Metric modulation question

[rpjazzguitar]

I think you are over-complicating this, if you count all the signatures in 8th notes, you need only add or subtract micro-beats: 7/8 > 8/8 (4/4) > 6/8 - etc. You would just accent the beats differently in each time signature.

Two things change. One is the number of eighth notes in the bars. The second thing that changes is the tempo. My question is about how to get the new tempo in your mind on the fly.

[rpjazzguitar]

One of the things I was looking for was the correct way to translate the equation (e.g. quarter = dotted-quarter) into plain English.

So, if the equation is "X=Y"

It means:

"The duration (as measured with a stopwatch) of X before the equation is the same as the duration of Y after the equation."

Where X and Y are note values.

I'm guessing this was already obvious to anybody with even a casual interest in music, but I got there late.

So, if q=q. (quarter = dotted quarter), then three new eighth notes now take the same length of time as two old eighth notes. So, one way to get there is to count eighth note triplets at the old tempo. Those become the new eighth note. If the tempo was 60, now it's 90. 1.5x as fast.

If the equation is reversed, q.=q that means the new quarter note takes the same length of time as the previous dotted quarter. Or, 2 new eighth notes now take the same length of time as three old eighth notes. Tempo slows in a ratio of 3:2. 2/3 of the prior tempo.

If the melody was written in dotted quarters it would be straightforward to find the new tempo. But, if the melody is, say, in quarters, you'd have to play quarters while thinking ahead in dotted quarters. Is there a simple, easier way?

All of the above assumes no change in time signature. If there's a change in time signature it adds another layer.

Suppose the equation is quarter=dotted eighth. So the equation states that 3 16ths in the new tempo will be spread over the time taken by 4 16ths in the old tempo. So the new tempo is slower in a ratio of 4:3. One way would be to count 8th note triplets in the old tempo. That becomes the new sixteenth note.

[Mick-7]

Two things change. One is the number of eighth notes in the bars. The second thing that changes is the tempo. My question is about how to get the new tempo in your mind on the fly.

The tempo may or may not change, one can change the time signature without changing the tempo just as one can do the reverse.

So, if q=q. (quarter = dotted quarter), then three new eighth notes now take the same length of time as two old eighth notes.

The duration of a note does not change when the tempo changes, e.g., the duration of an 1/8th note in 4/4 is one eighth of a measure at any tempo, the duration of an 8th note in 7/8 is one seventh of a measure at any tempo, etc. You seem to be conflating note/measure duration and the tempo at which they are played, they are separate considerations.

[rpjazzguitar]

I think we're talking about two different things.

In the most recent posts I have been talking about "metric modulation" which is a tempo change. The new tempo is defined by an equation which relates the new tempo to the old one.

It can happen with or without a change in time signature. I've talked about both situations. The one in that version of Surrey combined a time signature change with a tempo change.

When the equation states that the new dotted quarter is the old quarter, that is the same as saying the tempo has gone up by 50%. Once you're at the new tempo you just read what's there.

The issue for me has been getting the feel of the new tempo. Sometimes the necessary counting seems difficult enough that I'm hoping for a better technique.

I made a point about the definition of duration being measured in clock time, as with a stopwatch, not as a fraction of the measure. That's what it is. A change in how long (on a stopwatch) a certain note lasts.

[Christian Miller]

Nice job in figuring that out. I have a chart a friend did (I don't have permission to share it) and it agrees with everything you wrote.

I also appreciate the tip about "eyes will pop". The melody there is three quarter notes a 16th rest and a sixteenth note. The bass line is 3 quarters and an eighth rest.

So, now I'm trying to think this through. If I follow your line of thinking, the 7/8 is counted 12 12 123. 7 eighth notes.

Now, two things change. The time signature goes to 4/4. and the dotted eighth note becomes the new quarter note. That implies that the dotted quarter note becomes the new half note.

So, the 12 12 123 is useful because the "123" is the correct length of the half note in 4/4.

At "weather" the time goes to 7/8 for just one bar. Easy enough, just 3.5 of the quarters you were counting (assuming you divided that half note from the previous paragraph).

After the one bar of 7/8, the time signature goes to 6/8 and
there's another metric modulation equation. This time, quarter note = dotted eighth.

So at the moment you hit the equation at the end of the 7/8 bar, how do you instantly, on the bandstand, find the pulse for the new eighth note?

