Jump to content
  • entries
    15
  • comments
    57
  • views
    1,622

"Is It Time For A 12th Note?"

tunesmithth

137 views

It’s common knowledge that both music & musical notation have their basis in mathematics.

Each note within the system is assigned a specific time value and each relates to the others in a logical, mathematical way.

·   One 1/16 note is equal to the value of two 1/32 notes

·   One 1/8 note equals two 1/16 notes

·   One 1/4 note equals two 1/8 notes……and so-on.

All very consistent, right? At first glance, it would seem so. Until you examine the way in which we deal with triplets. ^_^

 

For those of you not familiar with the concept of triplets, I’ll explain.

Essentially, triplets occur when 3 evenly spaced notes are played within a musical space designed to accommodate 2 notes.

For example…

·   In 4/4 time a 1/4 note occupies the space of 1-full-count, which equates to 1/4 of the total measure.

·  As was indicated previously, one 1/4 note = two 1/8 notes

·  But if 3 evenly spaced notes are played in place of those two 1/8 notes, the result is a “triplet”.

The way in which triplets are played doesn’t pose a problem for me. It’s our traditional notation of them that I question.

 

In my mind, the problem is simple. When the actual time value assigned to a note changes, so should the numeric value of the symbol (note) used to represent it.

But, that’s not the case with triplets!

When a 3-note-triplet is played in place of two 1/8 notes, the resulting triplet is shown by inserting three 1/8 notes in place of the original two.

 

So…to quickly summarize, two 1/8 notes = one 1/4 note…except in the case of a triplet??????

Who in the world thought that was a good idea? :blush:

It’s every bit as consistent as saying that two 1/8 notes = one 1/4 note, except on Tuesdays…when the moon is full.  

 

Wouldn’t it have been better to create a 12th note? If three 12th notes had been used to fill the space of a 1/4 note, that would have been mathematically consistent.

So why wasn’t it set up that way?

 

In recent years, I’ve constructed several video tutorials on shuffle rhythms. “Shuffles” happen to be built upon the same framework as triplets. That’s what got me thinking about this debacle.

Honestly, I haven’t a clue about why it was set-up this way. But, if we ever hope to inspire a change to the current system, I guess we need a viable alternative. As luck would have it, I have an idea or two.

·   As a drummer, I’m aware that 8th note triplets aren’t the only type in use. Double-time triplets (16th note triplets) are also common. Given that, we’d need a 24th note to use in conjunction with our 12th note. Simple enough!

  • So, how would we write our new notes? Our current system shows triplets in several ways. Generally, the number “3” is combined with either a half-moon shaped arch, or a straight-line bracket shown above, or below the staff. Well…we wouldn’t need that number “3” anymore, but it might be useful to hang onto one of the familiar remnants from our current system. So, what if we incorporated that traditional half-moon arch?

 

image.png.72901f70f10be2760d378aa5c01a95ca.png

 

Could that work?                                                                                                                             

·         It’s no more difficult

·         Players wouldn’t need to look above & below the staff to identify a triplet

·         It would re-establish mathematical consistency within the system

 

So, what’s your opinion? Is it worth changing?

After all, I’m just one guy with some impromptu thoughts on the subject?

Does it make sense, or have I neglected to consider some major obstacles in my quest to reinvent the wheel? :rolleyes: 

What’s your take on this & is it worthy of further consideration?

As always, comments are welcome!

 

Tom Hoffman

"About Me" Muse Member pg.

Tune-Smith.com

Tom Hoffman YouTube



5 Comments


Recommended Comments

Backwards notes... if I understand correctly, basically instead of a bracketed 3, you have a curved line with reversed stem, and instead of a bracketed 6, you have a double-curved line, right? 

 

Don't forget also the "reversed" system of this, having two beats in a "three beat" time, and representing it by brackets as well (with a 2). I guess it would have a curved line? 

 

So saying, I do understand that triplets can cause confusion. Heck, even in this day and age, some software don't work well with swing rhythms. 

