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emkay

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3 hours ago, rensoup said:

I kept waiting for it getting out of tune, or the drums killing everything else... It didn't happen 

 

nice ?

 

Originally, I tried this tune at 3 times VBI speed, to have the drums not too long. 

The latest discussions gave me ideas to shorten them and to play them at 1 x VBI.

To me the real advantage is the "Background voice" now is playing the notes at good frequency steps. 

So the main lead is followed by correct lower sounds. Just as it should be "normal" ;)

 

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8 hours ago, emkay said:

The point is the 220 440 880 Hz correctness. And this seems correct enough even in the 8 bit resolution.

The 432 Hz calculation is just wrong at this point. Always was , and I have been told "it's good" ;)

Synth tunes were always based on 440Hz calculations. 

Yeah, but that's 12-TET. We're talking just intonation here. If you base that on A=220,440,880,... songs in the key of C Major/A Minor, and some other keys will sound better. But try a tune in A# or G#m, and it will be all over the place and sound horribly out of tune.

 

Experiment: just for fun, transpose your whole song one semitone up or down and run it through RMT2LZSS with Vinscools tables.

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That's not what I asked. A# major is obviously quite in tune with these tables. Only the tonic is a bit off.

 

Now transpose this to E♭ major. It WILL be out of tune.

 

BTW nobody disagrees on this. It's the law of nature. 12-TET is a compromise. Vinscool's table is another compromise, but closer to just intonation in certain keys. (keys as is musical keys, not piano keys).

 

Also note that A=440Hz is arbitrary. Vinscool uses 443.9Hz. Philharmonic orchestras around the world use, and have used, widely varying tunings.

 

https://en.wikipedia.org/wiki/Concert_pitch

 

As low as 415Hz, as high as 470Hz.

 

 

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I would like to mention there's still a lot of stuff I have yet to fully understand in all of this, and many errors I could try to improve, as well as some compromises that could work better too.
Some things do sound better with my tuning, and some also sounds a little less good, there can only be so much possible with a limited pitch resolution :D 

For example, I know very well that G notes are out of tune, especially on octave 5, since there was so much to compromise, so it was either, be much lower and sound wrong, or higher and also sound wrong, I picked the option that sounded the most acceptable to me.
That's one of the few notes that caused me problems. I think of the sharps especially, due to what was mentioned earlier.
I'll link my most recent .txt file below, there will be some very clear examples of compromises, contradictions and many hesitations, so of course, a lot of improvements has yet to be done.


Here's an example of this kind of mess:
 

C-4  == (263.94)  == 77  == 266.3 --- 79  == 262.0??? nah
C#4  == (279.64)  == 71  == 280.4
D-4  == (296.27)  == 6B  == 295.9 ok
D#4  == (313.88)  == 65  == 313.3
E-4  == (332.55)  == 5F  == 332.9 ok
F-4  == (352.32)  == 59  == 355.1
F#4  == (373.27)  == 55  == 371.6
G-4  == (395.47)  == 50  == 394.6 ok
G#4  == (418.99)  == 4B  == 420.5 ok
A-4  == (443.90)  == 47  == 443.9 --- reference value for current tuning ---
A#4  == (470.30)  == 43  == 470.0 ok
B-4  == (498.26)  == 3F  == 499.4 ok
C-5  == (527.89)  == 3B  == 532.7 --- 3C  == 523.9??? nah
C#5  == (559.28)  == 38  == 560.7

C-5 there, was literally out of tune from the intention I had at first, so I had to pick a compromise, and adjusted as many notes as possible to still sound good with the others, but that comes at the cost of potentially making even more notes sound wrong...
So yeah, it's a long puzzle, but I admit I'm that kind of nerd to have fun in this, it's all math, in a way, hahaha

In theory it's also possible to get as close as possible to 12-ET using 443.9hz as a reference to A, this was my initial approach, but the number of notes that got bad were a little annoying... which was what lead me to tune several things based on interval instead, and pray that most things work well together.
And it does, somewhat, work okay, for the most part. But some tunes are likely to sound off, and that's partially my fault for the tuning, and mostly due to the limitation in pitches, same for distortion basses, a couple notes were pretty questionable compromises but worked okay as well.
In fact in my own (messy) notes complete with frequencies in hertz and my own comments, can give a good clue about how much compromises I faced so far.

