Re: Metric accents of 4-time


"Steve Latham" <llatham@xxxxxxxxxxx> wrote in message news:IwG1j.26586$9h.19233@xxxxxxxxxxx

Aren't we? I thought a 6/8 time signature meant that a bar contains 6 eighth notes? An eighth note six times over. Six times an eighth is six eighths.

6/8 meter tells us how many beats there are, ....it's got nothing to do with "how many of something there are".

?????

More complete quote:

No, 6/8 meter tells us how many beats there are, and what type of note gets one of those beats. It's got nothing to do with "how many of something there are".


Sorry, I was adopting logic:

A beat is an eighth note.
There are 6 beats.
Therfore (to me at least) there are 6 eighth notes and it has absolutely everything to do with "how many of something there are".

And 6 * (1/8) = 6/8

As I've said before, a 6/8 measure not only has 6 8ths notes, but 3 quarter notes (among other things). If we are going to name things by how many of X note type it contains, then we should treat meter signatures as fractions and simply reduce everything. There's no need for 6/8 then, 3/4 will suffice.

No. as I have said before (quite a number of times) it is a fraction but contains extra information by not being reduced to the lowest denominator.

Six 8ths are merely six of an item. That's not a fraction. A fraction is a portion of something, of which we need to know the whole.

6*(1/8) = 6/8
6/8 is a vulgar fraction.

A fraction is not necessarily a portion of something obvious - it is just a number. And a vulgar fraction (the sort of fraction I'm talking about) is the ratio of two integers.

Again, that assumes a "whole note" as some sort of universal value.

It is a reference value, - defined by the word "whole" in the name!

A "whole" measure of 6/8 is 6 8th notes long. The idea of a "whole" note that is 8/8ths long is completely useless in 6/8 meter.

It sounds like you're getting really desperate here, trying to confuse whole notes with a "whole measure". next you'#ll be talking about a "whole time signature".

A measure of 6/8 is not "6/8" or "3/4" of anything.

Its duration is 6/8 of a (reference) whole note. Or, more musically, 6 times that of a 1/8 note.

Nowadays, we even allow a whole rest to be a whole rest in whatever meter we want!

A full bar rest is drawn with the same symbol as a whole note rest but it is subtly different. It is drawn in the centre of the bar, and doesn't align with the first note or rest in a parallel part.

Tell me, is a half note half of a 3/2 measure?

It might form a *third* of one, and its symbolic duration is certainly a third of the duration of the 3/2 bar.

I know that it is a *third* and not a half because (1/3)*(3/2) = 1/2 and (1/2)*(3/2) is not 1/2. I worked it out by doing arithmetic on the fractions, you see. If you didn't realise they were fractions you might easily get the answer wrong :-)

Yes, but the point is, its name means nothing.

Relative to the names of time signatures and other notes, it means everything.

What about of a 2/4 measure.

A half note is not half of a 2/4 measure either. A half note would occupy a full 2/4 measure because arithmetically 2/4 = 1/2. The power of fractions again!

But see David, you're using fractions to determine what portion a note occupies of a measure.

Not quite. I'm using them to determine how many notes fit in a measure. 6/8 means 6 (1/8) notes fit becaus 6/8 = 6*(1/8).

Meter signatures don't tell use what occupies what portion of what. 3/4 just tells us that 3 quarter notes equal 3 quarter note. We don't really treat a 3/4 measure as being 75 percent of a 4/4 measure do we?

No. But with no tempo change the duration of a 3/4 bar is 3/4 of that of a 4/4 bar. Why would anyone want to think of one time signature as a fraction of another except in the sense of duration? In the sense of (symbolic) duration it is of course.

OK. here's your problem.

I don't have a problem.

A measure is 1 measure. Do you disagree?

Different measures are different.

In these
units (where 1 represents a whole note) the duration of a measure is expressed by the fraction which is the time signature. You're making my case for me here!

Only if you assume that a whole measure is not a whole measure, but a portion of some arbitrarily determined whole measure.

Not at all. I don't assume anything about a "whole measure" which is not given to me by its time signature. In fact talking about "whole measures" out of the context of the time signature has extremely limited value, as they're different.

The fault in this is going back to 4/4 as a starting point (especially for us in the way we've named them).

Who is going back to 4/4?

Because that's the arbitrary full measure.

You made that one up - not me.

If 3/4 is 3/4 of something, it must be 3/4 of 1. You're saying 1 is 4/4. I'm saying a Full measure is 1,

Well a full measure isn't 1 - that's where you're so confused. The time signature expresses the nature of the full measure.

and since 3/4 is a full measure, it's not 75 percent of anything.

Its duration is 75% of a whole note.

This is why a quarter note can be 1/3 of 3/4 or 1/4 of 4/4.

No. A quarter note can have those attributes becaiuse of the simple fractional arithmetic

3 * (1/4) = 3/4
4 * (1/4) = 4/4

You see David, it's not the notes that are constant, but the Measure.

No wonder you're confused. If you have a piece which changes time signature with no tempo indication, are you telling me you play all measures with the same duration? The correct musical default is that any given note (eg a quarter note) has the same duration before and after the change.

A whole measure is a whole measure. Does a meter signature not represent a whole measure?

Different time signatures define different measures. Making them all the same despite the time signature is a most unmusical thng to do.

6/8 simply means there are 6 of the notes we call 8th notes in a measure.

And in fractional terms, correspondingly, 6 times (1/8) = 6/8. Bingo!

Faulty logic.

No very precise logic.

It does not mean it is 6/8 or 3/4 of a 4/4 measure.

Its duration is.

Well if you change time from 4/4 to 6/8 (with no indication of a tempo change) the duration of the 6/8 bar is exactly 6/8 of the duration of the 4/4 bar, and so in that sense it is exactly that.

If the previous measure were 5/4 then what? 6/8 is now 3/5 of the length.

Correct!

Again, you're assuming that 4/4 is some sort of base unit for the calculation of meters. It's not.

Not at all - it is you who are hung up on 4/4 and a strange concept of a whole measure irrespective of its time signature. I am happy that durations obey 6/8 = (3/5)*(5/4) with no mention of 4/4.

It may help to learn to use the word 'fraction' with out always following it with the word 'of'. Use the more precise term "vulgar fraction" as no one ever says a "vulgar fraction of" something.

Dave
--
David Webber
Author of 'Mozart the Music Processor'
http://www.mozart.co.uk
For discussion/support see
http://www.mozart.co.uk/mozartists/mailinglist.htm

.

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