Getting Z3TA+ tuned to Pythagorean tuning at C4=256Hz (which results in A4=432Hz) is quite an easy task to do, since this soft synth supports scala (.scl) files. The steps in this tutorial can also be taken in any other soft synth that supports scala files.

This tutorial is for anybody that wants to try out this beautiful tuning in a soft synth, I will not go into detail explaining the actual tuning itself. You can read about Pythagorean tuning elsewhere or just try it out and see how it sounds. 🙂 Remember you will have a bad sounding interval between Eb – G#, the fifths and forths are otherwise perfect.

The other aspect of going down from A4=440Hz to A4=432Hz will give you more natural frequencies, I can warmly recommend this to anybody, wheter you’re using Pythagorean tuning or not.

Ok, back to the tutorial. Start by downloading the scala file for pythagorean tuning.

1. Download scala-file (zipped)

2. The next step is to unzip this file and load it into Z3TA+

3. Then as the third and final step you just need to tune the synth down by 37.5 cents. According to my calculations, the ideal would be 37.6 cents (corrected from 37.4), but the tuning slider in Z3TA+ is a bit coarse, ther maybe some way to fine tune the value but I couldn’t do it. In some soft synths you maybe set the A4 reference frequency, in this case you need to set it to A4=430.5Hz (corrected from 430.6Hz). These are the theoretical values and you may have to adjust these values in practice. Check with a tuner, for example the free CTuner by C-Plugs.

If you were to just tune down the synth to A4=432Hz with equal temperament, you need to go down 31.8 cents or of course set the reference frequency to A4=432Hz depending on the soft synth.

Tagged with:
 

28 Responses to Tutorial: Pythagorean tuning at C4=256Hz (A4=432Hz) for Z3TA+ and other soft synths

  1. Krustybeats says:

    Hi,

    Thank you for this excellent article! It’s concise and well very written.
    I still have a question thou if you could clarify me this.
    As i understand from your article, in order to get the Pythagorean scale working, one has to first of all use/load this scale type, and then as the second important step, lower the A=440 Hz to A=430.6Hz (or equivalently tune down by 37.5 cents, depending which option your daw or vst synth offers). Is this correct?
    I’m asking because let’s assume i have FL Studio and Luxonix Purity vst. Should I then turn down the master tuning in FL Studio to -32 cents (which i don’t know what exact Hz would that give me, i assume 431.942 Hz according to this cents to hz conversion chart here: http://home.broadpark.no/~rbrekne/referhtml/cents-hz.html),
    AND also set the tuning in Purity vst to exactly 432.0 Hz and change the scale to Pythagorean as well?
    I guess what i’m asking is that, if i set the scale to Pythagorean, do i tune down to A=360.6Hz or A=432.0Hz?
    I guess if i’m sticking to equal temperament, i only have to tune to A=432.0?

    I’d really appreciate if you could answer.
    Thanks,

    • Mick says:

      Thanks for your feedback!

      I have no experience how master tuning works in FL Studio (or other DAWs that have this feature). It’s a little confusing since you can tune most VST instruments in their graphical user interfaces and I’m not sure if all VST instruments react to master tuning in the DAW. I recommend that you leave the master tuning at 440Hz and tune the VST instruments instead.

      To your question:

      If you want to use Pythagorean tuning and keep A4 at 432Hz (and C4 at 256Hz) then you need to set the tuning of the VST instrument to -37.4 (corr: -37.6) cents or 430.6Hz (corr: 430.5Hz) and load the scale. (This may seem a bit illogical but the synths I have tried work like this).

      If you use equal temperament then you just need to tune the VST instruments to -31.8 cents or 432Hz.

      Does this answer your question? If not then I will happily try to give a better explanation.

    • Mick says:

      An explanation why you need to set A4=430.6Hz (corr: 430.5Hz) to get C4=256Hz and A4=432Hz when using Pythagorean tuning:

      Setting A4 to 430.6Hz (corr: 430.5Hz) will result in a C4 at 256Hz. When applying a custom scale file (Pythagorean) the C-note will be the base for the calculation of the frequencies for the other notes, which will result in A4 at 432Hz.

