Sorry, Adam. To be fair, I’m probably wrong, too…

Youtubers Adam Neely and 12tone recently posted videos about a concept they call “negative time signatures” (click on their names to see their respective videos). There is certainly no consensus on this, as far as music theory goes, and there maybe never will, but it’s an interesting hypothetical question nonetheless. I’m writing this post because I think I have a different way of seeing this concept from Adam and 12tone’s. It’s not better, it’s not worse, just different, as there is no widely accepted definition of the term. But before introducing my theory on the subject, let me first explain briefly each of the youtubers’ theories.

Adam Neely

Adam is a widely known and appreciated musician and youtuber. I myself am a subscriber of his channel and it’s always full of interesting content. His take on the “negative time signature” concept is basically that you would read the measure in reverse, from right to left, and play it as such. Therefore, strong beats would be found on weak beats – at least as far as even time signatures go… A 7/8 bar, for example, with strong beats on each time would feel the same forwards as backwards. Adam suggests using this in the middle of a positive time signature song, so that it creates interesting motion. That is indeed good advice, but no sane composer would write this using negative time signatures, and would just rearrange the notes in a regular measure accordingly.

The negative 4/4 bar to the left would be played the same as the positive 4/4 bar to the right.

12tone

12tone’s concept of negative time signatures has to do with the actual reversing of audio recordings. Thanks to electronic music and especially music production techniques, this is available to mostly anyone. What would happen if Smash Mouth’s “All Star” was all in negative time signatures? Fire up Audacity and reverse the song, essentially playing it backwards. This is not convincing to me, however. Would anyone notate a piece of music meant to be played backwards with a negative time signature? A redeeming statement he makes is when 12tones mentions what I’d like to call ambiphonic compositions – most commonly known as reversible compositions. Those are compositions that, when played backwards and forwards, offer an accompaniment to themselves.

12tone’s self-accompanying “Crab Canon” with the forwards and backwards voices shown together

This idea is not new at all, but is interesting nonetheless. I guess you could mention the forwards playing part as positive – say, 4/4 – and the backwards playing one as negative, -4/4. Still, that is quite a stretch.

My Concept

My concept is slightly different, and is perhaps based more off of mathematics than the practical (Adam’s version) and theoretical (12tone’s version) aspects of music, but I believe it is a valid third option. At least, it will be until some sort of consensus is reached on what negative time signatures are, what they mean, and how they’re used… If that day ever comes! But here I’ll explain what my vision entails.

When you add a negative number to a positive number, what you get is the difference between the two.

\[-4 + 7 = 3\]

is the same as

\[7 – 4 = 3\]

Similarly, my vision of negative time signatures would effectively subtract beats from the performance. Here’s an example.

\[-3/4 + 4/4 = 1/4\]

When applied to music notation, that would mean that the three beats of the “-3/4” bar would cancel the first three beats of the “4/4” measure, and thus only the last beat of that bar should be played.

“The Lick™”, preceded by a random -3/4 measure to demonstrate my point.

In the above figure, only the black notes should be played, I have whitened the ones who should not be played to highlight them. So, basically, whatever is found within the negative time signature measures, and whatever is subtracted in the following ones would not be played.

But… what purpose would that serve? Well, aside from being a constant challenge to the performer, who would have to make mental calculations to know what they should play (which could be an entertaining and interesting challenge in and of itself), this vision of time signatures could also serve the composer who would like to hide information in the notation.

For example, some parts or entire songs could be hidden from the listener, and instead only accessible to those who read the music sheet. This is somewhat similar to how some artists hide parts of a song in negative playtime: to listen to the hidden parts you need to segue from the previous song, if you skip to the beginning of the song, the negative playtime part won’t be played. Similar, indeed, but with negative time signatures this could happen anywhere in a song, and not only at the beginning.

Moreover, I think it would be a powerful new tool for composers to portray their themes, concepts, and characters. As an example, let’s take any kind of opera – rock opera so that no one falls asleep! One of the characters is a scheming, secretive personage. In regular pieces, their plans are spoiled to the audience – one wonders how good they are at keeping their secrets –, but with negative time signatures, the composer can successfully hide information to the average listener. The parts of the schemer, well hidden in -11/16 bars, are available only to the more dedicated listeners, and the more avid seekers of truth.

Conclusion

I am not one to define what negative time signatures musically are. However, I hope that my answer brings a worthy third option to the discussion. I find it interesting to get lost in theoretical questions, even if they often are pretty useless, and the videos of Adam – and consequently 12tone – sparked my imagination. Please subscribe to these two fantastic music theory channels, I’m sure you won’t regret it!