Metric modulation question

[Mick-7]

It's funny that your thread has now shifted to konnakol. Carnatic rhythms are great, but that is not what you need in order to master metric modulation (true metric modulation is not even an element of fundamental Carnatic rhythmic vocabulary, though feel modulation - giving the illusion of being at a different rate through switching between different divisions of the beat - what we would call rhythmic superimposition - certainly is). I have a few youtube clips on this topic, but it is better to learn the whole picture than to spend a few moments with a youtube clip (and some I've seen on this topic are woefully bad and filled with errors!). Apologies that this sounds self-promotional, but if you really want to understand metric modulation, practice many fun exercises, see many examples you can find on recordings, and train in it systematically, please take a look at the 6th volume in rhythm book series (therhythmbooks.com) - it's the one with the blue cover. I developed and taught the rhythm curriculum for nearly 30 years at what was a top jazz program, so I was fortunate to get a lot of experience teaching this material in different ways and seeing what works best. Please at least give it a look if you are interested in this topic (there are previews at the website).

Actually, it became clear right away in this conversation that the OP's question was not about metric modulation but about counting uncommon or unfamiliar rhythms or meters, and counting micro-beats a la the konnakal system was recommended as a good way to do that.

[TearItDown]

Hi Christian - did not mean to rub you the wrong way! And no argument about it being preferable to use ta-ka, ta-ki-ta, and ta-ka-di-mi rather than "1 2" "1 2 3" and "1 2 3 4" as syllables. If I understand the process you're describing, you would practice feeling the clap as each of the different number of syllables, and rehearse going from one rate to the next. Although you did not explain to others reading this how you would determine which to use for each tempo, that is easy enough, so your system works fine, if you have enough advance time to practice/rehearse it.

FYI, there are a couple other approaches that would let you perform the metric modulation correctly the first time through in sight-reading this. But no problem if you are happy with your approach and find the Carnatic syllables help.

Also, did not mean to disparage traditional hand and finger counts for Adi Talam, etc., that's great, it's just a different topic than metric modulation, at least in my eyes.

[Christian Miller]

So the first time that dotted quarter thing in the melody comes back it’s the quarter in the old tempo? And we wind up in double time by the second modulation.

Anyway, I found it mostly intuitive to follow your exercise without doing any counting or subdividing at all. The tricky bit was that phrase starting on the syncopation. I daresay you have to be feeling the superimposed pulse and it’s not so much of an intellectual thing?

Fun exercise, I might work on this with a few tunes.

So provided I've actually heard it right, I have probably been a bit too mathematically literal about this.

If we see a modulation half note = dotted quarter the mathematical operation is multiply all note durations by 3/4. So we do this for a dotted quarter and we end up with a little change above a quarter note in the original tempo. But its like 1/32nd note

On the other hand if we repeat the operation we end up with something that isn't quite double time (1/2 durations) - we have 3/4 * 2 = 9/16, which is 1/16th more than a half.

But musically, that's probably not worth worrying about, and we naturally end up in double time?

Anyway..

[TearItDown]

Christian - Glad you find the exercise fun. Incidentally, about the math, you might want to re-think that (we're going from quarter to dotted quarter to half and back, so the 3rd chorus is exactly double time with respect to the 1st). It's performed quite precisely on the youtube clip.

Mick-7 - You make a very good point! I think I was overly swayed by the thread being called "metric modulation," but actually, you are right about the OP's question having nothing to do with metric modulation. (I must have gotten too excited thinking that some guitarists were actually talking about metric modulation! ) So your point is well taken!

[Christian Miller]

Christian - Glad you find the exercise fun. Incidentally, about the math, you might want to re-think that (we're going from quarter to dotted quarter to half and back, so the 3rd chorus is exactly double time with respect to the 1st). It's performed quite precisely on the youtube clip.

Mick-7 - You make a very good point! I think I was overly swayed by the thread being called "metric modulation," but actually, you are right about the OP's question having nothing to do with metric modulation. (I must have gotten too excited thinking that some guitarists were actually talking about metric modulation! ) So your point is well taken!

that makes more sense because that is exactly what you are singing lol.

