Master tune - Hz offset?

  • Hey all! The Virus synths have finally become available in New Zealand and so I'm starting to look very seriously into buying a Ti2 Desktop for my first hardware synth! I've been interested in buying one for quite some time but I'm hung up on one little point. I'm one of those fellows who produce with slight Hz offsets, usually A=432Hz and A=415Hz. I have a few reasons for this, I have a bit of a thing for classical/baroque music/instruments and their tunings so I like to produce in those sorts of tunings, and generally my ears prefer the slightly lower tuning, finding it a bit more mellow. I know there's a lot of debate about doing this in an esoteric context but I'd rather avoid that side of things and keep this query technically orientated.

    So, I know the Virus Ti2 doesn't have this functionality built in. The soft synths I use allow me to use .tun files to adjust the tuning exactly to my needs, and I know I can use cents microtuning to approximate the pitch shift but it's not exact, and I can hear the slight dissonance no matter how close I get. Does anybody have any suggestions for working around this? I'm not sure if I can microtune MIDI note data before it goes into the synth via say, Max4Live but I'm willing to explore that possibility as a workaround. Ideally though I'd love to be able to do the microtuning inside the synth itself as a global parameter.

    Representatives of Access themselves, what are your opinions on the possibility of this as a feature update?

    Looking forward to hearing some thoughts! ^^

  • Before I explain how to get the tuning you are after I'd like to start off by saying that a "Hz offset" is meaningless in terms of music - since the human perception of frequency (or pitch) is logarithmic. If we were to take a standard scale of pitches and add the same amount of Hz to each pitch, it would not sound like a scale anymore, the relations between notes would change, e.g. two notes that originally were an octave apart would not sound in unison anymore. Instead, in order to move the scale around as a whole, all the pitches of the notes have to be multiplied by the same ratio (dimentionless!). For example, to get the tunings you are looking for, you'd have to multiply the A440 pitches by 432/440=0.981818182, and 415/440=0.943181818. Maybe the feature you were talking about is reference tuning, where you tune one note (e.g. A below middle C), and all the other notes are derived from it by reference.
    So now let's solve your problem using the instrument at hand. The master tuning lets you change the tuning in cents, which devide the semitone by 100 logarithmically, the same way the semitone divides the octave by 12 logaritmically. To get a pitch to jump to the next octave you multiply it by 2. Therefore: 1 cent change applied 100 times (or 1cent to the power of 100) = semitone; 1 semitone change applied 12 times (or 1 semitone to the power of 12) = octave (or 2) => cent^1200 = 2 => 1 cent = 1200th root of 2 = 1.00057779; That's the ratio of 1 cent.
    As stated before, in order to get from 440 to 432, we have to multiply by 0.981818182, or in cents, cent^n=0.91818182 => n=log_cent(0.981818182)=-31.76665363 which we can round to -32 cents. This will give you A=440*(cent^-32)=440*0.981685855=431.9417763. Which is 0.06Hz away from the target (or less then 0.02% out of tune in general). If you can perceive such a difference then I'm really impressed. There is still a solution in this case, but I'll get there later. First let's see how we get to 415: log_cent(0.943181818 )=-101.2706247, which we can round to -101 cents. Oops, the global tuning allows only values between -64 and +63! There is still hope - you can tune a part by itself (independently of other parts) to go down one semitone (=100 cents) and one cent. Thus we get A=440*(cent^-101)=440*0.943329267=415.0648774, again, 0.06Hz away from our target (or less then 0.02%).
    If you are still dissatisfied with this, you can control the tuning with pitch bend messages you can send out of Max4Live. You can set the pitch bend range to 1 semitone each way, and the pitch bend message can sub-divide this range by 16384! And it can be set to do this either linearly or logarithmicly. I have another use for this. When I want to put some Arabic influence into my music I use the pitch bend wheel in this configuration, to put some quarter-tone notes in.

  • That's a fantastic reply flabberbob! Thank you very muchly! You are very right about my misuse of the term 'Hz offset', I wasn't quite sure which term to use at the time but yes I was talking about reference tuning/'standard' concert pitch.

    I went back in to Alchemy (my usual software synth) and had a play with tuning in cents again. One of the cool things about Alchemy is that you can tune more precisely (to say, -31.8cents like I could approximate from your mathematics) and still I did notice a tiiiiiny dissonance. To be totally honest I'm also immensely amazed that I can pick this out, especially seeming I don't have the best ears on the planet by a long shot. It may have something to do with the fact that i'm referencing from a perfect A=432Hz .tun file in Alchemy and i'm probably picking up on the slight unison-esque dissonance.

