analmux

As long as it's aimed at a playfield/BG (even in theory), then it has the same worth. If the code of a moving ball runs, then it's not that hard to add a playfield.

Thanks.

@ makary It seems that you also don't like the standard 64 kHz mode. The 15 kHz mode gives a possibility for 8-bit AUDF values and square bass notes. Do you have new PoKey ideas? Then maybe you can study RMT 1.28 Patch 8, which is especially made for the 15 kHz mode. Here you can find patch 8, some example tunes and YouTube links: http://atariage.com/forums/topic/234769-rmt-patch-8/

@ others Ehm ... Font and screen tricks are too easy, with BAS sitting idle most of the time. Just look at Mamutisko's BAS program. He's dealing with some numerical mathematics and practical physics (classical mechanics) to mimic realistic movenents of a ball.

I tested your code, and it seems quite heavy running it with the standard basic. Anyway, do you have an XL or XE computer? Then you can use turbobasic instead, which gives more possibilities. It also runs faster and the PAUSE command can lock the program to a fixed run frequency by vertical blank. If it's still too slow, then you can try a compiler / runtime.

@ thorfdbg I've made some new simple tests. See TEST2.BAS (picture 201601241.png). The input is again a theoretical AUDF+1 type starting number. The output is the complete table of errors in %'s of the 38 table steps. See picture 201601242.png and see the difference between 3 starting numbers. Start 256.08 is related to the approximate minimal L2 REL. Start 255.91 is related to the approximate minimal LI REL at 441 Hz (1 Hz steps). Start 255.84 is related to the approximate minimal LI REL at 441.12 Hz (0.01 Hz steps). This shows that the indivual errors look similar with respect to L2 RES (my method) and to LI RES (your method). See TEST3.BAS (201601243.png). This shows the absolute error sums (AES). Picture 201601244 shows its solution. It is remarkable that my minimal L2 RES (at 256.08) has the lowest AES value. Your minimal LI RES (at 255.91) the AES value is a bit higher. The better LI RES solution at 255.84 is even a bit higher again.

@ thorfdbg At first, thanks for your answers. I didn't use any absolute linear minimum error ($l^1$) at all. I used the L2 REL (thus the relative least mean square error) and the LI REL (thus the relative minimal maximum error) all the time. It's no problem if you are unsure, but it's rather obscure that you nevertheless made a choice which claimed that I made a mistake. See here: About your answer to my QUESTION I. Then we finally agree, as we should do. Indeed, we shouldn't argue at all. Even if you used a discrete linear frequency domain (or 'frequency quantization') and if I used a discrete linear time domain (or 'inverse frequency quantization'). Then I still don't understand why you didn't agree at first: However, discussing about quantizations isn't that important anyway. The correct measure is the most important here. Only the n-measure (n for 'note space') counts: f=1/T and n=log(f)=-log(T) so that f=exp(n) and T=exp(-n). About your answer to my QUESTION II. To change from 1 Hz sampling to 0.01 Hz sampling gives a better, more correct and significant final solution. About your answer to my QUESTION III. The L2 (least mean square error) also has its benefits; the LI (minimal maximum error) also has its weakness. The L2 solution often gives the possibility to minimize all the 'individual' errors at the same time. It is clear that the LI is only a projection map from the table of errors and to (just) the maximum value in this table. When you found the minimal LI (or 'LI solution'), then it is still possible that all the (other) errors are equal to the maximal error at the same time. The map image itself doesn't show or minimize that. But on the other hand it also has its weakness: in many cases the minimal LI is still too large, so it won't help in all cases. You cannot just bend the information. Yes, but that applies for both L2 and LI. And in many cases the information itself determines the structure of a sequence of individual errors.

Ehm, LI is not l^1. Just read again my post #19. It's better to rewrite your reply.

