Stromian Tuplet Notation

Nested tuplet from polyriddim by phonon

Stromian tuplet notation is a system for expressing tuplets. The main purpose of STN is to convey complicated tuplet ideas over text. The system strikes a balance between legibility and efficiency.

It can get frustrating when you send your homie a Fizz WIP and they ask “what’s that rhythm 8 seconds in?” To which you reply “It’s a bar long triplet but the first and last of those 3 beats are both nonuplets, and the beat in the middle is just filled with 8th notes. Or 8th note triplets rather... Never mind, you get what I mean. Actually I'll draw a picture and send it...". STN allows you to reply with "it's 3[9:1+4:1+9:1]:2/2" like an absolute chad.

Nested Tuplets

Nested tuplet used frequently in The Black Page by Frank Zappa

In STN, the nest tuplet (outside tuplet) is written with the numerator at the beginning and the denominator at the end, the contents of which are written in a bracketed section in between, which includes the nested tuplet and however many beats come before and or after it. In this page's main image, the "11[ ]:8" is the nest tuplet, the "8:6" is the nested tuplet, and the "+5" is the leftover beats in the nest tuplet.

The nested tuplet's denominator and leftover beats will always add up to the nest tuplet's numerator, making the nest tuplet's numerator redundant. The purpose of writing the nest tuplet's numerator at all is to make it more legible. The idea is for the human reader to glance at "7[1+3:2+4]:4", see the "7[ ]:4" and immediately think "So it's a septuplet. Now to figure out what's inside". The notation system used by the MeTr music tool on ChamberCode is very similar to STN for nested tuplets, except it doesn’t have STN’s redundant nest tuplet numerator.

Stromian vs. MeTr notation

	Tuplet	Notation
Stromian	11:8 with a nested 8:6 at the beginning	11[8:6+5]:8
MeTr	11:8 with a nested 8:6 at the beginning	[8:6+5]:8

Non-Dyadic Tuplets

@ symbol method

The most clear and concise method is to use the @ symbol. For example, a non-dyadic sextuplet consisting of only 5 sextuplets could be written as "5@6:4".

Time signature method

Another way of notating non-dyadic tuplets in STN is to use a time signature as a denominator. For example, a non-dyadic sextuplet consisting of only 5 sextuplets could be written as "7:5/6". This method is usually more confusing to read than the @ symbol method, but is sometimes useful when clarifying the exact length of the tuplet.

Bridge Tuplets

[7:4+6:4][5+6:4+4]:8

Bridged bridge tuplet [6:4], [6:4][2+5:3+1], [6:4][2+5:3+1][1+3:2+5]

One way of notating bridge tuplets in STN is by using two bracketed sections, the first one laying out the two tuplets being bridged, and the second one laying out where the bridge tuplet starts, its ratio, and where it ends. For example, a bridge tuplet in which a 7:4 and a 6:4 are being bridged by a 6:4 somewhere in the middle could be written like [7:4+6:4][5+6:4+4].

This step of adding another box to create another bridge tuplet can be repeated indefinitely. For example, the top-to-bottom sequence of progressively complex tuplets shown in the "bridged bridge tuplet" image can be written as such:

[6:4]

[6:4][2+5:3+1]

[6:4][2+5:3+1][1+3:2+5]

The benefit of laying it out in a sequence is legibility. If the whole thing is overwhelming to parse, you can work on grasping the first couple of boxes first, instead of taking it in all at once.

Limitations

Nested nested triplet

8[[4:3+7:5][2+7:6+3]]:8/7

Ambiguity

When written with STN, the exact length of the tuplet can be ambiguous. If there’s a 4 in the denominator, that could mean that the tuplet is 4 quarter notes long, but it could also be 4 eighth notes, 4 sixteenth notes, etc. This ambiguity can be solved by writing the nest tuplet's denominator as a time signature instead of a plain number.

11[8:6+5]:8 —> 11[8:6+5]:8/8

Legibility

A triplet inside of a nested triplet is pretty easy to conceptualize when reading it on sheet music, as opposed to STN, where it would be written like “3[3[3:2+1]:2+1]:2”. STN has its limitations, but it allows those familiar with it to glance at “11[6+9:5]:8” and think “ah yes, a 11:8 tuplet with a nested 9:5 at the end”.