analmux Posted January 26, 2015 Share Posted January 26, 2015 Remember RMT's 'pure frequency table', for a discrete approximation of a modern chromatic tone ladder: FRQTABPURE DTA $F3,$E6,$D9,$CC,$C1,$B5,$AD,$A2 DTA $99,$90,$88,$80,$79,$72,$6C,$66 DTA $60,$5B,$55,$51,$4C,$48,$44,$40 DTA $3C,$39,$35,$32,$2F,$2D,$2A,$28 DTA $25,$23,$21,$1F,$1D,$1C,$1A,$18 DTA $17,$16,$14,$13,$12,$11,$10,$0F DTA $0E,$0D,$0C,$0B,$0A,$09,$08,$07 DTA $06,$05,$04,$03,$02,$01,$00,$00 I'm studying an alternative "NOTE-2-PITCH" table (see below), to compare with the already existing above. See also BASIC or TURBOBASIC download at the bottom. I'm looking at 'absolute least mean square' and 'relative least mean square' to find a minimal distance series, to find an improved table: One of my solutions is just starting at AUDF+1=256, and I'm surprised that it's not equal to RMT's table. However, maybe RaSter used another optimization, because the distortion 12 basses need to define the minimal solution, not distortion 10. FRQTABBASS2 DTA $FF,$F1,$E4,$D8,$CA,$C0,$B5,$AB DTA $A2,$99,$8E,$87,$7F,$79,$73,$70 DTA $66,$61,$5A,$55,$52,$4B,$48,$43 DTA $3F,$3C,$39,$37,$33,$30,$2D,$2A DTA $28,$25,$24,$21,$1F,$1E,$1C,$1B DTA $19,$17,$16,$15,$13,$12,$11,$10 DTA $0F,$0E,$0D,$0C,$0B,$0A,$09,$08 DTA $07,$06,$05,$04,$03,$02,$01,$00 Does any of you have another idea? TEST2015.ATR 1 Quote Link to comment Share on other sites More sharing options...
Synthpopalooza Posted January 26, 2015 Share Posted January 26, 2015 I don't know if this will help, but I also compiled my own POKEY note table, covering distortions 2, 10, 12a and 12b (the last one being (freq+1)mod 3 = 0, for less buzzy bass sounds). http://atariage.com/forums/topic/216807-complete-pokey-note-table-for-all-distortion-settings/ I did this, based on the already existing distortion 10 note tables in 8 and 16-bit mode, and matching the pitches by ear. As it's based on distortion 10, I've probably gotten the same results as Raster's table. Shame he isn't around for us to ask anymore. 1 Quote Link to comment Share on other sites More sharing options...
analmux Posted January 26, 2015 Author Share Posted January 26, 2015 (edited) Thanks for another detailed reference. And, indeed, RaSter's table and the "COMPUTE! ISSUE 34 / MARCH 1983 / PAGE 214" table looks the same. Edited January 26, 2015 by analmux Quote Link to comment Share on other sites More sharing options...
analmux Posted January 26, 2015 Author Share Posted January 26, 2015 My next step will be:• Create a new set of "note-2-pitch" tables• PHI = PAL or NTSC base clock• Base frequency will be 15 kHz, thus PHI / 256*114 ~ 60 Hz will be the lowest note in this table. Thus using my alternative table, starting with AUDF+1=256, may give a best approximation of a real chromatic modern western scale. 1 Quote Link to comment Share on other sites More sharing options...
analmux Posted January 27, 2015 Author Share Posted January 27, 2015 (edited) ... And I'm just thinking about how to improve the whole-number-discretization: (1) Standard linear approximation (LINAPP): LINAPP gives us B := INT(A+0.5), and it is equivalent to: A0 := INT(A) so that A0 <= A < A0+1 B := A0 iff A-A0 < 0.5 thus iff A < A0+0.5 B := A0+1 iff A-A0 => 0.5 thus iff A => A0+0.5 (2) Logarith approximation (LOGAPP): A0 := INT(A) so that A0 <= A < A0+1 and LOG(A0) <= LOG(A) < LOG(A0+1) Define C := (LOG(A0)+LOG(A0+1))/2 = LOG(SQR(A0*(A0+1))) B := A0 iff LOG(A) < C thus iff A < SQR(A0*(A0+1)) B := A0+1 iff A => SQR(A0*(A0+1)) Now I think if A > 10 then the difference between LINAPP and LOGAPP is small enough, so that we can use LINAPP as a sufficiently approximation of LOGAPP. Then the LOGAPP idea can be ignored. But if A is critical, for example A=1.42, then B=1 gives the best LINAPP solution, but not w.r.t. LOGAPP. Edited January 27, 2015 by analmux Quote Link to comment Share on other sites More sharing options...
