Time Signature Woes

[Slant]

This post was inspired by the sub-conversation in Jay Norem's thread called "You've written a great head. Now what?". For those that haven't read it, the sub-conversation was about the differences between the "American" and "British" systems of nomenclature for note duration (ex. "quarter note" vs. "crotchet"; "8th note" vs. "quaver"; etc.).

This whole conversation got me thinking more on the subject, and finally brought me to a conscious confirmation of something that I've subconciously known to be correct for a long time. Get this: the "bottom" number of time signatures, as it is currently employed, is totally confusing and almost completely useless. It serves very little, if any, purpose whatsoever.

Before I give my rationale (for anyone not already yawning!), the following, in a nutshell, is how time signatures are usually taught: the top number is said to represent how many beats or pulses there are per measure, and the bottom number is said to represent what type of note gets applied to the beat. For those familiar with written music, that's easy enough, right?

So, the top number can feasibly be any number in the known universe, though usually you see the following: 4, 3, 2, 6, 9, 7, 5, 11, 13, and some others from time to time. But the fact remains that any number is possible.

The bottom number, on the other hand, again, refers to the value, or "weight", of the beat. Or does it? Just what is meant by the idea that the bottom number represents the "type of note that gets applied to the beat"?

Let's say you're reading/playing a tune in what's usually called 3/4 time. Here there are three quarter notes per measure. How is that possible? How can there be three quarter notes if a quarter note is = to 1/4 of a whole note? Numerically speaking, it just doesn't work, and it's certainly counter-intuitive. It's as if we are implying that, in an ideal tune, our measures would really have 4 beats, but in this case one beat was cut off. Nevertheless, we go ahead and retain reference to "/4" just in case some day our "discarded" quarter notes decide to jump back into the picture!

That certainly can't be the case. The composer must have intended the meter to get 3 beats, otherwise he/she would have written a different tune! So why retain reference to "quarter notes" in odd time? Can anyone logically explain it? If so, I'd love to hear it.

If, however, as I mentioned in Jay Norem's post, that at the core of the "American" system is the tendency to arbitrarily apply to odd meters the nomenclature local to 4/4, then, when playing in any other meter, the bottom number becomes useless and meaningless. Thus, the tendency to write the bottom number when notating time signature is also meaningless. The problem truly seems to revolve around the fact that the "American" tradition of notating and describing meter lacks a generic nomenclature, such as is used in the "British" system. In other words, the "American" system needs a nomenclature that doesn't require it to refer back to the meter 4/4, but can be equitably applied to all meters.

A natural argument to my rant would be as follows: if no bottom number is used, and the time signature changes mid-tune, how would someone understand the essence of the beat shift? Suppose a tune changes from 7/4 to 6/8. In other words, the value of the measure of 7 is greater than that of the measure of 6, but you wouldn't know that if it wasn't stated. Someone could just as easily apply the same metric division to the measure of 6/8 as he/she did to the measure of 7/4, yet the composer clearly meant for the beat in the 6/8 meter to be halved from 7/4.

So, what's the answer? The "British" system also seems to cover this problem. I doubt it's done this way currently, but it would be much less confusing (for the next generations of musicians at least) to see a shorthand such as the following (using the 7/4 vs. 6/8 example from the last para.): 7/c (for 7 chrochets per measure); then when the time changes to "6/8", you'd rather see 6/q (for 6 quavers per measure).

What do you all think? Is it too "radical" for us snooty jazz-types to consider? Are we way too set in our ways? Your band mates are definitely going to wonder what the hell has gotten into you when you hand them a chart that reads the time signature as: 4/c, or 7/q, or 3/sq (semiquaver) or what have you...

On the other hand, what am I missing? What have I overlooked w/ this proposal?

[Jay Norem]

Hi Slant...I'm thinking, I'm thinking...will return.

