Atari 2600 Frequency And Tuning Chart (NEW V1.1)

[diogoandrei]

VERSION 1.0 HAD A MAJOR ERROR ON THE SETUPS. PLEASE, DELETE THAT ONE AND GET NEW VERSION 1.1 (NOW ALSO WITH PAL CHART)

 

Hello there,

 

I am here to share a musical chart for TIA frequencies and channels that I've created. I've been using it for sometime now. It really helped me out when planning the key of a particular theme or when looking for ways to surpass those tuning issues we all know about. I finally thought that it's current design is decent enough to be shared in here.

 

Based on Paul Slocum's "Atari 2600 Music And Sound Programming Guide", I've gathered his three (handy and really good) setups in one single and printable chart. The main idea was to have a common musical scale where all his setups would relate to each other. I've asked his permission to use his material (and share this with AtariAge) and he kindly welcomed me to do so.

 

FEATURES:

 

- Paul Slocum’s tuning Setups all in one single printable page;

- Setups are identified by colors, making the chart easy to read;

- Data values for both TIA registers and Slocum’s Sequencer Kit;

- NTSC and PAL are in separated charts.

 

SMALL PART OF THE INTRODUCTION:

 

(...)

 

My ”Atari 2600 Frequency And Tuning Chart” came to be because I would always find myself looking up and down my printed version of Slocum’s guide, flipping through the pages and Setups when trying to find a path of notes that could be desirable. I always felt that one day I should figure out a way to put all that information in one single page.

 

One day I finally did it. I poured the three Setups on MS Excel, linked all then to one shared scale and granted an id color to each of them (plus two id colors to notes common to two Setups).

 

With the chart ready I could, with one single glimpse, found out that there’s no distortion able to play D#5, if that was a possible pitch I was aiming for, for example. Or, let’s say, I need the bass to go C2, D2 and E2 in ascending fashion for a brief fill. Looking at the chart I can easily see that the bass cannot play D2, but the saw distortion can. I can then achieve my desired effect doing bass C2, saw D2, bass E2. Also, if I want to have an idea of how the Setups are related to the octaves (or how the distortions are related to the Setups) I can easily check that out by observing the colors of the notes. And of course, if I just want to stay within a particular Setup, I just go about my business looking at the colors too.

 

(...)

 

PRINTING TIPS

 

If anyone is planning on printing it out, I would recommend using A4 coated paper (300gr or higher) and then applying a plastic laminate in it. Sometimes it will be better to print that on A3 sized paper and then trim the borders. More tips on printing the chart inside the document. Besides being useful, it looks really pretty!

 

 

DOWNLOADS

 

Attached follows some pictures of my printed version, as well as the fully documented chart in PDF (as well as single PDFs NTSC or PAL for the chart only).

 

Atari 2600 Frequency And Tuning Chart v1.1 (PDF FULL DOCUMENT).pdf

Atari 2600 Frequency And Tuning Chart v1.1 (PDF NTSC CHART ONLY).pdf

Atari 2600 Frequency And Tuning Chart v1.1 (PDF PAL CHART ONLY).pdf

 

 

I really hope this comes as a helping hand to those who enjoy writing music for the 2600. It is a chart that really helped me in identifying good in-tune possibilities as well as predicting out-of-key disasters. I think the main feature here is that it speeds up the composing process.

 

Comments, suggestions and corrections are always welcomed.

 

Best regards,

Diogo

Edited February 4, 2011 by diogoandrei

[RevEng]

Very nice work!

 

This went straight into my 2600 docs folder, and I'll be using it the next time I need to compose some music.

[diogoandrei]

Very nice work!

 

This went straight into my 2600 docs folder, and I'll be using it the next time I need to compose some music.

 

Thanks RevEng, I am really glad you liked it! Hope it helps out

[+Random Terrain]

Have you visited this page yet:

 

http://www.randomterrain.com/atari-2600-memories-batari-basic-music-sound.html

[SeaGtGruff]

Hi, diogoandrei!

