Pretty much stopped using Live for djing and using Traktor again, no real problems, just a matter of taste. Anyways, I have key and tempo info for all my tracks and was wondering if it'd be possible to make an Excel doc. or something that would allow you to calculate a track's key at the current tempo ie I know track A is in E at its original 124bpm, but what would the closest key be if synced to the currently playing track's 126.3bpm?
I know the math roughly but some kind of onthespot calculator would be filthy good. even better were it built into Traktor but don't see this happening anytime soon. Posted this as a feature request at NI but seeing as there's no shortage of smart 'uns here and this would be pretty useful generally, figured I'd ask here too.
Calculate track's key at current tempo? Howto ideas?

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The pitch shift applied by playing something in a known key at X bpm, at Y bpm, can be expressed in terms of ratios:
key/x bpm = newkey/y bpm
and can be rewritten:
(key * y bpm) / x bpm = newkey
Since we don't need a numeric value for 'key', we can consider it to equal 1 for the purpose of this calculation.
126.3/124 ~ 1.018.
Western music has very clearly defined semitones* that are neat ratios of two fairly low integers (http://en.wikipedia.org/wiki/Interval_(music) has a good table, but doesn't want to sit inside a url tag here). For example a full octave is 2:1 (2, which results when y = 2x in the above context); a fifth is 3:2 (1.5  try putting an Operator osc @ 500 to hear this). Here is where it gets tricky though; the semitone scale is logarithmic, not too easy to calculate in your head (well, at least not my head). The difference between the first and second semitones is 16:15 versus 9:8, not something I could tell without a calculator.
So if you're doing an Excel sheet I guess I'd suggest calculating the 11 semitones by solving:
+1 semitone :: 16/15 = z / 124(bpm, just an example) :: (z ~ 132.3)
+2 semitone :: 9/8 = z / 124 :: (z = 139.5)
...
My guess is this would give you the information you want, I think at this point guesstimates would be reasonably accurate.
*  There are a few tricks to the ratios underlying semitones as well, that result in some concrete audible effects resulting from how notes in a polyphonic context can modulate a little against each other, but culturally we live in one that has semitones.
I have a question here  how closely do keymatching DJs follow the rules? It seems to me like you're likely to find some harmonic / modal structures that might not look to be in 'key' with each other but can mesh in interesting ways, but also possible to have some accidents doing it this way.
key/x bpm = newkey/y bpm
and can be rewritten:
(key * y bpm) / x bpm = newkey
Since we don't need a numeric value for 'key', we can consider it to equal 1 for the purpose of this calculation.
126.3/124 ~ 1.018.
Western music has very clearly defined semitones* that are neat ratios of two fairly low integers (http://en.wikipedia.org/wiki/Interval_(music) has a good table, but doesn't want to sit inside a url tag here). For example a full octave is 2:1 (2, which results when y = 2x in the above context); a fifth is 3:2 (1.5  try putting an Operator osc @ 500 to hear this). Here is where it gets tricky though; the semitone scale is logarithmic, not too easy to calculate in your head (well, at least not my head). The difference between the first and second semitones is 16:15 versus 9:8, not something I could tell without a calculator.
So if you're doing an Excel sheet I guess I'd suggest calculating the 11 semitones by solving:
+1 semitone :: 16/15 = z / 124(bpm, just an example) :: (z ~ 132.3)
+2 semitone :: 9/8 = z / 124 :: (z = 139.5)
...
My guess is this would give you the information you want, I think at this point guesstimates would be reasonably accurate.
*  There are a few tricks to the ratios underlying semitones as well, that result in some concrete audible effects resulting from how notes in a polyphonic context can modulate a little against each other, but culturally we live in one that has semitones.
I have a question here  how closely do keymatching DJs follow the rules? It seems to me like you're likely to find some harmonic / modal structures that might not look to be in 'key' with each other but can mesh in interesting ways, but also possible to have some accidents doing it this way.
http://www.soundcloud.com/xherv
I know EVERYTHING that I know and you don't know, and don't know what I don't know that you know, so I'll ignore that stuff. Wassup now?
I know EVERYTHING that I know and you don't know, and don't know what I don't know that you know, so I'll ignore that stuff. Wassup now?
For a single excel formula, would this work:
Semitones Difference to New Key = LOG((NewBPM/CurrentBPM),2)*12
Examples:
CurrentBPM = 124
NewBPM = 132
Formula result = 1.08
So you're just over one semitone up compared to current key e.g. A > Asharp
CurrentBPM = 124
New BPM = 104
Formula result = 3.04
So you're just over three semitones down compared to current key e.g. A > Fsharp
xherv  you want to confirm whether I'm just talking rubbish or not?
Semitones Difference to New Key = LOG((NewBPM/CurrentBPM),2)*12
Examples:
CurrentBPM = 124
NewBPM = 132
Formula result = 1.08
So you're just over one semitone up compared to current key e.g. A > Asharp
CurrentBPM = 124
New BPM = 104
Formula result = 3.04
So you're just over three semitones down compared to current key e.g. A > Fsharp
xherv  you want to confirm whether I'm just talking rubbish or not?