[Jay Norem]

If, however, as I mentioned in Jay Norem's post, that at the core of the "American" system is the tendency to arbitrarily apply to odd meters the nomenclature local to 4/4, then, when playing in any other meter, the bottom number becomes useless and meaningless. Thus, the tendency to write the bottom number when notating time signature is also meaningless. The problem truly seems to revolve around the fact that the "American" tradition of notating and describing meter lacks a generic nomenclature, such as is used in the "British" system. In other words, the "American" system needs a nomenclature that doesn't require it to refer back to the meter 4/4, but can be equitably applied to all meters.

So, what's the answer? The "British" system also seems to cover this problem. I doubt it's done this way currently, but it would be much less confusing (for the next generations of musicians at least) to see a shorthand such as the following (using the 7/4 vs. 6/8 example from the last para.): 7/c (for 7 chrochets per measure); then when the time changes to "6/8", you'd rather see 6/q (for 6 quavers per measure).



First off, I love this as an idea for a thread. Odd meters have played a major role in my songs. A melody goes where it wants, and if it wants to be in 4/4, then veer off to 7, then 5, 4, 7 and end in 6, whose to argue with Mr. Melody? The bass is playing quarters throughout, and the drums are swinging, and it all works in a beautifully organic way.
I've never liked "hard syncopation" of odd meters. "Take Five"...what a horrible song. Do-dat do-dat doo-dat.
Now to your question. If the specific MEANING of quarters and eights is adhered to then it does, in fact, only apply in 4/4 time. I rememer from the other thread you mentioning double-think. That's pretty much what happens when the system is applied to odd meters, I think. And also, these terms have become basically generic terms anyway, much in the same way that the word "coke" can mean Pepsi or Dr. Pepper. So a quarter note really isn't really a quarter of anything in musicians' minds. It's twice what an eighth note is, yeah, and one quarter of a whole note, sure, or one sixth of a dotted whole note. Wait, how can a quarter also be one sixth? Double think, I think. But I think you'd have as hard a time getting American musicians to start using the quaver system as you would getting a national health care sytem established here, which is something I feel this country desperately needs and deserves. Anyway...
Jay

[Slant]

If the specific MEANING of quarters and eights is adhered to then it does, in fact, only apply in 4/4 time. I rememer from the other thread you mentioning double-think. That's pretty much what happens when the system is applied to odd meters, I think. And also, these terms have become basically generic terms anyway, much in the same way that the word "coke" can mean Pepsi or Dr. Pepper. So a quarter note really isn't really a quarter of anything in musicians' minds.

Jay,

I think you're right, in that basically the terms quarter, half, eighth, etc., really don't have specific meaning in this context. I have a hard time with it, however, because terms such as these are so specific in and of themselves. I mean, really, the word "half" couldn't be more specific, eh? No wonder time signature is such a huge hurdle for young musicians to deal with!!

By the way, speaking of odd time, the name Jay, jazz, drumming, etc., have you ever heard of the great drummer/composer Jae Sinnett?

Check it out: http://www.jaesinnett.com/

I heard about him on NPR one day. Great stuff.

[Slant]

Some audio from Jae Sinnett: http://www.npr.org/templates/story/story.php?storyId=5176440

Yeah!

[Jay Norem]

Oh yeah I checked out Jae Sinnet. Real nice, appreciate it man!

[LDGuy]

The thing about the quarter note thing being counter-intuitive is just because of the way music has evolved. There has been musical notation, and therefore notation of rhythm in some for or another, for thousands of years. I think there was a discovery of some supposed cuniform notation carved on a stone dated to be 2500BC a few years back. Certainly the Ancient Greeks had a system of musical notation, as well as the Chinese, Japanese, Javanese and Balinese, Indian and other peoples. We are familiar with western notation, which grew up from the system of neumes and plainsong notation, and modern notation is now considered to have been invented by the Italian monk Guido d'Arezzo. So rhythmical notation has been around for ages, and naturally there have been needs for differenciation between long and short notes, just like the grammar of language.