      • Krustybeats says:

        Thanks for the quick reply!

        Your explanations are clear.

        Yes, i was suspecting that it’s somehow necessary to set A4=430.6Hz as you suggested, for the Pythagorean scale to work out properly. And since you’ve tested this and made the calculations, i’ll buy that:)

        In regards to tuning VST instruments vs DAW, i also kind of assumed that maybe tuning only the VST will do. I tried it out, tuning both FL Studio to A=432Hz and Purity vsti to A=432Hz (and choosing Pythagorean scale), and as the result they kind of evened each other out, judging by the ear. So in my opinion it might not even matter which one i tune, but yeah, probably it’s best to tune the VST alone, if it has the function built into its user interface. And i take it then, that all midi data in the daw’s piano roll is then effected accordingly, that is, all midi will be tuned down to 432Hz as the reference point/frequency?

        One more thing. Do you know if loading Pythagorean scale and tuning the VST instrument down to -37.5 cents (or 430.6Hz) mean that now i will have Pythagorean scale in every key i choose to play. I mean, does the scala file apply to all keys, or only to the C major? Because, as i understand, the Pythagorean tuning itself is such that it needs to be retuned to every new i choose to play. I’m hoping it isn’t necessary in the digital realm and loading the Pythagorean scale will apply to all and every diatonic key, right?
        And i wonder, if there’s a way to verify if i’m using the correct scale and tuning. I now i can plug some tuning vst into my channel for tuning, but i guess there’s no other way to verify that my track is now indeed in pythagorean tuning but with my own ears:)

        • Mick says:

          You’re right about the midi data, you don’t need to worry about that. Midi note data only sends note numbers, no specific tuning or frequency information is included.

          Pythagorean tuning will give you perfect fifths (and fourths) all over the chromatic scale except for one fifth (the wolf’s interval). The scale file I included in this tutorial will have the wolf’s interval on the fifth of Eb – G#. This means that scales that include these notes should be avoided (for example C minor). Depending on which note the Pythagorean tuning is based you can move the wolf’s interval. This would require another scale-file.

          Try playing different fifths and then the fifth of Eb – G#, you can hear how out of tune that fifth is and all other fifths are perfectly tuned.

  2. Krustybeats says:

    Hi,

    Thanks for replying!
    I hope i’m not bothering too much with all my questions. All this different tempered tuning thing is still new to me. I’m starting to get the picture thou.

    So, basically, am i right to say, that the scale that is included in this article, is based on C maj scale (Pythagorean scale in C maj)? But in order to play in a different key, i would need another scale file? Btw, as i’ve managed to gather from other sources, there are tun files as well, besides the scala files. The tun files should allow me to use Pythagorean tuning in all keys. So, as i understand, one should load the .tun file instead of the .scl in order to have pythagorean in all keys. What is your understanding of that?

    Thanks, and i promise i won’t be bothering you too much longer:)

  3. Mick says:

    No problem, ask away, I’m also learning in the progress, I’m no expert on this either.

    Pythagorean tuning is not locked to a scale like C maj. It is a way to create a full chromatic scale of 12 notes in an octave. But depending on which note the Pythagorean tuning is based, you can move the wolf’s interval so other scales can be used. So you can play in different keys with that scale file as long as you avoid the wolf’s interval (Eb-G#). The ratios for the intervals will vary I think so you have to listen to how it sounds.

    I’m sorry I don’t have any experience with .tun files, they seem to include more specific information about the tuning, not only the scale.

  4. Krustybeats says:

    Thanks, Mick, for your replies!

    I’ve been digesting your answers, and feel like i understand alot more now about tuning.

    If i have any more questions/ideas in the future, i shall surely contact you…

    Thanks again for your help!
    Bye for now,

  5. Ben says:

    Hi Mick,

    Thank you very much for your clear explanation on tuning in 432Hz. I compose almost all my music in 432Hz for obvious reasons 😉

    However, I currently purchased Z3TA+2 and wanted to give this a try, but unfortunately your zip file isn’t available anymore. Do you happen to know how this scalar tuning is called? It probably comes already preloaded in Z3TA+2, because the list is pretty impressive to say the least.