  • Thanks 1

Share this comment


Link to comment
Quote

Backwards notes... if I understand correctly, basically instead of a bracketed 3, you have a curved line with reversed stem, and instead of a bracketed 6, you have a double-curved line, right? 

Basically, yeah!

More than anything, the article is a text representation of me thinking out loud. 

The chart is simply one possibility for replacement notation, but regardless of final notation form, it was the concept of "a 12th note" that intrigued me because it would resolve the mathematical inconsistency. 

The math is the part that never set comfortably in my brain. ;)

Appreciate the comment...have a good one!

 

Tom

Share this comment


Link to comment
42 minutes ago, tunesmithth said:

The chart is simply one possibility for replacement notation, but regardless of final notation form, it was the concept of "a 12th note" that intrigued me because it would resolve the mathematical inconsistency. 

I understand. The "math" I consider okay in common notation because a "12th" note and a triplet note are the same thing written only slightly differently. The "math" itself really isn't changing. The advantage with triplet notation is that it is a reminder that the pulse remains the same while the timing for something will be polyrhythmic for a section. Hence the simplicity, if I may use the word, of having them grouped into simple 2s, 3s, 6s... instead of 12th and 24th notes (or by logical extension 6ths and 3rds). There is the basic reminder of a simple polyrhythm over the primary pulse of the song. 

 

You also might run into problems with stems clashing. Maybe. 

I do appreciate the thought exercise, however. Very interesting. 

  • Thanks 1

Share this comment


Link to comment

Let me say right up front that I have 0 expectation of our system actually changing.

This same system has been in place since God was a baby & no one's going to change it to appease my sense of mathematical correctness.

But, I don't agree that my argument is without merit.

Perhaps I didn't do a very good job of explaining myself? Let me have one more go at it, 'eh? ;)

 

Our system of musical notation is constructed of mathematical fractions. Everyone knows that...nothing earth-shattering new there.

Most of us learned about fractions in school & I imagine most of us recall the basics.

  • 1/8 + 1/8 = 2/8's ...reduce 2/8's to it's lowest form and you have 1/4...hence in musical notation 2 eighth notes = 1 quarter note. Makes total sense, right?
  • Triplets currently consist of 3 eighth notes (shown in fractional form, that would be 3/8). So here's my issue...in purely mathematical terms, 3/8's does NOT = 1/4. 3/8's is not a reducible fraction & is already in it's lowest form. Placing a curved line over the 3 eighth notes doesn't change their value mathematically...it's still 3 eighth notes. Placing a magic "3" over or under the group of notes doesn't change the math either...still 3 eighths.

Unless I'm truly missing something here, our current form of notation is mathematically incorrect because 3/8's cannot = 1/4.

As I mentioned earlier, folks accept it as it is because it's all we've ever known...most never give it a thought.

It just so happens, because I was writing those tutorials, I did think about it & the inconsistency bothered me a little...hence the article.

 

Had the people formulating our system created a 1/12 note, as I suggested, it would have remained mathematically viable.

A triplet would consist of 3 - 12th notes (in fractional form 3/12's).

3/12's reduced does NOT = 1/4 

 

Yes, when a musician is reading a current staff & comes upon a triplet, they do understand how it is to be played. Because it's been the way it is for so long, triplet notation is universally understood. But that doesn't change the math or the actual value of the written notes. Regardless of how they're played, they are still 3 eighth notes, NOT the mathematically required "2".

 

When the same musician comes across a dotted note, they understand the meaning of that also. But the dot actually changes the value of the note...triplet notation does NOT. It changes the way in which the grouping is interpreted & played, but not the underlying mathematical value of the individual notes.

The implementation of "a 12th note" would correct that inconsistency. That was my intended point.

 

Again, I fully expect nothing to change, but the inconsistency did seem worthy of a blog article.

Hey, I grew up in the 60's...we questioned everything! I guess old habits die hard. ;)

Appreciate the comments guys...have a good holiday!

 

Tom

Share this comment


Link to comment

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×