 

You had messaged me a week or so ago about a post I'd made in the stella mailing list regarding TIA sound, and I said I'd share my thoughts/notes about it, but I haven't finished yet. Here's an unfinished Excel spreadsheet file (zipped) that I'm working on to help me analyze the frequencies. It's just for the "pure" tones, and it's based on information taken from the TIA "hardware manual" and Stella programmer's guide, as well as from documentation about the TIA sound emulation.

 

The file contains five worksheets, which were mainly intended for my own use to help me in my analysis, so they aren't necessarily formatted in a way that's most useful for everyday reference, but maybe they will help you.

 

Sheet1 is a summary of what the 16 different AUDC0 and AUDC1 settings do (column A), as described in the TIA "hardware manual" and Stella programmer's guide (column B), and the documentation for the TIA sound emulation routines (columns C, D, and E). Below that are my own notes about the four or seven settings that produce "pure" tones, showing the "base frequency" for NTSC 2600s and PAL/SECAM 2600s.

 

Sheet2 is a summary of the frequencies that should be produced for these four "pure" voices by setting AUDF0 or AUDF1 to the appropriate value (0 to 31) so as to divide the base frequency by a value from 1 to 32. Column A shows the values for the first voice (division by 2, or setting AUDC0 or AUDC1 to 4 or 5). These values are listed using a kind of shorthand, such as /2/1, /2/2, /2/3, up to /2/32. The first part (/2) means it is the "divide by 2" voice, and the second part (/1, /2, /3, up to /32) is for the value of AUDF0 or AUDF1. For example, to get /1 you would set AUDF0 or AUDF1 to 0. To get /2 you would set them to 1, and so on, because the actual divisor is 1 plus the value of AUDF0 or AUDF1. Column B shows the values for the second voice (division by 6, or setting AUDC0 or AUDC1 to 12 or 13). Some of these values coincide with values in column A-- for example, /2/3 is the same as /6/1, and /2/6 is the same as /6/2, etc. Column C is the third voice (AUDC0 or AUDC1 equals 6 or 10), which is division by 31. Again, some of these values coincide with values in column A or column B-- for example, /2/31 equals /31/2, and /6/31 equals /31/6. Column D is for the fourth voice (AUDC0 or AUDC1 equals 14), which is division by 93. Again, some of these values coincide with values in other columns. Column E shows the resulting divisor that will be applied to the base frequency-- for example, /2/1 equals division by 2, /2/3 or /6/1 both equal division by 6, and so on. Column F shows the frequency you get when you divide the NTSC base frequency (shown in row 1) by the divisor in column E, and column G shows what you get when you divide the PAL/SECAM frequency by column E. The rows are shaded in white or yellow to help show the different octaves-- for example, division by 16 through 31 would fall within one octave, whereas division by 32 through 62 would fall within a different octave.

 

Sheet3 is kind of spastic, with a lot of blank space, but it arranges the different notes (divisors) by octave-- each section of columns (separated by orange dividers) is a separate octave. The NTSC and PAL/SECAM frequencies are shown. Way over to the right (you have to scroll to see it) is a listing of what the divisors and frequencies would be in the lowest octave, even though some of the notes don't actually fall within that octave. For example, the first entry (in row 3, column BQ) says divisor 2048, which is what you would get if you extend the row 3 divisors for the higher octaves down to the lowest octave-- that is, the highest pitch has a divisor of 2, and each time you go down one octave the divisor is doubled (4, 8, 16, 32, and 64), so continuing that down to the lowest octave would give you a divisor of 2048. Then it shows the resulting NTSC frequency followed by the closest note in the standard tuning scale with the cents high or low, then the PAL/SECAM frequency, closest note, and cents. These notes and cents will be the same for all frequencies on a given row, only the octave will be different. The very last column lists the actual frequencies of the twelve standard notes for reference and for calculating the cents.

