To calculate frequency of a note you should know the amount of semitones between the note and A4.

2x/12 * ffixed = fgiven

x – is the quantifier, based on amount of semitones between given note and fixed one (A4);
ffixed – is the frequency of fixed note (~A4 = 440 Hz);

For example, since C4 is nine semitones lower than A4, the quantifier for it will be -9.

So, whether it is possible to calculate its frequency without knowing of this interval? Is there any other frequency-of-a-pitch equation that doesn't use intervals in it?

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    I have no idea, how you want to specify the tone for which you want the frequency if not counting to some reference. You could use a MIDI mapping from note number to frequency but even MIDI counts semitones. – guidot Mar 21 '16 at 12:41
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    What problem are you trying to solve? Is this an XY problem? meta.stackexchange.com/questions/66377/what-is-the-xy-problem – Dave Mar 21 '16 at 13:47
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    There are no inherent mathematical properties in the letters A-G that can enable them to be translated to frequencies without the use of a constant. The letter assignments are completely arbitrary; thus you need some kind of constant to define them — 440 Hz. Your equation makes use of the number 12, so you clearly have the ability to define a constant value in your equation; if all you're trying to do is create a function definition f(p) where p is the pitch, the frequency of which is being calculated, then this is really an algebra question. – NReilingh Mar 21 '16 at 13:47
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    I do think this is an XY problem, frankly. What are you trying to accomplish by answering this question? Are you just having trouble translating note names into numeric values? – NReilingh Mar 21 '16 at 17:48
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    The answer to your question as written is "No, it's not possible." This is because a pitch->frequency conversion actually requires a second argument that defines the tuning system in use. When you omit this, we assume that the tuning system will be 12-tone equal temperament at A=440Hz, and so this information must be embedded in your formula as constants. – NReilingh Mar 21 '16 at 18:18

You either needed a reference pitch to calculate all other notes or you need to have all the pitches defined. Every formula to obtain a pitch needs a reference pitch and you need to know how that pitch relates to the one you are calculating.

The pitch you are using is relative to a system whether it is equal temperament, just, Pythagoras, ect. The pitches you build off each Not even every A4 is 440 Hz. There are a lot of different groups that use other frequencies like 435 or 441.

As long as you have a way to figure out which of the 12 notes you are dealing with (if you are using equal temperament like you seem to be) the rest is easy. You must have some method to know the difference between an A, A#, B, C, ect.

After you figure out the 12 base reference pitches of each note the calculations are simple as you only need to calculate one octave then double the frequencies to get an octave up and half to get an octave down which is valid regardless of system. For example, A3 which is an octave below A4 would map to the pitch 220 Hz and A5 which is an octave above A4 would map to 880 Hz.

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