There's also the "theoretical" frequencies I put as a reference in parantheses... it's actually just what if everything was 12-ET based on 443.9, and to my surprise.

It turns out the same tables also worked really well in PAL for being closer to 440, so there's some good surprises at least :P 

Anyway, there's always room for improvements, hopefully :) 
I would say 1 or 2 tables aren't enough for this kind of situation. Like Ivo said, there will be keys that will work well in my tuning, and some that will most likely work fine, but sound... a tiny bit odd, or out of tune at worst, not that this cannot be done on purpose too!
There was some tunes I had tested and those got a new layer of harmonisation, or even dissonance, and sounded great that way, so we never know :D 

POKEY Table 1.79mhz (Octave Pattern, Distortion C 1.79mhz) v1.txt

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There's also the possibility of resorting to a quick oscillation between two pitches to in essence "dither" a pitch between the two pitches. I have yet to hear how they would sound with RMT at a 50hz refresh rate rather than 100hz. It's a quick and dirty fix, but that's what I would resort to if I can't seem to find any pitches close enough to a certain note and don't want it detuned.

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A few years back, I wrote a short program to make some comparisons of the commonly-used "pure tone" note table(s) for Ataris with an accurate tempered scale. I also planned to examine some other starting points besides A-440, to see about producing some more accurate overall tables; but never found time to continue examining things. I posted a table output in one of Analmux's threads [about using variations on A-440 for a more accurate (16-bit?) note table].

 

The program sends table output to the line printer; so, it can be examined by copy/pasting output from Altirra into Notepad or whatever. The main point was to find out if a calculated table would match up with what was commonly used on the Ataris, but to also evaluate their closeness to an actual calculated tempered scale. So, it outputs both at the same time and then gives the cents error for the Atari value. I was planning to use this to evaluate the 16-bit scale -- and then the variations from A-440. It could easily be modified for whatever use.

 

I could have done the same thing using a spreadsheet, but I thought it was interesting to see what Atari BASIC would come up with (actually, it's TBXL).

 

Anyway, here it is, if anyone's interested, with a little excerpt from the table output, and then the common Atari table from some magazine is included below. The program basically just outputs the table, then plays through the resulting notes that were calculated.

 

Sample Output

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

 

Program

100 c10 = 10 : c49 = 49

110 ScaleIndexOffset = 39 : Clock = 63921
120 PrincipalFreq = 27.5 : Intervals = 12

130 DIM FreqDivisor (c49), ScaleNote$ (24)
134 ScaleNote$ = "A A#B C C#D D#E F F#G G#A A#B "
136 ScaleIndex = 7 : Octave = %3

140 FOR I = %0 TO c49

150     TemperedFreq = PrincipalFreq * %2 ^ ((ScaleIndexOffset + I)/ Intervals)
160     FreqDivisor (I) = Clock / TemperedFreq

170     IF FRAC (FreqDivisor (I)) >= 0.5
180         FreqDivisor (I) = INT (FreqDivisor (I)) + %1
190     ELSE
200         FreqDivisor (I) = INT (FreqDivisor (I))
210     ENDIF

220     AtariFreq = Clock / FreqDivisor (I)
230     CentsError = (Intervals * 100 / CLOG (%2)) * (CLOG (AtariFreq / TemperedFreq))

232     LPRINT
234     LPRINT "Octave - Note      = " ; Octave ; " - " ; ScaleNote$ (ScaleIndex, ScaleIndex + %1)
240     LPRINT "Frequency Divisor  = " ; FreqDivisor (I); ", $" ; HEX$ (FreqDivisor (I))
250     LPRINT "Atari Frequency    = " ; AtariFreq
260     LPRINT "Tempered Frequency = " ; TemperedFreq
270     LPRINT "Cents Error        = " ; CentsError
280     IF I <> c49 THEN LPRINT : LPRINT "------------------------------"

284     ScaleIndex = ScaleIndex + %2
286     IF ScaleIndex > 24 THEN ScaleIndex = %1 : Octave = Octave + %1

290 NEXT I

300 FOR I = %0 TO c49

320     SOUND %0, FreqDivisor (I), c10, c10

340     PAUSE c10

350     FOR Volume = c10 TO 0 STEP .2
360         SOUND %0, FreqDivisor (I), c10, Volume
370     NEXT Volume

390     PAUSE c10

400 NEXT I

 

Commonly Used Atari Note Tables

1643053329_AtariNoteTables(edited).thumb.png.3426e83a2c0ab7442fe98d5bbe4af45a.png

 

Edited by MrFish
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Actually, I have no idea of "new" conversion. 