+MrFish Posted January 29, 2015 Share Posted January 29, 2015 (edited) This is interesting to me, because I'd always wondered how the Atari 12 note scales were derived, especially in relation to RMT. I was mainly just curious if it was all based on equal temperament. So I wrote a little program today in order to produce a table to compare with a precise equal temperament for Middle C at 440, and then compare the produced table with what you've posted above for RMT (which coincides with the article in Compute that you pointed out). The results by comparison look to show the scale used by RMT / Compute has been shifted up in pitch for the lower notes, most likely to compensate for the unavoidable sharpness in the higher notes -- although quite a few are flat as well. All the values produced below are exactly +1 (= lower in pitch) compared to RMT's table, until you get to a certain point in the higher notes, then everything coincides. I checked the values by hand to see whether they were actually closer than RMT's to the precise equal tempered scale, and they were. Whether or not this would actually sound better in practice or not I don't know, as it would need a real-world test. Never the less it's satisfied my curiosity about the data. [Note: The octave numbers listed do not coincide with what's shown on the article in Compute, but are based on octaves for an actual 88 key piano/keyboard.] I like the idea you have, even though it doesn't attempt to match up with Middle C = 440, as it looks like you're trying to get the most accurate scale based on fitting to the available values on the Atari. Next I'll perform the same comparison on the 16-bit values to see how things match up with the article in Compute. OCTAVE - NOTE = 3 - C FREQUENCY DIVISOR = 244, $F4 ATARI FREQUENCY = 261.971311 TEMPERED FREQUENCY = 261.625561 CENTS ERROR = 2.2863857 ------------------------------ OCTAVE - NOTE = 3 - C# FREQUENCY DIVISOR = 231, $E7 ATARI FREQUENCY = 276.714285 TEMPERED FREQUENCY = 277.18262 CENTS ERROR = -2.92762851 ------------------------------ OCTAVE - NOTE = 3 - D FREQUENCY DIVISOR = 218, $DA ATARI FREQUENCY = 293.215596 TEMPERED FREQUENCY = 293.664761 CENTS ERROR = -2.64998176 ------------------------------ OCTAVE - NOTE = 3 - D# FREQUENCY DIVISOR = 205, $CD ATARI FREQUENCY = 311.809756 TEMPERED FREQUENCY = 311.126975 CENTS ERROR = 3.7951002 ------------------------------ OCTAVE - NOTE = 3 - E FREQUENCY DIVISOR = 194, $C2 ATARI FREQUENCY = 329.48969 TEMPERED FREQUENCY = 329.627548 CENTS ERROR = -0.7242334751 ------------------------------ OCTAVE - NOTE = 3 - F FREQUENCY DIVISOR = 183, $B7 ATARI FREQUENCY = 349.295081 TEMPERED FREQUENCY = 349.22822 CENTS ERROR = 0.3314137507 ------------------------------ OCTAVE - NOTE = 3 - F# FREQUENCY DIVISOR = 173, $AD ATARI FREQUENCY = 369.485549 TEMPERED FREQUENCY = 369.994416 CENTS ERROR = -2.38269943 ------------------------------ OCTAVE - NOTE = 3 - G FREQUENCY