Western music eventually came to form itself into a system that was most commonly in simple quadruple time. Long pulse-like notes, which I suppose a crotchet would be, were analysed in the american system and called quarter notes, because the most common time is 4/4 (it's even called common time or common meter). This is all glaringly obvious, but the point I'm making is that the american system of rhythm is an analysation of what had already formed. That is, a quarter note is not really what it says it is - it may form one quarter of a whole bar of 4/4, but as a synonym for a crotchet, it also forms one third of a bar of 3/4. A quarter note does not mean a note that is one quarter of a bar. It means note that commonly is one quarter of a bar of four quarter notes. There is a subtle difference between these two, but it is a difference.

Thus the entire american system is built from common time. But it could have been anything. Indian classical music is in four sometimes (the teental is probably the most common tala), but also appears in 12, 9, 11, 5, anything. And the tala is strictly adheared to, much like a meter (although there are subtle differences). Indian classical music nowadays is rarely notated, if it is it is in written bols, and rags are sometimes written in conventional staff notation. A lot of traditional African music is also very rarely notated, and musical forms are often in complex times. Ghanaian drumming especially is often in a series of different percieved times at once, employing the duality of compound and simple time. So trying to notate Ghanaian music is extremely difficult, because some pieces will be in 12, 3, 4, and 6 at once (depending on the player or listener's perception). It seems in western classical music the players all agree on a set percieved meter.

This all seems obvious now you see it, but context is everything.

[Jakeweiser]

trying to come up with a system of measurement that is finite for something that has unlimited permutations is obviously not possible.

So we have a system based off the idea that in general, a quarter note is considered to be the guage in which all other beats are measured regardless of what happens to be the true subdivision of a beat. Time signatures exist to aid in musicality and phrasing rather then a way to write down something to explain the finer points of our notational system.

But on a mathmatics level, obviously the system doesn't work. However reading music with no clear delination of a pulse given by bar lines ceratinly is challenging. I did a transcription of Abercrombie's quartet playing freely with no pulse and notation was only possible (to me) if all time signatures were eliminated and note values were only to be observed in terms of a guess, how can a note be an 8th note when there is no quarter note to guage it against, therefore I used a Quarternote as a common note length, 8ths as fast, 16ths as faster nd halfs and wholes to indicate held notes.

I guess we work with what we have ;)

[LDGuy]

The thing is, we have obtained what pretty much every other technical field needs - unification, or the explanation of all complexity using a series of fundemental rules which all explain each other. Or at least we think we have. As jakeweiser says, there is a great deal of music which is difficult to notate with standard western notation. We are getting there, slowly, with knob tweaking and with the invention of new notation techniques in the 20th century. However, we can never truly represent everything about music on a page. And really musical notation wasn't designed to do that. Written language, on face value, conveys no meaning. It is a sequence of understood symbols, arranged to rules, which can then be interpreted. Meaning cannot be transcribed, it can only be interpreted through mutual understanding. Similarly, you cannot put a sound onto a piece of paper. And anyway, notation wasn't really designed to do that. Like written language, it is designed to convey ideas, musical ideas. These ideas of course need interpretation, by a player (or by a computer). So whether it truely is unification is difficult to say. We have a unified system of representation of musical ideas. But we cannot truely reduce the complexity of music to a page.

But you know what, I'm glad of it.

[Jay Norem]

These ideas of course need interpretation, by a player (or by a computer).

Or by a conductor. To me, sheet music is just a way to start rehearsing a tune. By the end or the rehearsal, most players have written all kinds of interpretive little scribbles on their charts.

[Tarquin1986]

While we're on the subject of notation: I'm not sure I like the way triplets are notated. To write '3' over a group of 3 quavers is on the one hand stating the obvious, and on the the other counter intuitive. You could write '2' over the three quavers to show that they take place in the space of 2 standard quaver beats. Makes more sense to me. Can you guys follow this? I don't know how well I explained myself.

[Slant]

While we're on the subject of notation: I'm not sure I like the way triplets are notated. To write '3' over a group of 3 quavers is on the one hand stating the obvious, and on the the other counter intuitive. You could write '2' over the three quavers to show that they take place in the space of 2 standard quaver beats. Makes more sense to me. Can you guys follow this? I don't know how well I explained myself.

