Forums

Sega Master System / Mark III / Game Gear
SG-1000 / SC-3000 / SF-7000 / OMV
Home - Forums - Games - Scans - Maps - Cheats - Credits
Music - Videos - Development - Hacks - Translations - Homebrew

View topic - Tuning the PSG to itself

Reply to topic
Author Message
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Tuning the PSG to itself
Post Posted: Wed Jun 11, 2008 5:43 pm
Last edited by Maxim on Wed Aug 19, 2009 4:28 pm; edited 1 time in total
As you may know, the PSG's not-quite-1024 possible frequencies are based on the wavelength of the sound produced. This does not map linearly to the 12-tone equal temperament scale commonly used by musicians, which is logarithmic compared to wavelength or frequency. In particular, the PSG's resolution is relatively poor at high frequencies - a change of 1 produces ~3 semitones difference, compared with about 0.005 semitones - aka 0.5 cents - at the low end.

Thus, any mapping of a musical scale onto the PSG will always be somewhat "out of tune". This doesn't matter so long as it's not trying to be in tune with something else, or so long as the amount it's out of tune is very small. Wikipedia says a trained musician can only hear a difference of 5-6 cents. In particular, an exact octave difference can normally be represented on the PSG with relatively high accuracy, so the most noticeable cases are less bad.

You can see a mapping to the standard notes here:

http://www.smspower.org/maxim/forumstuff/psgtable.html

There is a concept of "tuning something to itself", whereby it's not matching the standard (where A4 = 440Hz), but instead it's off-tune in a way that allows it to overall be more self-consistent in its tuning. I wondered if the PSG could be "tuned" this way.

I made an unpublished modification of that page that, rather than using the standard A4=440Hz, ran through many possible values, from 415 to 467Hz (one semitone flat to 1 semitone sharp), in small steps. For each it calculated the RMS error, to find the value for A4 that produces the most self-consistent musical scale, for the lowest 5 octaves of the PSG (to exclude the always-pretty-bad higher frequencies).

The result is:

A4 = 436.67Hz

produces an RMS error of 4.346 cents compared to 6.166 cents at the "standard" 440Hz tuning.

So: for the lowest 5 octaves of the PSG, this is the best reference point to minimise the average out-of-tune-ness. However, even if you chose the very worst one, a trained musician would struggle to hear it, on average.

But we're not dealing with averages; if all the notes are in tune but one, it'll have a low RMS and sound awful. So I ran another analysis that looked for the tuning that minimised the biggest out-of-tune-ness in the first 5 octaves. This gives the result:

A4 = 437.23Hz

has a maximum error of 12.6 cents; the worst case is about 25 cents. At 440Hz the maximum is 17.2 cents, at 436.67 it's 14.8.

So, what's the conclusion?

Whatever tuning standard you use, they're all pretty bad; 440Hz and the two results I gave above are all good ones to use, for various reasons, but the difference between them is not very much.
  View user's profile Send private message Visit poster's website
  • Joined: 14 Aug 2000
  • Posts: 444
  • Location: Adelaide, Australia
Reply with quote
Tuning the PSG to itself
Post Posted: Thu Jun 12, 2008 3:30 am
"Tuning the PSG to itself" makes perfect sense (unless you're going to have the SMS playing in an ensemble of other instruments of computers) there should be less dissidents between the 3 notes produced by the PSG using this method, over using register values 'as close to' the actual musical note frequencies.

There are also other techniques to reduce dissidents, like applying a gentle vibrato to extended notes. This technique is used by string instrument players like violinists.
  View user's profile Send private message
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Post Posted: Thu Jun 12, 2008 8:18 am
Yeah, but I was somewhat surprised at how little difference it makes to do so.