    Thank you very much in advance.

    Kind regards,
    Ben

  6. Ben says:

    Thank you SO much, Mick! Much appreciated.

  7. Hi Mick, I recently started using the excellent product M-Tron Pro from Gforce. However – I really want this thing to work on 432hz., but don’t know how to tune it. The master tuner is set from 0.0 to 1.0. The default position is 0.51. I’ve set it on 0.17 now and it seems OK, but I’m not 100% sure if this is correct though. Can you perhaps help me out? Thank you so much!

  8. Sorry, the default position is 0.50 of course, NOT 0.51. Cheers!

  9. Thank you SO much Mick. It seems that it’s quite impossible to properly tune a Mellotron as every sound is recorded in a different pitch obviously 😉 Some of them even are recorded in 432Hz. so it seems!

    On another note I’m using the Gforce Minimonsta (Moog) as well, but I have to set the tuning at -31.4 to get 432Hz. My Logic template is set to 432Hz. already, so to properly tune the VST instrument accordingly the above setting is apparently what is needed. Is this correct?
    I’m using the Logic X Tuner (set to 432 of course).

    Thank you for your responses. Much appreciated!

    • Mick says:

      Ok, I see, that’s interesting to know. 🙂

      So -31.4 in Minimonsta you say? Theoretically -31.8 cents down from 440Hz will give you 432Hz, maybe the Minimonsta is somewhat detuned to give an analog feel. I’m using Sonar myself and don’t set the tuning on project level. I find it quite confusing the way it works in Logic etc. because not all VST instrument will “obey” the project tuning, so you still need tu tune some VSTs manually. If you need to tune Minimonsta even if you have set the tuning in Logic I’m assuming that Minimonsta doesn’t take that tuning into account at all, because if it did you should be able to leave the VST tuning at default.

      But anyway it’s always good to check with a tuner.

      UPDATE 2014-04-25: It seems that my Yamaha AN1X will give me A4=432Hz when I tune down -31.3cents so it’s always good to check with a tuner. Minimonsta mentioned above needs tuning to be set to -31.4cents, I wonder why, since the theory gives us -31.76665cents.

  10. Yes, you are quite right about this. Logic’s own VST/AU instruments obey the rules, but the third party plugs don’t. I suppose I just have to live with that. 😉

    Thanks Mick, for your answers!

  11. I’ve got another question for you, Mick. Sorry to bother you, but it’s REALLY difficult to find anything on this on the net. How do I tune instruments in Kontakt? There is a tuning knob present obviously, but it only deals with semitones. How can I accurately tune the samples to 432Hz using Kontakt? Any experience in doing this perhaps? Thank you SO much!

    • Mick says:

      Did you get this sorted already? There is a master tuning knob for kontakt that lets you set the tuning in Hz, at least in Kontakt 5 as far as I remember, in the toolbar above the instruments. What version of Kontakt do you have?

  12. Thank you, Mick. I already sorted it. You’ll have to set the tuning in increments. I figured this out shortly after I posted my question here. Thanks again!

  13. Bass Traffic says:

    Hi, I’m really interested in this tuning method. Firstly do you know of a list I can get of VSTs that are tune-able in this way and secondly, how many decimal places are your calculations accurate to using 37.4 cents and A4=430.6Hz.
    I’d also be really interested in seeing the calculations that you used.
    I’m busy doing an album that’s taken me 6 years so far so I wanna get everything really accurate for obvious reasons. I was gonna resample everything from sine waves using the chart on this video at 13 minutes odd:
    http://www.youtube.com/watch?v=FY74AFQl2qQ
    Importantly noting that there’s a couple of mistakes in it has like B 234 – 456 that should be 468.
    Any more help would be really ace!
    Cheers.

  14. Mick says:

    I don’t know of a list with VST intruments that support scala tuning files, but if you are interested in a particular soft synth it needs to support general tuning (in cents or by setting a specific A4 frequency), most soft synths do so this shouldn’t be a problem, but secondly it need to support scala tuning files or otherwise support custom tuning, this is usually stated when reading the features.

    Those cent and frequency values are rounded, more exact values and calculations are given below.

