Vari-Speed - calculating speed percentage relative to semi-tone...

miroslav

miroslav

Cosmic Cowboy
Trying to get my head around something, but I'm just not seeing the math (though I'm sure it's a simple answer).

OK...so I have my MX-80 running at 15ips.
I want to simply slow down or speed up the IPS so that I can pitch-shift by a semi-tone.

Now....I've found some charts for this, but for some reason, if I go down, the percentage is -5.61%, but if I speed up a semi-tone, it would be +5.95%....according to the charts...???
I'm not seeing the reason in the slight difference between up/down.
Now, lets say you want to go further up or down...2-3 semi-tones....it's even more strange. There is no predictability in the percentage numbers.

Look at these charts....can anyone see why this is the case?

Semi-Tone Pitch/IPS/Percentage Relationship Chart 1
Semi-Tone Pitch/IPS/Percentage Relationship Chart 2

Just look at the percent column and the numbers at the 0.0, 1.0, 2.0 or 0.0. -1.0, -2.0....etc...etc.
If the steps between semi-tones are the same...why wouldn't the IPS percentage change be the same interval...??? Like 2x, 3x, etc.....and why the percentage differences when going up/down a semi-tone. I would think that at least there it would just be a + or -...but the percentage would be the same...???

The Otari decks have a percentage readout, so these charts are great, I can just set the Vari-speed with the correct percentage, depending how far I want to go up/down...but I just don't get why the difference.
Not to mention...the pecentage step between say C and C# (5.95%) is not the same as it is between D and D# (6.67%).......????????
To me...it's all one semi-tone, regardless of the note...so wouldn't the percentage steps be identical between any two semi-tones...?

I feel like there's a valid reason for the small differences....I just can't put my finger on why it's valid.
I'll have to think about it a bit...it will probbaly hit me when I wake up tomorrow...or when I'm in the shower. :D
 
OK....so I didn't have to wait to wake up in the morning, or the shower....but I was in the bathroom when I realized what the answer was. Something about the bathroom that makes for clear thinking! :D

It just came to me out of nowhere....it's all about the speed.
As you start to decrease or increase the speed of the tape...the percentage of what speed you have left or that you're adding to is always changing....therefor the percentage has to change with it.

IOW....
Lets make the speed 100, just to keep it simple. It doesn't matter what the units are....IPS, MPH, whatever.
If you drop the speed by 10 from 100, it will be a 10% drop.....but if you want to then deduct another 10 off the remaining 90 of the speed, that second drop of 10 = 11.11% as change in speed.
So as you drop with each increment, the percentage of drop increases.
Same thing if your adding speed....just in the opposite direction.

DUH.....I knew it was something simple, I was just too focused on the semi-tones and not thinking about what was happening to the speed.
Now I can go to sleep and wake up with the answer already in my head. :)
 
Also, frequency count doubles with every octave, I'm sure that has something to do with it too.

Oh wait, that wouldn't change percentage, would it? Oh well...
 
Yeah...I know about the frequency/octave...but it doesn't apply to the speed percentage.

I was initially expecting that once I calculated the percentage for a single semi-tone drop or rise, it would be a constant percentage for every semi-tone up/down, and I would just multiple by number of semi-tones desired for the vari-speed pitch shift.
I just didn't see the obvious, that once you drop it or raise it by one semi-tone, the speed has changed and therefor the percentage for the next semi-tone step will also change..and so on.

I knew it was simple...I just had to see it. :)
 
Yeah....OK. :D

Were talking about the speed of the tape....not sure what that equation has to do with it.
 
Sorry, posted from my Kindle, and it was frustrating me, so I cut it short.

F1 = F0 * 2^(x/12)
where F0 is the original frequency, F1 is the new frequency, and x is the number of semitones (positive or negative)

This will give you a decimal scaling factor, for 1 semitone up, that's 1.05946, for 1 down, it's 0.94387.

Multiply by 100 to get a percentage - up is 105.946, down is 94.387. Then realize that the percentage numbers on your varispeed control are added to 100%, such that when it's set at 0, it's actually running at 100% speed.

So, subtract 100 from the percentage number - up is 5.946%, down is -5.613%. Pretty much exactly what your charts said, no?
 
ashcat_lt said:
Sorry, posted from my Kindle, and it was frustrating me, so I cut it short.

F1 = F0 * 2^(x/12)
where F0 is the original frequency, F1 is the new frequency, and x is the number of semitones (positive or negative)

This will give you a decimal scaling factor, for 1 semitone up, that's 1.05946, for 1 down, it's 0.94387.

Multiply by 100 to get a percentage - up is 105.946, down is 94.387. Then realize that the percentage numbers on your varispeed control are added to 100%, such that when it's set at 0, it's actually running at 100% speed.

So, subtract 100 from the percentage number - up is 5.946%, down is -5.613%. Pretty much exactly what your charts said, no?
Click to expand...



That equation works better. :)
Though I wasn't asking how you compute the scaling factor.
The equation is right at the top of the chart.
Octave: a^12 = 2 (a = 1.059463)

What was initially puzzling me is why the speed percentage factor was changing with each step...regardless of any specific pitch used. You can completely remove the semi-tone pitch thing from it....just looking at the speed of the tape and how any change affects the percentage of change. Then I realized the obvious...whatever percentage of change occurs, it changes the speed...so the next computation for percentage of change will be different, and so on....


Anyway...it was just one of those late-night mind ticklers, and as I stood there playing around with the vari-speed and "tuning it it" to different semi-tones....looking at the speed percentage readout made me wonder.
 
Looking at the logic from Miro, this makes sense. The percentage has to change as the speed is now different. If going lower, if you start at 100 and change 10% and it equals some distance, the same distance would require I higher percentage at a lower speed. Inverse of that going higher. Plus, gravity and resistance. (I just made that up based)
 
Yeah...got it. :D

It was a temporary brain cramp last night.....couldn't see the forest for the trees.
I was happy though that it came to me without any need to look at the math, and the common sense logic just popped into my head while in the bathroom....ahhhhh...."library". A place where thoughts flow freely (among other things). :)
 
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