For some reason I thought you I saw on the chart you were going half to dotted quarter each time, duh.

I now see on the chart wrote rhythmically exactly what you did. It’s been a long day, daughter’s birthday party etc.

It’s musically a useful thing to work on as an improviser I can see its value as a transformation of material.

You could put other metrical relationships in there as the second stage.

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[rpjazzguitar]

The OP's first question was about changes in time signature.

Later, in the first post, he posed a question about metric modulation (as other posts later called it), with an acknowledgement that he might have been using the term incorrectly.

As the OP, I can say that much with confidence. I was tempted to define "metric modulation" in this post, but I still wasn't sure about the exact definition. Here's what Wikipedia thinks:

"In music, metric modulation is a change in pulse rate (tempo) and/or pulse grouping (subdivision) which is derived from a note value or grouping heard before the change. Examples of metric modulation may include changes in time signature across an unchanging tempo, but the concept applies more specifically to shifts from one time signature/tempo (metre) to another, wherein a note value from the first is made equivalent to a note value in the second, like a pivot or bridge."


After watching TearItDown's video, I could hear what he did but I still wasn't sure how to approach it.

Call it two bars of tresillo. Identical bars. The first time, you tap your foot four times and hit 1 2& 4.

Then, the equation shows q=q. (quarter equals dotted quarter).

In the video, the clapping stays the same. But the notes are played faster. By 50%?

At that point, I was tempted to try tapping my foot according to the q. (my symbol for dotted quarter). So I tapped on the first and second notes of the tresillo. But then, I couldn't figure out where the third note would go, or how many foot-taps there actually are in the bar if you think about it that way.

So, that's a blind alley.

I could play it by using the first two notes of the tresillo in the second bar to establish the rhythmic feel and then feel the third. But what is the best way to think about the math?

I have mixed feelings about people selling things on here, but when somebody has published something relevant, is clear about the financial interest and participates in the discussion, maybe that's ok. (I do think every post needs the financial disclaimer). Since I have a couple of shelves of books that weren't very useful, I'm now careful about what I buy.

[Mick-7]

So... I remember from my study of South Indian rhythms that the pace/speed at which a time signature is played is called it's "diri."

You change the diri by changing the accent of the beats.

Using syllables, that looks like: (Bold beats are accented)

3/4 ||: Ta-ki-ta | Ta-ki-ta :||

1st speed (diri) = 3/4 (x 1.5)
||: Ta-ki-Ta | ta-Ki-ta :||

2nd speed (diri) = 3/4 (x 2)
||: Ta-ki-ta ta-Ki-ta | ta-ki-Ta ta-ki-ta :||

3rd speed (diri) = 3/4 (x 4)
||: Ta-ki-ta ta-ki-ta ta-ki-Ta ta-ki-ta| ta-ki-ta ta-Ki-ta ta-ki-ta ta-ki-ta :||

[rpjazzguitar]

So... I remember from my study of South Indian rhythms that the pace/speed at which a time signature is played is called it's "diri."

You change the diri by changing the accent of the beats.

Using syllables, that looks like: (Bold beats are accented)

3/4 ||: Ta-ki-ta | Ta-ki-ta :||

1st speed (diri) = 3/4 (x 1.5)
||: Ta-ki-Ta | ta-Ki-ta :||

2nd speed (diri) = 3/4 (x 2)
||: Ta-ki-ta ta-Ki-ta | ta-ki-Ta ta-ki-ta :||

3rd speed (diri) = 3/4 (x 4)a||: Ta-ki-ta ta-ki-ta ta-ki-Ta ta-ki-ta| ta-ki-ta ta-Ki-ta ta-ki-ta ta-ki-ta :||

Thanks for this. I'm trying to understand it.

