 |
Welcome to the Piano World Piano Forums
Over 3 million posts about pianos, digital pianos, and all types of keyboard instruments.
Over 100,000 members from around the world.
Join the World's Largest Community of Piano Lovers
(it's free)
It's Fun to Play the Piano ... Please Pass It On!
|
|
|
|
57 members (brdwyguy, accordeur, Carey, AlkansBookcase, 20/20 Vision, Charles Cohen, 36251, benkeys, bcalvanese, 6 invisible),
1,896
guests, and
276
robots. |
|
Key:
Admin,
Global Mod,
Mod
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
Yes - I mentioned tuplets earlier, and I suspect that he doesn't really know what they are. They are groups of a certain kind of note in the length of the regular note like eight note triplet in the length of an eighth note for example or 2 quarters in the length of 1.
|
|
|
|
|
Joined: Mar 2013
Posts: 9,328
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Mar 2013
Posts: 9,328 |
Nope. We seem to have discovered the source of the issue. 
Regards,
Polyphonist
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
I see no point in a 4/3 time signature if it would serve exactly the same purpose as 4/4. The reason they exist is so that there are more polyrythms possible.
|
|
|
|
|
Joined: Mar 2013
Posts: 9,328
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Mar 2013
Posts: 9,328 |
Regards,
Polyphonist
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
4/4 and 4/3 together, 2/6 and 3/4 together, and even 2/5 and 2/3 together.
With the 4/4 and 4/3 you have 3 beats in 4/3 for every 4 beats in 4/4.
With the 2/6 and 3/4 you have 6 beats of 2/6 for every 4 beats of 3/4.
With the 2/5 and 2/3 you have 5 beats of 2/5 for every 3 beats of 2/3.
Last edited by caters; 04/05/14 04:52 PM.
|
|
|
|
|
Joined: Mar 2013
Posts: 9,328
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Mar 2013
Posts: 9,328 |
How would that work? In one measure of 4/3 you would have one measure of 4/4 plus an extra third, now would you cut that off and start it over or would you finish the 4/4 measure at the same time as you started the next 4/3 measure? Then that 4/4 measure would finish halfway through the 4/3 measure, and the 4/3 measure would finish 2/3 of the way through the third 4/4 measure...
Regards,
Polyphonist
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
With the 4/4 and 4/3 you have 3 beats in 4/3 for every 4 beats in 4/4.
You would just continue with the polyrhythm and not cut it off every time a 4/4 or 4/3 measure starts.
Last edited by caters; 04/05/14 05:01 PM.
|
|
|
|
|
Joined: Mar 2013
Posts: 9,328
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Mar 2013
Posts: 9,328 |
So you would have 4 4/4 measures against 3 4/3 measures? That would just be a normal 4 on 3 with some distorted bar placements.
Regards,
Polyphonist
|
|
|
|
|
Joined: Mar 2013
Posts: 9,328
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Mar 2013
Posts: 9,328 |
I know what a polyrhythm is. You seem not to understand that your 4/3 time signature doesn't allow you to do anything you can't already do.
Regards,
Polyphonist
|
|
|
|
|
Joined: Oct 2012
Posts: 1,031
1000 Post Club Member
|
|
1000 Post Club Member
Joined: Oct 2012
Posts: 1,031 |
Yes but that gives me 3/128 = (3/2)/64 or a dotted 64th.
512 = 2^9
256 = 2^8
128 = 2^7
64 = 2^6
32 = 2^5
16 = 2^4
8 = 2^3
4 = 2^2
So per whole note these are the dotted notes:
Dotted 256th: 170 2/3(256th notes have been used in early classical music. Some of Mozart's pieces include these. An example is Variations on Je suis Lindor, K. 354.)
Dotted 128th: 85 1/3
Dotted 64th: 42 2/3
Dotted 32nd: 21 1/3
Dotted 16th: 10 2/3(this is what the LCM gave me for dotted 32nds. I guess the LCM does work just not the way I thought it did)
Dotted 8th: 5 1/3
Dotted quarter: 2 2/3
Dotted half: 1 1/3
Dotted whole: 2/3
Dotted double whole: 1/3
Dotted Quadruple whole(longa): 1/6
Dotted Octuple Whole: 1/12(octuple whole is 8 and longa added to it makes 12)
You notice how with each of these as the note gets longer there are half as many per whole note. Thus the number of dotted notes per whole goes at the same pace as the powers of 2 but instead of increasing it decreases. You need to recheck your math...
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
It is correct. I would have gotten those same numbers have I divided the number of regular notes per whole by 6 and than multiplied that by 4.
|
|
|
|
|
Joined: Oct 2012
Posts: 1,031
1000 Post Club Member
|
|
1000 Post Club Member
Joined: Oct 2012
Posts: 1,031 |
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
Really I have no mistakes in those numbers, especially the ones for notes greater in length than a whole note.
