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2/2, 4/4, 8/8 etc. are equivalent time signatures. Why? Well if you multiply the tempo by 2 going from 4/4 to 2/2 it sounds the same. It also sounds the same going that way if you keep the tempo but multiply the note length by 2. Opposite true for 2/2 -> 4/4 and 4/4 -> 8/8.
60 quarters per minute = 30 halfs per minute = 120 eighths per minute so halfing the tempo for the 8/8 and multiplying the tempo for 2/2 would make them all 60 BPM.
Similar things go for 3/4, 6/8, 12/16 etc. and 2/4, 4/8, 8/16 etc. and 5/4, 10/8, 20/16 etc. and so on for every existing time signature with quarters as the beat.
It gets a little more complicated once you enter dotted notes and double dotted notes and triple dotted notes into the mix but overall for 1 time signature to sound the same as a different one, if the different one has notes twice the length as the beat than either multiply the tempo by 2 with the same note length or multiply the note length by 2 keeping the same tempo and opposite if the other time signature has beats half the length.
Last edited by caters; 07/09/14 08:14 PM.
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2/2, 4/4, 8/8 etc. are equivalent time signatures. That's right, they are all the same as 97/97. I like that time signature (I've just completed my magnum opus using it), because it uses the highest prime number that's below 100. My next Mega-magnum opus will have a time signature of 997/997. Following that, I'll use 9973/9973.
If music be the food of love, play on!
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and there have been irrational time signatures like e/pi and (1/pi)/sqrt 2 and (sqrt 2)/2. But how could you have a note of length pi be played at exactly length pi or a note of sqrt 2 be exactly sqrt 2? How do they get e pi length notes or 1/pi sqrt 2 notes or sqrt 2 half notes?
Last edited by caters; 07/09/14 08:30 PM.
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2/2, 4/4, 8/8 etc. are equivalent time signatures. That's right, they are all the same as 97/97. I like that time signature (I've just completed my magnum opus using it), because it uses the highest prime number that's below 100. My next Mega-magnum opus will have a time signature of 997/997. Following that, I'll use 9973/9973. The best piece I ever wrote was in the time signature Infinity/4. I started it in 3800 BCE and as of now I've barely finished the introduction. And I haven't used a single barline.
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Polyphonist
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Before this thread goes away, Caters, are you asking something? Cause I didn't see a question there, but your notion on what a time signature is, is WAY off!
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2/2, 4/4, 8/8 etc. are equivalent time signatures. Why? Well if you multiply the tempo by 2 going from 4/4 to 2/2 it sounds the same. ... Just the opposite. Take a piece in 4/4 with tempo specified as 60 beats per minute. Change the signature to 2/2. If you want it to sound "the same" you would specify the tempo as 30 beats per minute. You cut the tempo in half, not double it.
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And 2/2 does not sound like 4/4, even if the notes are played at the same speed. If you do not know that, you do not know music.
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Well if you multiply the tempo by 2 going from 4/4 to 2/2 it sounds the same. It also sounds the same going that way if . . . Time signatures do not have a sound, meter does.
Michael
"Genius is nothing more than an extraordinary capacity for patience." Leonardo da Vinci
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Writing music in 4/4 and 2/2 looks the same on the page, but it is implied that the feel is different. 2/2 is generally a march (2 beats per bar - S w | S w |, while 4/4 is the more common feel of S w w w | S w w w ).
Anyway, that's the way I've come to think of it.
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Caters - What a waste of 'time'! The only 'time' signature YOU need is 1/1, since you state all other fractions following the sequence 2/2,3/3,4/4,... are equivalent, including pi/pi, red/red, salmon/salmon, nerd/nerd, psycho/psycho, et cetera.
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Saying that 3/4 and 6/8 are the same is particularly misguided, since 6/8 is a compound time signature, divided into 2 groups of 3, giving it a completely different feel than the three distinct pulses in 3/4.
"If peeing your pants is cool, consider me Miles Davis."
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And yet, there is sense to be made from the OP's statement.
3/4 and 6/8 are "equivalent" in the sense that both signatures contain the same number of quarter notes per measure, the same number of eighth notes per measure, etc. From the point of view of pure counting, they are, perhaps, the same.
But from the point of view of the way the signature feels, and how many "beats" it has, of course they're different, as people have mentioned. But I think this additional idea is often not taught carefully.
-J
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2/2, 4/4, 8/8 etc. are equivalent time signatures. Why? Well if you multiply the tempo by 2 going from 4/4 to 2/2 it sounds the same. ... Just the opposite. Take a piece in 4/4 with tempo specified as 60 beats per minute. Change the signature to 2/2. If you want it to sound "the same" you would specify the tempo as 30 beats per minute. You cut the tempo in half, not double it. you do double it. Let me show you again: 60 quarters per minute = 30 halfs per minute = 120 eights per minute. This is all assuming 60 BPM to the quarter in 4/4. If you want them all to be 60 BPM(and thus sound the same)than you half the tempo in the 8/8 so that the eighths feel like quarters and you double the tempo in the 2/2 to make the halfs feel like quarters. Similar things for 3/4, 6/8, 12/16 etc. Take a 6/8 time signature and a certain tempo. The 3/4 is going to sound slower at 60 quarters per minute and the 12/16 is going to sound faster at that same QPM(quarters per minute) because in the 3/4 the beats are quarters and in 12/16 the notes played at the length of a quarter in 4/4 or any x/4 time signature are 16ths. Thus the same math applies as with 2/2, 4/4, and 8/8. also 6/8 can be viewed as compound triple or compound duple or simple sextuple. why can it be viewed as simple sextuple? Because 4/8 = simple quadruple and 3/8 = simple triple and so because sextuple meter does in fact exist all the 6 beat time signatures like 6/2, 6/4, 6/8 etc. can be viewed as simple sextuple. In the same way 4/4 can be viewed as simple quadruple(because it has 4 distinct beats), compound duple(because at fast speeds you hear 2/2 in 4/4), or simple duple(because it is simply 2 2/4 measures and 2/4 is simple duple)
Last edited by caters; 07/10/14 04:36 PM.