I think I get the "3/4 (x1.5)" case. Where there were two accents, now there are three, which is 1.5 x 2 = 3. So, if I tap my foot on the bolded syllables, I'm tapping 1.5 times as fast. Would that be notated as q=q. (quarter=dotted-quarter)?

In the "3/4 (x2)" case, is that the same as double time? It looks like it's something else. I see the pattern, which is that there are three non-accented syllables in between the accented ones, but I don't see how you arrived at that. Did the duration of each syllable change? How would the change be notated in standard (European?) notation?

Might you be kind enough to explain it? Thanks in advance.

[Mick-7]

Thanks for this. I'm trying to understand it.

I think I get the "3/4 (x1.5)" case. Where there were two accents, now there are three, which is 1.5 x 2 = 3. So, if I tap my foot on the bolded syllables, I'm tapping 1.5 times as fast. Would that be notated as q=q. (quarter=dotted-quarter)?

In the "3/4 (x2)" case, is that the same as double time? It looks like it's something else. I see the pattern, which is that there are three non-accented syllables in between the accented ones, but I don't see how you arrived at that. Did the duration of each syllable change? How would the change be notated in standard (European?) notation?

Might you be kind enough to explain it? Thanks in advance.

Um, now I'm questioning my own explanation, doesn't sound right. Sorry, it's been a while since I thought about this.

The conversion from 1/4 note to dotted 1/4 note would be: 1/4 >1/4 >1/4 becomes: [1/4+1/8] (tied notes) >[1/8+1/4] (tied notes). That is, you first subdivide the 1/4 notes into 1/8th notes to count them, so [1/8th+1/8th+1/8th] = a Dotted 1/4 note, and three 1/4 notes become two dotted 1/4 notes.

I may have to write these out on a staff and get back to you, I have only my old shorthand notes to refer to.

[rpjazzguitar]

To take a simple case ...

Say the equation is q=q. (quarter = dotted-quarter) ... and you've been tapping your foot in quarter notes in 3/4. Now comes the equation and each tap becomes a dotted quarter.

There are two dotted-quarters in a bar of 3/4. So, now you're tapping twice for a bar that still is written with 3 beats. Stated another way, you now get through the second bar in two taps and the taps haven't changed speed. That seems to be correct because the equation shortens the duration of the written quarter note.

But, it's not so easy to read something that looks like 3/4 while tapping your foot in dotted-quarters. It would be easier to read the rest of the chart if you could tap your foot in the new quarter note.

So, the problem becomes how do you make the transition in your foot? It's not difficult to play 2 over 3 by thinking dotted quarters. But this is like playing a triplet over the 2, which becomes the new tapping speed.

Where I end up is thinking dotted quarters in the first bar and trying to feel a triplet over them for the second bar.

I won't attempt to translate that into the Indian system, since I don't know anything about it beyond what I've read on this forum.

In some cases it may work better not to tap your foot (not my personal preference but if you watch horn sections you'll see some non-tappers). Or, better, to tap only on 1 and feel the rest.

Sorry, did I say simple? It gets thick pretty quick.

[Mick-7]

So... you don't want to change your foot tapping routine, that way madness lies.

You're not changing the base meter, just the rhythms you play over/against it.

The formula, as I mentioned earlier in this thread, is simple.

Here is an example:



P.S. - Beat Accent = ^ (down arrow)

This example I posted earlier is 3/2 - or 2 over 3 upside down:

-----Ta-ki--Ta-ki-Ta-ki--|
3/8:-o--o--o--o--o--o--|
Bt---1........2.......3.......|
2/4:-o--o--o--o--o--o--|
Bt....1............2............|

[rpjazzguitar]

I'm still struggling with the q=q. case.

You're tapping 3/4 in quarter notes before the equation. In the last bar before the equation you tap dotted quarters and get that pulse in your head.

Then, when you hit the equation you tap in quarter note triplets based on that dotted-quarter pulse.

I haven't figured out how to diagram that yet.

[Mick-7]

I'm still struggling with the q=q. case.