Certainly, if you can customise the vibrato for each note to take consideration of its error (effectively, making the average frequency be dead-on by distributing between the available values appropriately) it'd be a big help. But if you can really get away with 5-6 cents then you don't really need to care for at least the bottom 4 octaves. Maybe that's the source for the old inaccurate "4 octaves range" spec?
  View user's profile Send private message Visit poster's website
  • Joined: 07 Aug 2007
  • Posts: 190
  • Location: Yach, Germany
Reply with quote
Post Posted: Thu Jun 12, 2008 1:27 pm
Since the PSG is poor at low frequencies (not accurycy-wise, but it just can't do them) I often change the tone to be able to just include the lowest frequency I need.
Last time I ended up with A slightly above 490Hz. Which is okay to me since it was a piece from Johann Sebastian Bach and as far as we know today (from the still existing organs he used) he placed A at about 480Hz. The pitch has changed a lot in the past. Today the standard is A at 440Hz, most professional musicians use 442 or 443 Hz, historically i varied between 380 and 480 Hz.

Philipp
  View user's profile Send private message Visit poster's website
  • Joined: 25 Jul 2007
  • Posts: 544
  • Location: Melbourne, Australia
Reply with quote
Post Posted: Thu Jun 12, 2008 2:03 pm
And here I was thinking the scales never changed.
  View user's profile Send private message
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Thu Jun 12, 2008 5:59 pm
No, not at all. Do we really know the Hz from Bach's time? I mean, they went with a different type of temperament then because they simply didn't have the science to pull anything else off. However, it should be noted, well temperament was and still is considered superior by some musicians. I always wonder what Clavier sounded like in its intended temperament. I wonder if applying well to this problem would lead to a solution? It could perhaps lead to a more accurate system. I want to do some work on this when I get to it, and since I have perfect pitch maybe I can come up with something more usable and defined so there's little error going from a musical arrangement to the PSG. Any error could possibly be accomodated for easily if it would work out as I think it could.
  View user's profile Send private message Visit poster's website
  • Joined: 01 Feb 2004
  • Posts: 1460
  • Location: Sunny ol Tamworth, New England NSW AU
Reply with quote
Post Posted: Fri Jun 13, 2008 12:31 am
Stan wrote
and since I have perfect pitch maybe I can come up with something more usable and defined so there's little error going from a musical arrangement to the PSG.

Can I have your perfect pitch?

As a musician myself I have been showing a lot of interest in this thread. Stan how do you clock the PSG to play lower frequencies, and is it possible to do this in Martins tracker?

Thanks
  View user's profile Send private message Visit poster's website
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Post Posted: Fri Jun 13, 2008 8:46 am
The PSG can't play lower frequencies (unless you go for periodic noise...), what he describes is the same as transposing the music you have up by just enough to let the lowest note equal the 109.35Hz that's the lowest regular tone the PSG can play. I have no idea if you can make Mod2PSG2 do that for you.

It is true that 12-TET is a fairly modern concept and there's plenty of music that wasn't composed for it; but if you're going to try to use it, you're going to have to be pretty musically talented as well as able to make a matching music engine.
  View user's profile Send private message Visit poster's website
  • Joined: 04 Nov 2004
  • Posts: 262
  • Location: Deutschland
Reply with quote
Post Posted: Fri Jun 13, 2008 11:35 am
Jacko,
You can't do that in Mod2PSG2, except if you manually do the transposing+detuning. But it would be a nice feature I think.

Maxim,
what would it look like if you made a graph with RMS and out-of-tune-ness (on Y-axis) for a range of A4 frequencies (on X-axis)? Would that give a useful graph to search for a good compromise between RMS and out-of-tune-ness?
  View user's profile Send private message Visit poster's website
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Post Posted: Fri Jun 13, 2008 12:51 pm
Martin wrote
what would it look like if you made a graph with RMS and out-of-tune-ness (on Y-axis) for a range of A4 frequencies (on X-axis)? Would that give a useful graph to search for a good compromise between RMS and out-of-tune-ness?


As you can see, it's periodic across a semitone, due to the logic that is looking only at the lowest 60 notes that can be produced. The max error trough at 437.2 lines up pretty well with a low RMS error.