Tarquin,

This is another issue I have too, and here's a small part of a post I made a while back on the same subject (the rest of it is here: http://forums.allaboutjazz.com/showthread.php?p=293831#post293831):
-------------
12/8 is, IMO, the key to understanding, and "getting into" the jazz rhythm. Writing jazz in 4/4 is, in reality, merely a "convenience" built on years and years of habitual tradition. It is not the most accurate time signature out there, and it gives rise to the un-warranted use of the dreaded TRIPLET BRACKET!!! This needs to be changed!
-------------

Anyway, the essence of the triplet bracket, in the case of swing-based music especially, is that it designates a place within a measure where 12/8 (12/q in my new terminology - I'm starting the culture here on this forum) is literally being super-imposed onto the measure. All of the sudden you're not reading the "8ths" as long-short, long-short, but you're reading them as one-trip-let, two-trip-let, etc. Confusing, eh? I hate it. I think it's crap to be quite honest.

But...enough about me! Let's look at the triplet bracket in another light: imagine you have a bar of 4/4 (4/c), filled with quavers throughout, except for beat three, which is filled with a quaver triplet. So, what you now have is a bar of 4/c with nine 8th notes. Ha! You probably have yourself wondering: how the hell do you fit nine 8th notes in one bar of 4/4? Well, my friend, that's the magic of the miraculous triplet bracket! Don't question it, just accept it. Besides, "that's how it's always been done"!!!

Seriously, the system really needs to be looked at from an objective view point. Many are going to say that there is nothing you can do, it's as good as it gets, etc., etc. But that's not for me. I'm all about ease of use. If I can find a more productive, easier method, one that especially makes it easier to grasp for newbies...I'm going with it!

[Jay Norem]

12/8 is, IMO, the key to understanding, and "getting into" the jazz rhythm. Writing jazz in 4/4 is, in reality, merely a "convenience" built on years and years of habitual tradition. It is not the most accurate time signature out there, and it gives rise to the un-warranted use of the dreaded TRIPLET BRACKET!!! This needs to be changed!


I always thought that it was the dotted-eighth-sixteenth note. Now that's never written. It's assumed that a string of eights is to be played "swung." Yes, the triplet feel is in there, but now you're talking about the first two notes in the triplet being tied. Too cumbersome. Just notate in eights and it works fine, unless I'm misunderstanding the point at issue here.

[Slant]

The thing is, we have obtained what pretty much every other technical field needs - unification, or the explanation of all complexity using a series of fundemental rules which all explain each other. Or at least we think we have. As jakeweiser says, there is a great deal of music which is difficult to notate with standard western notation. We are getting there, slowly, with knob tweaking and with the invention of new notation techniques in the 20th century. However, we can never truly represent everything about music on a page. And really musical notation wasn't designed to do that. Written language, on face value, conveys no meaning. It is a sequence of understood symbols, arranged to rules, which can then be interpreted. Meaning cannot be transcribed, it can only be interpreted through mutual understanding. Similarly, you cannot put a sound onto a piece of paper. And anyway, notation wasn't really designed to do that. Like written language, it is designed to convey ideas, musical ideas. These ideas of course need interpretation, by a player (or by a computer). So whether it truely is unification is difficult to say. We have a unified system of representation of musical ideas. But we cannot truely reduce the complexity of music to a page.

But you know what, I'm glad of it.

LD Guy,

I'm not sure I follow your main theme here, but I'm in no way trying to suggest that written music can somehow display the subtleties of actual music. No no no!!! I'm simply suggesting something that would, IMO, qualify as what you refer to as "knob tweaking". This is a simple change in how we apply note value to meter, and thus how we refer to it. It doesn't actually change anything other than making it easier to understand by removing numerically ambiguous terms such as half, quarter, 8th and so on. These terms clearly refer to quantity for most people. The idea that one should have to reconcile associations of quantity with the idea that quarter, musically speaking, means something completely different (in some cases it means 3 or 7 or 6 or hell it just depends), seems absurd and, quite honestly, almost sadistic now that I think more about it.

