count you enter into the period register . The length register
AUDxLEN should be set to 8 (16 bytes = 8 words). The sample should
represent one cycle of the waveform.
Table 5-7: Equal-tempered Octave for a 16 Byte Sample
NTSC PAL Ideal Actual NTSC Actual PAL
Period Period Note Frequency Frequency Frequency
------ ------ ---- --------- ----------- ----------
254 252 A 880.0 880.8 879.7
240 238 A# 932.3 932.2 931.4
226 224 B 987.8 989.9 989.6
214 212 C 1046.5 1045.4 1045.7
202 200 C# 1108.7 1107.5 1108.4
190 189 D 1174.7 1177.5 1172.9
180 178 D# 1244.5 1242.9 1245.4
170 168 E 1318.5 1316.0 1319.5
160 159 F 1396.9 1398.3 1394.2
151 150 F# 1480.0 1481.6 1477.9
143 141 G 1568.0 1564.5 1572.2
135 133 G# 1661.2 1657.2 1666.8
The table above shows the period values to use with a 16 byte sample to
make tones in the second octave above middle C. To generate the tones in
the lower octaves, there are two methods you can use, doubling the period
value or doubling the sample size.
When you double the period , the time between each sample is doubled so
the sample takes twice as long to play. This means the frequency of the
tone generated is cut in half which gives you the next lowest octave.
Thus, if you play a C with a period value of 214, then playing the same
sample with a period value of 428 will play a C in the next lower octave.
Likewise, when you double the sample size, it will take twice as long to
play back the whole sample and the frequency of the tone generated will be
in the next lowest octave. Thus, if you have an 8 byte sample and a 16
byte sample of the same waveform played at the same speed, the 16 byte
sample will be an octave lower.
A sample for an equal-tempered scale typically represents one full cycle
of a note. To avoid aliasing distortion with these samples you should
use period values in the range 124-256 only. Periods from 124-256
correspond to playback rates in the range 14-28K samples per second which
makes the most effective use of the Amiga's 7 KHz cut-off filter to
prevent noise. To stay within this range you will need a different sample
for each octave.
If you cannot use a different sample for each octave, then you will have
to adjust the period value over its full range 124-65536. This is
easier for the programmer but can produce undesirable high-frequency noise
in the resulting tone. Read the section called Aliasing Distortion for
more about this.
The values in Table 5-7 were generated using the formula shown below. To
calculate the tone generated with a given sample size and period use:
Clock Constant 3579545
Frequency = --------------------- = ----------- = 880.8 Hz
Sample Bytes * Period 16 * Period
The clock constant in an NTSC system is 3579545 ticks per second. In a
PAL system, the clock constant is 3546895 ticks per second. Sample bytes
is the number of bytes in one cycle of the waveform sample. (The clock
constant is derived from dividing the system clock value by 2. The value
will vary when using an external system clock, such as a genlock.)
Using the formula above you can generate the values needed for the
even-tempered scale for any arbitrary sample. Table 5-8 gives a close
approximation of a five octave even tempered-scale using five samples. The
values were derived using the formula above. Notice that in each octave
period values are the same but the sample size is halved. The samples
listed represent a simple triangular wave form.