Dear thorfdbg, Have a look at one example: So you said that it isn't correct, so you think it is a problem. But here's again my explanation which you can also find in post #18. I used the AUDF+1 index, which is the real pitch number. Not AUDF itself. So in reality you made a little mistake. Thus this problem doesn't exist. QUESTION I: Do you think that your LI REL in frequency space and my LI REL in inverse frequency space are different? QUESTION II: What is the proper quantization you used in your code? You're wrong. I'm sorry, but the 1 Hz step you used wasn't good enough. See again my post #21. Frequency 441.12 Hz is a better approximation to find the minimal maximum relative error, with respect to your solution 441 Hz. The table results of 441 and 441.12 are different. Only partially. My last program LMS9.BAS is a summary of the most important previous ones. Column 2 shows L2 REL and column 3 shows LI REL, both at the inverse frequency space, so only column 2 is different. Column 3 should give the same result, as it's my way to compute the LI REL. The L2 REL doesn't need to be the same. See again my post #21 and the main definition here: I agree, but that doesn't say that my L2 REL method gives a wrong solution in the objective way. The L2 REL and LI REL are different, but they can both be used for this research. No, it doesn't hit only one specific frequency. From the chosen frequency at the start, a chromatic scale is constructed. No, there is no problem. Just try to understand my simple LMS9.BAS program. Especially the variable SUM1. Then you will see that the table (of 38 or 48 notes) gives a summation, pointed at the base frequency, but also the chromatic scale, up to the last note. Anyway, I know that the L2 ABS and L2 REL is quite common to minimize the difference between the measure data and the ideal data. I used it for practical physics. So: QUESTION III: Could you explain why you think L2 approximation is not correct in this situation? No, I don't miss anything and I am not too much only a mathematician. To conclude: it would be really interesting when you show your answers to my questions I, II and III.

Yes, I found it. Data is 25600 bytes, and the TBB program is only appr. 1 kB at max. @ dmsc Simple, but interesting. It is possible to write the data table directly into memory as a binary file. You made a small TBB file, and you can write it from page 64. Then only change the 3 LMS indexes on the display list per frame.

Interesting. What's the total size of your programm and data?

Dear thorfdbg, You started mentioning problems, but that won't say that they suddenly exist in reality. I really don't understand your attitude. When I only had interests and fun to check your computations, at the beginning of this topic, I added many substantive ideas, just to compare your method with mine. But as time goes on, I got the feeling you don't really like my substantive comments. I guess it feels very personal for you. It is so weird that you feel personally affected when I was just pointing you to your mistakes and correcting your mathematical ideas. Do you still say my method is not a suitable solution? One of the many many courses I got was about mathematical physics, during my second year Physics and Astronomy, Bachelor of Science. If you understand mathematical physics, then you should immediately understand what I was talking about and agree with me. But I'm afraid you're still trying to put me down personally. In general I don't mind at all when people don't agree with me. But you didn't mention any alternative conclusion or counterproof, to show that I made a mistake. It is weird that you just claimed that my methods are wrong. That is no scientific discussion at all. You just turned the discussion into personal. So there is no scientific dispute anyway. I wrote down a scientific proof which shows that some of your mathematical ideas aren't correct. But you just ignored my ideas and you didn't present your alternative conclusion and counterproof. Then you stopped discussing substantively and you just responded personally. This is just ridiculous. It's a pity that a substantive discussions is impossible.

We just don't fit together, and I don't need him anyway, so no thanks.

Now it's time to pay

That's why a 16-bit bass should never have been the standard setting. The 15 kHz mode gives always more possibilities.

I understand that my problem only exists in your phantasy. I understand your C code, but you yourself have indicated that you do not understand my work. But you claimed that my test are incorrect. That makes your comments a little ridiculous.