Also, please don't misunderstand: I don't think this is something novel either. I'm simply trying to apply an already-used system of nomenclature to time signature notation. For all I know this is already being used somewhere...??? Certainly I'm not the first to get sick of trying to explain to students why 7/4 has 7 quarter notes in it!!

[Slant]

I always thought that it was the dotted-eighth-sixteenth note. Now that's never written. It's assumed that a string of eights is to be played "swung." Yes, the triplet feel is in there, but now you're talking about the first two notes in the triplet being tied. Too cumbersome. Just notate in eights and it works fine, unless I'm misunderstanding the point at issue here.

Jay,

A 4/4 quarter note transltes to a dotted quarter in 12/8. The underlying triplet structure ("swing feel") is always present in 12/8 because there are literally 4 groups of three quavers (4 beats X 3 notes = 12). This way the triplet bracket is eliminated. Actually, some big-bands still use 12/8, but it's not as common as it used to be...especially post-Real Book.

[LDGuy]

LD Guy,

I'm not sure I follow your main theme here, but I'm in no way trying to suggest that written music can somehow display the subtleties of actual music.

I wasn't really responding to your comments, I'm sure you know more than I do; I was just trying to add to the discussion. No harm ment!

L.

[markweliky]

12/8 is, IMO, the key to understanding, and "getting into" the jazz rhythm. Writing jazz in 4/4 is, in reality, merely a "convenience" built on years and years of habitual tradition. It is not the most accurate time signature out there, and it gives rise to the un-warranted use of the dreaded TRIPLET BRACKET!!! This needs to be changed!


Most jazz players now a days play their eighth notes more straight than swung. The swing is still there, but it's not as rigid as a 12/8 type of feel. That is why there is the use of 4/4 and triplets and so forth. What's the big deal? it's really not that difficult.

[Bill Robinson]

••• It seems to me that the problem lies in having to put a number which represents a note value in the bottom of the time signature. For instance, 8=eighth note, 4=quarter note, 2=half note...what happened to 3? And notice how it progresses by 2's? I agree fully with Slant on notating jazz or blues shuffles in 12/8. There are too many imprecise explanations floating around, such as playing "behind the beat" and other vague descriptions (that might mean something different in Kansas City than it does in New York if its all transmitted orally). I never liked "shuffle feel". And who said 12/8 is inherently stiff? Just write in "play loosely, behind the beat", and stop counting every eighth note. I transcribed some Gatemouth Brown and did it in 12/8. I was stumped for several years pondering this problem. The key to the shuffle, and the jazz beat, is that being in 12/8 it can be subdivided by two OR three (3x4 or 4x3, 2x6, etc.). This gives it its complexity and flexibility, and I'm sure this all started in Africa with their drum ensembles. I'm not familiar with the British system, but it looks interesting, and I like the way it has an actual note in the bottom. ••• Ever notice how a shuffle has a strong 1-2-3-4 pulse, like a walking bass plays on, but has all the little subdivisions of 3 (123-223-323-423)? Each main pulse beat is divided by 3, which confounds our 2-4-6-8 Company HO! up-and-down military-march system (it was all started by Army drummers back in 1341). "Does anybody here in boot camp know how to march?" "Yes sir! I was in marching band in high school!" ••• What if instead of 12/8, in order to emphasise that 1234 pulse & still have groovy subdivisions of 3, you notated the shuffle as 4/with a dotted quarter note in bottom? Charles Ives did some experimenting in this area; I think I remember seeing 4-1/2 over 4 in one of his scores. The notes themselves are arbitrarily divided into 2s so you have to add dots. Question Authority! Ignore Alien Orders! ••• Peace, BR

[Slant]

I wasn't really responding to your comments, I'm sure you know more than I do; I was just trying to add to the discussion. No harm ment!

L.