Edit: I wasted a lot of time in Excel now. Depending on how you weight the errors, you can get different results, but they're all close to 437.2. Spreadsheet attached.
graph.png (10.12 KB)
graph.png
PSG.zip (438.83 KB)
Excel spreadsheet for PSG error graphing

  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Sun Jun 15, 2008 4:49 pm
Just so you know, I haven't actually started working the PSG yet, that was just an idea that popped in my head. When I work on it I'll see what I come up with, but I need to become uber familiar with it, like I did my drum machine. Once I figured out the inner workings of that computer, 2 on 3 became my bitch.
  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Sun Jun 15, 2008 5:39 pm
Speaking of all this music, I doubt not, but if you h haven't, you should check out what some guy (I think from here) did withthis.
  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Sun Jun 15, 2008 5:52 pm
So I'd like to mess around, but I'm a bit confused. I swear I found a link before to some program you can use to write SMS music. If this is merely a dream of mine that I remember as reality, can someone give me a link to a program that I can use to ONLY program music? Perhaps there is something I can use so I can hear tones as I work with them, similar to drum machine programs like Fastrack?
  View user's profile Send private message Visit poster's website
  • Joined: 31 Oct 2007
  • Posts: 811
  • Location: Estonia, Rapla city
Reply with quote
Post Posted: Sun Jun 15, 2008 6:22 pm
MOD2PSG2 is something you can use to make music for GG/SMS...
  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Mon Jun 16, 2008 12:34 am
That's the link I was looking for originally, thanks a bunch.
  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Tue Jun 17, 2008 2:55 pm
Well, finally downloaded the PSG and had a chance last night to start working on it. Reminds me of my drum machine, and with that in mind, I will, in time, be able to TOTALLY destroy this thing. I was able to make a track last night and mixed some tunes with brief noise tones for an awesome effect. At any rate, it gave me a chance to compare this whole tuning issue. Really, as a musician whose been clasically trained for over 10 years, I found it quite easy to take something I wrote and put it to the PSG, it just takes a little tweaking to get it close, and when you do there's hardly any difference from even tempered tuning. If you have an ear for music, you can easily put your songs on this thing with no problem.
  View user's profile Send private message Visit poster's website
  • Joined: 20 Dec 2004
  • Posts: 187
Reply with quote
Post Posted: Tue Jun 17, 2008 4:31 pm
Also, does anyone know of a good overview guide of how this thing works in detail? I'd hate to have to trudge through figuring out another piece of technology without some sort of manual. Just a simple thing describing how everything works is all I need. If not, whatever, I'll figure it out.
  View user's profile Send private message Visit poster's website
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Post Posted: Tue Jun 17, 2008 5:44 pm
I'm not sure what you're referring to, given that the thread is somewhat off-topic. How to use a tracker? How the PSG works? How to write a music engine? Feel free to start a new topic if it feels like something worth sharing/discussing.
  View user's profile Send private message Visit poster's website
redman
  • Guest
Reply with quote
Post Posted: Fri Oct 03, 2008 5:36 pm
Hi guys,

I was just doing scale mappings for the psg all day and then i found this thread.
It's nice to see other people busy with the same concerns :)

Anyway,
i'm doing this stuff because i'm writing a tracker/player for MSX.
What interested me was that people mention the psg cannot go lower than 109Hz or so.

This does not seem the case for me!
I can go almost 2 octaves lower (altho you would be just above 27Hz with that which is nt very usefull, especially because the output is a square and the harmonics will dominate heavily)

Sounds in the 54Hz~109Hz octave sound good to me, although typical squarish.

I was wondering, is there something about the SMS that prevents you from setting the full 12 bits of the registers?
 
  • Joined: 04 Nov 2004
  • Posts: 262
  • Location: Deutschland
Reply with quote
Post Posted: Fri Oct 03, 2008 5:42 pm
Yes, it's only 10 bits ;)
  View user's profile Send private message Visit poster's website
redman
  • Guest
Reply with quote
Post Posted: Fri Oct 03, 2008 6:33 pm
well, makes sense then :)
thanks for the info!
 