    Would you be able to assist/guide me a little further on the Max4Live approach to doing this? I'm not immensely skilled with Max (I bought it for university use but I found myself gelling with Reaktor a great deal more, the way my mind works seems to prefer it) so I'd really appreciate some guidance there, especially in this task!

    Thank you again, muchly appreciated assistance! Still curious to hear what Access might have to say on the matter, and the possibility of this reference tuning offset in a future firmware update.

  • Actually you don't REALLY need MAX or any other addition to your DAW, any standard MIDI strip has the possibility to add pitch bend MIDI messages, the same way you can add MIDI CC-s. You can also record the movement of the pitch wheel of your controller if you have one. The Virus' response to the pitch wheel is configured from under the common tab of VC, if I'm not mistaken. So by applying the same math I used above, if you set the pitch bend to +/-1semitone logarithmic, the 16384 "grey levels" are spread over 2 semitones, so, extrapulated to an octave we have a total of 98304 pitch wheel steps => pitch_wheel_step^98304 = 2 => pitch_wheel_step = 98304th root of 2 = 1.000007051.
    For A432, we need n so that pitch_wheel_step^n=0.981818182 => n=log_pitch_wheel_step(0.981818182)=-2602.324266, therefore sending a pitch bend message at the start of the song, with the value of -2609, will tune A of the MIDI channel in which it is sent to 440*pitch_whell_step^-2609=432.0009877Hz.
    For A415, n=log_pitch_wheel_step(0.943181818 )=-8296.089579, and 440*pitch_whell_step^-8296=415.0002621. The problem is, that a pitch bend message is limited in its minimal value to -8192, which, in our configuration is equal to one semitone down, so what you do is, as we did with the cent tuning, first tune the part one semitone down, then send the rest of the tuning as a pitch bend message with value -4. You should remember that if you plan to use the pitch bend wheel as a part of your performance/recording you should find a way to always return it to the tuning value.
    You should consider the fact that it could be that you heard a difference in tuning because you EXPECTED to hear one, and in a double blind test you might have not noticed it. Actually, frequencies that are very very close, like the ones we calculated in this thread, when played together, actually produce an "amplitude modulation" or "pulsating" effect rather than a dissonance. Furthermore, it is impossible to tune physical instruments such as the ones used in the baroque period, so perfectly. The tuning changes with time, as the temperature and mechanical strains change. Personally, I prefer music that's just a tiny bit out of tune, it sounds more interesting - take for example what we know as a super- or hyper-saw oscillator: when the sawtooth waves are very close in frequency it sounds very dull, but as you spread them apart, just before they begin to sound out of tune, they sound very rich and lush together.

  • Master pitch 440 as with most synths can be set in 1Hz increments. Tuning rations (either equal temperament, pure tuning or a combination of the two for Virus's) are calculated from master pitch and not each element of the cycle of fifths. 440 is convenient but not in resonance with anything and many other pitching's have great reasons for use.

    I've found tuning many instruments and a DAW differently for different songs if too much time spent in left brain for creative ease so tend to tune by other means. Plugins etc..

    Would be great though if more synths followed DAW master pitch so this could be stored with song settings which the Virus currently does not... Hopes for the future!!!



  • In cents yes, apologies was sure it was in hz last time I looked :S

    Was some time ago..…read&postID=7468#post7468

    Perhaps its time for that feature request. Will put one in asap.

    So we have 128 steps of 100 cents in master tuning and could also add semitone transpose to this to have a effective 100 cents each way.

    100 / 128
    = 0.78125

    So 128 steps of 0.78125 Cents or

    Master tuning in Hz :

    0.1986025941951 +1
    0.3972051883902 +2
    0.5958077825853 +3
    0.7944103767804 +4
    0.9930129709755 +5
    1.1916155651706 +6
    1.3902181593657 +7
    1.5888207535608 +8
    1.7874233477559 +9
    1.986025941951 +10
    3.972051883902 +20
    5.958077825853 +30
    7.944103767804 +40
    9.930129709755 +50
    11.916155651706 +60
    12.511963434291 +63

    A little off here and too sleepy to fix my math but a good idea of possible accuracy and not exact enough for my purposes. Its either VC following DAW global tuning update or other means of pitch adjustment for me..