You can get the new dotted eighth from the old quarter note, or better yet, the new dotted quarter from the old half note. The new measure of 6/8 lasts as long on the clock as the old measure of 4/4.

Is that much correct?

Yes I’d get the new dotted quarter note after the bridge from the bridge half note.

You are just feeling the overall pulse then.

If I saw this on the bandstand I think I would have trouble deducing any of this right away lol.


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[Mick-7]

In the most recent posts I have been talking about "metric modulation" which is a tempo change. The new tempo is defined by an equation which relates the new tempo to the old one.

Oh sorry, I did not listen to your example (Surrey with a Fringe) .... What is the cue for the change in tempo? How is the tempo "equation" you spoke of expressed?

I have a chart a friend did (I don't have permission to share it) and it agrees with everything you wrote.

It would help a great deal to see a written example (music notation) of the question you're trying to answer, words are a poor descriptor.

[rpjazzguitar]

The video I linked in post #100 has some examples.

I watched some other videos, mostly by drummers. One made the point that for some modulations it can seem like you're pulling the new tempo out of thin air.

[rpjazzguitar]

Yes I’d get the new dotted quarter note after the bridge from the bridge half note.

So, we're in 4/4 at "in case there is a change in the".

Then a bar of 7/8, which I'll think of as 3.5/4. The dropped 8th note won't throw me off.

Now, two things happen. Time signature changes to 6/8 and there's the equation q=e. (quarter = dotted 8th). The equation says "The new dotted 8th will last the same amount of stopwatch time as the prior quarter note".

Presumably, finding the old half note isn't difficult since you had some time to relax in 4/4. Since 6/8 can be counted as two dotted-quarters, four of the old quarter notes are the entire new bar. If the melody was in 8th notes, for a moment, it might sound like you were playing two sets of (old) quarter note triplets in 4/4.

The "two bright sidelights" bar is in 6/8, but the melody is dotted 8ths. That's the old quarter note. I find it easy enough to feel my way through that bar and then feel the 5/8 bar which follows. But, I want to also know the easiest way to count it.

So, I start by playing the melody according to the old quarter note. Tap my foot on "two" and "side" and then overlay the triplet. Now I've got the 8th note.

Which is a long way of saying the same thing. You get the new dotted quarter from the old half note -- as you pointed out.

[Christian Miller]

I think you may even be over thinking it.

Basically the overall 2/4 pulse of the song doesn’t change.

If we ignore the various dropped and added eighth notes, 2/4 divided into three notes is 6/8 for the A and into 2 notes is the swing four in the bridge right? So that basic ‘macro beat’ to use Mick7s term (I think it’s an Edwin Gordon term?) doesn’t change. In a way there is no metrical modulation just a change in subdivision.

So you’ve had plenty of time to feel that pulse even with the dropped and added eighth notes.

I would practice switching from 6/8 to 4/4 and back and once that’s intuitive, working on the whole arrangement. You can have that dialled in so you don’t have to think about it.

That 6/8 to 4/4 relationship is good to know in any case. It’s one of the basic rhythmic relationships in swing (quarter triplets). Pete Bernstein also teaches to use the 4/4 against 6/8 on waltz time tunes, for phrasing.

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[Mick-7]

Microbeats is a term used for polyrhythms in South Indian Music. There were quite a few exercises re: metric modulation in the lessons I took from Jim Loveless (since it's very common in South Indian Classical music) but unfortunately I can no longer decipher most of the old notes I took - use 'em or lose 'em.

One study he gave me is a Bulgarian folk song that goes from: 11/8 > 13/8 > 5/8 > 15/8 > 13/8 > 5/8 > 4/8.

It is counted like....

11/8--13/8--5/8--15/8--13/8--5/8--4/8 :
|1.2.3.4.5../1.2.3.4.5.6../1.2../1.2.3.4.5.6.7../1.2.3.4.5.6../1.2../1.2.|

Notice that the microbeats ( . ) in the last measure of each time signature are counted/accented as 1 beat to prepare the shift to the new time signature.

[Christian Miller]

I doubt it’s South Indian…. I mean it obviously isn’t a Sanskrit term, but I can see how it’s useful and relates to Konnakol.

I did however recognise it from Gordon’s “learning sequences in music” which is an interesting book if frighteningly uncompromising.

Learning Sequences in Music: Skill, Content, and Patterns : a Music Learning ... - Edwin Gordon - Google Books

Another Gordon coinage - “audiation”. Influential guy.