Using the new software, I have an idea of a new challenge.

 

Someone could suggest a MOD  file , and I try to resemble it to the Atari.

The only rule is that the MOD file needs to use real notes, not self playing sample rips of other music. 

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On 4/12/2021 at 7:03 PM, ivop said:

That's not what I asked. A# major is obviously quite in tune with these tables. Only the tonic is a bit off.

 

Now transpose this to E♭ major. It WILL be out of tune.

 

BTW nobody disagrees on this. It's the law of nature. 12-TET is a compromise. Vinscool's table is another compromise, but closer to just intonation in certain keys. (keys as is musical keys, not piano keys).

 

Also note that A=440Hz is arbitrary. Vinscool uses 443.9Hz. Philharmonic orchestras around the world use, and have used, widely varying tunings.

 

https://en.wikipedia.org/wiki/Concert_pitch

 

As low as 415Hz, as high as 470Hz.

 

 

I'm still not sure what to write here. 

But low notes have to fit to high notes.

And the "440Hz" solution is way correct there. 

The "432Hz" solution is like some old ruined cellar stairs...

 

It's still horrible to listen to those:

 

 

 

 

or 

 

 

It's like someone is pulling your gums through a needle eye. 

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2 minutes ago, emkay said:

I'm still not sure what to write here. 

But low notes have to fit to high notes.

And the "440Hz" solution is way correct there. 

The "432Hz" solution is like some old ruined cellar stairs...

 

It's still horrible to listen to those:

This is still something I have been playing around with, and honestly, as far as thing were going for me, most of my Alternate table actually has several things wrong now after reconsideration, but I have made an interesting observation.
I was actually really close to it, 443.9hz (or 439.8hz in PAL) is indeed the most in-tune solution by far, and while I went with tuning intervals in the process, I realise now several notes became wrong as a result, but the initial idea is pretty much as good as it could be for the 8-bit pitch resolution.
You are also correct, 432hz, or anything trying too hard to meet 440hz (that is more like 433.4 for PAL and 437.8 in NTSC if everything still use the 1983 documentation) don't work very well, after the first 2 octaves it goes wrong really quick.
I honestly thought I went too hard into it, but it turns out I was getting very close, there will be unfortunately several notes that are off, but compared to a majority of them being wrong, it's only a few that get several hz away from the intentions, and that gets only really bad on the octave 6, unlike the original tables being offtune as early as octave 4.

Just some things I had been looking again and hopefully could be improved with some changes here and there for later :D 
That also gives me the green light to tune 16-bit that way as well, since I know 443.9 will become 439.8 in PAL, which is pretty much as close as 440 could be.
Most of the values are cross compatible too, so it really is close to the best it could be now.


I must say thanks to Ivo's spreadsheet, I was able to play with it properly now and I was amazed to find out a majority of my Alternate Tuning was in reality quite good for the most part, and the interval problems mentioned earlier did indeed show up for a couple notes, the same ones I tried too hard to tune, it simply caused more issues on the long run, haha.
Sooo I guess it's just to do a few changes here and there, adjust the other tables if necessary, and that should be good enough, hopefully.
16-bit definitely gives a much smaller error margin, thankfully.

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20 minutes ago, emkay said:

And the "440Hz" solution is way correct there. 

Again, 440Hz is arbitrary. It all depends on the circumstances. Vinscool proved you wrong by tuning his table to A=443.9Hz, because in the musical keys he used, it sounds more in tune with the Dist C basses, which sadly are at fixed frequencies.

Edited by ivop
frequencieS
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8 minutes ago, ivop said:

Again, 440Hz is arbitrary. It all depends on the circumstances. Vinscool proved you wrong by tuning his table to A=443.9Hz, because in the musical keys he used, it sounds more in tune with the Dist C basses.

Why is Vinscool proving me wrong?

Fact is simply that NTSC needs the given calculation, while PAL needs the "440Hz" adjustment. 

It's correct for 99% of Synthesizer music... so what?