Last edited by caters; 04/05/14 09:23 PM.
|
|
|
|
|
Joined: Apr 2009
Posts: 6,427
6000 Post Club Member
|
|
6000 Post Club Member
Joined: Apr 2009
Posts: 6,427 |
I think you might have missed the sarcasm.  Thanks to quick action on the part of my velum I avoided having beer spit out my nose whilst reading this post.
Learner
|
|
|
|
|
Joined: Nov 2007
Posts: 9,395
9000 Post Club Member
|
|
9000 Post Club Member
Joined: Nov 2007
Posts: 9,395 |
You can just have a 4/4 bar, write 5 quarter notes,and then write a little 5 underneath....I don't understand why all you need all of the dots. Indeed - the standard tuplet notation works. Unless an example can be described where already-established ways of notation will not work, this thread seems to be an exercise in wasting time. I have nothing against experimental approaches, if there's a point to them, but I don't see the point of trying to re-invent the wheel.
|
|
|
|
|
Joined: Apr 2007
Posts: 999
500 Post Club Member
|
|
500 Post Club Member
Joined: Apr 2007
Posts: 999 |
any note dotted would represent a different integer. Any double dotted note would represent a different integer Example:
dotted quarter = quarter + eighth which equals 1/4 + 1/8 = 3/8 time per beat if based on dotted quarter. That would give you this set of time signatures:
2/(3/8) = 16/3 which is the reciprocal of 3/16, 3/(3/8) = 8 so no good here, 4/(3/8) = 32/3 for 4 dotted quarter beats, 64/3 for 8 dotted quarter beats, 40/3 for 5, 56/3 for 7, 80/3 for 10,and 88/3 for 11 dotted quarter beats.
You just have to take the duration in this case 3/8, put it in the denominator of a fraction and simplify the complex fraction with whichever numerator you want. as long as it does not turn into a whole number its fine.
So dotted half would have a 5 in the denominator and so 5 would represent dotted half beat because it is 5/8 time per beat based on dotted half which would give you this set of time signatures: 16/5 for 2, 24/5 for 3, 32/5 for 4, 48/5 for 6, 56/5 for 7, 64/5 for 8, 72/5 for 9, 88/5 for 11, and 96/5 for 12 dotted half beats. By similar rules dotted whole beats would be represented by a 13 in the denominator,dotted wholes with 24. Dotted quarters to dotted double wholes add 8 for each number of beats.
Similar things would go for double dotted notes except you now have to do it with complex fraction in which the denominator of the denominator is 16.
But this clearly illustrates that time signatures can be numbers that aren't powers of 2 No, it does not illustrate that at all (assuming you mean that time signatures can have denominators that are not powers of 2.) The construction you describe is not consistent with the established definition of time signature. Suppose you were explaining to a complete beginner what a time signature is. You would say, start with a fraction of a whole note, and decide how many of those units shall make up one measure. Multiply the two numbers to yield a new fraction, and the result is the time signature. For example, a quarter-note is 1/4 of a whole note, and if we want two per measure then multiply 1/4 x 2 to yield the time signature 2/4. If instead we take a dotted quarter as the unit, that is 3/8 of a whole note. If we want two per measure, multiply 3/8 x 2 to yield the time signature 6/8. In your construction, you are dividing the number of units by the unit fraction, instead of multiplying. What is the justification for this? There is no basis for these odd-numbered denominators. By the way, a dotted half is 6/8 of a whole note, not 5/8 as you wrote. Even following your construction rule, there would never be a 5 in the denominator.
Last edited by Ferdinand; 04/06/14 01:06 AM. Reason: fixed error
|
|
|
|
|
Joined: Feb 2014
Posts: 262
Full Member
|
|
OP
Full Member
Joined: Feb 2014
Posts: 262 |
any note dotted would represent a different integer. Any double dotted note would represent a different integer Example:
dotted quarter = quarter + eighth which equals 1/4 + 1/8 = 3/8 time per beat if based on dotted quarter. That would give you this set of time signatures:
2/(3/8) = 16/3 which is the reciprocal of 3/16, 3/(3/8) = 8 so no good here, 4/(3/8) = 32/3 for 4 dotted quarter beats, 64/3 for 8 dotted quarter beats, 40/3 for 5, 56/3 for 7, 80/3 for 10,and 88/3 for 11 dotted quarter beats.
You just have to take the duration in this case 3/8, put it in the denominator of a fraction and simplify the complex fraction with whichever numerator you want. as long as it does not turn into a whole number its fine.
So dotted half would have a 5 in the denominator and so 5 would represent dotted half beat because it is 5/8 time per beat based on dotted half which would give you this set of time signatures: 16/5 for 2, 24/5 for 3, 32/5 for 4, 48/5 for 6, 56/5 for 7, 64/5 for 8, 72/5 for 9, 88/5 for 11, and 96/5 for 12 dotted half beats. By similar rules dotted whole beats would be represented by a 13 in the denominator,dotted wholes with 24. Dotted quarters to dotted double wholes add 8 for each number of beats.