DIVISOR = 163, $A3 ATARI FREQUENCY = 392.153374 TEMPERED FREQUENCY = 391.995428 CENTS ERROR = 0.6974091715 ------------------------------ OCTAVE - NOTE = 3 - G# FREQUENCY DIVISOR = 154, $9A ATARI FREQUENCY = 415.071428 TEMPERED FREQUENCY = 415.304681 CENTS ERROR = -0.9726206825 ------------------------------ OCTAVE - NOTE = 4 - A FREQUENCY DIVISOR = 145, $91 ATARI FREQUENCY = 440.834482 TEMPERED FREQUENCY = 440 CENTS ERROR = 3.280263 ------------------------------ OCTAVE - NOTE = 4 - A# FREQUENCY DIVISOR = 137, $89 ATARI FREQUENCY = 466.576642 TEMPERED FREQUENCY = 466.163747 CENTS ERROR = 1.53271051 ------------------------------ OCTAVE - NOTE = 4 - B FREQUENCY DIVISOR = 129, $81 ATARI FREQUENCY = 495.511627 TEMPERED FREQUENCY = 493.883285 CENTS ERROR = 5.6985076 ------------------------------ OCTAVE - NOTE = 4 - C FREQUENCY DIVISOR = 122, $7A ATARI FREQUENCY = 523.942622 TEMPERED FREQUENCY = 523.251124 CENTS ERROR = 2.2863857 ------------------------------ OCTAVE - NOTE = 4 - C# FREQUENCY DIVISOR = 115, $73 ATARI FREQUENCY = 555.834782 TEMPERED FREQUENCY = 554.365251 CENTS ERROR = 4.58313622 ------------------------------ OCTAVE - NOTE = 4 - D FREQUENCY DIVISOR = 109, $6D ATARI FREQUENCY = 586.431192 TEMPERED FREQUENCY = 587.32952 CENTS ERROR = -2.64998176 ------------------------------ OCTAVE - NOTE = 4 - D# FREQUENCY DIVISOR = 103, $67 ATARI FREQUENCY = 620.592233 TEMPERED FREQUENCY = 622.253959 CENTS ERROR = -4.62946556 ------------------------------ OCTAVE - NOTE = 4 - E FREQUENCY DIVISOR = 97, $61 ATARI FREQUENCY = 658.979381 TEMPERED FREQUENCY = 659.255104 CENTS ERROR = -0.7242334751 ------------------------------ OCTAVE - NOTE = 4 - F FREQUENCY DIVISOR = 92, $5C ATARI FREQUENCY = 694.793478 TEMPERED FREQUENCY = 698.456448 CENTS ERROR = -9.10314599 ------------------------------ OCTAVE - NOTE = 4 - F# FREQUENCY DIVISOR = 86, $56 ATARI FREQUENCY = 743.267441 TEMPERED FREQUENCY = 739.988843 CENTS ERROR = 7.65346401 ------------------------------ OCTAVE - NOTE = 4 - G FREQUENCY DIVISOR = 82, $52 ATARI FREQUENCY = 779.52439 TEMPERED FREQUENCY = 783.990861 CENTS ERROR = -9.89124021 ------------------------------ OCTAVE - NOTE = 4 - G# FREQUENCY DIVISOR = 77, $4D ATARI FREQUENCY = 830.142857 TEMPERED FREQUENCY = 830.609375 CENTS ERROR = -0.9726605457 ------------------------------ OCTAVE - NOTE = 5 - A FREQUENCY DIVISOR = 73, $49 ATARI FREQUENCY = 875.630136 TEMPERED FREQUENCY = 880 CENTS ERROR = -8.61833051 ------------------------------ OCTAVE - NOTE = 5 - A# FREQUENCY DIVISOR = 69, $45 ATARI FREQUENCY = 926.391304 TEMPERED FREQUENCY = 932.327514 CENTS ERROR = -11.05819368 ------------------------------ OCTAVE - NOTE = 5 - B FREQUENCY DIVISOR = 65, $41 ATARI FREQUENCY = 983.4 TEMPERED FREQUENCY = 987.766582 CENTS ERROR = -7.6701858 ------------------------------ OCTAVE - NOTE = 5 - C FREQUENCY DIVISOR = 61, $3D ATARI FREQUENCY = 1047.885245 TEMPERED FREQUENCY = 1046.502231 CENTS ERROR = 