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I couldn't seem to find this anywhere - I'm a Berklee Music Theory Student (in 4th level) and I need to be able to do Nested Tuplets say for example a quarter note triplet where the 2nd quarter note is itself an eighth note triplet (or more like a 5 etc).

When I follow the instructions I found online for this with Notion (using the example above) when I try to modify the 2nd quarter note in the quarter note triplet (say into the new eighth note triplet) it "breaks" the quarter note triplet into two triplets (one on the left and one on the right) of what I modified in the middle.

I came to Notion from using MuseScore and LOVE Notion but I'm stuck for this assignment :( help is much appreciated.
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by Surf.Whammy on Sun Jul 14, 2019 3:22 am
Can you afford 24x7 armed security guards? :P

THOUGHTS

There are a few musicians and singers on this planet who can sight-read and play or sing nested tuplets; and after careful consideration I think there at least two . . .

It's an interesting way to have a bit of FUN with rhythm patterns, and it probably is useful at one time or another; but overall it's very confusing if one is a musician or singer . . .

Of course, when one considers the popular music of the so-called "Youth of Today" over the past century or so, nearly every song is performed with rhythm patterns based on nested tuplets; but very few of the songs actually have nested tuplets in a formalized way . . .

It's more of a "feel" type of thing, and in many instances the ability to "feel" intricate rhythm patterns is one of the primary characteristics that distinguishes what we colloquially consider to be 'great performers" in one way or another . . .

Two examples come to mind in more recent popular music--"recent" in the sense of being over 50 years ago, but so what--and the key to understanding the rhythm patterns are the rhythm guitar players (John Lennon and Keith Richards, respectively) . . .

[NOTE: The Beatles and Rolling Stones are highly orthogonal in the sense that the various instrumental parts are designed specifically not to overlap most of the time, which from this perspective means one can suggest that all the instrumental parts essentially are solos occurring in isolated and sharply constrained spaces which for the most part happen in discrete instances or quanta of time, but with two exceptions: (a) singing and (b) electric bass, which are what one might call the "sustaining" or "continuous" vocal and musical instruments. In the Beatles video, watch the way John Lennon strums (or pretends to strum) his rhythm guitar. In the Rolling Stones video, watch two things: (a) the way Charlie Watts (drummer) plays what appear to be awkward snare drum rimshots for emphasis, where he only plays the snare drum rimshots and no cymbals or hi-hats, and (b) the way Keith Richards plays and sustains rhythm guitar chords at what appear to be odd times, starting or ending early or late . . . ]

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Jumping forward to the past few months, drinking a cup of very strong coffee, and enjoying a bottle of Tiger Sauce, there's Metallica, where the key is to focus on Lars Ulrich (drummer) and James Hetfield (rhythm guitar, lead vocals) . . .

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[NOTE: Metallica is the definitive tuplet and syncopation Metal musical group . . . ]

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It's a virtual festival of tuplets and syncopation, but it's done "by ear" and "by feel" . . .

They do this intuitively, because they are pristinely precise time machines . . .

EXPERIMENTS

I did a few experiments toward the goal of determining what happens when you attempt to input nested tuplets (two-level only) in NOTION 6.5 . . .

As you observed, you can't do it in what one might expect is the logical way, where first you create the high-level tuplet and then create the second-level nested tuplets . . .

You can create the second-level nested tuplet first, and then put it all in a higher-level (or "first level") tuplet, but as best as I can determine so far, the second-level nested tuplet is discarded and reverts to being notes at the same level as the other notes . . .

In the example, three quarter notes in a tuplet are notated as either "3:2" or "6:4", where the latter is based on the units being eighth notes, hence a quarter note is two eighth notes, which makes a bit of sense . . .

The problem is that for the example you provided, NOTION makes the tuplet "7:4" rather than "6:4", where "6:4" is what I think the first-level tuplet should be, since you begin with three quarter notes and then change one of the quarter notes to three eighth notes in a "3:2" tuplet . . .

One can suggest that the first number in the ratio can be virtually any reasonably sized integer and that so long as the second number in the ratio is the same for a set of tuplets, the timing will be preserved correctly, which it is . . .