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Time signatures A and B such that A = m/n for some positive integers m and n, and B = cm/cn for some positive integer c are mathematically equivalent. The implication when writing a score in B instead of A is a musical one, not a mathematical one.
Mathematical equivalence, musical non-equivalence.
Lol, I thought every musician knew this.
Last edited by Atrys; 07/10/14 05:51 PM.
"A good intention but fixed and resolute - bent on high and holy ends, we shall find means to them on every side and at every moment; and even obstacles and opposition will but make us 'like the fabled specter-ships,' which sail the fastest in the very teeth of the wind." R. W. Emerson
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Lol, I thought every musician knew this. Every musician does know this.
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Take a 6/8 time signature and a certain tempo. The 3/4 is going to sound slower at 60 quarters per minute and the 12/16 is going to sound faster at that same QPM(quarters per minute) because in the 3/4 the beats are quarters and in 12/16 the notes played at the length of a quarter in 4/4 or any x/4 time signature are 16ths.
Thus the same math applies as with 2/2, 4/4, and 8/8.
also 6/8 can be viewed as compound triple or compound duple or simple sextuple.
I'd be laughing out loud if this wasn't so sad. You are either ignoring music theory and history or are ignorant of it. The math may be equivalent, but the music is not. A previous poster defined the strong and weak beat differences between 2/2 and 4/4. Other have stated the musical differences between 3/4 and 6/8. Allow me to reiterate 6/8 is always a compound duple meter. If you really want a sextuple you'd write in sixteenth notes in 3/8 as Bach did in the d minor invention.
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Gary
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2/2, 4/4, 8/8 etc. are equivalent time signatures. That's right, they are all the same as 97/97. I like that time signature (I've just completed my magnum opus using it), because it uses the highest prime number that's below 100. My next Mega-magnum opus will have a time signature of 997/997. Following that, I'll use 9973/9973. The best piece I ever wrote was in the time signature Infinity/4. I started it in 3800 BCE and as of now I've barely finished the introduction. And I haven't used a single barline. On a serious note, Satie frequently wrote pieces without bar lines. For instance: http://petrucci.mus.auth.gr/imglnks/usimg/d/d5/IMSLP00904-Gnossienne_1-a4.pdf
Last edited by Brad Hoehne; 07/11/14 11:39 AM.
1999 Petrof 125-111 (upright) Casio Privia PX-330
Currently working on: Chopin Etude op 25 #2 and op 10 #5 Schubert Op 90 #2, #3 Playing by ear and "filling out" pop tunes
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2/2, 4/4, 8/8 etc. are equivalent time signatures. Why? Well if you multiply the tempo by 2 going from 4/4 to 2/2 it sounds the same. ... Just the opposite. Take a piece in 4/4 with tempo specified as 60 beats per minute. Change the signature to 2/2. If you want it to sound "the same" you would specify the tempo as 30 beats per minute. You cut the tempo in half, not double it. you do double it. Let me show you again: 60 quarters per minute = 30 halfs per minute = 120 eights per minute. This is all assuming 60 BPM to the quarter in 4/4. If you want them all to be 60 BPM(and thus sound the same)than you half the tempo in the 8/8 so that the eighths feel like quarters and you double the tempo in the 2/2 to make the halfs feel like quarters. ... Now I'm gathering that by "going from 4/4 to 2/2" you don't mean just changing the signature, so I'm trying to understand what you're getting at. Take for example Chopin's c minor Prelude no. 20. It's in 4/4 with the left hand part proceeding in quarter notes, say for the sake of argument at 60 per minute. How do you propose to change this to 2/2? Rewrite it so the left hand chords are half notes, and make the piece twice as many measures long? And set the metronome at half note = 60?
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basically and if you were wanting it in 8/8 and to feel like 8/8 you would do the exact opposite of making there be half as many measures, halfing the length of each note so that quarters become eighths and setting the tempo at eighth note = 60
now would 8/8 be a compound quadruple(because of how 1 8/8 measure = 2 4/8 measures and 4/8 is a quadruple meter just like how 1 4/4 measure = 2 2/4 measures), simple quadruple(because at slow tempos you can hear 8 distinct beats and 8 is a multiple of 4), or simple octuple(because of the 8 beats per measure)?
And why is 4/4 always viewed as a simple meter when you could say it is compound duple because of how 2 2/4 measures fit into 1 4/4 measure and at very fast tempos you might hear only 2 beats instead of the whole 4.
and at slow tempos you can hear all 6 beats in 6/8, all 9 in 9/8, and all 12 in 12/8. Same thing for 16th time signatures and time signatures with shorter notes. Thus a slow 6/8 is basically sextuple and a slow 9/8 is nonuple and a slow 12/8 is dodecuple.
Last edited by caters; 07/13/14 02:18 AM.
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