2.28640245 ------------------------------ OCTAVE - NOTE = 5 - C# FREQUENCY DIVISOR = 58, $3A ATARI FREQUENCY = 1102.086206 TEMPERED FREQUENCY = 1108.730485 CENTS ERROR = -10.4059929 ------------------------------ OCTAVE - NOTE = 5 - D FREQUENCY DIVISOR = 54, $36 ATARI FREQUENCY = 1183.722222 TEMPERED FREQUENCY = 1174.659043 CENTS ERROR = 13.30620873 ------------------------------ OCTAVE - NOTE = 5 - D# FREQUENCY DIVISOR = 51, $33 ATARI FREQUENCY = 1253.352941 TEMPERED FREQUENCY = 1244.507888 CENTS ERROR = 12.26081231 ------------------------------ OCTAVE - NOTE = 5 - E FREQUENCY DIVISOR = 48, $30 ATARI FREQUENCY = 1331.6875 TEMPERED FREQUENCY = 1318.510184 CENTS ERROR = 17.21622161 ------------------------------ OCTAVE - NOTE = 5 - F FREQUENCY DIVISOR = 46, $2E ATARI FREQUENCY = 1389.586956 TEMPERED FREQUENCY = 1396.912899 CENTS ERROR = -9.10314599 ------------------------------ OCTAVE - NOTE = 5 - F# FREQUENCY DIVISOR = 43, $2B ATARI FREQUENCY = 1486.534883 TEMPERED FREQUENCY = 1479.97765 CENTS ERROR = 7.65349869 ------------------------------ OCTAVE - NOTE = 5 - G FREQUENCY DIVISOR = 41, $29 ATARI FREQUENCY = 1559.04878 TEMPERED FREQUENCY = 1567.981687 CENTS ERROR = -9.89120035 ------------------------------ OCTAVE - NOTE = 5 - G# FREQUENCY DIVISOR = 38, $26 ATARI FREQUENCY = 1682.131578 TEMPERED FREQUENCY = 1661.218732 CENTS ERROR = 21.65820486 ------------------------------ OCTAVE - NOTE = 6 - A FREQUENCY DIVISOR = 36, $24 ATARI FREQUENCY = 1775.583333 TEMPERED FREQUENCY = 1760 CENTS ERROR = 15.26116116 ------------------------------ OCTAVE - NOTE = 6 - A# FREQUENCY DIVISOR = 34, $22 ATARI FREQUENCY = 1880.029411 TEMPERED FREQUENCY = 1864.654995 CENTS ERROR = 14.21579423 ------------------------------ OCTAVE - NOTE = 6 - B FREQUENCY DIVISOR = 32, $20 ATARI FREQUENCY = 1997.53125 TEMPERED FREQUENCY = 1975.533144 CENTS ERROR = 19.17121828 ------------------------------ OCTAVE - NOTE = 6 - C FREQUENCY DIVISOR = 31, $1F ATARI FREQUENCY = 2061.967741 TEMPERED FREQUENCY = 2093.004471 CENTS ERROR = -25.86435939 ------------------------------ OCTAVE - NOTE = 6 - C# FREQUENCY DIVISOR = 29, $1D ATARI FREQUENCY = 2204.172413 TEMPERED FREQUENCY = 2217.460987 CENTS ERROR = -10.4059929 ------------------------------ OCTAVE - NOTE = 6 - D FREQUENCY DIVISOR = 27, $1B ATARI FREQUENCY = 2367.444444 TEMPERED FREQUENCY = 2349.318064 CENTS ERROR = 13.30622587 ------------------------------ OCTAVE - NOTE = 6 - D# FREQUENCY DIVISOR = 26, $1A ATARI FREQUENCY = 2458.5 TEMPERED FREQUENCY = 2489.015828 CENTS ERROR = -21.35647639 ------------------------------ OCTAVE - NOTE = 6 - E FREQUENCY DIVISOR = 24, $18 ATARI FREQUENCY = 2663.375 TEMPERED FREQUENCY = 2637.020386 CENTS ERROR = 17.21620487 ------------------------------ OCTAVE - NOTE = 6 - F FREQUENCY DIVISOR = 23, $17 ATARI FREQUENCY = 2779.173913 TEMPERED FREQUENCY = 2793.825787 CENTS ERROR = -9.10314599 ------------------------------ OCTAVE - NOTE = 6 - F# FREQUENCY