You only get 5 extra notes on a 7 string.

[eaeolian]

I've mostly played 7 string for the last 10 years, tuned E,A,D,G,C,F,Bb, with a special high treble string.

I'm thinking of converting one of my 7 string guitars to a low string instead of a high treble.

My purpose in this post was asking fellow 7 stringers if it was worth changing for the extra 5 bass notes?

I'm nearly convinced, due to advantages in playing chords and positional playing, but I find 6 string much easier to play, having played guitar for over 45+ years.

We use them in Division because it allows to use lower root notes for songs while still playing our full catalog, since we use chord forms that have the open high E in some songs.

 

[bostjan]

That's not what any of that means.

LOL, well, not precisely, except kinda yeah. You're just being a fun governor, and your criticism seems very silly to me, and I'll get to why in a moment. If you had left it at this, you would have made me feel bad for posting what I posted, but as it stands, I more or less feel bad for you, who seems like the kid who stands up to correct someone making a joke and then proceeds to misspeak.

Infinity doesn't imply countability because there are countable and uncountable infinities.

This is absolutely correct. My language was reckless, but in my defense, I did carefully clarify.

Aleph one describes an uncountable infinity. To say it's bigger than infinity makes no sense because it is infinity.

That's exactly what I said, though.

Uncountable infinities are "bigger" than countable infinities, but the word "bigger" has a different meaning in this context. The key point being that in two sets, say the reals R and the integers Z, you can systematically give a name to (count) every Z and but you can't give a name to every R. They both go on forever in both directions though so they both have infinity numbers in them. You can't do arithmetic with infinities for this reason and that is why "bigger" means a different thing here.

Which is also what I said.

Similarly, Z and N both have countably infinite numbers, and both aleph-0, but Z contains approximately twice as many numbers. But since every Z can be mapped onto an N they have the same number of elements. Because 2 times infinity doesn't have any meaning.

Which is, again, the same gist as what I said.

Same with "size". You're using its set theory meaning while talking about something outside of set theory. Cardinality of infinite sets is not the same as size in the lay sense. There is a different number of elements in R and Z because Z is a subset of R, but again infinity plus x is the same as infinity, by definition, and what is being described here is an endless number.

Firmly disagree with you here. Not sure why you would try to imply that the set of all reals is the same size as the set of all natural numbers, since you clearly grasp the concept.

All that is to say, uncountable notes is the same as infinity notes and this is some very bad maths.

I'd propose that me saying uncountable notes is more than countable notes is better mathematics than you saying they are the same size sets of notes.

Also "you have aleph-one notes" doesn't make any sense because that is not a number.

You saying aleph-one is not a number is also incorrect. It is a number that represents the size of a set of uncountable elements. If you disagree, then you've got some weird definitions of concepts. Feel free to have weird definitions, though. This is a guitar forum, not a mathematics forum, so you do you.

Overall, I agree that my post was silly. But your post has more egregious mistakes than mine. Take that however you'd like.

 

[CanserDYI]

Ahh yes, I understand, fully. Maybe explain for the rest of the forum, in like really small words so my, I mean their, brains can comprehend it?

 

[jaxadam]

Ahh yes, I understand, fully. Maybe explain for the rest of the forum, in like really small words so my, I mean their, brains can comprehend it?

If you lived for an infinite amount of time, you'll do everything an infinite amount of time, but some of the things you do would be a smaller infinity than the other. For example, you may brush your teeth twice a day, but eat three times a day (or in my case six). Your teeth brushing infinity will be smaller than your eating infinity. Now, all of the possibilities in between your teeth brushing and eating will be a much larger infinity of uncountable events.

 

[jaxadam]

Actually, let's just put this to bed with the following example:

The amount of threads vejichan starts vs the amount of threads vejichan replies to is a MUCH LARGER INFINITY.

 

[CanserDYI]

If you lived for an infinite amount of time, you'll do everything an infinite amount of time, but some of the things you do would be a smaller infinity than the other. For example, you may brush your teeth twice a day, but eat three times a day (or in my case six). Your teeth brushing infinity will be smaller than your eating infinity. Now, all of the possibilities in between your teeth brushing and eating will be a much larger infinity of uncountable events.

