Theoretical time signature

About 20 years ago a friend and I were talking music theory and time singatures. We came up with an idea. What if there was a note that mathematically was exactly 1/3 the time of a whole note and called a 1/3rd note. This would make a time signature of 3/3 possible in theory. So I am interested to hear if any of you have an idea of what a 1/3 note could look like (or is there a way to express this without downright inventing stuff) and what would 3/3 sound like?
 
I think you are already covered, with triplets of various denominations. There would be no difference between 3/4 and 3/3 in practical terms, except your magical 1/3 note would get one beat instead of a quarter note.

Sounds like interesting discussion with no new practical application, as far as I can tell.
 
That's kinda where we ended up, but it was a long time ago and I was 16 or so. It occured to me we may have missed something so it was worth asking.
 
A 1/2 note triplet would sound like 1/3 note in 4/4 music.

But IDdrummer would be correct. If you designated a symbol to be a 1/3 note, any note combinations could just as easily be written out using already existing notation. Making any usefulness limited at best.

Which is probably why 1/3 noted don't exist. At least not that I've seen.
 
I play in pi/i time signatures. Sometimes even e/i.
 
The other guy in the dicussion presented idea that as far as he could tell from an entirely mathematical standpoint there is no note symbol that is EXACTLY 1/3 of a whole note I think the consensus was that dotted quarters and eighth note triplets were close though. I had the musical theory but he had the math skills.
 
A triplet, if done properly, IS one third of the note. For example, an 1/8 note triplet is, mathematically, 1/3 of a quarter note. Dotted notes won't produce the even 1/3 subdivision you are looking for, though, as they add half a note value. Therefore the dotted note value will always be divisible by some multiple of 2, not 3. It's hard to explain, but triplets already do what you guys wanted from a 1/3 note. That's all we really need to know, lol.
 
The other guy in the dicussion presented idea that as far as he could tell from an entirely mathematical standpoint there is no note symbol that is EXACTLY 1/3 of a whole note I think the consensus was that dotted quarters and eighth note triplets were close though. I had the musical theory but he had the math skills.

There is a symbol for exactly 1/3 of a whole note:

Triplet-example-7.png


You could actually meter the above example as 3/3 if you wanted to. But since rhythm in western notation is based on halvings, and the symbol for a third note is a regular half note with a numeral 3 over it; so you might as well just take away the 3 and call it 3/2:

-nMdxxC_Q-SmQI_WKnOsrQ_m.jpg


They are functionally exactly the same, except there is no pointless, confusing bracketed 3 over the whole measure. The only case I know of where you might be able to justify using */3 meter would be if you wanted to throw a measure of an odd number of triplet partials into a piece in an otherwise normal meter.
 
I learned something today =) . The thought exercise actually stemmed from seeing my teacher at the time practicing a piece that had a 23/16 signature (still cant wrap my head around that one).

Wierdly now that I know that (thank you toddbishop) I can move on. Have Tommy Igoe's "Great hands for life" arriving thursday.
 
Question is "How portable is it?" Can you show this to someone else and have it make sense?

Just because I can envision a song as a cartoon character and play it as such, handing a person the Sunday comics and saying "play that on the drumkit" won't do you much good unless they also have that concept in mind.

The system that note and time values are built on (The imperial system) seem to be working rather well and rhythmic content is expressed within the context of those metrics.

Think about one inch (take your filthy jokes outside, LOL)... Within that inch are half inches, quarter inches, eighth inches, sixteenth, 32nd, etc. That in itself is easy to visualize (unless you're a metric system snob, GOTCHA...finally!) so if you can begin to work on that small act of attaching a visual to an audible then you're getting the right idea...

Basically what you speak of doing when you talk about creating "1/3 notes" is redefining the system of measurement that's already there.

Learn what's there already and THEN break the rules. :D
 
I had this same thought last year in music theory. My thinking is that it is currently impossible to notate any non-2-divisible subdivision taking partial beats and have that constitute a measure. Since that didn't make any sense, let me explain further:

Outside of a one-bar tempo and meter change, there's no way for me (in popular notation) to say that, for example, I want 13 eighth note triplets in a measure. If the time signature is 4/4, I can fit in 12 eighth note triplets easy, but there's no system in place to add a non-3-divisible number of those triplets to the bar- i.e. I could go up to 15 notes with a bar of 5/4 but I couldn't do 13 or 14.

Techncially, triplets, quintuplets, what have you are just different numerical notes anyways, just notated differently. A whole note equals 1 bar of 4/4, a half note half, quarter is a quarter, etc. So it follows that a third note (currently only recognized as a half note triplet) is a third of a bar, a 12th note is a 12th of a bar (8th note triplet), a 20th note is a 20th (16th note quintuplet). There's no way to say "I want twenty-four 20th notes in this bar" outside of the clunky one-bar tempo & meter change I mentioned before. Todd understands this concept.

It seems to be just an oversight in musical notation. The only conceivable problem with this system is the note appearances- there's already a (frankly somewhat silly) system in place for 1/(2^x) note values, and we don't want more strange noteheads, especially given that those serve a purpose already. I haven't figured out a good system yet, but I think it must be algorithmically based so as to be infinitely expandable (so composers down the line don't run into the same limitations we have come to in the current western system).

I will probably return to this topic if I find a suitable solution. Glad to know that others have considered it!
 
I had this same thought last year in music theory. My thinking is that it is currently impossible to notate any non-2-divisible subdivision taking partial beats and have that constitute a measure. Since that didn't make any sense, let me explain further:

Outside of a one-bar tempo and meter change, there's no way for me (in popular notation) to say that, for example, I want 13 eighth note triplets in a measure. If the time signature is 4/4, I can fit in 12 eighth note triplets easy, but there's no system in place to add a non-3-divisible number of those triplets to the bar- i.e. I could go up to 15 notes with a bar of 5/4 but I couldn't do 13 or 14.

Tuplet ratios have been around since forever... While highly rare in popular music outside Frank Zappa, these have been used in modern orchestral music. With ratios, you can have any number of notes over any other number of notes -- and you can stack them within tuplets.

Ratios.png
 
Hey, Porter, here somebody has been fiddling with this question:

Micro-Metric-Modulation.jpg


The 'difficult' way is the normal way for doing the kind of thing you're talking about; this guy's 'easy' way-- using triangle note heads for triplets, and a meter change to 5/6 is actually not bad. The thing that makes odd */3, */6, or */12 meters so screwed-up to look as is that you have something bracket as a triplet with less than three notes in it; the triangle note heads solve that, and seem to be easy enough to read (in a short example, at least), if you can get everyone to recognize them. I'm not sure if it's a great idea to revamp a system that works pretty well, even if it's not the most elegant thing possible, just to make this very rare thing look nicer on the page, though.
 
Thanks for that, Todd! After a little messing around with the concept of an 'algorithmic' notehead, and other ways to display value based on the notehead, I think that's probably the easiest solution- just a special notehead to show its difference and a time signature change with the presupposition that the reader knows how to interpret it. That works easily for other metric divisions as well (5, 7, etc.)- simply have the prime division (1/3, 1/5) be an open notehead, a halving of that (1/6, 1/10) be a blacked-out one, and add stems past that for additional halvings.

Now to find interesting and listenable ways to employ it, haha!
 
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