I have a quick question as far as depths go in terms of the vibratos. Do you know the ratio of cents to depth percent for each waveform? Some of my records do a little sweep here and there, some just upwards, some just downwards. I correct the sweep by: 1) Determining the length of the selection; 2) Subtracting the end-length in seconds from the beginning-length in seconds using Calculator; 3) Take 1 and divide it by that number to get the Hertz reading for the vibrato; and 4) After the vibrato has been applied, change the speed of the rest of the file to the right of the selection (command "Cursor to track end) by approximately the number of cents. As I understand it, each depth percent is 2 cents. So if I had a depth of 100 percent, then would the sound change by 200 cents (or 2 half-steps)? If not, I’d like to know what exact number of cents is used for a given depth percentage, so that I don’t have sudden pitch changes in my de-warped records. Maybe it depends on the waveform as well, but if it’s consistent number, that’s cool. Thanks,
100 percent gives a vibrato “width” of 4 semitones. That is, the difference between highest and lowest bend is 4 semitones. The pitch bend in Hz in the upward direction is equal to the pitch bend down. For example, a 100 percent vibrato applied to a 1000 Hz tone produces a pitch bend of +/- 115 Hz.
I don’t think I was clear. I meant as far as the deviation from the original pitch, not the entire range. I meant to say, if I had a vibrato of 100 percent depth, would it go 200 cents higher (from the original pitch) and 200 cents lower (from the original pitch)? I know where you’re coming from, it totals 400 cents, but what about from the original pitch? I think I’m probably right.
No it wouldn’t. As you say, the “width” (maximum deviation) totals 400 cents, but it’s the same frequency difference above and below, not the same frequency ratio. For small variations the “pitch” above is very close to the pitch below, but it’s not exactly equal because pitch is matter of ratio, not of absolute difference. Using my previous example, a 100 percent vibrato applied to a 1000 Hz tone produces a pitch bend of +/- 115 Hz. That works out as about 188 cents above and 212 cents below. For smaller shifts, say 10%, it’s very close to +/- 20 cents.
Hmm - let me get this straight. So there is no real factor to convert depth percentages to exact number of cents? I wasn’t talking about converting depths to Hertz, but cents, so that after part of a file sweeps up, for instance, I’d know how many cents to lower the rest of the file after counteracting the original sweep. For instance, let’s say that we have a sound that’s fine for most of the file, but then quickly sweeps 20 cents lower and stays there for the rest of the file. My original approach was to take the length of the sweep in seconds and subtract the end position from the start position, and take 1 and divide it by that number to get the vibrato cycle frequency so that it has only one cycle in the whole selection. In the example I said it sweeps about 20 cents lower, so I apply a Sawtooth vibrato so that the whole selection would sweep up by about 20 cents. Because of the start of the selection being 20 cents too low, I increase the speed of the selection (using Calculator I find the factor from cents to pitch-percentages). After the sweep has been counteracted I realize that the selection ends at 20 cents too high - or is it 40. I then change speed of everything to the right of the selection by 40 cents, and after listening to the file the sweep is hardly noticeable at all. However, since you said that there isn’t really an exact factor of depth versus number of cents, I’m afraid I won’t be able to find the exact number of cents to change the pitch by, at least when it isn’t 2 cents = depth number. When you said “linear scale”, I thought you were referring to semitones and cents rather than Hertz, so that’s what I figured. Would I have to modify or add anything to the code so that a depth of X = exactly 0.5X the depth number? I think I’m quite confused.
The conversion from Hz to cents is not simple. Hz is a measure of frequency and cents (pitch in general) is a ratio of frequencies. Hz is relatively easy to measure and work with; it’s the number of times that a waveform completes a full cycle in one second. Pitch is a ratio, so to measure pitch you always need a reference. In other words, pitch compares one frequency with another frequency and the pitch difference is the ratio between the two frequencies. One of the standard frequencies for measuring the pitch of a note, is to compare the frequency with a frequency of 440 Hz, which is the most commonly used standard for the note “A” above “middle C” (often called “A440”).
When comparing two frequencies, we look at the ratio of one frequency (in Hz) to another frequency (in Hz). For example, if one tone has a frequency of 440 Hz, and another tone has a frequency of 880 Hz (double the frequency of the A440 reference tone), then the ratio is 1:2, which we call an octave. Whenever the ratio is 1:2 (or 2:1), the pitch difference is one octave. Doubling (or halving) the frequency again is another octave. Thus a ratio of 4:1 (or 1:4) is a pitch difference of 2 octaves (the frequency has doubled (or halved) twice).
Historically there have been a number of ways to sub-divide octaves into smaller amounts. In Western music we have used 12 sub-divisions for a very long time, which we call “semi-tones”). Over the centuries there have been a number of different ways to sub-divide an octave into 12 semi-tones. The method that is used almost universally today is to sub-divide an octave such that the ratio of frequencies from one semi-tone to the next is constant. In other words, pitch is a logarithmic scale, which is called “Equal Temperament”. The idea of equal temperament goes back thousands of years, and was popularised in European culture in about the 18th century.
Mathematically, as an octave is defined as a ratio of 2:1, so a semitone is defined as a ratio of 2^(1/12):1. Cents were defined in the mid 19th century, as 1/100th of a semi-tone. Note that this is also on the same logarithmic scale, so a cent is not a fixed frequency difference, but a fixed frequency ratio of 2^(0.01/12):1 which is a ratio of approximately 1.00057779 : 1