Table 5-8: Five Octave Even-tempered Scale
NTSC PAL Ideal Actual NTSC Actual PAL
Period Period Note Frequency Frequency Frequency
------ ------ ---- --------- ----------- ----------
254 252 A 55.00 55.05 54.98
240 238 A# 58.27 58.26 58.21
226 224 B 61.73 61.87 61.85
214 212 C 65.40 65.34 65.35
202 200 C# 69.29 69.22 69.27
190 189 D 73.41 73.59 73.30
180 178 D# 77.78 77.68 77.83
170 168 E 82.40 82.25 82.47
160 159 F 87.30 87.39 87.13
151 150 F# 92.49 92.60 92.36
143 141 G 98.00 97.78 98.26
135 133 G# 103.82 103.57 104.17
Sample size = 256 bytes, AUDxLEN = 128
254 252 A 110.00 110.10 109.96
240 238 A# 116.54 116.52 116.43
226 224 B 123.47 123.74 123.70
214 212 C 130.81 130.68 130.71
202 200 C# 138.59 138.44 138.55
190 189 D 146.83 147.18 146.61
180 178 D# 155.56 155.36 155.67
170 168 E 164.81 164.50 164.94
160 159 F 174.61 174.78 174.27
151 150 F# 184.99 185.20 184.73
143 141 G 196.00 195.56 196.52
135 133 G# 207.65 207.15 208.35
Sample size = 128 bytes, AUDxLEN = 64
254 252 A 220.00 220.20 219.92
240 238 A# 233.08 233.04 232.86
226 224 B 246.94 247.48 247.41
214 212 C 261.63 261.36 261.42
202 200 C# 277.18 276.88 277.10
190 189 D 293.66 294.37 293.23
180 178 D# 311.13 310.72 311.35
170 168 E 329.63 329.00 329.88
160 159 F 349.23 349.56 348.55
151 150 F# 369.99 370.40 369.47
143 141 G 392.00 391.12 393.05
135 133 G# 415.30 414.30 416.70
Sample size = 64 bytes, AUDxLEN = 32
254 252 A 440.0 440.4 439.8
240 238 A# 466.16 466.09 465.72
226 224 B 493.88 494.96 494.82
214 212 C 523.25 522.71 522.83
202 200 C# 554.37 553.77 554.20
190 189 D 587.33 588.74 586.46
180 178 D# 622.25 621.45 622.70
170 168 E 659.26 658.00 659.76
160 159 F 698.46 699.13 697.11
151 150 F# 739.99 740.80 738.94
143 141 G 783.99 782.24 786.10
135 133 G# 830.61 828.60 833.39
Sample size = 32 bytes, AUDxLEN = 16
254 252 A 880.0 880.8 879.7
240 238 A# 932.3 932.2 931.4
226 224 B 987.8 989.9 989.6
214 212 C 1046.5 1045.4 1045.7
202 200 C# 1108.7 1107.5 1108.4
190 189 D 1174.7 1177.5 1172.9
180 178 D# 1244.5 1242.9 1245.4
170 168 E 1318.5 1316.0 1319.5
160 159 F 1396.9 1398.3 1394.2
151 150 F# 1480.0 1481.6 1477.9
143 141 G 1568.0 1564.5 1572.2
135 133 G# 1661.2 1657.2 1666.8
Sample size = 16 bytes, AUDxLEN = 8
256 Byte Sample
---------------
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94
96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126
128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98
96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66
64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34
32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2
0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30
-32 -34 -36 -38 -40 -42 -44 -46 -48 -50 -52 -54 -56 -58 -60 -62
-64 -66 -68 -70 -72 -74 -76 -78 -80 -82 -84 -86 -88 -90 -92 -94
-96 -98-100-102-104-106-108-110-112-114-116-118-120-122-124-126
-127-126-124-122-120-118-116-114-112-110-108-106-104-102-100 -98
-96 -94 -92 -90 -88 -86 -84 -82 -80 -78 -76 -74 -72 -70 -68 -66
-64 -62 -60 -58 -56 -54 -52 -50 -48 -46 -44 -42 -40 -38 -36 -34
-32 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2
128 Byte Sample
---------------
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124
128 124 120 116 112 108 104 100 96 92 88 84 80 76 72 68
64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124
-127-124-120-116-112-108-104-100 -96 -92 -88 -84 -80 -76 -72 -68
-64 -60 -56 -52 -48 -44 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4
64 Byte Sample
--------------
0 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
128 120 112 104 96 88 80 72 64 56 48 40 32 24 16 8
0 -8 -16 -24 -32 -40 -48 -56 -64 -72 -80 -88 -96-104-112-120
-127-120-112-104 -96 -88 -80 -72 -64 -56 -48 -40 -32 -24 -16 -8
32 Byte Sample
--------------
0 16 32 48 64 80 96 112 128 112 96 80 64 48 32 16
0 -16 -32 -48 -64 -80 -96-112-127-112 -96 -80 -64 -48 -32 -16
16 Byte Sample
--------------
0 32 64 96 128 96 64 32 0 -32 -64 -96-127 -96 -64 -32