Love it. Where were you three when I was sleeping in high school math?

 

[bostjan]

Ahh yes, I understand, fully. Maybe explain for the rest of the forum, in like really small words so my, I mean their, brains can comprehend it?

Probably not worth it at this point, but, wtf, I'm into all things that aren't worth it:

In mathematics, there is a concept called a "set," which is more or less exactly what it sounds like. All of the things in the set have (mathematicians call the things in a set "elements" of the set) a relation that puts them in the set, like "the set of all numbers" - is a set that contains anything that is a "number." Or the set of all numbers that begin with the letter "f," which would be four, five, fourteen, fifteen, forty, forty one, etc. Both of those sets are infinite, meaning that they have no end. The concept of infinity is a little bit wacky, since playground kids will use it like it's a usual number "I call dibs," "oh yeah, I call dibs times two!" "I call dibs times infinity" "I call dibs times infinity times two!!!" But, well, all numbers are just a concept, but infinity is a different sort of concept. Infinity is really a number, but it's a number defined as exceeding assignable quantity, such that "infinity plus one" is just infinity, or, probably more correctly, nonsense.

So, the set of all numbers that are the number one, has one element, the number one. The set of all sets that contain the number one can also be a set, because a set doesn't have to contain just numbers - it can contain whatever things you want. You could also make a set that is the number one and the set of all things that contain the number one, so that set would contain numbers and sets and even itself.

You can also have an empty set that contains nothing. The set of the number zero is not an empty set, because it contains a number, zero, so the concept of an empty set is distinctly different from the concept of zero. But the two concepts are linked, because the number of elements (how many things) inside of the empty set is zero. Going back to a goofy example, the set of all empty sets is not an empty set, because it contains an empty set.

So a lot of sets are infinite sets. Those are sets that contain more elements than you could ever assign a numerical value to represent. The set of all "natural numbers" is the set that contains 1, 2, 3, 4, 5, 6, 7, ..., where the "..." means that it just keeps going. If you assign a value to a number, "x", such that x is a natural number, no matter which number you choose, you can always do something to make x bigger and still have x be a natural number. Pick the biggest number you can think, and then add one, and it's still a natural number, so the set of all natural numbers is an infinite set.

But, mathematicians call the set of all natural numbers a countable set, because, even if you can't actually count all of the elements in the set, the concept of counting still applies, in that you could start counting the natural numbers, you could just never stop. So, that particular type of infinite set is said to have aleph-naught elements in it. Where aleph-naught is defined as the number of elements in the set of natural numbers. It is, by consequence, the smallest infinite number. I wasn't clear about that in my last post, which is what seems to have caused someone to take exception to what I said, rightfully so, I suppose.

Anyway. You might be prone to think about the set of all whole numbers next. The whole numbers are just the natural numbers, except that zero is also included. So, you might think that there are more elements in the set of all whole numbers than in the set of all natural numbers. This is where things get sticky with the logic. Since you can start counting at one or start counting at zero, and never stop counting, it's the same concept, logically. So the number of elements in the set of whole numbers is still aleph-naught.

You could also move on to the set of all "integers," defined as the set of all natural numbers, all of the negative natural numbers, and zero. Now you might want to think that you have a necessarily larger number of elements, since there is not starting point. You can't start at negative infinity and count up, but, you could be a little clever and say, start with one, and just count two at a time, one for each positive number and one for each negative number, keeping in mind that zero adds one to the total. So, again, logically, it's the same concept of infinity as trying to count all of the natural numbers.

So, where you first see an actual difference is when you move on to the set of "real numbers." So a real number is all of the natural numbers, all of the negative natural numbers, zero, all of the fractions, and all of the "irrational" numbers (numbers like pi or the square root of two or whatever, which can be approximated by decimals, but have infinite digits in them). And the difference is that you cannot even start counting them. Choose any arbitrary number, like 4.7175. What is the very next number? Is it 4.7176? Nope, because you could say 4.71751 or 4.717501 or 4.7175001 or 4.717500000000...00001... Aha, so now it's a different concept, where you have an infinite number of elements like before, you can place those infinite number of elements in order from largest to smallest like before, BUT, you can't say which element is "the next one" after any arbitrarily chosen element. So, that set has a different number of elements in it, which is what they call aleph-one.