L,

No harm taken! I appreciate your comments. I just wanted to make sure we're on the same page, that's all. Regarding me knowing more than you...nope. I'm just trying to make sense of some chaos, nothing more.

[bassist]

I'm not familiar with the British system, but it looks interesting, and I like the way it has an actual note in the bottom.

hey, just to correct you here... the british system does not have an actual note on the bottom. time signatures are written the same as they are in america. slant was just coming up with a new system based on the british nomenclature that would have an actual note on the bottom. this is slants new system, not a system actually currently employed in england.

Question Authority! Ignore Alien Orders!

sir, yes sir! (errrrrrr.....)

dan

[Slant]

Most jazz players now a days play their eighth notes more straight than swung.

Huh? This really takes me off guard for a couple of reasons: 1) it's a hell of a blanket statement, and 2) it's not really relevant to what I'm saying at all.

The swing is still there, but it's not as rigid as a 12/8 type of feel.

Since when is 12/8 "rigid"? I've stated elsewhere on this forum, and I'd like to state again, that there is nothing "rigid" or "loose" about ANY time signature. They mean nothing in that regard!! The term "12/8" means nothing more than 'twelve 8th notes per measure'. Play them as rigid or as hang loose as you want...the time signature doesn't care.

That is why there is the use of 4/4 and triplets and so forth. What's the big deal? it's really not that difficult.

You mean to say that because today's cats have tightened up their swing, that's why we have such prolific use of 4/4? Hmmm.... I'm not so sure, principally because the use of 4/4 has been used for a long time to describe swinging tunes (long before we were born).

I never meant to state (if I did) that anything is "difficult" or a "big deal". Hell, there are a thousand quadzillion bigger problems in this world. All I'm saying is that, when it comes to swing-based music, the time signature 12/8 does a vastly better job of describing what is actually occuring than does 4/4. Does it describe what is exactly occuring? Hell no. Just like the sense of sight doesn't relate to the brain exactly what is in front of the eyes, so too does written music only somewhat approximate via symbol a piece of music.

But...this is, like most threads, running off topic. My initial post is more to the point here.

[Bill Robinson]

••• Remaining on topic here, as I always do, there's one little conceptual glitch I noticed. I'm not a math expert, so forgive me if my explanation is not 100% kosher. Even though ratios, or fractions, are derived by going backwards on the number line from 1 and approaching zero, they do not represent absolute quantities. For instance, 1/2 can be one-half of any quantity, not just one: one-half of a million, one-half of 500, and so on. I really "grokked" this concept after studying Harry Partch's book "Genesis of a New Music", where he explains intervals as ratios. A guitar neck gets more crowded and spaces get smaller as you go up the octaves, but a "G" is still a "G". That's why we have the "cents" system in tuning, because the Hz "number line" keeps getting proportionally bigger, i.e. A-110, A-220, A-440, A-880, etc. and the cents line evens it all out. ••• So back to quarter notes: one-quarter of a whole note, sure, but that's a proportion, not an absolute quantity like "one bar". Ratios are relationships between things, not fixed quantities. Hey, that's Art; the Greeks and their Golden Mean. Might I suggest you read "The Divine Proportion" or one of the many "layman's math" books on the subject of the Golden Ratio, nature's numbers, etc. ••• I started studying all this stuff harder when I was faced with some problems at work (a tuned wind chime factory) making tunings from customers who submitted their requests in Hz, not notes; or "solfeggio" tunings and other weird requests. ••• A musician friend of mine examined the Harry Partch book and commented "What practical use could this be?" It turns out that Partch's info on ratios and tuning tables has been invaluable in my job, and somewhat ironically, this friend now makes his living as a piano tuner. (?) Maybe someday all this info will sneak up and bite him on the ass. •••• I know I'm veering off-topic, but "it's all related, man...it's all one." I'll go start another thread if you'd like. Peace, BR •••

[Slant]