The problem is that the durations of the individual notes are different when the ratio is "7:4" than it is when the ratio of the high-level tuplet is "6:4" or "3:2" . . .

[NOTE: Ratio arithmetic can be a bit confusing, but the ratio "6:4" is equivalent to the ratio "3:2", so in the example you can replace "2/3" with "4/6", which is the way you compute the duration of a quarter note in the "6:4" examples. It took a few tries to determine how to compute the "7:4" ratio times, but after noticing that the numbers didn't add correctly the first way I tried it, I switched to arithmetic mode and got it right, which overall took about an hour or so, mostly because I don't mess with ratios so often. I like fractions but not ratios. Ratios are useful, but I think the same folks who thought having many variations of the name of the same note on a piano expressed in various convoluted permutations involving from one to four sharps or flats nudged their ways into the team meeting on "Ratios vs. Fractions" and proclaimed proudly that "A### is D♭♭", which was widely recognized as a "bright observation" by all in attendance . . . ]

Code: Select all
4/6 = 0.67

4/7 = 0.57

These are the equations for the "7:4" tuplet:

x = (1/7) * 2 = duration of eighth note (0.29)

y = 3x = duration of three eighth notes (0.86)

z = 2x = duration of one quarter note (0.57)

t = y + 2z = 2 beats

[The decimal values of these fractions are rounded to keep everything as simple as possible, but so what . . . ]

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In other words, it's a matter of 0.67 versus 0.57 for the quarter notes and 0.67 for the eighth note triplet versus 0.86, which is significant and changes the timing dramatically, as heard in the YouTube video (see below) . . .

This means that the eighth notes done correctly will have durations of approximately 0.22, not the eighth note durations of 0.29 when it is done incorrectly (or perhaps more graciously is overridden and not done at all in terms of nesting) . . .

MORE THOUGHTS

This an interesting puzzle, and I think I understand what happens; but it's possible I don't understand it . . .

The way I determined everything is that I created a NOTION score with several instrument staves and set each one to a useful variation of the overall problem . . .

I set the temp to 20 beats per minute and used different pitch notes for the variations . . .

I also added a stave of maracas at a rapid but steady repetition and did the same with a woodblock staff, but at a slower repetition . . .

And after trying to make sense of it "by ear", which was somewhat productive, I switched to a graphic drawing application and did the mathematics and physics . . .

My thinking is that if NOTION supported nested tuplets, then it would not remove the tuplet nesting when a tuplet is later put inside a definitively higher-level tuplet . . .

To avoid the "splitting" problem, I moved the two quarter notes to the front and put them in a separate tuplet, which was useful except that it doesn't change the durations of notes in the eighth note tuplet, which need to be changed when they are nested . . .

Explained another way, I couldn't make sense of it "by ear" or visually by watching the various notes being played; so I switched to mathematics and physics and did the relevant arithmetic . . .

I might do a few more YouTube video examples, but the easy way to do this is to have two piano staves, where (a) one stave has a series of sequential tuplets, each comprising six eighth notes in the ratio "6:4" or whatever it happens to be and (b) the other piano stave has a series of sequential "7:4" tuplets like the last example (see above) . . .

An even easier experiment is to do this will all eighth notes, where there is a "7:4" ratio tuplet of seven eighth notes starting at the same time as a "5:4" ratio tuplet of six eighth notes, which you can do by inspection, since the timing of seven eighth notes over two beats will be different from the timing of six eighth notes over two beats . . .

When played, the notes don't start at exactly the same times; and what happens is that you hear what can be described as rapid "grace notes", leading or following the "on beat" notes of the "6:4" tuplets, more or less . . .

[NOTE: After doing a bit more thinking after listening to the YouTube video, I decided to remove the Reverb, although it doesn't have a dramatic affect on the tails of notes. It's important to remember that notes have attack, decay, sustain, and release phases, which for instruments like piano maps to the note ringing during the decay, sustain, and release phases, even though it is not so immediately and obviously audible. I think everything aligns correctly with respect to the last note of the two pianos when you consider decay, sustain, and release times; but since the attack phases are different, the timing differences are exaggerated or more prominent than the decay, sustain, and release phases . . . ]

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I am pondering this--and if I have an insight, then I will revise and extend my thoughts accordingly--but at present I do not think NOTION supports nested tuplets . . .