 

[Neon_Knight_]

If you lived for an infinite amount of time, you'll do everything an infinite amount of time, but some of the things you do would be a smaller infinity than the other. For example, you may brush your teeth twice a day, but eat three times a day (or in my case six). Your teeth brushing infinity will be smaller than your eating infinity. Now, all of the possibilities in between your teeth brushing and eating will be a much larger infinity of uncountable events.

Just like the infinite number of notes will be greater with a 7 stringer compared to a 6 stringer, if both are played for an infinite amount of time.

 

[Emperoff]

This thread:

 

[bostjan]

This thread:

You mean this thread started on the rails?!

 

[Emperoff]

You mean this thread started on the rails?!

If you take a closer look to the picture, you'll realize that it ends up on the rails, so we can still hope!

 

[odibrom]

I've mostly played 7 string for the last 10 years, tuned E,A,D,G,C,F,Bb, with a special high treble string.

I'm thinking of converting one of my 7 string guitars to a low string instead of a high treble.

My purpose in this post was asking fellow 7 stringers if it was worth changing for the extra 5 bass notes?

I'm nearly convinced, due to advantages in playing chords and positional playing, but I find 6 string much easier to play, having played guitar for over 45+ years.

... and that's how you should have started this thread... I see you're tuning everything in perfect 4th intervals, which is cool. The extra range you get on the higher pitch strings when comparing a 6 with a 7 string is exactly the same if you move for the lower strings instead, keeping your string to string tuning pattern as well...

I can't answer if it was worth it comparing to a higher pitch 7th string because I never navigated those waters, when comparing to a regular 6 stringer, I feel I gained range on the low end, specially on hand position range, it's like I can have 3 octave range runs without moving my hand all over the neck. Low end chugging is also nice. You have to be aware that the amp/effects settings for a low B1 must be different that those used for a regular 6 stringer. There's a lot more low frequencies in the air that need to be accounted for in order to get the mud out, either in clean or dirty sounds.

Out of curiosity, what's the scale length of your guitars so you can get up to Bb and what string gauge are you using for it. There are threads over here about reaching out A4 on the high string...

 

[StevenC]

LOL, well, not precisely, except kinda yeah. You're just being a fun governor, and your criticism seems very silly to me, and I'll get to why in a moment. If you had left it at this, you would have made me feel bad for posting what I posted, but as it stands, I more or less feel bad for you, who seems like the kid who stands up to correct someone making a joke and then proceeds to misspeak.



This is absolutely correct. My language was reckless, but in my defense, I did carefully clarify.



That's exactly what I said, though.



Which is also what I said.



Which is, again, the same gist as what I said.



Firmly disagree with you here. Not sure why you would try to imply that the set of all reals is the same size as the set of all natural numbers, since you clearly grasp the concept.



I'd propose that me saying uncountable notes is more than countable notes is better mathematics than you saying they are the same size sets of notes.



You saying aleph-one is not a number is also incorrect. It is a number that represents the size of a set of uncountable elements. If you disagree, then you've got some weird definitions of concepts. Feel free to have weird definitions, though. This is a guitar forum, not a mathematics forum, so you do you.

Overall, I agree that my post was silly. But your post has more egregious mistakes than mine. Take that however you'd like.

What you said was "uncountable is bigger than infinity" which is very incorrect. Uncountable infinity, which is what you were trying to say, is an infinity, which you did not say.

I'm not going to bother arguing the rest with you because you've made up your mind and I can't change that. I'll apologise for taking some liberties to explain a really complicated subject to someone who was obviously grossly misunderstanding it.

Ahh yes, I understand, fully. Maybe explain for the rest of the forum, in like really small words so my, I mean their, brains can comprehend it?

In most instances, it is really only relevant to talk about the two smallest kinds of infinity: discrete and continuous.