 

Sheet4 is a grid that shows how all the different frequencies relate to each other, where each row is a given octave, and each column is a particular frequency within that octave. At the bottom are several rows (unfinished) where I'm calculating the harmonic ratio between two notes. For example, you can see that the frequencies in column W have a 4:3 ratio to the frequencies in column A, that the frequencies in column AF have a 3:2 ratio to the frequencies in column B, that the frequencies in column AH have a 3:2 ratio to the frequencies in column C, and so forth.

 

Sheet5 is basically the same as Sheet4, except the rows at the bottom show the differences between the notes in terms of cents. The shaded cells show the closest frequency to a given note in terms of cents-- that is, 0.00 cents would be the same note, 100.00 cents would be up one note, 200.00 cents would be up two notes, and so on, up to 1200.00 cents (up 12 notes or one octave). The idea is to help you see which notes should sound most in tune with each other, even if they're actually quite sharp or flat in comparison to the standard notes. For example, column W is close to 500 cents (498.04) above column A, so /2/16 (column A) and /2/12 (column W) should sound pretty much in tune with each other (five semi-tones apart), even though column A is a B that's 11.49 cents flat (as seen from Sheet2) and column W is an E that's 13.44 cents flat, because they're both flat by amounts that are pretty close to each other.

 

As you can see, I have a long way to go before Sheet4 and Sheet5 are completed, and then I still need to present all of this in a manner that's useful to the average user. My goal is to hopefully show the best values to pick to get the notes for a particular key, such as the key of B flat or D sharp, even if the notes are technically off from the ideal pitch. And Sheet4 is specifically for use with harmonic tuning, or "just intonation." For example, two frequencies that have a ratio of 3:2 form a "perfect fifth," so they should sound very harmonious together.

 

Michael

 

 

TIA Sound Notes.zip

[diogoandrei]

Have you visited this page yet:

 

http://www.randomterrain.com/atari-2600-memories-batari-basic-music-sound.html

 

Yes, many many times, it's a wonderful material

[diogoandrei]

Hi, diogoandrei!

 

You had messaged me a week or so ago about a post I'd made in the stella mailing list regarding TIA sound, and I said I'd share my thoughts/notes about it, but I haven't finished yet. Here's an unfinished Excel spreadsheet file (zipped) that I'm working on to help me analyze the frequencies. It's just for the "pure" tones, and it's based on information taken from the TIA "hardware manual" and Stella programmer's guide, as well as from documentation about the TIA sound emulation.

 

(...)

 

As you can see, I have a long way to go before Sheet4 and Sheet5 are completed, and then I still need to present all of this in a manner that's useful to the average user. My goal is to hopefully show the best values to pick to get the notes for a particular key, such as the key of B flat or D sharp, even if the notes are technically off from the ideal pitch. And Sheet4 is specifically for use with harmonic tuning, or "just intonation." For example, two frequencies that have a ratio of 3:2 form a "perfect fifth," so they should sound very harmonious together.

 

Michael

 

Hello Michael, thanks for writing.

 

Your approach based on proportions (old fellow Pythagoras started all that, hm?) is probably the ultimate path to wield the TIA sound capabilities! In the end, it's more really about intonation as you said. Be it a perfect fifth (3:2) or a perfect fourth (4:3), once the proportion is right those intervals will sound right no matter how far each individual note might be off in relation to A 440Hz. After all, the equal tempered scale is about proportion inbetween scale degrees. After setting one single frequency, the proportions will bring all others.

 

It's funny... all this talk about tempered systems makes the TIA look like an issue from the Renaissance, when all kinds of math systems were being used to develop and achieve new musical tunings.

 

I will definitely print those sheets you sent me. I'll probably have to sit down and slowly read again each sheet description you wrote here so I can start to digest it's content. So please alow me a couple of days to get a grip of your material.

 

Overall, this looks like a really promosing project. If you need any help, please let me know!

 

Best regards,

Diogo

[SeaGtGruff]

It's funny... all this talk about tempered systems makes the TIA look like an issue from the Renaissance, when all kinds of math systems were being used to develop and achieve new musical tunings.