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 Joined: Mon May 15, 2006 12:15 pm
That's pretty clever and more accurate than using the ratios listed in the Wiki . . . I haven't visited this topic in quite a while, since I was in high school tuning a guitar a couple times a day, Wiki is really fascinating.
I'm tempted to demand Live 8 include Just, Even, Well Temperament as well as all other mathematical and crosscultural tuning maths. It's kinda like MPC swing, right? edit: Not even kidding, in the case of something like Tension modeling a guitar, I wonder if this is accounted for, I think you can definitely feel and hear some of those microtuning issues on the 'real' thing.
I'm tempted to demand Live 8 include Just, Even, Well Temperament as well as all other mathematical and crosscultural tuning maths. It's kinda like MPC swing, right? edit: Not even kidding, in the case of something like Tension modeling a guitar, I wonder if this is accounted for, I think you can definitely feel and hear some of those microtuning issues on the 'real' thing.
http://www.soundcloud.com/xherv
I know EVERYTHING that I know and you don't know, and don't know what I don't know that you know, so I'll ignore that stuff. Wassup now?
I know EVERYTHING that I know and you don't know, and don't know what I don't know that you know, so I'll ignore that stuff. Wassup now?

 Posts: 2233
 Joined: Fri Jan 10, 2003 5:28 pm
 Location: Tokyo
 Contact:
Wow, thankyou for all that, now to figure out how to apply all that in some kind of inthemix kind of format/process that my brain can deal with. For sure there are many uses for keymatching and not simply likewithlike. The Mixed In Key software uses an interesting nonmusical notation which suggests 4 mixfriendly keys at the most basic level. In a software such as Traktor which will displays tempo and key info. in the browser this kind of functionality would seem to be a very logical step.
A 6% change in tempo results in approximately a semitone shift in key.
When mixing, it's just a matter of doing a quick calculation in your head. Eventually when you've been doing it often enough, you kinda tend to get a rough idea as to which situations will and won't work
i.e. a track in B minor is going to work with a track in C minor, if say Bn is 125 and Cn is 130, or a F Minor at 132 may work with a B minor at 126. If you work out the bpm difference between the two however, you'll find that they are 4% and 4.7% respectively. As long as the difference is a bit more than 3%, there will be a discernible shift, and likewise, if it is leaning towards something less than 3%, there won't be a majorly discernible shift in pitch during your mix. However, I've noticed that some tracks are in fact keyed/detuned by as much as 50cents which puts the tune in a lil bit of a limbo zone, but it's always bound to work with something
When mixing, it's just a matter of doing a quick calculation in your head. Eventually when you've been doing it often enough, you kinda tend to get a rough idea as to which situations will and won't work
i.e. a track in B minor is going to work with a track in C minor, if say Bn is 125 and Cn is 130, or a F Minor at 132 may work with a B minor at 126. If you work out the bpm difference between the two however, you'll find that they are 4% and 4.7% respectively. As long as the difference is a bit more than 3%, there will be a discernible shift, and likewise, if it is leaning towards something less than 3%, there won't be a majorly discernible shift in pitch during your mix. However, I've noticed that some tracks are in fact keyed/detuned by as much as 50cents which puts the tune in a lil bit of a limbo zone, but it's always bound to work with something