••• Remaining on topic here, as I always do, there's one little conceptual glitch I noticed. I'm not a math expert, so forgive me if my explanation is not 100% kosher. Even though ratios, or fractions, are derived by going backwards on the number line from 1 and approaching zero, they do not represent absolute quantities. For instance, 1/2 can be one-half of any quantity, not just one: one-half of a million, one-half of 500, and so on. I really "grokked" this concept after studying Harry Partch's book "Genesis of a New Music", where he explains intervals as ratios. A guitar neck gets more crowded and spaces get smaller as you go up the octaves, but a "G" is still a "G". That's why we have the "cents" system in tuning, because the Hz "number line" keeps getting proportionally bigger, i.e. A-110, A-220, A-440, A-880, etc. and the cents line evens it all out. ••• So back to quarter notes: one-quarter of a whole note, sure, but that's a proportion, not an absolute quantity like "one bar". Ratios are relationships between things, not fixed quantities. Hey, that's Art; the Greeks and their Golden Mean. Might I suggest you read "The Divine Proportion" or one of the many "layman's math" books on the subject of the Golden Ratio, nature's numbers, etc. ••• I started studying all this stuff harder when I was faced with some problems at work (a tuned wind chime factory) making tunings from customers who submitted their requests in Hz, not notes; or "solfeggio" tunings and other weird requests. ••• A musician friend of mine examined the Harry Partch book and commented "What practical use could this be?" It turns out that Partch's info on ratios and tuning tables has been invaluable in my job, and somewhat ironically, this friend now makes his living as a piano tuner. (?) Maybe someday all this info will sneak up and bite him on the ass. •••• I know I'm veering off-topic, but "it's all related, man...it's all one." I'll go start another thread if you'd like. Peace, BR •••

BR,

I don't think you're off-topic at all. In fact, just the opposite; I think this is precisely the point. You are correct that the terms whole, half, quarter, etc. are ambiguous and don't necessarily refer to exact portions of a musical meter. Moreover, they don't necessarily mean any particular thing. Rather, they are applied (math is an "applied" science) to units or fractions of anything...including other fractions!! For instance, you could easily have 1/4 of 1/2 of something (and that's a relatively simple example!). Jay and I agreed on this point earlier.

BUT, when it comes to a group of musicians attempting to collectively interpret the work of some composer, it seems necessary that there be an agreed system so a "trainwreck" doesn't happen immediately after the count off. The system most often used today (universally, I think) is the statement of a time signature. Time signatures, as I already explained, borrow terminology local to the meter 4/4, and apply that terminology to any other meter regardless of its numeric base (thus Jay's remark about "double think"!!!).

Anyway, my personal problem w/ the system as used today is that the terms half, quarter, 8th and so on seem to refer to fractals of some given unit. That unit, in my estimation, is the whole note in 4/4. If someone knows that this ISN'T the case, please let me know!!! I can't help but think back to that note tree that gets crammed down everyone's throats when first learning music. You know:

whole =
half -- half =
quarter -- quarter -- quarter -- quarter =
8th -- 8th -- 8th -- 8th -- 8th -- 8th -- 8th -- 8th =
etc.

Later, when learning odd time, we apply the above system, but only change the top number of the time signature. Meanwhile, the bottom number remains in reference to the whole note in 4/4. Enter "double think", where the terms half, quarter, etc. no longer retain their original stated meaning, but, ironically, they retain the same names! The musician is expected to mentally adjust his/herself to the error in the system, when, in reality, there is a simple, much less confusing answer.

How did this come about? I mean, when you think about scales and how they are applied, why can't we be lax about that??? Ha! Not gonna work. Is the IV the same in C major as in F major? Nope! So we have a system in place whereby the IV is referred to generically via Roman Numerals, but if you check the key signature you'll come to know specifically what the IV refers to for a given piece.

Why can't there be an analogous system for time? Could it be that people, generally, don't take rhythm & meter as seriously as tonal concerns? Could be. I'd hope, however, that as music progresses rhythm becomes of serious concern so as to allow some really magical things to happen.