That is the 2 beats over 3 example I just posted. As I said, you can still tap your foot to the lower beat (quarter notes), while playing the 2 beats (dotted quarter notes) over it. It takes practice to master it.

[Christian Miller]

A recording might be helpful?


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[Mick-7]

I forgot I can export Guitar-Pro files as midi files, the two examples I posted are attached.

[rpjazzguitar]

I forgot I can export Guitar-Pro files as midi files, the two examples I posted are attached.

As far as speeding up a 2 over 3 rhythm by 50% so that it becomes 3 dotted quarter note beats over 2 beats (think that was the question), I think the notation involves dotted 8th notes, i.e., three dotted 1/4 notes over two 1/4 notes tied to 1/16th notes, or in 16th notes, 3x6 16th notes (three 8th notes) over 2x9 16th notes (four 8th notes + one 16th note)

Post deleted because I think I got it wrong.

[Mick-7]

As far as I can figure, it has to be done with triplets.

Let's suppose you're one bar before the equation. You count two dotted quarters. You hit the equation. Now, you have to find three equally spaced notes across those two dotted quarters. At that point, you'll be in 3/4 time, playing three notes (at the new tempo) in the space of two notes of the old tempo.

But, as I try to work out the math, it looks like it has to be done with triplets. Either three quarter note triplets, or, two sets of eighth note triplets and you play the first, third and fifth notes.

Actually, forget my first example, it is a mistake, I was counting a different time signature. Sorry for the confusion.

The 1st speed ("diri") is the normal 1 count per beat. In my 2 over 3 example, that's three 1/8th notes (or dotted 1/4 note) = one 1/4 note.

The 2nd speed is double-time, i.e., 2 counts per beat, so the three 1/8th notes become three 1/16th notes (or dotted 1/8th note), or viewed another way, two measures are now played as fast as one was.

The 3rd speed is 4 times as fast, i.e., 4 counts per beat. If the piece was not really slow to start with, that could be insanely fast.

Perhaps you've heard Ravi Shankar do that, the raga will start slowly and end at a breakneck speed. As I recall, he did that in his Monterey Intl. Pop Festival performance with Alla Rakha on tabla, Rakha's fingers were moving so fast near the finale that they were a blur.

Here is 2 over 3 played in double-time. As you can see, the dotted 1/4 note of 2 over 3 is now a dotted 1/8th note and it's now 4 over 6 beats.

[Christian Miller]

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[rpjazzguitar]

Maybe it's this:

You're in 3/4.
The metronome is playing q=100 bpm. Clicking quarters.

Then you hit the equation q=q.

The next bar is also written in 3/4, but the tempo goes up in a ratio of 3/2. So it's now 150 bpm. I think.

You get 3 notes where there were previously two notes.

What would the notation look like? You might ...

Write out three quarter notes at 100bpm. And, then, below them, write an eighth note triplet for each. That's 9 notes.

Play the first, third and fifth notes, then stop. You've just played three equally spaced notes over two beats. You're done. That's one bar at the new tempo.

So, the task might be conceptualized as hitting the bar before the equation, singing the triplets to yourself and then changing the tempo to be the first, third and fifth notes in the triplet -- if you can pick it apart like that.

The idea of continuing to tap or hear the metronome at 100bpm when you're reading 3/4 time at 150bpm, well I can't yet get my mind around that.

[Christian Miller]

I did have a video, but I realised on rewatching that I’d failed to button up my shirt correctly lol


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[rpjazzguitar]

If you're in 3/4 you can overlay 2/4 by playing dotted quarters.

But, if you start in 2/4 and you want to overlay 3/4, you can't do it with eighth notes, or sixteenth notes, because you can't divide, say, 8 sixteenth notes, by 3. You have to go to triplets.

Of course, this thread is about q=q. which is not a simple overlay, but a change of tempo. So, the issue is how to find the new tempo based on the old one. Which, I think requires triplets over two beats at the old tempo. That gives you six notes, which can be grouped into groups or two or three.

Doesn't strike me as easy to think about or read, but maybe easier to feel.