Here’s an article on the concept the way I used it above, website based on the Gordon approach
https://theimprovingmusician.com/cou...ntroduction-2/

These are all useful concepts that relate to other traditions so I can see why your teacher used them. The macrobeat/microbeat thing maps to taala/solkatu

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[Mick-7]

I doubt it’s South Indian…. I mean it obviously isn’t a Sanskrit term, but I can see how it’s useful and relates to Konnakol.

They call the subdivisions of the beat "laya."

Correction: A web search tells me that laya is the tempo, they do have a word for the microbeats/subdivisions of the beat but I don't know what it is.

"Laya can be explained as the distance between two beats. Hence, the lesser the distance, the faster the tempo of the song, and vice versa."

[rpjazzguitar]

I think you may even be over thinking it.

Basically the overall 2/4 pulse of the song doesn’t change.

If we ignore the various dropped and added eighth notes, 2/4 divided into three notes is 6/8 for the A and into 2 notes is the swing four in the bridge right? So that basic ‘macro beat’ to use Mick7s term (I think it’s an Edwin Gordon term?) doesn’t change. In a way there is no metrical modulation just a change in subdivision.

So you’ve had plenty of time to feel that pulse even with the dropped and added eighth notes.

I would practice switching from 6/8 to 4/4 and back and once that’s intuitive, working on the whole arrangement. You can have that dialled in so you don’t have to think about it.

That 6/8 to 4/4 relationship is good to know in any case. It’s one of the basic rhythmic relationships in swing (quarter triplets). Pete Bernstein also teaches to use the 4/4 against 6/8 on waltz time tunes, for phrasing.

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Useful insight. Thank you.

Do you see the 3/4 bars as any different? They each follow a 5/8 bar. No equation. Just a different subdivision.

If you're feeling 2/4 against the 4/4 and 6/8 sections (which makes sense), then to get the 3/4, you need to take the six 8th notes and group them in three groups of two 8ths rather than two groups of three 8ths.

That is, if you're feeling 2/4, you have to divide those two beats each into a triplet. And then group those 6 notes into groups of two.

There are several 3/4 bars, most notably "fringe on top".

[Christian Miller]

They call the subdivisions of the beat "laya."

Correction: A web search tells me that laya is the tempo, they do have a word for the microbeats/subdivisions of the beat but I don't know what it is.

"Laya can be explained as the distance between two beats. Hence, the lesser the distance, the faster the tempo of the song, and vice versa."

The way my teacher described it seemed it was more like the ‘feeling of the distance between two beats’. Either that or I failed to understand what he meant. Which is likely tbf.


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[Mick-7]

The way my teacher described it seemed it was more like the ‘feeling of the distance between two beats’. Either that or I failed to understand what he meant. Which is likely tbf.

That makes sense because it's not a rigid formula. This definition from a forum post matches my teachers use of the term:

"Layakari literally means skill or art of controlling laya in an artistic manner. Laya itself can be quantified as a numerical value, which is the ratio of beats actually played to the base beats. Base beats (or conceptual beats) in case of tabla solo are equivalent to beats played by the lehra in one cycle; and in case of accompaniment are the beats dictated or implied by the song/khayal. Hence if lehra is playing 4 beats in cycle and tabla player plays 8 beats in same time; the laya will be 8/4 which is 2; also called a dugun."
( From: Forums – chandrakantha.com )

[Christian Miller]

Useful insight. Thank you.

Do you see the 3/4 bars as any different? They each follow a 5/8 bar. No equation. Just a different subdivision.

If you're feeling 2/4 against the 4/4 and 6/8 sections (which makes sense), then to get the 3/4, you need to take the six 8th notes and group them in three groups of two 8ths rather than two groups of three 8ths.

That is, if you're feeling 2/4, you have to divide those two beats each into a triplet. And then group those 6 notes into groups of two.

There are several 3/4 bars, most notably "fringe on top".

I mean with 6 8 there’s two ways of grouping. You can do 2 groups of 3 or 3 groups of 2.

So the former is 6/8 and the latter is 3/4. But this is common throughout western music to go from the first to the second for variety. This is called a hemiola and is a common feature of Irish music for instance - think of the Irish Washerwoman - as well baroque music etc. and jazz. In fact the 2/3 duality is a basic feature of West African bell patterns as well as the Afro-Cuban Bembe pattern.

So il just hearing it as that. The 5/8 is just a shortened bar of 6

If that makes any sense….


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[Christian Miller]