Number of keys on a piano is a discrete number. You can, hypothetically, keep adding 12 keys onto the ends of the keyboard forever. That is to say, we can have a C1, C#, then D, then Eb, then E, ... then Bb, then B1, then C2, then... forever until we have as many notes as we want beyond even what we can hear. We can give a name to every single one of these notes, counting them.

Divisions of a vibrating string is a continuous number. You can take a fretless guitar, play a note anywhere on the neck, then move slightly in either direction and get a new note. The continuous part comes when I ask you to play the next note along. You can't play the next note because whatever note you play there will always be a note in between that and your first note.

Normally this is phrased as what is the first number between 0 and 1?, and you could say 0.1 but what about 0.05 or 0.001 or 0.0005? And the point is that wherever you start on the number line there is an infinite distance between there and not only the next whole number, but every number between and beyond you and that next whole number. There is as big a gap between 0 and 1 as there is between 0 and 0.1.

The first example is a countable infinity. There are infinite half steps higher than where we start and lower than where we start.

The second example is an uncountable infinity. There are infinite notes between C and D because the steps can be infinitesimally small.

Jaxadam's examples are both countable infinities, but they speak to the nature of infinity not being a number and the size of it being a different thing than the size of finite sets. Jaxadam has shown that you eat more than you brush your teeth, but these are both aleph-nought sized sets because they are both countable. This is an important nuance in the discussion.

 

[cardinal]

Infinite notes?

 

[TedEH]

In most instances, it is really only relevant to talk about the two smallest kinds of infinity: discrete and continuous.

In some fairness, this is what I thought of when I was reading Bostjan's post - being a non-expert, it sounds like you're describing the same thing just with different framing / semantics.

 

[GuyB]

Probably not worth it at this point, but, wtf, I'm into all things that aren't worth it:

In mathematics, there is a concept called a "set," which is more or less exactly what it sounds like. All of the things in the set have (mathematicians call the things in a set "elements" of the set) a relation that puts them in the set, like "the set of all numbers" - is a set that contains anything that is a "number." Or the set of all numbers that begin with the letter "f," which would be four, five, fourteen, fifteen, forty, forty one, etc. Both of those sets are infinite, meaning that they have no end. The concept of infinity is a little bit wacky, since playground kids will use it like it's a usual number "I call dibs," "oh yeah, I call dibs times two!" "I call dibs times infinity" "I call dibs times infinity times two!!!" But, well, all numbers are just a concept, but infinity is a different sort of concept. Infinity is really a number, but it's a number defined as exceeding assignable quantity, such that "infinity plus one" is just infinity, or, probably more correctly, nonsense.

So, the set of all numbers that are the number one, has one element, the number one. The set of all sets that contain the number one can also be a set, because a set doesn't have to contain just numbers - it can contain whatever things you want. You could also make a set that is the number one and the set of all things that contain the number one, so that set would contain numbers and sets and even itself.

You can also have an empty set that contains nothing. The set of the number zero is not an empty set, because it contains a number, zero, so the concept of an empty set is distinctly different from the concept of zero. But the two concepts are linked, because the number of elements (how many things) inside of the empty set is zero. Going back to a goofy example, the set of all empty sets is not an empty set, because it contains an empty set.

So a lot of sets are infinite sets. Those are sets that contain more elements than you could ever assign a numerical value to represent. The set of all "natural numbers" is the set that contains 1, 2, 3, 4, 5, 6, 7, ..., where the "..." means that it just keeps going. If you assign a value to a number, "x", such that x is a natural number, no matter which number you choose, you can always do something to make x bigger and still have x be a natural number. Pick the biggest number you can think, and then add one, and it's still a natural number, so the set of all natural numbers is an infinite set.

But, mathematicians call the set of all natural numbers a countable set, because, even if you can't actually count all of the elements in the set, the concept of counting still applies, in that you could start counting the natural numbers, you could just never stop. So, that particular type of infinite set is said to have aleph-naught elements in it. Where aleph-naught is defined as the number of elements in the set of natural numbers. It is, by consequence, the smallest infinite number. I wasn't clear about that in my last post, which is what seems to have caused someone to take exception to what I said, rightfully so, I suppose.