[Mick-7]

Maybe it's this:

You're in 3/4.
The metronome is playing q=100 bpm. Clicking quarters.

Then you hit the equation q=q.

The next bar is also written in 3/4, but the tempo goes up in a ratio of 3/2. So it's now 150 bpm. I think.

You get 3 notes where there were previously two notes.

What would the notation look like? You might ...

Write out three quarter notes at 100bpm. And, then, below them, write an eighth note triplet for each. That's 9 notes.

Play the first, third and fifth notes, then stop. You've just played three equally spaced notes over two beats. You're done. That's one bar at the new tempo.

So, the task might be conceptualized as hitting the bar before the equation, singing the triplets to yourself and then changing the tempo to be the first, third and fifth notes in the triplet -- if you can pick it apart like that.

The idea of continuing to tap or hear the metronome at 100bpm when you're reading 3/4 time at 150bpm, well I can't yet get my mind around that.

The 2 over 3 beats example I posted, in 9/8 time, was incorrect, because I sped up the top part of the time signature (2 beats) but not the bottom part (3 beats).

When you speed up 2 over 3 by 50%, you get 3 over 4, as notated below (this is incorrect, going from 2 over 3 to 3 over 4 would be a metric modulation).

[rpjazzguitar]

It would be something like this (3 > 4.5 beats) but don't try it without a helmet - or with your shirt unbuttoned.

Attachment 118044

I think that's right. It's now 4.5 beats in the space of three.
To simplify the math, suppose the metronome is at 60, one beat per second.

The bar before the equation takes 3 seconds. Then, the equation. The bar after the equation should take 2 seconds?

But it's still in 3/4. So, each new quarter note is 2/3 as long as the original quarter. Which means the new tempo is 90 bpm. Is that much right?

Back to the problem. You're counting 1 beat per second. How do you find 2/3 of a beat per second to transition to the new tempo?

Seemed to me initially that you count in eighth note triplets and set the new tempo by the first and third notes.

The idea to write it in 9/8 is great. That way, you can still notate it in eighth notes. Amounts to the same thing in the end, but may be easier to think about. Or so I think.

Xxx Xxx Xxx in the bar before the equation becomes

XxX xX / (it only takes up 2 beats of the original bar, because the tempo is faster. You tap the capital Xs and you're now reading 3/4 at the faster tempo.

Not so easy. I've seen some great players stumble over this stuff -- which does come up now and then.

[rpjazzguitar]

My 9/8 example was incorrect, please see my correction above - in 3/4 time.

For overlaying 4 onto 3, you divide the 3/4 bar into sixteenth notes. That gives 12 notes. And you can divide 12 into 3 parts or 4.

To overlay 3 onto 4, I think you have to divide the 4/4 bar into triplets.

But, neither of these addresses the difficulty of the metric modulation, or, at least, the difficulty I'm having. What I need to do is feel the new time after q=q. That is, feel exactly how much faster to tap my foot. Or, I'd have to read conventional notation with a different pulse in mind - which seems impossible, although that video seemed to demonstrate it.

There has to be an easier way.

[Mick-7]

So... I think I've been addressing the wrong question. If we want to play 2 beats over 3 beats 50% faster, than the number of beats per measure will not change, we'll just play 1 & 1/2 measures at the speed we were playing 1 measure.

I answered a different question, which is how to make 2 over 3 beats sound like 3 over 4 beats.

But, neither of these addresses the difficulty of the metric modulation, or, at least, the difficulty I'm having. What I need to do is feel the new time after q=q. That is, feel exactly how much faster to tap my foot. Or, I'd have to read conventional notation with a different pulse in mind - which seems impossible, although that video seemed to demonstrate it.

As I said earlier, the base beat will not change, so you would continue to tap your foot to it, it's the counter-beat that changes and that you must count differently, e.g., a 1/4 note counts as 1 beat in 3/4 time but it counts as 1.5 beats when you're playing 2 over 3 beats in 3/4 time.