There might be a way do determine what happens definitively; and one way might be to modify the experimental score in a specific way, followed by recording the generated audio in Studio One Professional, which then should make it possible to observe the attack or start times of the respective notes in a very precise way using the Studio One Professional "timeline" . . .

I am primarily a "by ear" musician, which overall maps to being able to discern subtle differences in rhythm patterns and pitch patterns, so at present I am comfortable with the analysis so far, since I set the tempo to 20 beats per minute, which maps to a beat every 3 seconds and is very slow, although in the YouTube video the tempo was set to 40 beats per minute (not too slow, but slow enough to hear the start times of the notes clearly . . .

Lots of FUN! :)

P. S. Since you are studying Music Theory at Berklee, you might find my project on the Schillinger System of Musical Composition (SoMC) in this forum to be interesting, which is fabulous . . .

Project: SoMC ~ Paint a Song with Numbers (PreSonus NOTION Forum)

Fabulous! :+1

The Surf Whammys

Sinkhorn's Dilemma: Every paradox has at least one non-trivial solution!
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by Surf.Whammy on Mon Jul 15, 2019 9:09 am
As a bit of follow-up, I think there is a way to approach solving the puzzle from a different perspective . . . :)

THOUGHTS

Based on the hypothesis that NOTION does not support simple nested tupelos (two-level tupelos, if you prefer), what can you do to provide a solution when you need to play a phrase with notes timed as if they were notated with a nested tupelo, where the focus is on playing the notes rather than on producing printed music notation?

(1) As shown in my previous post to this topic, you can do the ratio and fraction arithmetic to get what essentially are decimal numbers without units . . .

The units actually are time, but time is based on the tempo . . .

More to the point, it's relative time, which is relative to the tempo . . .

For example, in a 4/4 time signature a quarter notes has a duration of one, and this is the value regardless of the tempo . . .

Mapping it to wall clock time requires knowing the tempo . . .

(2) It's important to understand that timing in music notation primarily is binary but not in the sense of binary computers . . .

Instead, it's "binary" in the sense of being multiples of two in one way or another . . .

For example, an eighth note has half the duration of a quarter note; and a sixteenth note has half the duration of an eighth note, which are "divide by two" activities . . .

There are dots (single and double, for practical purposes), and they extend the duration of a note by one or two "divide by two" fractions . . .

Switching to decimals for a moment, if a quarter note in 4/4 is 1.0, then an eighth note is 0.5; a sixteenth note is 0.25; a thirty-second note is 0.125; and so forth . . .

A single dotted eighth note is equivalent to an eighth note plus a sixteenth note and has a duration of 0.75, while a double-dotted eighth note is equivalent to an eighth note plus a sixteenth note and a thirty-second note, which is 0.875; and so forth . . .

(3) Non-nested tuplets provide a way to create notes with what one call "in-between" or "odd" durations, as contrasted to the "even" durations of non-tuples notes . . .

For example, in 4/4 time when you want three notes to have individual durations of two-thirds (or 0.67), then you put them in a "3:2" ratio tuple, which also is called a "triplet" . . .

(4) A series of notes can be "tied" together to create a longer duration note, and "dotting" is a shortcut for some of the simpler ways to "tie" notes, where a single "dotted" eighth note is equivalent to an eighth note "tied" to a sixteenth note . . .

(5) A ratio expressed as "A:B" has two parts, where "A" is the antecedent and "B" is the consequent. The consequent in music notation in NOTION can be one of several positive integer values, for practical purposes in the set {1, 2, 3, 4, 5, 6, 7}, although it might span all the single-digit positive integers. This can be useful, for example, if you need five notes, each having a duration of 0.8, which you do by putting five identical duration value notes into a "5:4" ratio tuplet (4 divided by 5 is 0.8) . . .

Combining these rules, you can create a table of different decimal durations toward the goal of devising a system which at least will be a good approximately of having complete control over the durations of notes . . .