DIVISOR = 22, $16 ATARI FREQUENCY = 2905.5 TEMPERED FREQUENCY = 2959.95535 CENTS ERROR = -32.1467898 ------------------------------ OCTAVE - NOTE = 6 - G FREQUENCY DIVISOR = 20, $14 ATARI FREQUENCY = 3196.05 TEMPERED FREQUENCY = 3135.963407 CENTS ERROR = 32.85748934 ------------------------------ OCTAVE - NOTE = 6 - G# FREQUENCY DIVISOR = 19, $13 ATARI FREQUENCY = 3364.263157 TEMPERED FREQUENCY = 3322.43747 CENTS ERROR = 21.65820486 ------------------------------ OCTAVE - NOTE = 7 - A FREQUENCY DIVISOR = 18, $12 ATARI FREQUENCY = 3551.166666 TEMPERED FREQUENCY = 3520 CENTS ERROR = 15.26116116 ------------------------------ OCTAVE - NOTE = 7 - A# FREQUENCY DIVISOR = 17, $11 ATARI FREQUENCY = 3760.058823 TEMPERED FREQUENCY = 3729.310035 CENTS ERROR = 14.21577709 ------------------------------ OCTAVE - NOTE = 7 - B FREQUENCY DIVISOR = 16, $10 ATARI FREQUENCY = 3995.0625 TEMPERED FREQUENCY = 3951.066322 CENTS ERROR = 19.17120114 ------------------------------ OCTAVE - NOTE = 7 - C FREQUENCY DIVISOR = 15, $0F ATARI FREQUENCY = 4261.4 TEMPERED FREQUENCY = 4186.008887 CENTS ERROR = 30.90252296 ------------------------------ OCTAVE - NOTE = 7 - C# FREQUENCY DIVISOR = 14, $0E ATARI FREQUENCY = 4565.785714 TEMPERED FREQUENCY = 4434.922002 CENTS ERROR = 50.34529293 Edited January 29, 2015 by MrFish 2 Quote Link to comment Share on other sites More sharing options...
+MrFish Posted January 29, 2015 Share Posted January 29, 2015 (edited) Ah, that's what I get for posting after midnight... I should have said A of the 4th octave at 440, not "Middle C", which would be the first A coming after Middle C while ascending in pitch. Middle C is actually the first (lowest) note in this scale. Also, the octaves are numbered starting at zero. Edited January 29, 2015 by MrFish Quote Link to comment Share on other sites More sharing options...
+MrFish Posted January 29, 2015 Share Posted January 29, 2015 Here's a table using the 15kHz clock. I suppose one possible use for these tables, or any related tables, is that compositions can be created based on avoiding notes with too high of an error ratio. I believe Paul Slocum created a composition tool for the 2600's TIA -- which has more tuning problems than Pokey -- for assisting in doing just this. Also, notes which are "out" by similar ratios can be used together for compositions, being in tune with each other, but being more limited in number. However, working with limitations can often produce interesting and unique results. I'll probably end up formatting these tables for putting into spreadsheets. I'll also probably make up some tables based on RMT's selected frequency divisors, since the tables I've created so far are only useful in the above stated sense if RMT is patched to use them. OCTAVE - NOTE = 1 - B FREQUENCY DIVISOR = 254, $FE ATARI FREQUENCY = 61.81062992 TEMPERED FREQUENCY = 61.73541192 CENTS ERROR = 2.10803524 ------------------------------ OCTAVE - NOTE = 1 - C FREQUENCY DIVISOR = 240, $F0 ATARI FREQUENCY = 65.41625 TEMPERED FREQUENCY = 65.40639077 CENTS ERROR = 0.2609301434 ------------------------------ OCTAVE - NOTE = 1 - C# FREQUENCY DIVISOR = 227, $E3 ATARI FREQUENCY = 69.16255506 TEMPERED FREQUENCY = 69.29565665 CENTS ERROR = -3.32853208 ------------------------------ OCTAVE - NOTE = 1 - D FREQUENCY DIVISOR = 214, $D6 ATARI FREQUENCY = 73.36401869 TEMPERED FREQUENCY = 73.41619065 CENTS ERROR = -1.23073449 ------------------------------ OCTAVE - NOTE = 1 - D# FREQUENCY DIVISOR = 202, $CA ATARI FREQUENCY = 77.72227722 TEMPERED FREQUENCY = 77.7817447 CENTS ERROR = -1.32413382 ------------------------------ OCTAVE - NOTE = 1 - E FREQUENCY DIVISOR = 191, $BF ATARI FREQUENCY = 82.19842931 TEMPERED FREQUENCY = 82.40688802 CENTS ERROR = -4.38494508 ------------------------------ OCTAVE - NOTE = 1 - F FREQUENCY DIVISOR = 180, $B4 ATARI FREQUENCY = 87.22166666 TEMPERED FREQUENCY = 87.3070572 CENTS ERROR = -1.69406373 ------------------------------ OCTAVE - NOTE = 1 - F# FREQUENCY DIVISOR = 170, $AA ATARI FREQUENCY = 92.35235294 TEMPERED FREQUENCY = 92.49860482 CENTS ERROR = -2.7394745 ------------------------------ OCTAVE - NOTE = 1 - G FREQUENCY DIVISOR = 160, $A0 ATARI FREQUENCY = 98.124375 TEMPERED FREQUENCY = 97.99885837 CENTS ERROR = 2.2159296 ------------------------------ OCTAVE - NOTE = 1 - G# FREQUENCY DIVISOR = 151, $97 ATARI FREQUENCY = 103.972847 TEMPERED FREQUENCY = 103.826173 CENTS ERROR = 2.44395472 ------------------------------ OCTAVE - NOTE = 2 - A FREQUENCY DIVISOR = 143, $8F ATARI FREQUENCY = 109.78951 TEMPERED FREQUENCY = 110 CENTS ERROR = -3.31597519 ------------------------------ OCTAVE - NOTE = 2 - A# FREQUENCY DIVISOR = 135, $87 ATARI FREQUENCY = 116.295555 TEMPERED FREQUENCY = 116.540938 CENTS ERROR = -3.64907157 ------------------------------ OCTAVE - NOTE = 2 - B FREQUENCY DIVISOR = 127, $7F ATARI FREQUENCY = 123.621259 TEMPERED FREQUENCY = 123.470823 CENTS ERROR = 2.10803524 ------------------------------ OCTAVE - NOTE = 2 - C FREQUENCY DIVISOR = 120, $78 ATARI FREQUENCY = 130.8325 TEMPERED FREQUENCY = 130.81278 CENTS ERROR = 0.2609472846 ------------------------------ OCTAVE - NOTE = 2 - C# FREQUENCY DIVISOR = 113, $71 ATARI FREQUENCY = 138.937168 TEMPERED FREQUENCY = 138.591313 CENTS ERROR = 4.31491392 ------------------------------ OCTAVE - NOTE = 2 - D FREQUENCY DIVISOR = 107, $6B ATARI FREQUENCY = 146.728037 TEMPERED FREQUENCY = 146.83238 CENTS ERROR = -1.23073449 ------------------------------ OCTAVE - NOTE = 2 - D# FREQUENCY DIVISOR = 101, $65 ATARI FREQUENCY = 155.444554 TEMPERED FREQUENCY = 155.563489 CENTS ERROR = -1.32413382 ------------------------------ OCTAVE - NOTE = 2 - E FREQUENCY DIVISOR = 95, $5F ATARI FREQUENCY = 165.262105 TEMPERED FREQUENCY = 164.813776 CENTS ERROR = 4.70292734 ------------------------------ OCTAVE - NOTE = 2 - F FREQUENCY DIVISOR = 90, $5A ATARI FREQUENCY = 174.443333 TEMPERED