Anyway. You might be prone to think about the set of all whole numbers next. The whole numbers are just the natural numbers, except that zero is also included. So, you might think that there are more elements in the set of all whole numbers than in the set of all natural numbers. This is where things get sticky with the logic. Since you can start counting at one or start counting at zero, and never stop counting, it's the same concept, logically. So the number of elements in the set of whole numbers is still aleph-naught.

You could also move on to the set of all "integers," defined as the set of all natural numbers, all of the negative natural numbers, and zero. Now you might want to think that you have a necessarily larger number of elements, since there is not starting point. You can't start at negative infinity and count up, but, you could be a little clever and say, start with one, and just count two at a time, one for each positive number and one for each negative number, keeping in mind that zero adds one to the total. So, again, logically, it's the same concept of infinity as trying to count all of the natural numbers.

So, where you first see an actual difference is when you move on to the set of "real numbers." So a real number is all of the natural numbers, all of the negative natural numbers, zero, all of the fractions, and all of the "irrational" numbers (numbers like pi or the square root of two or whatever, which can be approximated by decimals, but have infinite digits in them). And the difference is that you cannot even start counting them. Choose any arbitrary number, like 4.7175. What is the very next number? Is it 4.7176? Nope, because you could say 4.71751 or 4.717501 or 4.7175001 or 4.717500000000...00001... Aha, so now it's a different concept, where you have an infinite number of elements like before, you can place those infinite number of elements in order from largest to smallest like before, BUT, you can't say which element is "the next one" after any arbitrarily chosen element. So, that set has a different number of elements in it, which is what they call aleph-one.

My thread has been highjacked by irrelevant nonsense. I've been a member here for over 12 years, I was just asking relevent questions about 7 string guitars on a Sevenstring.org forum.

 

[jaxadam]

Just like the infinite number of notes will be greater with a 7 stringer compared to a 6 stringer, if both are played for an infinite amount of time.

Pick any Nobel Prize from the middle shelf!

 

[jaxadam]

My thread has been highjacked by irrelevant nonsense. I've been a member here for over 12 years, I was just asking relevent questions about 7 string guitars on a Sevenstring.org forum.

Pick any Nobel Prize from the bottom shelf!

 

[bostjan]

I'll apologise for taking some liberties to explain a really complicated subject to someone who was obviously grossly misunderstanding it.

Read what you said and read the original post that so offended you again, and you'll see that that is not what I said. Clearly, you misunderstood what I wrote. I'll admit that's partially my fault, since I wasn't clear. However, I was clearly making a light joking discussion about a very non-serious topic. Anyway, now you are doubling down that I said things that I didn't say, and trying to be a dick about it. So, clearly, the general "you" cannot make light of anything these days, even guitar playing or especially set theory. I'm sorry for trying to have a little bit of fun. Clearly that is not allowed.

My thread has been highjacked by irrelevant nonsense. I've been a member here for over 12 years, I was just asking relevent questions about 7 string guitars on a Sevenstring.org forum.

IDK, if you've been active here for 12 years, I would have thought it would be safe to assume you had seen this same sentiment expressed dozens of times already, but I guess it's been a pretty long time since a thread like this one has surfaced. I think the question you asked was already answered, and the rest of the discussion could be equivocation or off topic.... but I propose that, well...

Your OP only asks one actual question "Is it really worth it?" My "irrelevant" post might have a lot to do with that question that either of us would like to admit.

No, it's not worth it. It's not worth playing guitar at all, or trying to have discussions at all, about anything at all, really. Because worth is entirely in the eye of the beholder, and there will always be someone out there thinking that what you have to say musically, verbally, technically, or otherwise, is worthless. People are jerks. I am one, too, clearly. So, if you base the worth of anything off of what other people think about it and not off of how much you yourself enjoy it, then the answer is always going to be "no, it's not worth anything."

 

[AwakenTheSkies]

Hahaaaa bet you all wish you paid attention in school now