@ thorfdbg Could you explain what you mean with one of your replies? See: "Yet, I would argue that the error metric I have chosen is a better choice as you can hardly hear the l^2 error but only individual notes." (See post 6 in this topic.) Remember one of my replies: "It could also depend on the size of the table." (See post 5 in this topic.) I understand how you restricted the size of your table to 38 tones. Then your solution and mine are different. But it is striking when you expand the table size to 48 notes. Then the result of a local minimum of your maximum relative error (LI REL) and the result of my global relative least mean square (L2 REL) coincide. Then your minimum approximation is 256.03 and my minimum approximation is 256.07: then the results are identical. Note that I used table size of 48 notes for RMT Patch 8. Compare to the table size of 61 notes for the standard RMT, by RaSter. Anyway, I still don't understand why you have this attitude. To be precise, you wrote my computation methods and solutions aren't correct. If you don't understand my methods, then just ask a neat question. I agree that at first it seems that the LI REL minimum in frequency (f) space is not related to the LI REL minimum in time (T) space. Indeed: f=1/T (thus T=1/f), so that f-quantization and T-quantization have no linear relation. But in fact you didn't use f-quantization, but n-quantization (for 'notes'). Then the relation is f=exp(n)=1/exp(-n). Thus T=exp(-n). Then the log function is the inverse of the exp function. Now note that the 1-st order approximation of the Taylor series of log(x) is equal to x-1 for x0=1 and x~x0. The x can be replaced by A/B. So in fact there is an equivalence between your example "error = targetfreq / outfreq" (see findFreq) and my example "ABS(1-B/A)". So if you want to minimize the LI-error of the frequency, the answer is in fact "note space". Thus relative f-error, relative T-error and absolute n-error are equivalent. For me this is just children's mathematics. I posted some advanced mathematics on the internet. See here for example: http://math.stackexchange.com/questions/1177583/quotient-spaces-so3-so2-and-so3-o2/1358628#1358628 Do you have other questions? Best regards, 'Analogue Multiplexer', MSc (Hons. Mult.) Theoretical Physics, Master of Science, Honours Programme (Final thesis about membrane instantons and non-perturbative superstring theory.) Mathematical Sciences, Master of Science, Honours Programme (Final thesis about symmetric monoidal categories and topological quantum field theories.) I know what I'm doing.

I hope this topic helps: http://atariage.com/forums/topic/234400-rmt-128-patch-8-theory/ (Especially post #32.)

Here's one of his works. The music still lives, and I like it.

Another test to compare some results. My approach was to find global minima of the L2 REL and the LI REL, but this time I replaced the LINAPP with the LOGAPP. The LINAPP is defined with: B=INT(A+0.5) And the LOGAPP is defined with: B=INT(A):IF A>=SQR(B*(B+1)) THEN B=B+1 Here is the test program called LMS9.BAS. See picture 31.png. After running LMS9.BAS and finding a minimum of the L2 REL, when focused at column 2, I found an approximate minimal solution MIN(L2 REL) = 256.08. See picture 32.png. After running LMS9.BAS and finding a minimum of the LI REL, when focused at column 3, I found an approximate minimal solution MIN(LI REL) = 255.84. See picture 33.png. Here is the test program called TEST1.BAS. See picture 34.png. Here you can start with an arbitrary pitch value (around 256, of type AUDF+1). I made 4 choices (256.08, 256, 255.91 and 255.84) to compare the results. See picture 35.png. This shows that 256.08 and 256 have the same result. But from 256 to 255.91 gives a change, at place 19 (1-based), value 91 to 90. But also from 255.91 to 255.84 also gives a change, at place 2 (1-based), value 242 to 241. @ thorfdbg I still don't see why you got 255.91 (which is equivalent to your minimal solution 441 Hz). You should find 255.84 (which is equivalent to solution 441.12). In your C++ code, you made integer steps: ...,440,441,442,... My solution doesn't say that 255.91 is the minimum, but 255.84. And then the resulting table is different.

I know ...

@ thorfdbg OK, I find it interesting to compare the L2 and LI methods, and wrote a simple expand of LMS1.BAS: Initially, you can assume that line 105,106,107,108,110 and 111 are inactive (REM mode) - For the L2 ABS method, turn on lines 105 and 110 - For the L2 REL method, turn on lines 106 and 110 - For the LI ABS method, turn on lines 107 and 111 - For the LI REL method, turn on lines 108 and 111 And here the minima: - The L2 ABS (2.png) method gives the approximate minimal solution at 256.09 with value 2.151... - The L2 REL (3.png) method gives the approximate minimal solution at 256.09 with value 0.0004158... - The LI ABS (4.png) method gives the approximate minimal solution at 256.77 with value 0.4387... - The LI REL (5.png) method gives the approximate minimal solution at 255.85 with value 0.007293... I do understand why the coordinates of the minimal L2 ABS and L2 REL are equal, as the non-linear relation (coordinate transformation) between ABS and REL doesn't generate a deformation. But the minimal LI ABS has no meaning. Only the LI REL can be correct. Thus, L2 ABS and L2 REL support my solution, and LI REL supports your solution. The L2 method is good enough. There is no real sign that the LI method is better, but just equivalent. ------------------ Some symbols: L2 = L^2 LI = L^infinity ABS = absolute REL = relative

I still doubt if the mid range notes (which start around 0:46) will sound better if you change it from PoKey distortion 10 (at 15 kHz) to PoKey distortion 2 (at 1.79 MHz).