FREQUENCY = 174.614112 CENTS ERROR = -1.69406373 ------------------------------ OCTAVE - NOTE = 2 - F# FREQUENCY DIVISOR = 85, $55 ATARI FREQUENCY = 184.704705 TEMPERED FREQUENCY = 184.997208 CENTS ERROR = -2.7394745 ------------------------------ OCTAVE - NOTE = 2 - G FREQUENCY DIVISOR = 80, $50 ATARI FREQUENCY = 196.24875 TEMPERED FREQUENCY = 195.997715 CENTS ERROR = 2.21594634 ------------------------------ OCTAVE - NOTE = 2 - G# FREQUENCY DIVISOR = 76, $4C ATARI FREQUENCY = 206.577631 TEMPERED FREQUENCY = 207.652344 CENTS ERROR = -8.98335726 ------------------------------ OCTAVE - NOTE = 3 - A FREQUENCY DIVISOR = 71, $47 ATARI FREQUENCY = 221.125352 TEMPERED FREQUENCY = 220 CENTS ERROR = 8.83308838 ------------------------------ OCTAVE - NOTE = 3 - A# FREQUENCY DIVISOR = 67, $43 ATARI FREQUENCY = 234.326865 TEMPERED FREQUENCY = 233.081876 CENTS ERROR = 9.22264013 ------------------------------ OCTAVE - NOTE = 3 - B FREQUENCY DIVISOR = 64, $40 ATARI FREQUENCY = 245.310937 TEMPERED FREQUENCY = 246.941646 CENTS ERROR = -11.47033866 ------------------------------ OCTAVE - NOTE = 3 - C FREQUENCY DIVISOR = 60, $3C ATARI FREQUENCY = 261.665 TEMPERED FREQUENCY = 261.625561 CENTS ERROR = 0.2609472846 ------------------------------ OCTAVE - NOTE = 3 - C# FREQUENCY DIVISOR = 57, $39 ATARI FREQUENCY = 275.436842 TEMPERED FREQUENCY = 277.18262 CENTS ERROR = -10.93832523 ------------------------------ OCTAVE - NOTE = 3 - D FREQUENCY DIVISOR = 53, $35 ATARI FREQUENCY = 296.224528 TEMPERED FREQUENCY = 293.664761 CENTS ERROR = 15.02512076 ------------------------------ OCTAVE - NOTE = 3 - D# FREQUENCY DIVISOR = 50, $32 ATARI FREQUENCY = 313.998 TEMPERED FREQUENCY = 311.126975 CENTS ERROR = 15.90225767 ------------------------------ OCTAVE - NOTE = 3 - E FREQUENCY DIVISOR = 48, $30 ATARI FREQUENCY = 327.08125 TEMPERED FREQUENCY = 329.627548 CENTS ERROR = -13.42534649 ------------------------------ OCTAVE - NOTE = 3 - F FREQUENCY DIVISOR = 45, $2D ATARI FREQUENCY = 348.886666 TEMPERED FREQUENCY = 349.22822 CENTS ERROR = -1.69402387 ------------------------------ OCTAVE - NOTE = 3 - F# FREQUENCY DIVISOR = 42, $2A ATARI FREQUENCY = 373.807142 TEMPERED FREQUENCY = 369.994416 CENTS ERROR = 17.74876362 ------------------------------ OCTAVE - NOTE = 3 - G FREQUENCY DIVISOR = 40, $28 ATARI FREQUENCY = 392.4975 TEMPERED FREQUENCY = 391.995428 CENTS ERROR = 2.21596428 ------------------------------ OCTAVE - NOTE = 3 - G# FREQUENCY DIVISOR = 38, $26 ATARI FREQUENCY = 413.155263 TEMPERED FREQUENCY = 415.304681 CENTS ERROR = -8.9833174 ------------------------------ OCTAVE - NOTE = 4 - A FREQUENCY DIVISOR = 36, $24 ATARI FREQUENCY = 436.108333 TEMPERED FREQUENCY = 440 CENTS ERROR = -15.38039419 ------------------------------ OCTAVE - NOTE = 4 - A# FREQUENCY DIVISOR = 34, $22 ATARI FREQUENCY = 461.761764 TEMPERED FREQUENCY = 466.163747 CENTS ERROR = -16.42572523 ------------------------------ OCTAVE - NOTE = 4 - B