We actually have a positive feature on PAL machines, as the 440Hz work "perfectly" . There are some glitches, but they can be "equalized" by adding a tone of a different octave at specific points. 

100% music with POKEY given on PAL Ataris, if just the "editor" software allows to listen to the real result while editing. 

Edited by emkay
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The 432Hz emkay references is nothing but a conspiracy theory. He's correct that it is not something better. 432Hz tuning is also arbitrary. Every tuning is arbitrary. Even during a two hour concert, the tuning of an orchestra might change due to changing circumstances.

 

6 minutes ago, VinsCool said:

I must say thanks to Ivo's spreadsheet, I was able to play with it properly now and I was amazed to find out a majority of my Alternate Tuning was in reality quite good for the most part, and the interval problems mentioned earlier did indeed show up for a couple notes, the same ones I tried too hard to tune, it simply caused more issues on the long run, haha.

Thanks. I really should do a diatonic or even Pythagorean tuning spreadsheet. Which means you select a frequency for the base note (1), and then 1, 1#, 2, 2#, 3, 4, 4#, 5, 5#, 6, 6#, and 7 are calculated for every octave with said ratios.

 

6 minutes ago, VinsCool said:

Sooo I guess it's just to do a few changes here and there, adjust the other tables if necessary, and that should be good enough, hopefully.
16-bit definitely gives a much smaller error margin, thankfully.

Definitely. Pokey's 16-bit value is exactly what you want for music. High resolution in the lows, less resolution in the highs. SID is the opposite, which is why they struggle with in tune basses.

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11 minutes ago, emkay said:

Fact is simply that NTSC needs the given calculation, while PAL needs the "440Hz" adjustment. 

That's correct. I was thinking you were thinking 440Hz was something special, but it appears that's not what you meant :)

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9 minutes ago, ivop said:

Even during a two hour concert, the tuning of an orchestra might change due to changing circumstances.

This is honestly the entire reason for my frequencies experiments: circumstances.

 

Something that works the best in a given situation ?

 

10 minutes ago, ivop said:

Thanks. I really should do a diatonic or even Pythagorean tuning spreadsheet. Which means you select a frequency for the base note (1), and then 1, 1#, 2, 2#, 3, 4, 4#, 5, 5#, 6, 6#, and 7 are calculated for every octave with said ratios.

I imagine it should be easy enough om the same sheet to add with a simple formula?

 

i was also wondering how could it work for tuning based on existing known frequencies, that will be especially useful for distortions and exotic combinations

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24 minutes ago, emkay said:

It's correct for 99% of Synthesizer music... so what?

If we had 16-bit resolution for each channel. But we have not. With our limitted 8-bit resolution, I'm sure just tuning will improve songs that don't use dist C basses, but just dist A at 15kHz, 64kHz or in 16-bit 1.77MHz. Especially the 64kHz notes will sound more in tune. But you'll need a table for each key.

Edited by ivop
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9 minutes ago, VinsCool said:

I imagine it should be easy enough om the same sheet to add with a simple formula?

Not really, because the first note of a tuning is not always C, or A, or whichever note. But I will add a 12-TET column where every frequency is 100 cents apart. And a few columns that calculate back to pokey timer values.

 

Quote

i was also wondering how could it work for tuning based on existing known frequencies, that will be especially useful for distortions and exotic combinations

The idea is that you fill in note '1' equals 55Hz, or something else, and it calculates all octaves according to different ratios.

Edited by ivop
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3 minutes ago, ivop said:

Not really, because the first note of your tuning is not always C, or A, or whichever note. But I will add a 12-TET column where every frequency is 100 cents apart. And a few columns that calculate back to pokey timer values.

Ahh I see, anything would work really.

 

 

 

 

 

3 minutes ago, ivop said:

The idea is that you fill in note '1' equals 55Hz, or something else, and it calculates all octaves according to different ratios.

Ohhh that could certainly do, I got a large amount of known frequencies I had noted down with more or less accuracy, so adding the few that are missing could then be used to calculate as well.

 

Thankfully Distortion A in 15khz, 64khz, 1.79mhz and 16-bit are very easy to calculate based on the clock, only these would give a huge reference point.