Code: Select all
1/4      1.0
1/8      0.5
1/16     0.25
1/32     0.125
1/64     0.0625
1/128    0.03125

In the original example, there is a two-level tuplet containing a quarter note, a nested eighth note triplet, and a quarter note . . .

We computed the values to be {0.67, 0.22, 0.22, 0.22, 0.67} . . .

The solution then becomes a matter of computing equivalents using the aforementioned rules, including the simple note duration table showing the decimal values . . .

For the quarter note durations, we need to get to 0.67, and one way to do this is to tie an 8th note, a 32nd note, and a single-dotted 128th note, which produces the duration 0.67185, which overall differs from 0.67 at a temp of 60 beats per minute by approximately 1.25 milliseconds; and at a faster tempo the difference essentially becomes inconsequential . . .

Using the same strategy, we can "tie" a 32nd note to a 64th note and a 128th note to get a duration of 0.21875, which at a tempo of 60 beats per minute differs from the target value (0.22) by 1.25 milliseconds, which again is nearly inconsequential . . .

PRACTICAL CONSIDERATIONS

One might suggest that using complexly tied notes to create non-standard durations requires more computing at runtime, but in what I call the "ReWire MIDI" strategy, I think this is not a problem . . .

Specifically, in the "ReWire MIDI" strategy, NOTION is used only for music notation on ReWire MIDI staves, which at runtime creates a stream of MIDI . . .

The virtual instruments are hosted in Studio One Professional and are played by the MIDI streamed from NOTION . . .

In this way, both of these PreSonus applications (a) are highly optimized and (b) are doing what they do most efficiently . . .

NOTION is focused solely on music notation and generating MIDI at runtime; and since in the "ReWire MIDI" strategy NOTION is not hosting any native or virtual instruments, it has the most "computing space" it can have . . .

Similarly, since Studio One Professional in the "ReWire MIDI" strategy is a player for streaming MIDI coming from NOTION and audio on already recorded Audio Tracks, it also is doing what it does best--noting that Studio One Professional has sufficient "computing space" to handle a reasonable set of hosted virtual instruments, which on the 2.8-GHz dual-core Mac Pro (Early 2008) here in the sound isolation studio is 12 or so virtual instruments at a time and is more than I ca see on the display, which works for me . . .

After doing a few experiments, I decided that working with virtual instruments in sets of 12 is convenient; and every time the Studio One Professional ".song" gets to 12 Instrument Tracks, I record the audio to Audio Tracks and then retire the current 12 Instrument Tracks, replacing them with a new set of hosted virtual instruments; and every so often I do submits of the Audio Tracks to add yet another level of consolidation toward the goal of keeping everything simple and uncluttered . . .

It takes a while to turn this into a "cookie template" from the perspective of arranging, producing, and audio engineering; but most of the key bits of information are discovered regardless of the particular strategy being used, where for example, after a while you develop an arranging, producing, and audio engineering strategy for bass, which can be a particular combination of bass instruments, which then becomes your "go to" bass sound . . .

FUTURE THOUGHTS

Being a formally trained software engineer, when I have to resort to doing arithmetic on a calculator and actually thinking, I see the opportunity to design a computer program to do the work--or at least to make it easier and faster . . .

Recognizing the utility of the scalar digital values, I think it should not be so difficult to design a program that determines the simplest way to use the aforementioned rules and table of decimal equivalents to answer the question, "What combination of stuff produces a notation entity which is equivalent or nearly equivalent to a specific scalar digital value?" . . .

Of course, having such a computer program is only part of the solution, since the more important part is determining why one might need to do what essentially are custom-timed phrases . . .

The key to this being intriguing occurred as I was doing initial experiments and noticed that some of the resulting rhythms were very nice . . .

Mostly this is focused on drums and lead guitar in the virtual universe; and it looks likely to provide a way to do with music notation and virtual instruments at least a few things that are not so easy to do with a real drum kit and lead guitar, which explained another way suggests that it's possible to be a better virtual drummer and virtual lead guitar player than doing it with real instruments in the real universe . . .

More importantly, it looks to provide a practical solution to making virtual music a bit less mechanical, or stated a different way, more human . . .