FREQUENCY DIVISOR = 32, $20 ATARI FREQUENCY = 490.621875 TEMPERED FREQUENCY = 493.883285 CENTS ERROR = -11.47033866 ------------------------------ OCTAVE - NOTE = 4 - C FREQUENCY DIVISOR = 30, $1E ATARI FREQUENCY = 523.33 TEMPERED FREQUENCY = 523.251124 CENTS ERROR = 0.2609472846 ------------------------------ OCTAVE - NOTE = 4 - C# FREQUENCY DIVISOR = 28, $1C ATARI FREQUENCY = 560.710714 TEMPERED FREQUENCY = 554.365251 CENTS ERROR = 19.7037575 ------------------------------ OCTAVE - NOTE = 4 - D FREQUENCY DIVISOR = 27, $1B ATARI FREQUENCY = 581.477777 TEMPERED FREQUENCY = 587.32952 CENTS ERROR = -17.3353223 ------------------------------ OCTAVE - NOTE = 4 - D# FREQUENCY DIVISOR = 25, $19 ATARI FREQUENCY = 627.996 TEMPERED FREQUENCY = 622.253959 CENTS ERROR = 15.90222338 ------------------------------ OCTAVE - NOTE = 4 - E FREQUENCY DIVISOR = 24, $18 ATARI FREQUENCY = 654.1625 TEMPERED FREQUENCY = 659.255104 CENTS ERROR = -13.42534649 ------------------------------ OCTAVE - NOTE = 4 - F FREQUENCY DIVISOR = 22, $16 ATARI FREQUENCY = 713.631818 TEMPERED FREQUENCY = 698.456448 CENTS ERROR = 37.21172147 ------------------------------ OCTAVE - NOTE = 4 - F# FREQUENCY DIVISOR = 21, $15 ATARI FREQUENCY = 747.614285 TEMPERED FREQUENCY = 739.988843 CENTS ERROR = 17.74872894 ------------------------------ OCTAVE - NOTE = 4 - G FREQUENCY DIVISOR = 20, $14 ATARI FREQUENCY = 784.995 TEMPERED FREQUENCY = 783.990861 CENTS ERROR = 2.21594634 ------------------------------ OCTAVE - NOTE = 4 - G# FREQUENCY DIVISOR = 19, $13 ATARI FREQUENCY = 826.310526 TEMPERED FREQUENCY = 830.609375 CENTS ERROR = -8.98335726 ------------------------------ OCTAVE - NOTE = 5 - A FREQUENCY DIVISOR = 18, $12 ATARI FREQUENCY = 872.216666 TEMPERED FREQUENCY = 880 CENTS ERROR = -15.38039419 ------------------------------ OCTAVE - NOTE = 5 - A# FREQUENCY DIVISOR = 17, $11 ATARI FREQUENCY = 923.523529 TEMPERED FREQUENCY = 932.327514 CENTS ERROR = -16.4257651 ------------------------------ OCTAVE - NOTE = 5 - B FREQUENCY DIVISOR = 16, $10 ATARI FREQUENCY = 981.24375 TEMPERED FREQUENCY = 987.766582 CENTS ERROR = -11.47033866 ------------------------------ OCTAVE - NOTE = 5 - C FREQUENCY DIVISOR = 15, $0F ATARI FREQUENCY = 1046.66 TEMPERED FREQUENCY = 1046.502231 CENTS ERROR = 0.2609644257 1 Quote Link to comment Share on other sites More sharing options...
analmux Posted January 29, 2015 Author Share Posted January 29, 2015 Thanks MrFish. Indeed it's more accurate to forget A3 = 440 Hz and compute an approximation table under 64 kHz or 15 kHz mode. See my TEST2015.ATR (at post 1) and LOAD "D:LMS1.BAS" to compare with my techniques. The Least Mean Square computing I used gives a better approximation to use base note AUDF+1 at 256 (see left picture, AUDF=$FF) w.r.t. base note AUDF+1 around 244 (see right picture, AUDF=$F3). 1 Quote Link to comment Share on other sites More sharing options...
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