Similar things would go for double dotted notes except you now have to do it with complex fraction in which the denominator of the denominator is 16.
But this clearly illustrates that time signatures can be numbers that aren't powers of 2 No, it does not illustrate that at all (assuming you mean that time signatures can have denominators that are not powers of 2.) The construction you describe is not consistent with the established definition of time signature. Suppose you were explaining to a complete beginner what a time signature is. You would say, start with a fraction of a whole note, and decide how many of those units shall make up one measure. Multiply the two numbers to yield a new fraction, and the result is the time signature. For example, a quarter-note is 1/4 of a whole note, and if we want two per measure then multiply 1/4 x 3 to yield the time signature 3/4. If instead we take a dotted quarter as the unit, that is 3/8 of a whole note. If we want two per measure, multiply 3/8 x 2 to yield the time signature 6/8. In your construction, you are dividing the number of units by the unit fraction, instead of multiplying. What is the justification for this? There is no basis for these odd-numbered denominators. By the way, a dotted half is 6/8 of a whole note, not 5/8 as you wrote. Even following your construction rule, there would never be a 5 in the denominator. Well dividing a number by a fraction the same as multiplying by the reciprocal of the fraction. Also there are irrational meters that are actually used occasionally like 4/3 for instance.
|
|
|
|
|
Joined: Apr 2007
Posts: 999
500 Post Club Member
|
|
500 Post Club Member
Joined: Apr 2007
Posts: 999 |
any note dotted would represent a different integer. Any double dotted note would represent a different integer Example:
dotted quarter = quarter + eighth which equals 1/4 + 1/8 = 3/8 time per beat if based on dotted quarter. That would give you this set of time signatures:
2/(3/8) = 16/3 which is the reciprocal of 3/16, 3/(3/8) = 8 so no good here, 4/(3/8) = 32/3 for 4 dotted quarter beats, 64/3 for 8 dotted quarter beats, 40/3 for 5, 56/3 for 7, 80/3 for 10,and 88/3 for 11 dotted quarter beats.
You just have to take the duration in this case 3/8, put it in the denominator of a fraction and simplify the complex fraction with whichever numerator you want. as long as it does not turn into a whole number its fine.
So dotted half would have a 5 in the denominator and so 5 would represent dotted half beat because it is 5/8 time per beat based on dotted half which would give you this set of time signatures: 16/5 for 2, 24/5 for 3, 32/5 for 4, 48/5 for 6, 56/5 for 7, 64/5 for 8, 72/5 for 9, 88/5 for 11, and 96/5 for 12 dotted half beats. By similar rules dotted whole beats would be represented by a 13 in the denominator,dotted wholes with 24. Dotted quarters to dotted double wholes add 8 for each number of beats.
Similar things would go for double dotted notes except you now have to do it with complex fraction in which the denominator of the denominator is 16.
But this clearly illustrates that time signatures can be numbers that aren't powers of 2 No, it does not illustrate that at all (assuming you mean that time signatures can have denominators that are not powers of 2.) The construction you describe is not consistent with the established definition of time signature. Suppose you were explaining to a complete beginner what a time signature is. You would say, start with a fraction of a whole note, and decide how many of those units shall make up one measure. Multiply the two numbers to yield a new fraction, and the result is the time signature. For example, a quarter-note is 1/4 of a whole note, and if we want two per measure then multiply 1/4 x 3 to yield the time signature 3/4. If instead we take a dotted quarter as the unit, that is 3/8 of a whole note. If we want two per measure, multiply 3/8 x 2 to yield the time signature 6/8. In your construction, you are dividing the number of units by the unit fraction, instead of multiplying. What is the justification for this? There is no basis for these odd-numbered denominators. By the way, a dotted half is 6/8 of a whole note, not 5/8 as you wrote. Even following your construction rule, there would never be a 5 in the denominator. Well dividing a number by a fraction the same as multiplying by the reciprocal of the fraction. Also there are irrational meters that are actually used occasionally like 4/3 for instance. I stand by my argument.* As for the actual use of 4/3, I'll take your word for it. However I still believe your exposition provides no mathematical basis for it. By the way 4/3 is not irrational. * though I made an error, which I fixed in my previous post, but not before you quoted it. It should say, if we want two per measure then multiply 1/4 x 2 to yield the time signature 2/4.
|
|
|
|
|
Joined: Jul 2013
Posts: 566
500 Post Club Member
|
|
500 Post Club Member
Joined: Jul 2013
Posts: 566 |
Also there are irrational meters that are actually used occasionally like 4/3 for instance. Would you mind giving an example of a piece or song with a time signature of 4/3? I have not come across music with such a time signature.
|
|
|
|
Forums43
Topics223,392
Posts3,349,293
Members111,634
| |
Most Online15,252
Mar 21st, 2010
|
|
|
|
|
|
|