I'd totally give it a shot, all I need to know is how the math formula would be done to produce something out of these :D

 

 

 

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6 hours ago, ivop said:

If we had 16-bit resolution for each channel. But we have not. With our limitted 8-bit resolution, I'm sure just tuning will improve songs that don't use dist C basses, but just dist A at 15kHz, 64kHz or in 16-bit 1.77MHz. Especially the 64kHz notes will sound more in tune. But you'll need a table for each key.

I'm still not sure, want you want to say. 

Of course the 8 bit resolution is rather limited.

 

I posted the two videos above. 

Why is no one else blaming this detuning ?

I'm talking of some 0.xxHz , while the tunes above shift the tuning in more than 10Hz difference from the high to the low tones. 

If an Orchestra is "tuned to 432Hz" , all notes at all instruments were adjusted to that. 

Not the high tones to 443Hz and the low tones to 432Hz. 

 

Also, particular the detuning in the basses is what made SID sound so "beloved". 

Things get nuts when people don't like modern remixes of the old tunes where everything is clean tuned.

I have several modern remakes of this music playing in my car audio (you might know remix.kwed.org / amigaremix.com). Some to them resemble the great arrangement of the chip tunes, but sound so "rich" played from modern music hardware.

 

 

 

  

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Continuation from earlier, after a bit of math I figured out what I wanted to do earlier today, so here's a spreadsheet that calculates both PAL and NTSC, Distortion A, 16-bit, 8-bit 15-64khz and 1.79mhz, All of this is going to be really useful soon :D 
This was based on @ivop's sheet, so most of the formating is the same but I adjusted the equations for the new columns I added.


I should start a new thread sometime...
I also was supposed to test some RMT2LZSS stuff but kind of got carried over oops. Good thing I don't need to get up early tomorrow hahaha 

Atari Tuned A4=X (8-16-bit-15-64khz-1-79mhz).ods

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10 hours ago, emkay said:

I'm still not sure, want you want to say. 

Of course the 8 bit resolution is rather limited.

 

Quote

I posted the two videos above. 

Why is no one else blaming this detuning ?

Oh, I am.  It seems we are not constantly on the same page :)

 

Vinscool's tables try to minimize the difference of dist A notes to dist C notes, more or less.

 

What I'm talking about it, leave dist C out of the mix, and be freed of the limitation of dist C. Now you can use just intonation for each musical key, and sound clearer, more open. I hope you watch the video on Scar Tissue.

 

Quote

I'm talking of some 0.xxHz , while the tunes above shift the tuning in more than 10Hz difference from the high to the low tones. 

If an Orchestra is "tuned to 432Hz" , all notes at all instruments were adjusted to that. 

Not the high tones to 443Hz and the low tones to 432Hz. 

Exactly. Here we agree. That's what Vinscool's tables fix.

 

Trying Pythagorean tuning is something completely different, and won't work properly with dist C because these notes are fixed.

 

I'll post a Calc sheet tonight. Almost finished.

Edited by ivop
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1 hour ago, ivop said:

 

 

 

The video explains exactly my point. 

My experience is more on expensive Pianos, where several strings build a chord (creating one tone)to solve this  effect. 

So you can play single keys or add "problematic" chords without problems.  

 

That's also what I'm writing about VinsCools notation . It fits to create a good scale , and if you use notes of different octaves, it adds nicely together.

 

And we have to make a clear point about adding "harmonics" to make the music better, or to add "harmonics" to create waveforms.

So, clean Syntehsizers can handle the start of every wave per channel. That's why the effect that is explained in the video won't happen by standard. But it is possible to change settings ;)

The analog strings build their own waves at different times. So every time the resulting tone will get different. 

That's why the detuning needs to be done until the waves won't logically add together into loud interferences.   

 

Edited by emkay
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Here's a spreadsheet to calculate Pythagorean tuning, or any other RA:TIO for that matter.

 

To keeps things manageable, I decided to base everything on a single clock. You can change that from NTSC to PAL, and vice versa. That's half the amount of columns ;)  I also skipped the HEX columns. And the delta columns are now in cents instead of hertz.

 

In this example, note '1' is tuned to 27.5 Hz, but you can change that to any frequency you want.

 

Just for fun, I created a second sheet with the exact 12-TET ratios.

 

The third sheet is an alternate Pythagorean tuning. Gb (1024:729) and F# (729:512) are different ratios. It's the devil's interval!!  :D

 

You can copy the sheet as many times as you want and try out different intervals.

 

Different Tunings.ods

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