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Lots of FUN! :)
Last edited by Surf.Whammy on Wed Jul 17, 2019 3:44 pm, edited 1 time in total.

The Surf Whammys

Sinkhorn's Dilemma: Every paradox has at least one non-trivial solution!
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by richardborio on Wed Jul 17, 2019 8:53 am
I don't believe that Notion supports nested tuplets. The only workaround that I could come up with is as follows:


1) using voice 1, enter your first tier tuplet
2) using voice 2, rest until you come to the point in time where you want your second tier tuplet to begin. Add that tuplet there. (You can go on to voice three for another tier, etc.)
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by richardborio on Wed Jul 17, 2019 9:12 am
I should note that this method is not 100% accurate. You would need to adjust the start times and durations of the second tier tuplet for 100% accuracy.
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by Surf.Whammy on Wed Jul 17, 2019 3:37 pm
This is a way to emulate the 2-level nested tuplet, as described and explained in my second post to this topic . . . :)

Image

[NOTE: I added a 128th note to the end of the measure to show that the total timings and durations are accurate to less than 0.03125 of a beat, where in this example the time signature is "4/4" and the tempo is 90 beats per minute (BPM). This is the finest granularity NOTION 6.5 supports. It's less than 20 milliseconds at 90 BPM. For reference, 20 milliseconds is in the medium range of the Haas Effect, and 1 millisecond is the generally lowest repetitive delay to create the Haas Effect, but primarily for clicks rather than for more complex sounds). Intuitively, I think the total rounding error probably is less than 5 milliseconds. In fact, I think the computed virtual nested tuplet duration differs from the true nested tuplet duration by less than 5 milliseconds at 90 BPM . . . ]

Haas Effect (Wikipedia)

Code: Select all
x = true nested tuplet duration

y = computed virtual nested tuplet duration

(x - y) < 5 milliseconds at 90 BPM

[NOTE: The wood blocks are native NOTION instruments, which suggests that the computing overhead is minimal for the tied notes. In the "ReWire MIDI" strategy, I think the NOTION computing overhead will be even smaller, since NOTION only is generating MIDI from the music notation at runtime and streaming it to Studio One Professional, which is hosting the virtual instruments . . . ]

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THOUGHTS

This strategy works, which is good . . . :+1

It makes the music notation a bit complex, but it provides a mostly straightforward solution to the problem of not being able to use 2-level nested tuplets . . .

I think it's accurate to suggest that the faster the tempo, the better the precision (or the smaller the error) . . .

Using the differences from (a) true nested tuplet note durations and (b) computed virtual nested tuplet note durations, which were provided in my previous post to this topic and are 1.25 milliseconds per note when the tempo is 60 BPM, this makes the total error approximately 6.25 milliseconds. At the faster 90 BPM tempo, the total error is approximately two-thirds of the total error at 60 BPM, which makes it approximately 4 milliseconds . . .

I plan to do a few more experiments, since this is an intriguing puzzle . . .

From my perspective, the interesting aspect is that once you hear the computed virtual nested tuplet, it's not particularly unusual . . .

It's a rhythmic sequence of notes a proficient drummer might play . . .

No matter how it's done with music notation, I think it's going to be a bit strange until you commit the music notation and the way the notes sound to memory, at which time the music notation becomes either (a) a succinct shortcut or (b) a not-so-succinct series of tied notes which are not nested and are not in tuplets . . .

Regardless, for musicians and singers performing these type of phrases from music notation, if nothing else it's one of the many reasons there are conductors who, at least in theory, should know how to read this stuff and tap it with a baton so everyone else has a clue . . . :P

Lots of FUN! :)

P, S. Since performing a song live is nearly always a bit different from the studio recording, it's useful to study the studio recording for the Metallica song specifically when listening with studio quality headphones like SONY MDR-7506 headphones (a personal favorite), which is fabulous . . .

[NOTE: The tuplets and syncopation are clearer and more distinct in the studio recording . . . ]

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Fabulous! :)

The Surf Whammys

Sinkhorn's Dilemma: Every paradox has at least one non-trivial solution!

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