    Todays standard is A4=440Hz and equal temperament. In this tuning C4 is 440×2^(-9/12) = 261.625565Hz. (-9 is the number of semitones from A4 to C4.) We need the value of C4 because that is the base for the calculations of scala files.

    Intervals in cents for two frequencies (f1 and f2) can be calculated with this formula: c = 1200 × log2 (f2 / f1). (There are 1200 cents per octave.)

    This gives us f1=261.625565Hz and f2=256Hz and the calculation:
    c = 1200 × log2(256/261.625565) = -37.631654 cents

    The following formula will give us the base frequency (-37.63cents down from A4=440Hz). f2 = f1 × 2^(c/1200) or in our case:
    f2 = 440 × 2^(-37.631654/1200) = 430.538965 Hz

    When I wrote this article I did testing with custom scales on my Roland XP-30 and to get C4=256Hz and A4=432Hz with Pythagorean tuning I needed to set the master tuning to 430.6Hz and calculated -37.4cents from that value, this is not theoretically correct and I have now corrected the values in the article. The reason for this was I could not set the master tuning to 430.5Hz on my XP-30, only 430.6Hz and 430.4Hz (increments of 0.2). The previous values were close but still just a little bit off, I’m sorry about that.

    It seems that the theory doesn’t work fully in practice and I advice you to check the tuning with a tuner to comfirm the correct frequencies. On my Yamaha AN1X virtual analog synth I have to set the tuning to -31.3 (equal temperament) to get A4=432Hz. Ben van Geest mentioned that he needed to set -31.4 to get A4=432Hz. I don’t know why but I’m going to try to find out.

    • Bass Traffic says:

      Thanks for the quick reply, I’m definitely gonna have to look into this on a deeper level. Have been working on an album project for 6 years now so I really want to get the tuning accurate, if I’ve spent this long on it then it would be a shame to have the tuning out, even by a tiny fraction.
      I’ll check back to this later cos my brain is a bit wasted from a heavy weekend so not really working at full capacity.

  15. Hey Mick. Do you happen to use the Cakewalk Z3TA 2 Plus by any chance? It seems like you can’t properly tune this synth well, because of the lack of increments between the steps (from -50 to +50, but no in- between values like for instance -37.6). Thanks.

    • Mick says:

      Sorry, I haven’t tried it, but that’s too bad, I’m not surprised though, it seems like a lot of vsti makers don’t take exact tuning to seriously.

  16. Rain Wilber 36 says:

    Thanks for writing up this useful info Mick. This was helpful for me: “We need the value of C4 because that is the base for the calculations of scala files.”

    Found:List of Microtonal Software and Vst’s

  17. Zack says:

    Hey there,

    Just coming across this post. I got a TX-802 recently and I was wondering if anyone had any knowledge on micro tuning it in HZ? I’d like to get all the notes to 432hz if possible, as the master tune won’t allow me to get to it perfectly. The closest I can get it to is 431.9hz in the master tune.

    If I changed the master tune to 431.9hz, would the micro tune be that much closer, or would it still start from 440hz? I’m assuming it will be at 431.9hz, but I could be wrong.

    I realize this is a bit off topic as it’s a hard synth, but I thought someone might be able to shed some insight. 🙂

    Any help is appreciated.

    Thanks!

    Here is what the manual says:
    “Here you can edit a Micro Tone scale. You can specify the pitch that will be produced for each not (C-2 to G8). Use the +1/-1 keys to raise or lower the pitch for each note. You can move in steps of a semi-tone (Coarse) or steps of 1.1719 cents (Fine). Select Coarse/Fine using ENTER + the cursor keys. The resulting pitch is shown as a note number +42/-43 and also as an absolute number 0 – 10794. (One octave is 1024 steps.)
    To store the Micro Tune scale you have edited, press STORE. Use the ten-key pad and INT/CRT to select the destination (INT 1-2 or CRT 1-63) and press ENTER. Press YES, and if you are sure, press YES again.”

Leave a Reply to Krustybeats Cancel reply

Your email address will not be published.

The annoying part... * Time limit is exhausted. Please reload the CAPTCHA.