[Bill Robinson]

••• Slant, thanks for explaining some of the earlier posts. I was having a hard time following what you guys were getting at, but it's beginning to make more sense now. I've got some pondering to do now. The analogy with Roman numerals was especially helpful, as I am more familiar with pitch-related phenomena. I guess what you mean by adjusting to an odd meter when reading is a matter of ignoring the literal nomenclature of "quarter", "eighth", etc. and seeing the notes simply as "entities" in the context of the meter. This can only be done by "just doing it" over and over, in different contexts. ••• There are instances where traditional musical terminology is discarded in favor of a more logically consistent method; for instance, the books "Basic Atonal Theory" by Rahn and "Introduction to Post-Tonal Theory" by Straus, in which a number line is used to identify pitches. These are concerned with pitch only as material for creation of new forms. If similar texts do not already exist for rhythm, perhaps you will be the one who writes it. ••• Talk about obscure tomes, but if you can find a copy of "die Reihe" number 3 /pub. Universal Edition (maybe a university library would have it), there's an essay in there by Karlheinz Stockhausen entitled "How Time Passes" that is very illuminating. Guys like this pondered the seemingly simple "givens" long and hard, and scrapped tradition when necessary. ••• By the way, pitch and rhythm are really aspects of the same vibrational continuum, as Stockhausen demonstrates (with sound, not theory) in "Kontakte" (on the Wergo label) when he takes a pitch gradually down until you can hear the beats of the frequencies morph into a rhythm. I have created similar effects by cranking up the tempo on a drum machine until it screams a pitch. That's almost as good as in "Hymnen" where he turns a goose-honk into the French National Anthem (I'm not kidding here). Keep exploring, and thanks again for your gracious reply. Peace, BR

[Phil Kelly]

Most jazz players now a days play their eighth notes more straight than swung. The swing is still there, but it's not as rigid as a 12/8 type of feel. That is why there is the use of 4/4 and triplets and so forth. What's the big deal? it's really not that difficult.


The normal contiuum of the progression of triplet to even eights feel in a "jazz" or "swing" genre is basically related to the prevailing tempo rate: The slower the tempo the more prounced the triple division will seem ..as the pace accelates , the notes tend to "flatten out" closer to even eighths.

Other styles ( like latin , bossa nova, R&B, and some fusion styles ) utilize more even eighth /sixteenth based divisions at all tempos. In fact, it's become the norm to notate "funk" rhythms in 16th based divisions.

The one digression I personally use is when notating hip -hop type lines ( which are basically funk rhythms played with a tight swing feel ), I put at the beginning of the chart a note that says:

"hip hop feel" ( four 16th notes = six 16th sextuplet
with the 2nd and 5th notes shown as rests )

[LDGuy]

math is an "applied" science.

Er, isn't science applied mathematics? Maths looks to describe interaction between numbers, through created mathematical techniques; science uses these techniques to help create theories about the natural world, right?

[Slant]

Er, isn't science applied mathematics? Maths looks to describe interaction between numbers, through created mathematical techniques; science uses these techniques to help create theories about the natural world, right?

LD,

You might be right, but here's my take on it: the "natural" world gave rise to the idea of number in the mind. In fact, it was necessary that we should distinguish one thing from another, primarily so as to go about getting food. So, really, getting to know numbers at one time was seen as much better than the alternative!! It's almost as though Man, once he/she recognized them, tried to apply numbers so as to overcome nature...if you get my drift.

By compiling these numbers (things) together we came to recognize addition, and by consuming things we uncovered the notion of subtraction. Likewise, by grouping things we came across multiplication and it's opposite, division. So, really, to call them 'created mathematical techniques' is quite correct, but not "created" as in a cabal of man's doing. We merely put a name on operations that were already occuring. The "4 operations", as they're called, were necessary and "natural" developments just like plant growth.

So you can see now what I meant when I said that math is an "applied" science. In other words, musicians apply math to sound patterns. It might have been better to say that numbers are an applied science.

As to your question about science, in the sense of university/government research, I can't really say. I'm definitely no scientist!