  • Site Admin
  • Joined: 19 Oct 1999
  • Posts: 12005
  • Location: London
Reply with quote
Post Posted: Thu Aug 13, 2009 9:11 am
For completeness, here's the values used by most SMS games:

PSG     Freq /Hz    Nearest note    MIDI name   Error /cents
1023    109.346     45              A2          -10.3
 967    115.678     46              A#2         -12.9
 912    122.654     47              B2          -11.5
 861    129.920     48              C3          -11.9
 813    137.590     49              C#3         -12.6
 767    145.842     50              D3          -11.7
 724    154.504     51              D#3         -11.8
 683    163.779     52              E3          -10.9
 645    173.428     53              F3          -11.8
 609    183.679     54              F#3         -12.4
 575    194.540     55              G3          -12.9
 542    206.385     56              G#3         -10.6
 512    218.478     57              A3          -12
 483    231.596     58              A#3         -11.1
 456    245.309     59              B3          -11.5
 431    259.538     60              C4          -13.9
 406    275.519     61              C#4         -10.4
 384    291.304     62              D4          -14
 362    309.008     63              D#4         -11.8
 342    327.078     64              E4          -13.4
 323    346.318     65              F4          -14.5
 304    367.963     66              F#4         - 9.5
 287    389.759     67              G4          - 9.9
 271    412.770     68              G#4         -10.6
 256    436.956     69              A4          -12
 242    462.235     70              A#4         -14.7
 228    490.617     71              B4          -11.5
 215    520.283     72              C5          - 9.8
 203    551.038     73              C#5         -10.4
 192    582.608     74              D5          -14
 181    618.015     75              D#5         -11.8
 171    654.157     76              E5          -13.4
 161    694.787     77              F5          - 9.1
 152    735.926     78              F#5         - 9.5
 144    776.811     79              G5          -15.9
 136    822.506     80              G#5         -17
 128    873.912     81              A5          -12
 121    924.469     82              A#5         -14.7
 114    981.235     83              B5          -11.5
 108   1035.748     84              C6          -17.9
 102   1096.674     85              C#6         -18.9
  96   1165.216     86              D6          -14
  91   1229.239     87              D#6         -21.4
  85   1316.009     88              E6          - 3.3
  81   1380.997     89              F6          -19.8
  76   1471.852     90              F#6         - 9.5
  72   1553.622     91              G6          -15.9
  68   1645.011     92              G#6         -17
  64   1747.825     93              A6          -12
  60   1864.346     94              A#6         - 0.3
  57   1962.470     95              B6          -11.5
  54   2071.496     96              C7          -17.9
  51   2193.349     97              C#7         -18.9
  48   2330.433     98              D7          -14
  45   2485.795     99              D#7         - 2.2
  43   2601.414     100             E7          -23.5
  40   2796.520     101             F7          + 1.7
  38   2943.705     102             F#7         -9.5
  36   3107.244     103             G7          -15.9
  34   3290.023     104             G#7         -17
  32   3495.649     105             A7          -12
  30   3728.693     106             A#7         - 0.3
  28   3995.028     107             B7          +19.2
  27   4142.992     108             C8          -17.9
  25   4474.431     109             C#8         +15.4
  24   4660.866     110             D8          -14
  22   5084.581     111             D#8         +36.7
  21   5326.704     112             E8          +17.2
  20   5593.039     113             F8          + 1.7
  19   5887.410     114             F#8         - 9.5
  18   6214.488     115             G8          -15.9
  17   6580.046     116             G#8         -17

This seems to be based on tuning it so that the lowest note possible (PSG value 1023) is A2 (the nearest "correct" note) and trying to tune the rest of the notes to work with that, possibly with some dodgy rounding along the way.
  View user's profile Send private message Visit poster's website
Reply to topic



Back to the top of this page

Back to SMS Power!