I know! It's kind of funny that, in terms of the equal-tempered scale, the TIA is such a mess, yet its approach to creating different frequencies/pitches is actually more conducive to using "just intonation," which produces pitches that are more perfectly in tune from the harmonic viewpoint! The only problem is that just intonation works great for some notes/steps, but other steps can be represented by multiple ratios, so you have to pick the best one for the specific situation.

 

For example, using lowercase letters to represent notes at the 12 different semi-tone steps:

 

a = 0 semi-tones = perfect unity = P1

b = 1 semi-tone = minor second = m2

c = 2 semi-tones = major second = M2

d = 3 semi-tones = minor third = m3

e = 4 semi-tones = major third = M3

f = 5 semi-tones = perfect fourth = P4

g = 6 semi-tones = tritone = TT

h = 7 semi-tones = perfect fifth = P5

i = 8 semi-tones = minor sixth = m6

j = 9 semi-tones = major sixth = M6

k = 10 semi-tones = minor seventh = m7

l = 11 semi-tones = major seventh = M7

m = 12 semi-tones = perfect octave = P8

 

a to a (P1) is 1:1.

a to f (P4) is 4:3.

a to h (P5) is 3:2.

a to m (P8) is 2:1.

 

Since P4 is 5 semi-tones and P5 is 7 semi-tones, this suggests that 2 semi-tones (M2) is 9:8, since 4/3 * 9/8 = 3/2. Also, 3/2 * 3/2 = 9/4, which is a M2 plus 1 octave.

 

a to c (M2) is 9:8.

f to h (M2) is 9:8.

k to m (M2) is 9:8.

 

Then 10 semi-tones (m7) would be 16:9, since 16/9 * 9/8 = 2/1. Also, 4/3 * 4/3 = 16/9.

 

a to k (m7) is 16:9.

c to m (m7) is 16:9.

 

So far we have the following, which work perfectly together:

 

a = P1 = 1:1

b = m2

c = M2 = 9:8

d = m3

e = M3

f = P4 = 4:3

g = TT

h = P5 = 3:2

i = m6

j = M6

k = m7 = 16:9

l = M7

m = P8 = 2:1

 

But then things start to get more messy-- for example, c to f (m3) should be P4 / M2 = 4/3 / 9/8 = 4/3 * 8/9 = 32/27, which would give us the following:

 

a to d (m3) is 32:27 (ick!)

c to f (m3) is 32:27 -- indeed, 9/8 * 32/27 = 4/3

f to i (m3) is 32:27 -- so 4/3 * 32/27 = 128/81 (ick!)

h to k (m3) is 32:27 -- indeed, 3/2 * 32/27 = 96/54 = 16/9

 

That works out okay, except 32:27 isn't listed as one of the usual possible choices for m3, and 128:81 isn't listed as one of the usual possible choices for m6:

 

a = P1 = 1:1

b = m2

c = M2 = 9:8

d = m3 = 32:27 ? (usually listed as 6:5 or 19:16)

e = M3

f = P4 = 4:3

g = TT

h = P5 = 3:2

i = m6 = 128:81 ? (usually listed as 8:5, 11:7, 14:9, or 63:40)

j = M6

k = m7 = 16:9

l = M7

m = P8 = 2:1

 

And going backward from m (P8) we would get j (M6) as 2/1 / 32/27 = 2/1 * 27/32 = 54/32 = 27/16 or 27:16 (but M6 is usually listed as 5:3 or 12:7).

 

So filling in the gaps for the other steps gets progressively more messy, even though things started out so well for P1, M2, P4, P5, m7, and P8.

 

I guess if you're going to pick notes for a tune using just intonation, you should focus on the specific intervals that would be needed for that tune, and look for the TIA frequencies that would best fit the harmonics of those intervals.

 

Michael

[diogoandrei]

Bumping this so people can get to know the new version 1.1... previous version had an error.